RILEM_Connections_between_Steel_COncrete_Stutgart_2001
0_Preface by R. Eligehausen 1_Where structural steel and concrete meet by J.W.B. Stark, D.A. Hordijk 10_Study on standard test methods for post-installed anchors by Y. Hosokawa, K. Nakano, Y. Oohaga, S. Usami, K. Imai 100_Experimental investigations on the bahaviour of strip shear connectors with powder actuated fasteners by M. Fontana, H. Beck, R. Bärtschi 101_Design concept of nailed shear connections in composite tube columns by G. Hanswille, H. Beck, T. Neubauer 102_An experimental study on shear characteristics of perfobond strip and its rational strength equations by U. Yoshitaka, H. Tetsuya, M. Kaoru 103_Behavior of lying shear studs in reinforced concrete slabs by U. Kuhlmann, K. Kürschner 104_Composite bridge with compression joint connection concrete end slab to steel girder finite element method by M.V. Lammens 105_Perfo-bond connection and tests by S. Poot 106_Development and application of saw-tooth connections for composite structures by J. Schlaich 107_Geometry, behaviour and design of high capacity saw-tooth connections by V. Schmid 108_Composite bridge with compression joint - Connection concrete end slab to steel girder - Dowels divided in groups by D. Tuinstra 109_TH~1 11_Static behavior of anchors under combinations of tension and shear loading by D. Lotze, R.E. Klingner, H.L. Graves, III 110_Influence of fatigue loads in tension on short cast-in-place anchors in concrete by E. Cadoni 111_A test proposal for fatigue experimental studies on stud shear connectors by G. Natalino, E. Giuriani 112_Innovative interface systems for steel-girders-concrete-deck connection by M.K. Tadros S.S. Badie, A.M. Girgis 113_Non-linear analyssis of steel-concrete composite beams a finite element model by C. Faella E. Martinelli E. Nigro 114_Connections between prestressed concrete bridge decks and composite bridge decks - Hybrid construction by D. Jankowski, O. Fischer, M. Matthes 115_Anchorage behavior of 90-degree hooked beam bars in reinforced concrete wall-beam intersections by O. Joh, Y. Goto, A. Kitano 116_Embedded steel bearings instead of concrete NIBS by M.R. Kintscher 117_Anchorage zone in a steel-concrete composite slab with unbonded tendons by H. Koukkari 118_Connections for continuous framing in precast concrete structures by G. Krummel 119_Standoff screws as shear connectors for composite trusses push-out test results and analysis by J.R.U. Mujagic W.S. Easterling T.M. Murray 12_Improved structural model for channel bars with more than 2 anchors by J. Kraus, J. Ozbolt, R. Eligehausen 120_EX~1 122_Design and construction of a concrete-filled steel tube joint by S.P. Schneider, D.R. Kramer, D.L. Sarkkinen 123_Friction slipping behavior between concrete and steel - Aiming the development of bolted friction-slipping joint by T. Yoshioka, M. Ohkubo 124_AN~1 125_Low-cycle fatigue behaviour of pull-push specimens with headed stud shear connectors by S. Erlicher, O.S. Bursi, R. Zandonini 126_Static tests on various types of shear connectors for composite structures by H.C. Galjaard, J.C. Walraven 127_Structural monitoring of hybrid specimens at early age using fibre optic sensors by B. Glisic, D. Inaudi 128_Development of innovative composite system- Between steel and concrete members by K. Kitagawa, H. Watanabe, Y. Tachibana, H. Hiragi, A. Kurita 129_An experimental study on the bond-slip relationship between the concrete and steel with stud by K. Konno, A. Farghaly, T. Ueda 13_Anchors in low and high strength concrete by J. Kunz, Y. Yamamoto, M. Berra 130_The behavior of beam-to-box column connection of CFT with air cavity by M.-J. Lee, M.-S. Choi, J.-H. Kim, S.-W. Jun 131_Sheet reinforcement by O. Matthaei, H.-P. Andrä, N.V. Tue 132_Composite girders of reduced height by U. Khulmann, J. Fries, A. Rieg 133_Innovative development of light steel composites in buildings by R.M. Lawson, S.O. Popo-Ola, D.N. Varley 134_Intentional and unintentional shear connections in shallow floor composite structures by M.V. Leskelä 14_Development of common uniform regulations in Europe for the assessment of metal anchors by K. Laternser 15_Behavior of multiple-anchor fastenings subjected to combined tension_shear loads and bending moment by L. Li, R. Eligehausen 16_Load bearing capacity of torque-controlled expansion anchors by L. Li 17_Behaviour and design of anchors close to an edge under torsion by R. Mallée 18_Fixing new anchors concerning relevant base plate thickness by R. Mallée, F. Burkhardt 19_Installation verification of mechanical and adhesive anchors by L. Mattis 2_Fastening technique - Current status and future trends by R. Eligehausen, I. Hofacker, S. Lettow 20_Steel capacity of headed studs loaded in shear by N.S. Anderson, D.F. Meinheit
21_The analysis of fastener strength using the limit state approach by J.J. Melcher, M. Karmazínová 22_Behavior of shear anchors in concrete stastical analysis and design recommendations by H. Muratli, R.E. Klingner, H.L. Graves, III 23_Study on shear transfer of joint steel bar and concrete shear key in concrete connections by K. Nakano, Y. Matsuzaki 24_Performance of undercut anchors in comparison to cast-in-place headed studs by P. Pusill-Wachtsmuth 25_Shear anchoring in concrete close to edge by N. Randl, M. John 26_Behavior of tensile anchors in concrete statistical analysis and design recommendations by M. Shirvani, R.E. Klingner, H.L. Graves, III 27_Performance of single anchors near an edge under varying angles of loading by R.E. Wollmershauser, U. Nestler, V. Smith 28_The prequalification of anchors in the united states of america past, present and future by R.E. Wollmershauser 29_On the ratio of plate thickness to stud diameters for steel concrete stud shear connectors by H.D. Wright, A. Elbadawy, R. Cairns 3_Anchoring to concrete_the new ACI approach by J.E. Breen, E.-M. Eichinger, W. Fuchs 30_INC~1 31_Corrosion behavior of materials in fixing applications by N. Arnold 32_Behaviour of post-installed anchors in case of fire by K. Bergmeister, A. Rieder 33_Durability of galvanized, post-installed fasteners to concrete by K. Menzel, B. Hagmayer 34_Durability of stainless steel connections with respect to corrosion by U. Nürnberger 35_Fibre resistance of steel anchors in concrete by M. Reick 36_Anchoring with bonded fasteners by R.A. Cook, R.C. Konz 37_Experimental study on performance of bonded anchors in the low strength reinforced concrete by T. Akiyama, Y. Yamamoto, S. Ichihashi, T. Katagiri 38_Behavior of grouted anchors by R.A. Cook, N.A. Zamora, R.C. Konz 39_Long time load-carrying capacity of bonded anchors by L. Elfgren, G. Danielsson, I. Holm, G. Söderlind 4_Evolution of fastening design methods in Europe by W. Fuchs 40_Transmission of shear loads with post-installed rebars by J. Kunz 41_Design of anchorages with bonded anchors tension load by B. Lehr, R. Eligehausen 42_Load bearing bahavior and design of single adhesive anchors by J. Meszaros, R. Eligehausen 43_Rebar anchorage in concrete with injections adhesive by M. Reuter, T. Greppmeir, F. Münger 44_Investigations on bonding behaviour of the reinforcements in historic masonry by M. Raupach, J. Brockmann, A. Domink, M. Schürholz 45_Actual trends in chemical fixings from capsule to injection systems by J. Schätzle 46_PER~1 47_Study on the performance evaluation of the new capsule typed bonded anchor by M. Yonetani, A. Fukuoka, Y. Matsuzaki 48_Seismic behavior of connections between steel and concrete by J.O. Jirsa 49_Test on connectors for seismic retrofitting of concrete and masonry structures in Mexico by S.M. Alcocer, L. Flores 5_Probabilistic calibration of design methods by W. Fuchs 50_Design and construction of heavy industrial anchorage for power-plants by P.J. Carrato, W.F. Brittle 51_Dynamic behavior of single and double near-edge anchors loaded in shear by J.H. Gross, R.E. Klingner, H.L. Graves, III 52_Post-installed rebar connections under seismic loading by I. Hofacker, R. Eligehausen 53_An evaluation of tensile capacity of anchor system in NPPS by actual model tests by J. Jung-Bum, W. Sang-Kyun, S. Yong-Pyo, L. Jong-Rim 54_Structural behavior of SRC column - RC beam joint under monotonic and cyclic load by S.-H. Lee, Y.-K. Ju, S.-C. Chun, D.-Y. Kim 55_Dynamic behavior of tensile anchors to concrete by M. Rodriguez, D. Lotze, J. Hallowell Gross, Y.-G. Zhang, R.E. Klingner, H.L. Graves, III 56_Test methods for seismic qualification of post-installed anchors by J.F. Silva 57_Safety concept for fastenings in nuclear power plants by T.M. Sippel, J. Asmus, R. Eligehausen 58_Experimental study on seismic performance of beam members connected with post-installed anchors by R. Tanaka, K. Oba 59_Shallow shear anchor bolts for structural seismic strengthening of columns with wing wall by Y. Yamamoto, Y. Hattori, T. Koh, M. Kato 6_Current status of post-installed anchor application in Japan by R. Tanaka 60_Seismic response of multiple-anchor connections to concrete by Z. Yong-gang, R.E. Klingner, H.L. Graves, III 61_Smeared fracture Finite Element (FE) - Analysis of reinforced concrete structures - Theory and examples by J. Ozblot_ 62_Numerical and experimental investigations of the splitting failure mode of fastenings by J. Asmus, J. Ozbolt 63_Three dimensional modeling of an anchorage to concrete using metal anchor bolts by H. Boussa, G. Mounajed, B. Mesureur, J.-V. Heck 64_Influence of bending compressive stresses on the concrete cone capacity by M. Bruckner, R. Eligehausen, J. Ozbolt 65_ATENA - An advanced tool for engineering analysis of connections by V. Cervenka, J. Cervenka, R. Pukl 66_A computational model for double-head studs by A. Haufe, E. Ramm 67_Behavior and design of fastenings with headed anchors at the edge under arbitrary loading direction by J. Hoffmann, J. Ozbolt, R. Eligehausen 68_Evaluation of a bridge deck strengthening with shear connectors finite element analysis and experimental results by A.J. Leite 69_Numerical analysis of group effect in bonded anchors with different bond strengths by Y.-J. Li, R. Eligehausen
7_Design method for splitting failure mode of fastenings by J. Asmus, R. Eligehausen 70_Simulation of fastening systems utilizing chemical and mechanical anchors by J. Nienstedt, R. Mattner, U. Nestler, C. Song 71_Headed stud anchor - Cyclic loading and creep-cracking interaction of concrete by J. Ozbolt, J. Hofmann, R. Eligehausen 72_Numerical investigations of headed studs with inclined shoulder by P. Pivonka, R. Lackner, H.A. Mang 73_Simulating investigations of headed studs with inclined shoulder by R. Pukl, J. Cervenka, V. Cervenka 74_Non-supported crash barriers - Proof of the concrete resistances according to the concrete-capacity-method by J. Buhler 75_Reconstruction of multi-layer-walls by E. Dereser, J. Buhler 76_Load carrying capacity of fasteners in concrete railay sleepers by H. Thun, S. Utsi, L. Elfgren, P. Nilsson, B. Paulsson 77_Anchorage with headed bars with exterior beam-column joints by J. Hegger, W. Roeser 78_Halfen HDB-S bars as shear reinforcement in slabs and beams by J. Hegger, K. Fröhlich, R. Beutel, W. Roeser 79_Behaviour of fasteners in concrete with coarse recycled concrete and masonry aggregates by D.A. Hordijk, R. van der pluijm 8_Behaviour and design of fastenings of shear lugs in concrete by H. Michler, M. Curbach 80_Regarding strength of anchor bolts used for PCa Curtain wall fasteners by H. Kawamura, T. Otobe, S. Oka 81_New method of reconstruction - Strengthening of old buildings by M. Marjanishvili, T. Zuzadze, D. Ramishvili, A. Lebanidze 82_Fastening in masonry by A. Meyer, T. Pregartner 83_Study on design method of joint panels for hybrid railway rigid-frame bridges by H. Nishida, K. Murata, T. Takayama 84_Tension stiffening model based on bond by M.A. Polak, K. Blackwell 85_OVE~1 86_Redundant structures fixed with concrete fasteners by M. Rößle, R. Eligehausen 87_Numerical and experimental analysis of post-installed rebars spliced with cast-in-place rebars by H.A. Spieth, J. Ozbolt, R. Eligehausen, J. Appl 88_Dowel action of titanium bars connecting marble elements by E. Vintzileou, K. Papadopoulos 89_Case study - Application of high strength post-tensioned rods for anchoring aerial tram structures to rock by G.P. Wheatley 9_Safety relevant aspects for torque controlled expansion anchors by H. Gassner, E. Wisser 90_Behaviour and design of fastenings with concrete screws by J.H.R. Küenzlen, T.M. Sippel 91_Behaviour and design of anchors for lifting and handling in precast concrete elements by D. Lotze 92_Behaviour of plastic anchors in cracked and uncracked concrete by T. Pregartner, R. Eligehausen 93_TES~1 94_A new step forward for composite bridges - The Bras de la Plaine Bridge by E. Barlet, G. Causse, J.-P. Viallon 95_Anchorage of the steel elements to the concrete piers at the specific pipe bridges over a Danube-bay in Budapest by B. Csiki 96_BEH~1 97_Recent developments and chances of composite structures by U. Kuhlmann 98_Design of lying studs with longitudinal shear force by U. Breuninger 99_STU~1
Preface Anchorage by fasteners and composite structures of steel and concrete have seen dramatic progress in research, technology and application over the past decade. The understanding of the fundamental principles underlying both disciplines has significantly improved. Concurrently, there has been rapid growth in the development of sophisticated new products and the establishment of international directives and codes to ensure their safe and economical use in a wide range of engineered structures.
Although they deal with very similar problems, the two disciplines have developed independently from each other. To optimize the use of composite structures and fastenings to concrete, however, it is necessary to have knowledge of both: the local behavior of the fastening system and the global behavior of the structure. It became apparent that a forum offering the opportunity to expand and to exchange experience in the field of connecting steel and concrete would benefit all involved. Furthermore this forum would aid in the rapid dissemination of new ideas, technologies and solutions as well as explore new areas of research.
To meet these objectives the first symposium on 'Connections between Steel and Concrete' was conducted in Stuttgart, Germany from September 9 to 12, 2001 organized under the auspices of RILEM, the International Union of Testing and Research Laboratories for Materials and Structures and the University of Stuttgart. The event was cosponsored by the American Concrete Institute (ACI), the International Federation for Structural Concrete (fib) and the International Association for Bridge and Structural Engineering (IABSE). Experts from all facets of the research, design, construction and anchor manufacturing community from around the world were invited to present papers covering the topics of testing, behavior and design, durability, exceptional applications, strengthening and structures as well as related topics such as anchorage to masonry.
Regrettably, due to the limitation on the number of papers, dictated by the time frame of the symposium, not all worthy papers proposed for presentation could be accepted. 134 authors were invited by the scientific committee to address the topic of connections between steel and concrete at the symposium. Their papers are gathered in this volume. I hope this volume will significantly contribute to knowledge in the field of connecting steel and concrete, related design methods, code specifications and new applications.
I wish to thank the authors for their excellent contributions and the scientific committee for the useful technical advice. I would like to express particular thanks to Mr. Stefan Fichtner and Werner Fuchs for their essential assistance in the local organization of the symposium and the preparation of the present volume.
Rolf Eligehausen Stuttgart, September 2001
WHERE STRUCTURAL STEEL AND CONCRETE MEET J.W.B. Stark*, D.A. Hordijk** *Delft University of Technology CiTG, The Netherlands **Adviesbureau ir. J.G. Hageman B.V., The Netherlands
Abstract Traditionally "steel structures" and "concrete structures" formed more or less two different worlds in structural engineering. However, fortunately this situation is changing rapidly. It is now recognised that each of the two materials have advantages and disadvantages and that often an optimal solution is found by combining both materials in for example a "Composite steel-concrete construction" or a "Mixed construction". It is important that the design rules for the two materials are consistent, especially for those components connecting both materials. However, in the past the design standards and recommendations for concrete and steel have been developed separately. So evidently at this moment there are still considerable differences in design assumptions and treatment of various aspects. During drafting of the Eurocodes and the conversion of the ENV's into EN's these inconsistencies became apparent. As the Eurocodes, additional to level national differences, also aim at harmonisation over the materials, it is now urgent to trace inconsistencies and find solutions for improvement. In this paper situations in modern buildings are described where steel and concrete meet. On the basis of an overview of the historic situation in education and practice, differences in approaches for concrete and steel design can be explained. Then for some aspects of steel-concrete-connections the present approaches will be discussed and compared with emphasis on inconsistencies, gaps and possibilities for harmonisation of design rules.
1. Introduction In the past for the design of a building the choice was normally between a concrete structure or a steel structure. Looking at recent practice in Europe there is an evident tendency that designers also consider the combined use of concrete and steel in the form of composite or mixed structures as a serious alternative. Use of composite elements in
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the form of beams, columns and composite slabs is already common practice in many countries (see Figure 1). Composite slab
Composite beam Composite column
Fig. 1: Composite elements Applications are supported by accepted National Standards or Recommendations, including rules for the design and verification of the connection between the concrete and steel parts. These National Standards will be replaced by a Harmonised European Standard: EN 1994 - Eurocode 4 [1], now being in a final stage of completion. However, this supporting material is not available for mixed constructions where (reinforced or prestressed) concrete elements and structural steel elements are used in combination. The elements itself are covered by the respective design standards for concrete and steel. But in many cases the joints where the elements meet form a black spot as far as Design Standards and information is concerned. So the designer has to develop design models based on a creative interpretation of methods and rules in use for concrete and steel. It is of course a complication when these design methods for the different materials are not consistent. In the past the Design Standards and Recommendations for concrete and steel have been developed separately. So evidently at this moment there are still considerable differences in design assumptions and treatment of various aspects. Some examples of these differences will be illustrated in this paper. That this situation exists is understandable from the historic perspective where separation existed for education and design practice between concrete and steel. At Universities students were (are) separately educated by professors specialised in concrete or steel. Each had (have) separate academic chairs and departments. Also in practice often difference is made between concrete designers and steel designers rather than structural engineers. This is also caused by the fact that for concrete most often the complete design is made by the design consultant while for steel the task of the design consultant is limited to the overall structural design. Detailing for steel structures, inclusive connection design, is often carried out by the fabricator or a specialised design office. Also professional organisations act separately. In Germany, for example, “Betonverein” and “DAST” and on an international level CEB and FIP (now merged to fib) and ECCS act respectively for the concrete and the steel society. Incidentally there are examples of co-operation between these organisations as for example in the “Joint
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Committee on Structural Safety” and the “Joint Committee for Composite Structures”. It would be useful to form a similar Joint Co-operation for connections between concrete and steel (and possibly other materials).
2. Typology Many different details exist depending on the type of members to be connected, the actions to be transferred and the performance requirements. An exhaustive treatment of all possible details is not possible in the context of this paper. Just to give an idea an arbitrary selection is made. 2.1 Column bases This is one of the most commonly used details. The steel column is connected to a base plate, which is attached to the concrete foundation by some form of so-called “holding down” assembly. A typical detail is shown in Figure 2. The system of column, base plate and holding down assembly is known as a column base. The holding down assembly comprises two, but more commonly four (or more) holding down bolts (anchors). These may be cast-in-place, or post-installed to the completed foundation. Cast-in-place bolts sometimes have some form of tubular or conical sleeve, so that the top of the bolts are free to move laterally, to allow the base plate to be accurately located.
base plate
anchor grout
Fig. 2: Typical detail of a column base
Base plates for cast-in assemblies are usually provided with oversized holes and thick washer plates to permit translation of the column base. Anchor plates or similar embedded arrangements can be attached to the embedded end of the anchor assembly to resist pull-out. Post-installed anchors may be used, being positioned accurately in the hardened concrete. Post-installed assemblies include, for instance, torque-controlled expansion anchors, under-cut anchors and bonded anchors (see also [2]).
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2.2 Connections of steel beams to concrete walls or columns A stiff concrete core often provides the stability of a multi-storey steel frame. The steel beams of the floors are connected to the wall of the concrete core (see Figure 3a). To provide sufficient fire resistance sometimes (prefabricated) concrete columns are used instead of steel columns with fire protection. In Figure 3b a connection is shown as used in a refurbishment project where new steel floor beams are connected to existing concrete columns by means of an extended end plate connection.
concrete core
anchor
a
b
Fig. 3 Connection composite beam-concrete core (a) ; steel beam-concrete column (b). A great number of different forms of connection details are possible for these types of connection. The choice of the most appropriate solution is dependent of the following aspects of consideration: • Sequence of construction • Method of fabrication of the core or column. • Tolerances of both concrete and steel • Type of action effects (shear, tension or compression, moment) • Static or variable loading • Reversal of loading • Support conditions (degrees of freedom) • Required static properties (resistance, stiffness and deformation capacity) • Behaviour under elevated temperature caused by fire 2.3 Outrigger in a high rise building In some structures taylor-made solutions have to be invented by the designer. As an example in Figure 4 an outrigger structure in a high rise building is shown. The steel outrigger had to be connected to a concrete core and to a composite column.
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Outrigger
Composite column
Concrete core
Fig. 4: Outrigger in a high rise building
3 Standards and Recommendations The European Standards Organisation (CEN) has planned to develop a complete set of Harmonized European Building Standards. This set includes Standards for concrete, steel and composite steel-concrete buildings and bridges. The Eurocodes, being the Design Standards, form part of this total system of European Standards, together with Standards for fabrication and erection and Product Standards. After a period of experimental use of the ENV(European Pre Standard)-versions of the Eurocodes, a start has been made with the conversion to EN’s (European Standards). At the time of the conference, draft prEN versions of the relevant parts covering – "General Rules and Rules for Buildings" will have been completed [1,3,4]. The Eurocode-programme is aiming at a two dimensional harmonization: 1) Harmonization across the borders of the European Countries; 2) Harmonization between different construction materials, construction methods, types of building and civil engineering works to achieve full consistency and compatibility of the various Codes with each other and to obtain comparable safety levels. Especially the 2nd item is relevant for the topic of this paper. The designer of a “mixed structure” is concerned with the Eurocodes listed in Table 1. A check of the present drafts shows that he will find not many detailed rules specific for the design of joints between concrete and steel elements. Table 1: Eurocodes relevant to “mixed” structures Standard Subject Material General EN 1990 Basis of Design “ EN 1991-1 Actions on structures Concrete EN 1992-1-1 Concrete - General & Buildings Steel EN 1993-1-1 Steel - Common rules “ EN 1993-1-8 Steel – Design of joints “ EN 1993-3 Steel – Buildings Composite EN 1994-1-1 Composite steel & concrete – General & buildings
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•
•
•
prEN 1992-1-1 (Eurocode 2 – 2nd Draft Jan. 2001) [3] In Eurocode 2 no specific section for the design of connections is included. This situation will change since recently within CEN/TC250/SC2 a new Working Group ‘Design of fastenings’ started their activities. prEN 1993-1-8 (Eurocode 3 – 2nd Draft Dec. 2000) [4] Eurocode 3 has a separate part for the design of steel joints. The present draft contains design rules for fasteners (bolts, rivets and welds) but also principles and application rules for the design of joints. The principles are so general that they apply globally to ”mixed” joints as well. For example clause 2.5 states: “2.5 Design assumptions (1)P Joints shall be designed by distributing the internal forces and moments to fulfill the following criteria: (a) the assumed internal forces and moments are in equilibrium with the applied forces and moments; (b) each element in the joint is capable of resisting the forces or stresses assumed in the analysis; (c) the deformations implied by this distribution are within the deformation capacity of the fasteners or welds and of the connected parts, and (d) the deformations assumed in any design model based on yield lines are based on rigid body rotations (and in-plane deformations) which are physically possible. (2)P In addition, the assumed distribution of internal forces shall be realistic with regard to relative stiffnesses within the joint.” The design method for joints in EN1993-1-8 is based on the so-called “component method”. The advantage being that the rules for “all steel” joints can easily be extended to ”mixed” joints. Detailed rules are given for the application of the component method for typical steel joints but also for column bases. prEN 1994-1-1 (Eurocode 4 – 3rd Draft April 2001) [1] Composite joints in frames for buildings are covered in Section 8 (and Annex A) of prEN1994-1-1. This Section is consistent with prEN 1993-1-8. A great advantage is that the design method in EN1993-1-8 is based on the component method so only rules for properties of specific composite components had to be given in EN19941-1. The proposed EN provisions therefore deal only with what is peculiar to composite joints. It is assumed that the user of EN1994 will be familiar with EN 1993-1-8. Design moment resistance and rotational stiffness are each to be “determined in a manner analogous to that for steel joints”. No attempt is made to present detailed modifications to the provisions of the Steel Code.
So far Design Standards as covered by the Eurocodes. Other groups also produce design guidance. A CEB Task Group (since the merging of CEB and FIP in 1998 now a fib Group) prepared a Design Guide for fastenings in concrete [5]. It only covers the load transfer into the concrete. For the design of the fixture (f.e. a base plate) the designer is referred
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to “the appropriate code of practice”. In [5] so far only rules for cast-in-place headed anchors and post-installed expansion and undercut anchors are given. Work is in progress for other types of anchor, like bonded anchors and channel bars. Many types of anchor are special products. The determination of the characteristic properties is not covered in the Eurocodes. They either refer to Harmonized Product Standards or ETA‘s (European Technical Approvals). For ETA‘s, guidelines (ETAG’s) are being produced by the European Organisation for Technical Approvals (EOTA). In the ETAG for “Metal anchors for use in concrete” [6] a Design Guide is given in an Annex. The motivation for including design rules was the fact that there is a relation between the anchor properties and the design and that a Design Guide was not yet provided by CEN. With the new Working Group of CEN/TC250/SC2, as mentioned before, this situation will change. The elastic design approach in the ETAG Design Guide [6] is similar to the CEB guideline [5]. However the CEB document is more comprehensive than the ETAG design guideline, since also a plastic design approach is included, while cast-in-place anchors are also covered. As a result of a joint project of ECCS/TWG10.2 “Semi-rigid connections” and COST/C1/WG2 a publication [7] was issued. This publication gives details of a design method for column bases. It covers the calculation of characteristic values for the resistance and rotational stiffness. An evaluation of the CEB Design Guide model is included.
3. Comparison of some fastener aspects in different Codes 3.1 General As mentioned before, in Eurocode 2 connections are not treated. Therefore, for some aspects the rules in Eurocode 3 are compared with the CEB/EOTA Design Guidelines. In Section 3.2 rules for the resistance of the steel part of a single anchor fastening are compared. In Section 3.3 some aspects related to a base plate connection are discussed. 3.2 Anchor strength In table 2 resistances for the steel part of a single anchor according EC3 and EOTA/CEB are compared. Values are given for the design tension resistance Ft.Rd (NRd.s) and the design shear resistance Fv.Rd (VRd.s). For some cases there are significant differences. The design shear strength according to EC 3 is always greater than that according to CEB and EOTA. It should be noted that in case of shear there is a difference between a bolt connecting two steel parts and an anchor connecting a steel component to concrete. The design resistance to combined tension and shear load is according CEB [5] and EOTA [6] to be determined with the following interaction equation:
N N Sd VSd + ≤ 1,2 but Sd ≤ 1 and N Rd VRd N Rd
VSd ≤1 VRd
(1)
It is noted that this yields conservative results for steel failure and that when NRd and VRd are governed by steel failure more accurate results are obtained by:
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2
2
N Sd VSd + ≤ 1 N Rd VRd
(2)
For bolts subjected to combined tension and shear Eurocode 3 [4] gives the following interaction equation :
Fv.Sd Ft .Sd + ≤ 1,0 but Fv.Rd 1,4 ⋅ Ft .Rd
Ft .Sd ≤1 Ft .Rd
(3)
The resistance functions in Eurocode 3 have been developed by statistical evaluation of a international collection of test results evaluated in accordance with the procedure given in Annex D of prEN1990 : “Basis of Design” Table 2 Comparison of the design resistance of the steel part of a single anchor according to Eurocode 3 [4] and the CEB/EOTA [4,5] Design Guidelines. tension ‘Code’ ‘original equation’ 4.6 5.8 8.8 10.9 EC 3 Ft.Rd = 0,9⋅fub⋅As / γMb = 0,72⋅As⋅fuk 288⋅As 360⋅As 576⋅As 720⋅As CEB/EOTA NRd,s= As⋅fyk / γMs = 0,83⋅As⋅fyk 200⋅As 333⋅As 533⋅As 750⋅As Note: fyk = characteristic steel yield strength (nominal value) fuk = characteristic steel ultimate tensile strength (nominal value) The ‘original equation’ differs between CEB and EOTA, but the result is, except for 10.9 anchors, equal; CEB result is shown. shear ‘Code’ ‘original equation’ 4.6 5.8 8.8 10.9 EC 3 384⋅As Fv.Rd= 0,6⋅fub⋅As / γMb = 0,48⋅As⋅fuk 192⋅As 200⋅As 400⋅As Fv.Rd= 0,5⋅fub⋅As / γMb = 0,40⋅As⋅fuk CEB/EOTA VRd,s= 0,6⋅As⋅fyk / γMs = 0,5⋅As⋅fyk 120⋅As 150⋅As 320⋅As 360⋅As Note: CEB/EOTA: for 10.9 anchors γMs=1,5 instead of 1,2 for lower classes. In the CEB and EOTA Design Guidelines steel failure under a shear load with a lever arm (causing combined shear and bending stresses in the anchor) is treated separately. This is not covered by Eurocode 3. 3.4 Base plate connection Probably the most common connection between concrete and steel is the base plate connection of a column (see Figure 2). Quite a lot of steel research into the structural behaviour was carried out in the past. These research activities mainly focussed on the strength and stiffness of the steel base plate, while for the behaviour of concrete under concentrated loads use was made of knowledge provided by the‘concrete-colleagues’. For tensile loading “holding down bolts” have to be used, as they are named in the
8
normative Annex L of Eurocode 3 [4]. For the anchorage of these bolts reference is made to Eurocode 2. This means that the anchorage should be such that steel yielding governs anchorage failure. One could speak of an anchorage according to the reinforced concrete technique. With the fastener technique relative shorter anchorages with other governing failures modes (break out of concrete cone, pull-out and concrete splitting), are introduced. The length of short anchors is normally about 10 times their diameter, while for anchorages of reinforcing steel according to the concrete codes lengths of 20d to 30d, depending on cover and concrete strength, are required. Now two items from the CEB Design Guide will be discussed more in detail. These items were selected because the authors expect that a combined effort of experts from the steel and fastener groups shall lead to improvement of the design rules . Base plate stiffness and load distribution over the anchors. In the CEB Design Guide [4] distinction is made between an elastic design approach and a plastic design approach. The plastic approach is only acceptable when the anchor has sufficient deformation capacity. For short anchors with a high steel strength this is often not the case. Furthermore, in many situations the resistance of the concrete is reduced by edge effects of the concrete element. This may also cause that the requirement for the plastic approach is not fulfilled. For an elastic approach it is required that the fixture does not deform under the design actions. It may be assumed that this is valid when the base plate is rigid and in full contact with the concrete or with a layer of mortar. Furthermore, the base plate may be assumed to be rigid when the maximum steel stress under the design actions does not exceed fyk/γMs with γMs = 1,1. It is expected that in practice this requirement will sometimes not be fulfilled and/or even not checked in many cases. The guidance in [5] on this aspect is rather limited, which can be understood since the document mainly deals with the load transfer into the concrete. According the CEB Design Guide the use of flexible end plates is permitted, provided that the non-linear load distribution over the anchors and the associated prying forces are taken into account. Shear strength and contribution of friction According the CEB Design Guide for base plates with a grout layer thicker than 3 mm plastic design is not allowed, friction forces underneath the base plate should be neglected and the shear capacity has to be calculated for the mechanism ‘shear load with lever arm’. For column bases usually a grout layer with a thickness greater than 3 mm is used. Though it is realised that there may be uncertainties about the strength and quality of the grout layer, the CEB method will be very conservative in many practical cases. This was confirmed by COST/WG2 [7] that compared design values with test results for column bases loaded in shear and with a varying thickness of the grout layer [8]. In particular in case of low strength bolts and a thick grout layer (60 mm) the experimentally obtained maximum shear load was many times (between 10 and 25 !!) greater than the calculated characteristic shear strength of the connection.
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5. Concluding remarks In daily practice the two main structural materials concrete and steel are often used in combination. When steel is fully incorporated in the concrete, as is the case with reinforcement the interaction between these two materials is treated properly. This also applies to composite elements. However, when concrete and steel elements are used in combination in a mixed structure the designer is not supported with sufficient design guidance. Significant improvement can still be achieved as far as Codes, engineering practice and education is concerned. Though things are changing rapidly in a positive direction, to some extent there are still two separate “worlds”. As far as the joint is concerned, both “worlds” tackle the aspects related to their one material in detail and look a little bit over the border to the other world. Since at the joint the interaction between the two worlds play an essential role, it is of prime importance that the treatment on both sides of the border is consistent. This is not the case yet. As a result of the “two-world-situation” inconsistencies in Codes still exist and properties of connections may not be fully utilised. Some examples have been given. The authors of this paper, one with a steel and the other with a concrete background, are of the opinion that with joint co-operation for several aspects of steel-concrete connections improvement can be achieved. In that respect, this symposium is a perfect initiative and may be a bases for new combined activities.
6. References 1. 2. 3. 4. 5. 6.
7. 8.
prEN 1994-1-1, ‘Eurocode 4: Design of composite steel and concrete structures – Part 1: General rules and rules for buildings’, CEN, 3rd Draft, April 2001. CEB ’Fastenings to concrete and masonry structures – State-of-the-art’ CEBbulletin no. 216, Thomas Telford, July 1994. prEN 1992-1, ‘Eurocode 2: Design of concrete structures – Part 1: General rules and rules for buildings’, CEN, 2nd draft, January 2001. ENV 1993-1-1: 1992, ‘Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings’, CEN, April 1992. CEB, ‘Design of Fastenings in Concrete. CEB Guide - Part 1 to 3’ CEB-bulletin no. 233, Thomas Telford, January 1997. Guideline for European Technical Approval of Anchors (metal anchors) for use in concrete. Part 1, 2 en 3 and Annexes A, B en C (Final Draft). EOTA, Brussels, February 1997. COST C1, ‘Column bases in steel building frames’, ECCS Technical Working Group 10.2 ‘Semi-rigid connections’ and COST C1 WG 2, February 1999. Bouwman, L.P., Gresnigt, A.M. and Romeijn, A., Research into the connection of steel base plates to concrete foundations, Stevin report 25.6.89.05/c6, 1989 (in Dutch).
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FASTENING TECHNIQUE – CURRENT STATUS AND FUTURE TRENDS Rolf Eligehausen, Isabelle Hofacker and Steffen Lettow Institute of Construction Materials, University of Stuttgart, Germany
Abstract In the paper the current status and future trends of modern fastening technique are described. Fastening technique is used in a wide range of the construction industry. By cooperation between industry and research more economical and safe fastening systems have been and will be developed, which work well in cracked and uncracked concrete. Engineers use special software for the selection of fastening systems and the design of fastenings according to the CC-method. For the installation of anchors technicians are more and more supported by manufacturers with descriptive technical manuals and in some cases with training courses. This will lead to an expanding field of application of modern fastening technique.
1. Introduction Modern fastening systems are becoming more important in civil engineering constructions. In Figure 1 on basis of a simple graph an overview of the wide area of applications of fastenings is given. Fastenings are used in all types of constructions. Because the failure of a fastening may lead to an endangerment of human life or major economic consequences, reliable fastenings are necessary. To ensure reliable fastenings a good co-operation of producer, engineer and user is needed (Figure 2). The producer has to supply efficient and well functioning fastening systems, the engineer must choose the optimal fastening system for the application in question and proof the adequate safety of the fastening by accurate design methods and the user has to ensure a correct installation of the fasteners.
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Figure 1. Examples of the field of application of fastenings
Figure 2. Requirements to ensure reliable fastenings
2. Fastening Systems The fastening systems currently in use in concrete structures may be classified in cast-inplace installations and post-installed installations for applications (Figure 3). Cast-inplace systems are typically positioned in the formwork before the concrete is cast and thus may also be used in members with dense reinforcement. Post-installed systems may either be installed into drilled holes (drill installation) or be driven into the base material with impact energy (direct installation). They are very flexible in application. For tension loading the load-transfer mechanisms employed by the fasteners may be identified by three different types: friction, mechanical interlock and bond (Figure 4).
Figure 3. Fastening methods in concrete
Figure 4. Load transfer mechanisms
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Cast-in-place systems like headed anchors (Figure 5a) and channel bars (Figure 5b) transfer tension load mainly by mechanical interlock to the concrete. Typical postinstalled fasteners based on the above mentioned load-transfer mechanisms are shown in Figure 6. In case of expansion anchors (Figure 6a), the load is transferred to the concrete mainly by friction. The frictional resistance depends on the expansion force generated by the expansion of the anchor. Undercut anchors (Figure 6b) transfer tension load to the concrete principally through mechanical interlock between a local undercut and the expansion element which results in locally high bearing stresses. The load transfer of bonded anchors (Figure 6c) is ensured by bond stresses between threaded rod and mortar and mortar and concrete along the embedment length. Often fastenings systems employ a combination of load transfer mechanisms, e.g. bonded expansion anchors for use in cracked concrete. During the last decade many innovative and well functioning fastening systems have been developed by the industry often in close contact with research institutes which cover almost all applications encountered in practice (e.g. fastenings in noncracked and cracked concrete as well as fastenings in different types of masonry under static and cyclic loading).
(a)
(b)
Figure 5. Typical cast-in-place anchors
(a)
(b)
(c)
Figure 6. Typical types of post-installed anchors
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A survey at about 50 German engineering offices revealed that engineers consider the availability of detailed technical data (e.g. Technical Approval) on anchors as the most important criteria for anchor selection (Figure 7). Furthermore they ask for fastening systems that can be used in a large variety of appli- Figure 7. Selection criteria of fastenings cations. In contrast to the general believe the low price of a fastening system seems not to be an important selection criteria.
3. Testing of Fasteners Fasteners must function properly in the application in question. To ensure this prequalification testing is necessary. During the last years test programs to check the suitability of anchors and to evaluate allowable conditions of use have been worked out by EOTA (1997) and ACI (1985). They will be explained in detail during the conference. In the suitability tests the behavior of fasteners under unfavorable conditions that may occur during installation or the service life of the fastening (e.g. behavior in a wide crack with w=0.5 mm) is checked. In Europe anchors that have passed the approval tests which are mainly performed by an independent testing institute receive an European Technical Approval (ETA) which is required for the use of anchors in safety related applications.
4. Design of Fastenings Fastenings may be loaded by tension-, shear-, or combined tension and shear loads and bending moments. The loads may be static or dynamic. Fastenings may fail in several different modes.
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Under tension loading mechanical fasteners may be pulled out of the hole (Figure 9e), whereby the concrete at the surface may be damaged. This failure mode will occur only if with expansion anchors the expansion force and with headed and undercut anchors the bearing area is too small. The most common failure mode is the pulling of a concrete cone (Figure 9b + d). For anchor groups the individual cones may overlap (Figure 9b) and for fastenings at the edge the cone is truncated by the edge (Figure 9d). With fastenings close to an edge or in a thin concrete member splitting of the concrete Figure 8. Load directions and failure modes might occur (Figure 9a) and headed anchors very close to an edge may generate a local blow-out failure (Figure 9f). The maximum capacity of the fastening is governed by steel failure (Figure 9c). Fastenings with a sufficiently large edge distance and embedment depth loaded in shear will fail by a local concrete spall in front of the anchor followed by steel rupture (Figure 10a). If the embedment depth is not large enough, the concrete behind the anchor will fail (pry-out failure, Figure 10b). Fastenings close to an edge often fail by a brittle edge failure (Figure 10c, d + e).
Figure 9. Failure modes under tension loading
Figure 10. Failure modes under shear loading
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While in reinforced concrete constructions in general tensile forces are taken up by reinforcement this is often not possible with fastenings. Therefore fastenings without special reinforcement utilize the concrete tensile capacity which – in case of concrete failure governs the failure load. This must be taken into account in the safety considerations. In the design it must be shown that in the serviceability limit state the displacements of the fasteners are smaller than allowable values and that in the ultimate limit state the load acting on the fastening can be safely transmitted into the concrete. Furthermore the fasteners must be durable during the expected service life. The design of fastenings – as the design of structures – is based on the concept of partial safety factors. It must be demonstrated that the design actions Sd are not larger than the design resistance Rd (Equ. (4.1)). Formelabschnitt 4
S d ≤ Rd
(4.1)
The design actions are distinguished between permanent or variable actions and actions induced by restraint of imposed deformations (e.g. by temperature variations). In the simplest case with one variable load Qk acting in the same direction as the permanent load Gk we get
S d = γ G ⋅ Gk + γ Q ⋅ Qk
(4.2)
The partial safety factors γG for permanent loads and γQ for variable loads are independent of the material or failure mode. They may be different in different countries. In Europe γG = 1.35 and γQ= 1.50 are used. The design resistance is equal to the characteristic resistance (5%-quantile) divided by the material safety factor γM (Equ. (4.3))
Rd ≤ Rk γ M
(4.3)
The partial safety factor γM depends on the accepted probability of failure. It is influenced by the failure mode (ductile steel failure or brittle concrete failure). In case of concrete failure the value of γMc should reflect the utilization of the concrete tensile capacity. Furthermore it should take into account the sensitivity of a fastening system to installation inaccuracies often observed in practice and to unfavorable conditions (e.g. hole drilled with drill but with a diameter of the cutting edge at the upper tolerance limit). In Europe values γMc = 1.80 (fastener with high installation safety) to γMc = 2.50 (fastener with low installation safety) are used.
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To calculate characteristic resistances for different load directions and failure modes sound engineering models should be available that are sufficient accurate and generally accepted. A comprehensive design method has been published by ACI 349 (1985). It is based on the 45° cone model and assumes a constant tensile stress ( k1 ⋅
f c0.5 ) over the failure
surface ( k2 ⋅ hef ) (Equ. (4.4)). 2
N u ,c = k1 ⋅ f c0.5 ⋅ k2 ⋅ hef2
(4.4)
Intensive research has shown that in case of concrete structures failing in tension the failure load should not be based on the theory of plasticity. But on fracture mechanics to account for the size effect (Bažant (1984)). According to the size effect the failure load of geometrical similar specimens will increase less than proportional with increasing member size. Because of the very high strain gradient in the region of the load transfer area the size effect is very pronounced in fastening technique (Eligehausen/Sawade (1989), Eligehausen/Ožbolt (1990)). It can be taken into account by multiplying 0.5
Equ. (4.4) with the factor ( k5 / hef ) (Equ. (4.5)).
N u ,c = k3 ⋅ f c0.5 ⋅ k4 ⋅ hef2 ⋅ k5 / hef0.5 = k ⋅ f c0.5 ⋅ hef1.5 with:
(4.5)
k1 - k5 = constants fc = concrete compressive strength hef = embedment depth
Figure 11 shows the concrete cone failure loads measured in tests can be predicted with sufficient accuracy by Equ. (4.5). In contrast to that the failure loads are underestimated by Equ. (4.4) for small embedment depths and are overestimated for large embedment depths. Furthermore the angle between the failure cone and the concrete surface is not 45° but approximately 35° (Figure 12). Therefore assuming α = 45° the failure load of anchor groups or fastenings at the edge may be overestimated.
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3.0 Eligehausen et al. (1992/1) and (1992/2)
Failure load [MN]
2.5
CC-method ACI-349 (1985)
2.0 1.5 1.0 0.5 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Embedment depth [m]
Figure 11. Concrete cone failure loads of headed Figure 12. Angle of the failure cone as a anchors under tensile load as a function of the function of the embedment depth (Fuchs, embedment depth (fcc=33 MPa), (Eligehausen et al. Eligehausen, Breen (1995/2) (1992/1), (1992/2))
The above described and other research results have been incorporated into the κ-method for the design of fastenings which is described in the CEB State-of-the-Art-Report (1994). In this method the influence of different parameters on the failure load (as edge distance, spacing, eccentricity of the resultant force, surface reinforcement, cracked concrete) is taken into account by κ−factors. Fuchs/Eligehausen/Breen (1995/1) developed the CC-method, which is based on the same mechanical models as the κ-method. The CC-method visualizes the κ-factors of the κ−method. Furthermore, more recent research results (e.g. Fuchs (1990), Eligehausen/Furche (1991), Lehmann (1993), Zhao (1993), Furche (1994), Asmus (1999)) have been taken into account to cover all failure modes. The CC-method is very user friendly and in most cases gives sufficiently accurate results. The CC-method has been incorporated in several design guides in Europe ((DIBt (1993), EOTA (1997), CUR (2000) and SIA (1998)) and the USA ((IBC (2000) and ACI 318 (2001)) and is currently discussed in China. It is described in several papers of this conference and open problems are discussed. Recent research results (e.g. Cook et al. (1998), Meszaros (2001) and Lehr (2001)) demonstrate that for fastenings with bonded anchors a modification of the CC-method is needed to cover their load transfer mechanism. These modifications will also be discussed during this conference.
5. Cracked Concrete In concrete structures often cracks will occur due to a variety of reasons (Beeby (1991)). The most important are tensile stresses due to loads and due to restraint of imposed
18
deformations (e.g. caused by shrinkage, creep, temperature variations or support settlements). Therefore according to codes for structural concrete in the serviceability limit state the width of cracks must be limited to acceptable values by reinforcement. Extensive measurements in practice demonstrate that under quasi-permanent load the characteristic crack width is wk ≈ 0.3 mm (Bergmeister (1988), Eligehausen/Bozenhardt (1989)), which agrees with the value generally accepted by codes.
Figure 13. Crack pattern at service load. The anchors were installed in uncracked concrete, after Lotze (1987)
There is a high probability that fasteners installed in uncracked concrete will be located in a crack if the concrete cracks (Figure 13), because high tensile stresses are caused in the region of the fastening by prestressing and loading of anchors and the notch effect. The influence of concrete cracking on anchor behavior depends on the type of anchor. The failure load of anchors transferring tensile loads by mechanical interlock (e.g. headed and undercut anchors) and failing by breaking a concrete cone is reduced by about 25 % by a crack with a width w ≈ 0.3 mm (Figure 14) due to the disturbance of the distribution of the tensile stresses around the anchor by the crack. A slightly larger reduction must be expected for torque controlled expansion anchors that function well in cracked concrete (Figure 15).
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Figure 14. Load-displacement curves of headed Figure 15. Load-displacement curves of anchors in cracked and uncracked concrete torque controlled expansion anchors de(Furche, Dieterle (1986)) signed for use in cracked concrete in cracked and uncracked concrete (Dieterle, Bozenhardt, Hirth, Opitz (1990))
Figure 16. Load-displacement curves of torque controlled expansion anchors designed for use in non-cracked concrete in cracked and uncracked concrete (Dieterle, Bozenhardt, Hirth, Opitz (1990))
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Figure 17. Load-displacement curves of fully expanded displacement controlled expansion anchors in cracked and uncracked concrete (Dieterle, Opitz (1988))
However torque controlled expansion anchors that are designed for use in uncracked concrete may not function at all if anchored in a crack (Figure 16). With deformation controlled expansion anchors the failure load in cracked concrete (w = 0.3 mm) is on average only 50 % of the value valid for non-cracked concrete (Figure 17). The reduction of the failure load is even more pronounced if – as often in practice – the anchors are partly expanded only.
Figure 18. Interference of bond between mortar Figure 19. Influence of cracks on the and concrete caused by a crack failure load of capsule-type bonded anchors under tension loading (Meszaros (2001))
With bonded anchors the bond between mortar and concrete is partly destroyed by a crack (Figure 18) which results in rather low failure loads and a large scatter (Figure 19). With bonded expansion anchors expansion forces are generated by pulling the cone into the mortar after crack opening (Figure 20). Therefore the failure load is only reduced by about 30 % compared to non-cracked concrete (Figure 21). If fastenings must be installed in reinforced concrete that may crack only fasteners with a predictable behavior in cracked concrete (demonstrated in pre-qualification tests) should be used and the influence of cracks on the failure load should be taken into account in the design. Whether in a certain application the concrete may be considered as cracked or non-cracked over the expected service life of the fastening should be decided by the designer based on the rules for reinforced concrete.
21
Figure 20. Interference of bond between Figure 21. Load-displacement curves of bonded mortar and concrete caused by a crack and expansion anchors in cracked and uncracked load transfer mechanism of a bonded expan- concrete (schematically) sion anchor
6. Installation of Fasteners Fasteners must be installed correctly according to the design specifications and the installation instructions of the manufacturer. To reach this goal the installation instructions - preferably in form of pictograms - should be detailed and clear and the installer should be well trained. The mistakes may not always be as severe as shown in Figure 22. However, even smaller mistakes (e.g. use of improper drill bit, no or too little cleaning of the hole, too small installation torque, improper compaction of the concrete in the region of a cast-in-place fastening) may influence the anchor behavior significantly. During the last decade especially manufacturers have done a lot to improve the situation by distributing adequate installation instructions. However the biggest problem is that many fasteners are installed by untrained workers. According to a recent survey in Germany, 45% of the
Figure 22. Fastening of column. According to the design the fastening should be installed directly on the concrete surface, after Steiner (2000)
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polled engineers believe that fastenings are installed by inexperienced personal resulting in an incorrect installation in about 50% of all applications (Schade (2001)). In other countries the situation is probably not much better. According to the authors opinion the situation will only improve significantly if only workers with proper training are allowed to install safety related fastenings. And if this is checked by supervision the proper training should be demonstrated by a certificate that is issued after passing a corresponding test. Very good experiences have been made in Germany with this approach for the post-installation of rebars.
7. Open Problems and Future Trends With the CC-method fastenings under arbitrary loading can be designed. However, in some applications (e.g. fastenings close to an edge and loaded in shear parallel to or away from the edge) the design models are rather conservative and should be improved. Furthermore the influence of special reinforcement on the strength and ductility of fastenings should be taken into account by improved design models. Until now most of the research has been done for monotonic loading including sustained and fatigue loading. However, much less research has been performed to study the behavior of fastenings under seismic excitations. The results until about 1990 are summarized in the CEB State-of-the-Art Report (1994) and the results of a recently finished extensive study are given in Klingner et al. (1998). It should be clarified if the test procedures and evaluation criteria for post-installed anchors and the design models valid for monotonic loading are adequate in case of seismic loadings, especially if fastenings are installed in regions where very wide cracks must be expected in the structure. Fastenings may be subjected to fire. While some results have been published (e.g. Reick (2001)), more research is needed in this area. In many regions of the world a large number of existing structures must be strengthened to resist future earthquakes. Modern fastening technique will play an important role in this work. However, more research is needed to develop new strengthening techniques and rational design models for the actions on and the resistance of fastenings. During the last two decades many new types of anchors have been developed (e.g. undercut anchors, bonded expansion anchors, concrete screws) to cope with new requirements (e.g. cracked concrete, fatigue and seismic loading). In the future more systems will be developed by combining different working principals to reach more economical solutions, better performance or both satisfy new demands by the user.
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Figure 23. Procedures used in praxis for the design of fastenings, after Schade (2001)
According to a recent survey in Germany about 70% of the polled engineers design fastenings according to the CC-method by using software provided by manufacturers and in only 20% of applications a hand calculation is done according to a simplified design method (Figure 23). In the future the design of fastenings with the help of a computer will be common all over the world.
Several committees all around the world work on test procedures and evaluation criteria for fasteners and on design methods for fastenings. The authors hope that because of modern information technologies, communication between the acting persons and – last but not least – conferences like this one the provisions will be harmonized world wide. The knowledge on fastening technique has increased significantly over the last two decades which is demonstrated by an increasing number of papers, reports, text books and conferences. However, the subject is often not taught in engineering schools. The authors believe that this will change in the future when more design guides are published by code committees.
8. Summary Modern fastening technique is increasingly used in the building industry. New and innovative fastening systems have been developed by the industry and reliable design methods have been incorporated in design guides. This will go on in the future. However, the training of designers and installers should be improved. Currently fastenings to concrete structures with cast-in-place or post-installed fastening systems are often not used in practice with the same confidence as other connections (e.g. welding or screwing in steel structures). It is hoped that this will change in the future, thereby expanding the field of application of modern fastening technique.
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9. References 1. American Concrete Institute, ACI Committee 318: Proposed Canges to Building Code Reqiurements for Structural Concrete. Appendix D – Anchoring to Concrete, scheduled to be published in edition of Concrete International, June 2001. 2. American Concrete Institute, ACI Standard 349-85: Code Requirements for Nuclear Safety Related Concrete Structures, Appendix B – Steel Embedments, 1985 3. Asmus, J.: Verhalten von Befestigungen bei der Versagensart Spalten des Betons. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1999. 4. Bažant, Z.P.: Size Effect in Blunt Fracture: Concrete, Rock, Metal. Journal of Engineering Mechanics, ASCE, 110, No. 4, S. 518-535, April 1984. 5. Bergmeister, K.: Stochastik in der Befestigungstechnik mit realistischen Einflußgrößen. Dissertation, Universität Innsbruck, 1988. 6. Civieltechnisch Centrum Uitvoering Research en Regelgeving (CUR): Aanbeveking 25, Korte Ankers in Beton; berekening en uitvoering. Redactionale Bijlage bij Cement 4/2000. 7. Comité Euro-International du Béton (CEB): Design of Fastenings in Concrete. Bulletin D’Information No. 226, Lausanne. Thomas Telford, London 1995. 8. Comité Euro-International du Béton (CEB): Fastenings to Concrete and Masonry Structures. State-of-the-Art-Report, Bulletin D’Information No. 216, Lausanne. Thomas Telford, London 1994. 9. Cook, R.A.; Bishop, M.C.; Hagedoorn, H.S.; Sikes, D.; Richardson, D.S.; Adams, T.L.; De Zee, C.T.: Adhesive Bonded Anchors: Bond Properties and Effects of InService and Installation Conditions. Bericht Nr. 94-2A, University of Florida, Department of Civil Engineering, Collage of Engineering, Gainsville 1994. 10. Cook, R.A.; Kunz, J.; Fuchs, W.; Konz, R.C.: Behavior and Design of Single Adhesive Anchors under Tensile Load in Uncracked Concrete. ACI Structural Journal, V. 95, No. 1, 1998, S. 9-26. 11. Deutsches Institut für Bautechnik (DIBt): Bemessungsverfahren für Dübel zur Verankerung in Beton (Anhang zum Zulassungsbescheid). Berlin, Ausgabe Juni 1993. 12. Dieterle, H.; Bozenhardt, A.; Hirth, W.; Opitz, V.: Tragverhalten von Dübeln in Parallelrissen unter Schrägzugbeanspruchung. Bericht Nr. 1/45-89/19 (nicht veröffentlicht). Institut für Werkstoffe im Bauwesen. Universität Stuttgart, 1990. 13. Dieterle, H.; Opitz, V.: Tragverhalten von nicht generell zugzonentauglichen Dübeln, Teil 1: Verhalten in Parallelrissen. Bericht Nr. 1/34-88/21 (nicht veröffentlicht). Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1988. 14. Eligehausen, R.; Bouska, P.; Cervenka, V.; Pukl, R.: Size Effect of the Concrete Cone Failure Load of Anchor Bolts. In Bažant, Z.P. (Herausgeber), Fracture Mechanics of Concrete Structures. S. 517-525, Elsevier Applied Science, London, New York, 1992/2. 15. Eligehausen, R.; Bozenhardt, A.: Crack Widths as Measured in Actual Structures and Conclusions for the Testing of Fastening Elements. Bericht Nr. 1/42-89/9, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1989.
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16. Eligehausen, R.; Fuchs, W.; Ick, U.; Mallée, R.; Reuter, M.; Schimmelpfennig, K.; Schmal, B.: Tragverhalten von Kopfbolzenverankerungen bei zentrischer Zugbeanspruchung. Bauingenieur 67, S. 183-196, 1992/1. 17. Eligehausen, R.; Mallée, R.: Befestigungstechnik im Beton- und Mauerwerkbau. Bauingenieur-Praxis. Ernst & Sohn, Berlin 2000. 18. Eligehausen, R.; Ožbolt, J.: Size Effect in Anchorage Behavior. Proceedings, ECF8, Fracture Behavior and Design of Materials and Structures, Turin, 1990. 19. Eligehausen, R.; Sawade, G.: A Fracture Mechanics based Description of the PullOut Behavior of Headed Studs embedded in Concrete. Fracture Mechanics of Concrete Structures, From Theory to Application. S. 281-299. Herausgeber: Elfgren, L. Chapmann and Hall, London, New York, 1989. 20. European Organization for Technical Approvals (EOTA): Guideline for European Technical Approval of Metal Anchors for Use in Concrete. Part 1, 2, 3 & 4, Brüssel, 1997. 21. Fuchs, W.: Tragverhalten von Befestigungen unter Querlast im ungerissenen Beton. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1990. 22. Fuchs, W.; Eligehausen, R.; Breen, J.E.: Concrete Capacity Design (CCD) Approach for Fastening to Concrete. ACI Structural Journal, Vol. 92, No. 1, S. 73-94, 1995/1. 23. Fuchs, W.; Eligehausen, R.; Breen, J.E.: Concrete Capacity Design (CCD) Approach for Fastening to Concrete, Authors’ Closure to Discussion. ACI Structural Journal, Vol. 92, No. 6, S. 794-802, 1995/2. 24. Furche, J.: Zum Trag- und Verschiebungsverhalten von Kopfbolzen bei zentrischem Zug. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1994. 25. Furche, J.; Dieterle, H.: Ausziehversuche an Kopfbolzen mit unterschiedlichen Kopfformen bei Verankerungen in ungerissenem Beton und Parallelrissen. Bericht Nr. 9/1-86/9 (nicht veröffentlicht), Institut für Werkstoffe im Bauwesen. Universität Stuttgart, 1986. 26. Furche, J.; Eligehausen, R.: Lateral Blow-out Failure of Headed Studs Near the Free Edge. In: Senkiw, G.A.; Lancelot, H.B. (Herausgeber), SP-130, Anchors in Concrete, Design and Behavior. American Concrete Institute, S. 235-252, Detroit, 1991. 27. International Building Code (IBC): International Code Council. Fall Church, Virginia, March 2000. 28. Klingner, R.E.; Hallowell, J.M.; Lotze, D.; Park, H.-G.; Rodriguez, M.; Zhang, Y.G.: Anchor Bolt Behavior and Strength During Earthquakes. Report No. NUREC/CR-5434. The University of Texas at Austin, 1998. 29. Lehmann, R.: Tragverhalten von Metallspreizdübeln in ungerissenem und gerissenem Beton bei der Versagensart Herausziehen. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1993. 30. Lehr, B.: Bemessung von Befestigungen mit Verbunddübeln. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 2001. 31. Lehr, B.; Eligehausen, R.: Vorschlag eines Bemessungskonzeptes für Verbundanker. Bericht Nr. 20/25-98/6, (nicht veröffentlicht). Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1998.
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32. Lotze, D.: Untersuchungen zur Frage der Wahrscheinlichkeit, mit der Dübel in Rissen liegen – Einfluß der Querbewehrung. Bericht Nr. 1/24-87/6 (nicht veröffentlicht), Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1987. 33. Meszaros, J.: Tragverhalten von Einzelverbunddübeln unter zentrischer Kurzzeitbelastung. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 2001. 34. Ministry of Construction of People’s Repuplic of China: Anchors for Use in Concrete (Draft). China, 2000. 35. Rehm, G.; Eligehausen, R.; Mallée, R.: Befestigungstechnik. Betonkalender 1988, Teil II, Verlag Wilhelm Ernst & Sohn, Berlin 1988, S. 569-663. 36. Rehm, G.; Lehmann, R.: Untersuchungen mit Metallspreizdübeln in der gerissenen Zugzone von Stahlbetonteilen. Forschungsbericht, Forschungs- und Materialprüfungsanstalt Baden-Württemberg, Stuttgart 1982. 37. Reick, M.: Brandverhalten von Befestigungen in Beton bei zentrischer Zugbeanspruchung. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 2001. 38. Schade, P.: Stand der Befestigungstechnik in der Praxis. Diplomarbeit am Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 2001. 39. Schweizerischer Ingenieur- und Architekten-Verein (SIA): SIA 179, Befestigungen in Beton- und Mauerwerk. Zürich, 1998. 40. Steiner, J.: Vermeidbare Qualitätseinbuße – Erfahrungen mit der Planung und der Ausführung von Verankerungen mit Dübeln. IBK-Bau-Fachtagung, Dübel- und Befestigungstechnik, Darmstadt 2000. 41. Studiengemeinschaft für Fertigbau e.V.: Verankerungen am Bau. Technisches Merkblatt der Arbeitskreise “Dübel” und “Verankerungen am Bau”. Wiesbaden 2000. 42. Zhao, G.: Tragverhalten von randfernen Kopfbolzenverankerungen bei Betonbruch. Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1993.
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ANCHORING TO CONCRETE: THE NEW ACI APPROACH John E. Breen*, Eva-Maria Eichinger** and Werner Fuchs*** *Ferguson Structural Engineering Laboratory, The University of Texas at Austin, USA **Institute for Structural Concrete, Technical University of Vienna, Austria ***Institute for Construction Materials, University of Stuttgart, Germany
Abstract This paper outlines the general approach of a new appendix for design of anchoring to concrete in the American Concrete Institute (ACI) Building Code. It covers cast-in-situ anchors and mechanical post-installed anchors. ACI 318 and the ACI Technical Activities Committee have approved this proposal, and it is being published for public comment as part of the ACI 318-2001 revision. The proposed design procedures are in general harmony with provisions being developed by fib.
1. Foreword It is a great privilege to participate in this Symposium. It is fitting that it is being held at the University of Stuttgart where Professors Gallus Rehm, Rolf Eligehausen and their coworkers, established the extensive scientific basis for modern approaches to Anchoring to Concrete. While ACI has long had recommendations for the design of anchors when used in nuclear related structures (ACI 349) the ACI 318 Building Code has been silent on this subject. In 1970, ACI Committee 355, Anchorage to Concrete, was established to report on performance and recommend design and construction practices for anchorage to concrete. Because of trade conflicts, no design related code recommendations ever came to ACI 318. In 1989 ACI 318 Sub B formed a task force to develop anchoring to concrete design provisions. Anchor qualification provisions were left to ACI 355 and ASTM. The design approach adopted by ACI 318 stems directly from the interaction with Dr. Fuchs as a DFG post-doctoral fellow at The University of Texas in 1990-1991. His visit resulted in major integration of the European and North American test data on cast-in-place and post-installed anchors reported in comparison studies of Reference 1. Detailed discussions led to adaptation of the previously proposed Stuttgart κ method to
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make it more “designer friendly,” a most important factor in subsequent adoption by ACI 318. Now, twelve years later that challenge is virtually done, at least in its first phase. This paper describes where ACI 318 is and its general approach. But, in structural concrete, doors never truly close. While the new recommendations cover much and represent a great improvement, they are still only first steps. The search is just beginning for similar design provisions for adhesive and grouted anchors.
2. Introduction In 1995 when setting the goals for the 2001 ACI 318 Building Code, the membership voted overwhelmingly to add specific design provisions for anchoring to concrete. This reflects the increased demand for such design guidance by code users, the considerable research and design development stimulated by ACI Committees 349 and 355, and the increased cooperation with CEB (now fib). Main decisions in the ACI 318 approach were based on the unanimous technical advice from Committee 355. The approach had to be compatible with the load and resistance factor format of the present code. The nominal resistance expressions should be consistent with the observed accuracy of the design formulae or values from comprehensive tests. A design approach should be found that accommodates brittle failure as well as ductile failure modes. The design provisions that envision brittle failure should use load and resistance factors appropriate for brittle failure modes. The nominal resistance design formulae should account for the effects of the type of anchor, anchor material, anchor diameter, edge distance, spacing, concrete strength, embedment depth and for the effects of cracking. An alternate approach using site specific testing to determine design values should be included. The basic approach of the ACI 318 Building Code provisions is to express all possible modes of failure for the anchors, to require the use of conservative design provisions based on the 5 percent fractile, and to provide some limited spacings, edge distance minimums and minimum thicknesses for the concrete member. Then, while the user is allowed to choose any design models or design by test values that meet these general requirements, for practical use a “deemed to satisfy” procedure is included. This latter procedure for steel failures is based on the method of AISC LRFD [2] while for concrete failures, it is based on the Concrete Capacity Design (CCD) procedure [1,3] that is accurate, designer friendly and in good agreement with tests. Special provisions for seismic applications and enhanced ductility through use of supplementary reinforcement are included. The ACI 318 Building Code provisions are applicable in scope to cast-in-place headed studs and headed or hooked bolts as well as a variety of post-installed anchors such as expansion anchors and undercut anchors [See Fig. 1]. Committee 318 plans to include provisions for adhesive anchors in a future code revision. A key element in the design philosophy is that the post-installed anchors must be prequalified by acceptance testing
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using performance standards developed by ASTM or ACI 355 (ACI 355.2-00) [4]. This testing differentiates between post-installed anchors according to their installation sensitivity, behavior in oversize holes, low and high strength concrete, or with partial torque or expansion in cracked or uncracked concrete. These standards are similar to European EOTA (ETAG) requirements but adapted to American certification procedures. The anchors are placed in one of three categories according to their performance in tests. The ACI Code gives reduced resistance factors (φ) for the poorer performing categories. Designers may specify allowable categories to be used according to their safety requirements. The ACI 318 Appendix passed all voting procedures of Committee 318 and was approved by the ACI Technical Activities Committee pending final approval of the reference testing standard. A version for cast-in-place anchors that does not require such acceptance testing was adopted and included in the International Building Code 2000 [9]. An almost identical version has been adopted by ACI 349B for cast-in and post-installed anchors for nuclear-related structures. Since the Nuclear Regulatory Commission prescribes test procedures for fastening acceptance, the ACI 349B-1999 version did not have to wait for completion of the reference acceptance testing standard. Thus, ACI has now replaced the traditional 45º cone approach of ACI 349B with the new CCD procedures. The overall approach has also been adopted by the Fastening to Concrete committee of NEHRP (National Earthquake Hazard Reduction Program) for inclusion in NEHRP 2000 [10].
hef
hef (a) post-installed anchors
(b) cast-in-place anchors
Figure 1 – Types of anchors The proposed Appendix provides design requirements for structural anchors used to transmit structural loads from attachments into concrete members by means of tension, shear, or a combination of tension and shear. Several failure types of fasteners can be differentiated [See Figs. 2 and 3]. Strength design of structural anchors is based on the computation or test evaluation of the steel tensile and shear strengths of the anchor and the attachment, the concrete breakout tensile and shear strengths, the tensile pullout strength of the anchor, the side-face blowout strength, the concrete pryout strength and required edge distances, spacing and member thickness to preclude splitting failure. The minimum of these strengths is taken as the nominal strength of the anchor for each load condition. Regardless of the mode which governs for a given anchor at a given embedment depth, the suitability of post-installed anchors for use in concrete must be demonstrated by the prequalification tests of ACI 355.2 [4].
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Many possible design approaches exist and the user is always permitted to “design by test” as long as sufficient data are available to verify the model. If test results are used these must be evaluated on an equivalent statistical basis to that used to select the values for the concrete breakout method in the “deemed to satisfy” provisions. The basic capacity shall not be taken greater than the 5 percent fractile. When the failure of an anchor group is due to breakage of the concrete, the behavior is brittle and there is limited redistribution of the forces between the highly stressed and less stressed anchors. In such a case the theory of elasticity must be used for determining the force on the anchor, assuming the attachment that distributes loads to the anchors is sufficiently stiff. The forces in the anchors are considered to be proportional to the external load and its distance from the neutral axis of the anchor group.
Nn
Nn
(a) Steel Failure
Nn
Nn
(b) Pullout
Nn
(c) Concrete Breakout
Nn
Nn
Nn
Nn
(e) Concrete Splitting (d) Side-Face Blowout
Figure 2 — Failure modes for fasteners under tensile loading
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Vn
Vn
(b) Concrete Pryout for Fasteners Far From a Free Edge
(a) Steel Failure Preceded by Concrete Spall Vn
Vn
Vn Vn
Vn Vn
Vn
(c) Concrete Breakout
Figure 3 — Failure modes for fasteners under shear loading If an anchor failure is governed by ductile failure of the anchor steel, significant redistribution of anchor forces may occur. In such a case, analysis assuming the theory of elasticity will be conservative. A non-linear analysis, using theory of plasticity, is allowed for the determination of the ultimate loading conditions of ductile anchor groups. The levels of safety defined by the combinations of load factors and resistance factors (φ) are appropriate for structural applications. The designer may use lower levels of safety in design for non-structural applications and may wish to use more demanding safety levels for particularly sensitive structural connections. The safety levels are not intended for handling and construction conditions. The φ factors proposed for use with the current load factors given in the 1995 ACI Code Section 9.2 are given in Table 1. Condition A applies where the potential concrete failure surfaces are crossed by supplementary reinforcement proportioned to tie the potential concrete failure prism into the structural member. Condition B applies where such supplementary reinforcement is not provided or where pullout or pryout strength governs. Higher φ factors are given for anchors that have supplementary reinforcement in the direction of the load to increase overall ductility, i.e. Condition A [See Fig. 4].
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Table 1: φ factors a) Anchor governed by tensile or shear strength of a ductile steel element .................... 0.90 b) Anchor governed by tensile or shear strength of a brittle steel element...................... 0.75 c) Anchor governed by concrete breakout, blowout, pullout or pryout strength Condition A Condition B i) Shear Loads ...................................................................... 0.85 0.75 ii) Tension Loads Cast-in headed studs, headed bolts, or hooked bolts ........ 0.85 0.75 Post-installed anchors with category as determined from ACI 355.2 Category 1 (Low sensitivity to installation and high reliability) ...................................................................... 0.85 0.75 Category 2 (Medium sensitivity to installation and medium reliability) ........................................................ 0.75 0.65 Category 3 (High sensitivity to installation and lower reliability) ...................................................................... 0.65 0.55
Figure 4 – Influence of reinforcement on the load-displacement behavior of headed anchors loaded in shear (from Ref.5)
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For a post-installed anchor to be acceptable in seismic loading situations, the system must be proven to have adequate ductility. The anchor must demonstrate the capacity to undergo large displacements through several cycles as specified in the seismic simulation of the ACI 355.2 prequalification tests. If the anchor cannot meet these requirements or if substantially reduced design loads are being applied which assume substantial ductility in the structure, then the attachment must yield at a load well below the anchor capacity.
3. Steel Based Resistance For the calculation of steel failure, an approach based on the AISC LRFD [1] approach was “deemed to satisfy” (See Reference 6). In case of steel failure the shear and tensile strength of an anchor are evaluated based on the properties of the anchor material and the dimensions of the anchor. Values based on the 5 percent fractile of test results may also be used.
4. Concrete Based Resistance The basic design concrete capacities for any anchor or group of anchors must be based on design models which result in predictions of strength in substantial agreement with results of comprehensive tests and which account for the size effect. They are to be based on the 5 percent fractile of the basic individual anchor capacity, with modifications made for the number of anchors, the effects of close spacing of anchors, proximity to edges, depth of the concrete member, eccentric loading of anchor groups, and presence or absence of cracking. Limits on edge distances and anchor spacing in the design models shall be consistent with the tests that have verified the model. The “deemed to satisfy” design method used for the calculation of the concrete breakout capacities under tensile or shear loading was developed from the Concrete Capacity Design (CCD) Method [1,3], which was an adaptation of the κ method [7,8] and is considered to be accurate, relatively easy to apply, and can be extended to irregular layouts. For single anchors, it assumes a breakout prism angle of about 35 degrees [Figs. 5, 6]. Both the CCD and the κ methods include fracture mechanics theory, which indicates that in the case of brittle concrete failure the failure load increases at a rate less than the increase in the available surface and that the nominal stress at failure (peak load divided by failure area) decreases with increasing member size. The method predicts the load-bearing capacity of an anchor or group of anchors by using one basic equation for a single anchor in cracked concrete, and multiplying by factors which account for the number of anchors, edge distance, spacing, eccentricity and absence of cracking [1,6]. A very important attribute of the CCD approach is that it is reasonably “transparent” and hence designer friendly. Rather than working with the complex intersection of 45º cones as previously required by the ACI 349B approach, the CCD method when applied to groups uses values of AN/ANo or AV/AVo that are based on projected areas of
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quadrilaterals. These areas are illustrated in Figure 7 for tension loads and in Figure 8 for shear loads.
The critical edge distance for headed studs, headed bolts, expansion fasteners, and undercut fasteners is 1.5hef . 1.5 hef
1.5hef
1.5 hef
1.5hef
≈ 35° h ef
1.5hef
1.5hef
Section through failure cone Plan view
A No = 2 * 1.5 h ef × 2 * 1.5 h ef = 3 h ef × 3 h ef = 9 h ef2
Figure 5 – CCD concrete cone breakout model for tensile loading
1.5c1
≈35o
Vn Center of fastener where it crosses the free surface
1.5c1
The critical edge distance for headed studs, headed bolts, expansion fasteners, and undercut fasteners is 1.5c1
1.5c1
c1
Edge of concrete
1.5c1
Plan view
Vn
1.5c1
hef
Side section
A Vo = 2 ∗ 1.5c 1 × 1.5c 1 = 3c1 × 1.5c 1 = 4.5c 12 Front view
Figure 6 – CCD concrete cone breakout model for shear loading
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c1 1.5 hef 1.5 hef 1.5 hef
AN AN = (c1 + 1.5hef) (2 x 1.5hef) if c1 < 1.5hef
s1 1.5 hef
1.5 hef 1.5 hef
c1
AN AN = (c1 + s1 + 1.5hef) (2 x 1.5hef) if c1 < 1.5hef and s1 < 3hef
s1 1.5 hef
c2
s2 1.5 hef
c1
AN AN = (c1 + s1 + 1.5hef) (c2 + s2 + 1.5hef) if c1 and c2 < 1.5hef and s1 and s2 < 3hef
Figure 7 – Projected areas for single anchors and groups of anchors for tension loads
5. Other Design Concepts A comparison with the extensive test database indicated that the CCD method gave good results over the full range of applications [Figs. 9, 10]. While the ACI 349-85 procedure had very much the equivalent accuracy in some ranges, it was very unconservative in other ranges, particularly with group effects, and the geometry of intersecting circles was much more complex in group applications [Fig. 11]. However, recognizing that widely accepted procedures such as the earlier ACI 349-85 model as well as the PCI model can give satisfactory results in certain ranges, the proposed ACI 318 Appendix allows any “design models which result in substantial agreement with results of comprehensive tests” to be used. This generalized wording
39
allows previous procedures like the ACI 349 or PCI techniques to be used in applicable ranges if desired.
if h < 1.5c1
if h < 1.5c1
Vn/2
Vn Av
Av
c1
h
Vn/2 c1
h 1.5c1 1.5c1
1.5c1 1.5c1
AV = 2 x 1.5c1 x h
AV = 2 x 1.5c1 x h Note:One One assumption of the Note: assumption of the distribution forces indicates distribution of of forces indicates that that half half thewould shear be would be on critical the shear critical front on front anchor its projected fastener and its and projected area. area.
if c2 < 1.5c1 Vn Av
c1
1.5c1
if h < 1.5c1 Vn
c2 1.5c1 Av
AV = 1.5c1 (1.5c1 + c2)
c1
h 1.5c1
if h < 1.5c1 and s1 < 3c1
Av = 2 x 1.5c1 x h
Vn Av
Note:Another Another assumption of the Note: assumption of the distribution forces applies distribution of of forces thatthat applies onlyonly where anchorsare arerigidly rigidly connected where fasteners connected to to theattachment attachment indicates the total the indicates thatthat the total shear would critical on the shear would be be critical on the rearrear anchor and itsand projected area. area. fastener its projected
c1
h 1.5c1
s1
1.5c1
1.5c1
AV = (2 x 1.5c1 + s1) x h
Figure 8 – Projected areas for single anchors and groups of anchors for shear loads
Typical cast-in-place headed studs, headed anchor bolts and hooked anchors have been tested and have proven to behave predictably, so calculated pullout values are acceptable.
40
Post-installed anchors do not have predictable pullout failure loads, therefore they must be tested. The pullout strength of headed studs or headed anchor bolts can be increased by provision of confining reinforcement such as closely spaced spirals throughout the head region. This increase can be demonstrated by tests. The tensile and shear capacity can be increased by provision of supplementary reinforcement with resisting components in the direction of the applied force [See Fig. 4] [5].
a) Equation vs Tension Test Results for Post-Installed Anchors
b) Equation vs Tension Test Results for Headed Studs and Anchor Bolts
in uncracked concrete, and not affected by edges or spacing
in uncracked concrete, and not affected by edges or spacing
Mean CCD Equation for tension on post-installed anchors in uncracked concrete
Mean CCD equation for tension on headed studs and anchor bolts in uncracked concrete
1000
Failure Load, kN
Failure Load, kN
300
200
500
100
Design equation for anchors in uncracked concrete
Design equation for anchors in uncracked concrete 0 0
50
100
150
200
0
250
0
125
250
375
500
Effective Embedment Depth, hef, mm
Effective Embedment Depth, hef, mm
Figure 9 – Mean and design CCD equations for anchors in uncracked concrete compared to test data for a) post-installed anchors and b) headed anchors
41
625
Equation vs. Shear Test Results for single anchors in deep uncracked members (European Tests)
Failure Load, kN
150
Mean CCD equation for shear in uncracked concrete
100
50
0
Design equation for shear in uncracked concrete
0
75
150
225
300
Edge Distance in Direction of Shear, c1, mm
Figure 10 – Mean and design CCD shear equations for uncracked concrete compared to test data
N [kN] 3000
Symbol
1 4 16 36
Si
+ I3 AC
85 49-
fcc′ = 25 N/mm2 hef = 185 mm n = 1-36 headed studs
St
2000
n
hod Met CCD
1000
200
400
600
800
+
Mean value of a series
1000 Si [mm]
Figure 11 – Comparison of ACI 349-85 and CCD design equations for anchor groups
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Interaction of tensile and shear loads is considered in the design using an interaction expression which results in predictions of strength in substantial agreement with results of comprehensive tests [See Ref. 6 and Fig. 12]. The values used for the tension part of the interaction equation shall be the smallest of the anchor steel strength, concrete breakout strength, sideface blowout strength, or pullout strength. For the shear part, the smaller of the steel strength, the concrete pryout strength or the concrete breakout strength shall be used.
Nu Nu φ Nn
φ Nn
5
3
+ Vu φ Vn
5
3
=1
Trilinear Interaction Approach
0.2 φ Nn φ Vn
0.2φ Vn
Vu
Figure 12 – Shear and tensile load interaction equation
6. Status In North America, a task force of ACI 318 Subcommittee B developed and refined the current proposals that have been approved by ACI Committee 318. ACI 355 recently completed the post-installed anchor acceptance test standard [4], but it has been subject to procedural and legal challenges by one anchor manufacturer. Assuming resolution of this challenge, comprehensive design provisions will be in ACI 318-2001. Even if the challenge provides further delay in adoption of the provisions for post-installed fasteners, the new ACI 349B expressions will be widely used and cast-in anchors will be governed by the recently adopted IBC 2000 provisions. These are identical to the ACI 318 provisions given herein but are limited to cast-in applications. The proposed new Appendix to the ACI 318 Building Code is a very important step in harmonizing several existing design procedures. The user is allowed to choose any design models or design by test values that meet the general requirements. A design procedure based on the CCD design method is “deemed to satisfy.” The harmonization with the CEB task force leads to the hope that future fib recommendations and Eurocodes will be in close agreement with the new ACI approach.
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7. References 1. Fuchs, W., Eligehausen, R., and Breen, J., Concrete Capacity Design (CCD) Approach for Fastening to Concrete. ACI Structural Journal, 92(1), Jan.-Feb., 1995, pp. 73-93. 2. American Institute of Steel Construction (1986). Manual of Steel Construction – Load and Resistance Factor Design. 3. Eligehausen, R., and Balogh, T., Behavior of Fasteners Loaded in Tension in Cracked Reinforced Concrete, ACI Structural Journal, 92(3), May-June 1995, pp. 365-379. 4. ACI Committee 355, ACI Provisional Standard 355.2-00, Evaluating the Performance of Post-Installed Mechanical Anchors in Concrete, American Concrete Institute, Detroit, MI. 5. Comité Euro-International du Béton (1994). Fastenings to Concrete and Masonry Structures – State of the Art Report. Thomas Telford Services Ltd., London. 6. ACI Committee 318, Proposed Changes to Building Code Requirements for Structural Concrete, scheduled to be published in June 2001 edition of Concrete International. 7. Eligehausen, R., Fuchs, W., and Mayer, B., Load Bearing Behavior of Anchor Fastenings in Tension. Betonwerk + Fertigteiltechnik, 12(87), pp. 826-832, and 1/88, pp. 29-35. 8. Eligehausen, R., and Fuchs, W., Load Bearing Behavior of Anchor Fastenings under Shear, Combined Tension and Shear or Flexural Loadings. Betonwerk + Fertigteiltechnik, 2(88), pp. 48-56. 9. International Code Council, International Building Code 2000, Falls Church, Virginia, March 2000. 10. Proposed year 2000 revisions to the 1997 edition of the NEHRP (National Earthquake Hazards Reduction Program) Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Federal Emergency Management Agency 302, Building Seismic Safety Council, Washington, DC, 1997.
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EVOLUTION OF FASTENING DESIGN METHODS IN EUROPE Werner Fuchs Institute of Construction Materials, University of Stuttgart, Germany
Abstract Since antiquity there has been a demand for more flexibility in the planning, design and strengthening of concrete structures in Europe. Although a wide variety of fastening systems have been invented over the years to help achieve this goal, our understanding of the behavior of these systems and the corresponding development of design provisions has only in the past three decades made significant advances. This paper gives a brief overview of the evolution of fastener design. Emphasis is placed on the importance of understanding the physics behind these problems and the need for a unified design approach throughout Europe.
1. Foreword Stability, durability and aesthetics have always been primary concerns for buildings. These requirements have been equally important for fastening technology. In the 1st century B.C., Vitruvius described in his 10 books on architecture practical solutions for fastening applications. It can be assumed that fasteners played an important role in the construction of the Colosseum in Rome as evidenced by the ruins (Fig. 1). At many other excavation sites in Europe traces similar fastening devices have been found. At the beginning of the 20th century, the common thinking of the master builder with regard to fastening technology was: "leave well-enough alone". That is to say, use what has been proven to work. Consequently, fastening technology was restricted for many centuries to grouting or cast-in situ installation of steel parts. This dogma was thrown into turmoil as new construction methods were developed such as mixed constructions from concrete and steel or concrete and wood which placed higher demands on fastening technology. For the fulfillment of these tasks, new solutions in the fastening technology such as post-installed fasteners were provided.
45
Figure 1: Colosseum, Rome The diversity of products increased with the number of possible applications of fastening devices. For the user in the practice, it became difficult to find the correct fastening solution and to design safe connections. It became apparent that guidelines to aid in the design of structures using fastening systems was necessary.
2. Introduction The push over the last two decades to reduce construction duration has brought about increased use of fasteners for the transfer of concentrated loads in concrete structures. Various types of fastenings, such as cast-in-place headed anchors, as well as postinstalled mechanical and chemical fastening systems, are available to meet a wide range of strength and application requirements. Furthermore, installation techniques have been developed for certain fastening systems, which have features that can be tailored to fit special construction situations and offer added constructability and productivity advantages. These advances have been brought about through extensive scientific work and today myriad prequalified, quality controlled products with demonstrated repeatable performance characteristics meet the ever increasing demand for safe and secure fastening products in a wide field of applications. This paper surveys fastener design techniques from past to present. It illustrates how fastenings were historically used to meet project demands and the progress of products for new applications. Some developments in building design codes are also highlighted. The review focuses primarily on developments in Europe, however, similar trends can be observed in other parts of the world.
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3. Basic principles Plutarch (45-125 A.D.) reported that the building contractors who promise quality construction and fast execution, with the lowest costs, will receive the contract for the erection of a building. The trade-offs between quality, costs and deadlines have apparently existed for millenniums and are still valid today for the discipline of structural fastening technology. As the use of fasteners has increased in recent years, so has the need to ensure their correct use on site. Faced with a bewildering multitude of fastening systems, the first question one must ask one's self is: 'Which kind of fastening type is most appropriate for my application?'. The second question is: 'How do I use it to achieve its maximum effect?'. This work is the domain of the engineer. The best design method and the most careful design by engineer, however, are of no use if the fastening device specified by the designer does not function reliably or is not installed properly. The factors influencing the successful design of connections are illustrated in Figure 2. reliable fastening systems
satisfying design provisions
designer (accurate design)
installer (proper installation)
safe, economical, aesthetically pleasing connection
Figure 2: Success factors for connections It goes without saying that connections for safety relevant applications where fastening devices are used, should be planned and designed by experienced personnel. Reproducible calculations and drawings must be done. The fastening installation has to be carried out by properly trained workers. Reliable connections based on reliable fasteners and appropriate design procedures may be ensured only by cooperation of both: the designer and the installer. One should never lose sight of the fact that proper connection design and application are vital for the overall performance of a structure.
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4. Evolution of fastening systems As the development of new and innovative products in fastening technology has gained pace, design provisions have become considerably more accurate, more transparent and unfortunately, more time consuming. In Figure 3 the load-bearing principles of three commonly used fasteners are shown. Load transfer through mechanical interlock by anchor heads (Fig. 3a)) and grouting or glueing of steel parts to the base material (Fig. 3c)) are very old techniques. In the past the design of such fastening elements was based mainly on trial and error. Failure was to be avoided at all costs and it was for this reason that the fasteners were overdesigned in most applications. This poor engineering was due to a lack of understanding of the behavior of fasteners.
N
a)
N
N
N
b)
c)
Fig. 3: Load-bearing principles of fastening elements a) mechanical interlock (direct) b) expansion (friction) c) grouting, glueing (bond, shear) In 1920 a new era in fastening technique began, when John Rawlings applied a time tested scientific principle as a means of making fasteners. Namely, he used the principle of expansion (Fig. 3b)) to develop the first expansion anchors (Fig. 4). When a screw was turned into a threaded plug, the product expanded and tightly griped the side of the hole that had been made for it. The result was that the plug and screw become securely fixed. This invention immediately gained public favor for small fastener dimensions. It was not until the 1960's, however, that the real break-through for post-installed fasteners occurred: This was when the first electric compact hammer-drill tools were launched to the construction market. It became possible to drill large holes into concrete in a reasonable period of time. At about the same time the first post-installed glass-capsule
48
type adhesive anchors became available to the construction market and increased the range of applications for post-installed fastening systems. The use of post-installed anchors for structural applications began to soar, and today a big variety of fastening systems classified in cast-in situ fasteners and post-installed fasteners with different load-bearing principles are known and used in virtually every country of the world. The need for reliable design provisions taking into account the load-bearing principles is evident.
Fig. 4: One of the first expansion anchors
5. Development of design concepts Fastener design provisions must account for several influencing factors. For example they must consider the type of fastener, its load-bearing mechanism, fastener material, fastener diameter, edge distance, anchor spacing, concrete strength, embedment depth, as well as for the conditions of the base material (cracked or non-cracked concrete), the type of loading and the loading direction. Early on there was little known about the parameters mentioned above. The designer, liable for his work with his fortune and perhaps even his life, had to design according to experience and gut feeling. Therefore, he may have used lower levels of safety in design for non-structural applications and more demanding safety levels for particularly sensitive structural connections. With the development of post-installed fasteners this situation changed. It was necessary to promote new products and to convince the engineering community of their performance. The design of early post-installed fasteners was primarily based on test results. Tensile loading was thought to be the most critical application. Therefore, values obtained from static, short-duration tests with single fastenings under tensile loading were published as technical data in most manufacturers' product information brochures. The producers recommended to apply a global safety factor 4 ≤ γ ≤ 5 to the mean ultimate load of the tests to account for variations e.g. in concrete, steel and fastening reliability. For non-standard applications the designer had to refer to his own experience and limited common knowledge. Until about 1970, no guidelines or standards for fastener testing and evaluation were available. Testing was conducted based on an individual laboratories' experience or
49
according to the manufacturers' recommendations. It became apparent that depending on the testing laboratory, the same product could end up with different load-bearing behavior, ultimate capacity and consequently, a different recommended allowable load. The need for harmonization of testing and evaluation procedures became obvious. In response to several, in part severe accidents mainly due to improper use and installation of post-installed fasteners, an expert committee 'Channel bars and dowels' was set up in Berlin, Germany in 1972 to refine the application of fasteners to allow for greater safety and durability. Thus began the first true research work in fastening technology with the goal of understanding the influence of the test methods on the fastening systems. The focus was on the most common case of predominantly static loading. The investigations yielded testing guidelines. The experimental program included tensile tests and shear tests far away from edges. Furthermore, the experience from a large number of fastener tests showed that the load-bearing capacity of the fasteners approximates a normal Gaussian probability density function. This allowed for the use of statistical evaluation techniques, which could relate the allowable load to the reliability of the connection. Thus, design could be defined based on the 5%-fractile with a global safety factor γ = 3 for concrete failure and γ =1.75 for steel failure. The minimum strength after evaluation was taken as the allowable load for each load condition: tension, shear and combined tension and shear loading. Acceptable quality levels were defined and the era of approved fastening systems began. The design was founded on experimental results, corresponding evaluation method and allowable loads for certain applications. In addition it became necessary to the manufacturer to shown by internal (plant) and external quality control (testing agency), that the product samples used in the approval tests are conform with of the products marketed. Only fastening systems which were approved were permitted for use in safety relevant applications. In 1975 the first approvals for post-installed expansion and bonded anchors as single fastenings with large edge distances and anchor spacings for applications in non-cracked concrete were released. Both the admissible loads and the fields of application were limited, however, and not in accordance with practical requirements. This is illustrated by the technical data of a sleeve type expansion anchor M 12 with an embedment depth hef = 80 mm: The allowable load in non-cracked concrete C20/25 was 5.7 kN at a minimum edge distance c1 = 130 mm, a minimum distance to the corner c1 = c2 = 180 mm and the minimum anchor spacing s = 450 mm. As our knowledge of the behavior of structural fasteners increased the range of applications regulated by German approvals was extended. Approvals were granted for double fastenings with post-installed anchors in non-cracked concrete (1978) and for single fasteners with expansion anchors in cracked concrete (1979). Then, the allowable load for an expansion anchor M 12 situated in cracked concrete was just 1.5 kN.
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In the mid 1970's, the headed stud industry in the United States intensified testing and supported the development of the first design methods for applications in non-cracked concrete only [9]. The nominal tensile capacity of an anchor governed by concrete failure was assumed to be computed by the maximum concrete tensile strength acting equally distributed on the surface of an idealized truncated conical failure surface (Fig. 5). The inclination of the concrete break.-out surface was assumed to 45 degrees. The design of fastenings under shear loads was based on similar assumptions of the failure mechanism. Because this design approach was conceptually simple and in satisfactory agreement with the limited test results available at this time, it was adopted by ACI 349 [10]. Due to the lack of design aids for cast-in parts, the ACI 349 design method was often used by designers in Europe.
Fig. 5: Concrete tensile capacity of a headed stud [10] In the beginning of the '80s, comprehensive research in fastening technology started in Germany. The first physical models explaining the behavior and failure of different fastening systems were developed [4]. These models lead to the so-called κ-method for the design of fastenings (Fig. 6). The main research focus was on the load-bearing principles of mechanical interlock and the mechanics of anchor expansion (Fig. 3a, b). In 1983, the first approval incorporating the κ-method was published for cast-in-place headed studs in non-cracked and cracked concrete. In 1985 followed approvals, also based on the κ-method, for mechanical post-installed anchorage systems for use as fastenings in the tensile and compressive zones of slab-type and beam-type concrete and reinforced concrete structural members. Fasteners were placed in load classes according to their anchorage depth (Fig. 7). Fastening in the tensile zone (i.e. cracked concrete)
51
was regarded as the normal case. The permissible load in the compression zone (noncracked concrete) was about 1.33 times the value in the tension zone. The higher allowable loads in the compression zone could be used for design, if in each individual case it was shown, that the anchors were installed in a concrete member, which is under compression over the full embedment depth of the fastener. Then, for the example of an expansion anchor M12, installed to concrete C20/25, the admissible load in cracked concrete might be 6 kN (compare to 1.5 kN in 1979), in non-cracked concrete 9 kN (compare to 5.7 kN in 1975), the minimum edge distance c1 = 120 mm, a minimum distance to the corner c1 = c2 = 120 mm and the minimum anchor spacing s = 80 mm.
Fig. 6: κ-method for fastenings according to German approvals [6] The κ-method represented a significant advance in the design methods given in approval documents up until this point, which – with a few exceptions – were applicable only to single anchors in the compressive zone with large anchor spacing and edge distances. The κ-method permitted to determine the admissible load of a single anchor and of an anchor in a double or quadruple fastening far from and close to an edge. The admissible load for a fixture is calculated from the admissible load of an individual anchor located at considerable distance from other anchors and from an edge of a structural member by multiplication with coefficients κ (Fig. 6). The values for the admissible load of the individual anchor, the critical anchor spacings and edge distances, that prevent adjacent anchors from interacting with each other as well as the minimum spacings and distances were stated in the approval documents. However the κ-method of the German approvals still had the disadvantage, that the minimum of the capacities under shear and tensile
52
loading evaluated from test results regardless of the mode of failure was taken as the admissible load of the fastener for each load direction, i.e. the admissible load represented the most unfavorable case.
Fig. 7: Load classes for mechanical anchors in cracked concrete [6] In the mid '80s, approvals for mechanical expansion anchors were released by SOCOTEC in France, which allowed higher loads and a wider range of applications than given in the German approvals. The basematerial used to establish these approvals, however, was non-cracked concrete. The admissible loads for each product were derived directly from experimental results. Since the French system did not use load classes, allowable anchor loads were dependent on scatter of concrete strength and on the testing methods of the testing institute, where proof testing was performed. In other countries where no approval system existed the designer had to rely on information provided by the manufacturers. Most of these published data were based on fastener testing. The manufacturers believed that determining the ultimate or allowable loads for fasteners from 'theoretical (i.e. calculation) methods' e.g. the κ-method would not give satisfactory results because of the interrelationships of the many variables involved e.g. material strength, friction coefficients, etc.. Hilti developed a design concept very similar to the κ-method also taking into account product specific characteristics. In some cases even different sizes of a single product had different tuning factors. Furthermore, the Hilti design method distinguished between load
53
directions and in this respect was superior to the κ-method of the German approvals at this time. The various efforts to develop new design provisions reflected the increased need and demand to design reliable connections with cast-in-place and post-installed anchors at reasonable costs. Further improvements were necessary. The German design concept of one admissible load for all directions could be presented in a very simple form, however, it resulted in many cases in a considerable underestimation of the load-carrying capacity of the fastening. For reasons of economy, it was desired to optimally utilize the capacity of anchor-type fastenings in most applications. Thus it was necessary to develop a more application oriented approach. The first steps in this direction are documented in [6, 7 and 8]. In these documents expanded κmethods for the computation of concrete break-out failure of post-installed mechanical expansion and undercut anchors as well as cast-in-place headed studs under tension, shear and combined tension and shear loading fracture mechanics theory are explained in detail. Fracture mechanics indicated that the failure load increases less than the available concrete break-out failure surface. That means the nominal stress at failure (peak load divided by failure area) decreases. Furthermore, corresponding to widespread observations in tests, the κ-method is based on 35 degrees concrete break-out cones. Note, these are major differences to the ACI 349 design approach. It was determined that an improved design method should distinguish between different directions of loading, modes of failure and condition of the base material (cracked or non-cracked). In addition, modern design recommendations should consider all available test data and differences among already existing recommendations should be analyzed and reconciled. This task was performed at the University of Stuttgart and during the visit of the author to the Structural Engineering Laboratory at the University of Texas, Austin in 1990-1991. During his visit the European and North American test data for cast-in-place and post-installed mechanical fasteners were assembled and integrated into a database to facilitate comparison studies with different design approaches. Furthermore, the κ-method to predict concrete capacity was adapted to make the design process more transparent and user friendly by implementing a rectangular prism model (Fig. 8). The combination of the accuracy of the κ-method and the transparency analogous to the ACI 349 cone model yielded the Concrete Capacitymethod (CC-method). The CC-method not only improved computation for design with fasteners, it also helped to increase the accuracy of the computed fastener capacity in comparison to design provisions using test results. Detailed results of the comprehensive studies leading to the development of the CC-method are given in [11]. A summary is published in [1].
54
The critical edge distance for headed studs, headed bolts, expansion anchors, and undercut anchors is 1.5hef . 1.5 hef
1.5hef
1.5 hef
1.5hef
≈ 35° h ef
1.5hef
1.5hef
Section through failure cone Plan view
A No = 2 * 1.5 h ef × 2 * 1.5 h ef = 3 h ef × 3 h ef = 9 h ef2
Fig. 8: Concrete cone surface idealized by a 35° prism, according to CC-method [11] To predict the capacity of other failure modes, such as steel failure, additional design models may be used. The pull-out capacity for typical cast-in-place headed studs has proven to be predictabe by calculation. Post-installed anchors on the other hand do not have predictable pullout failure loads and therefore they must be tested. Tests are also necessary to determine the minimum concrete member dimensions, minimum spacing and edge distances of fasteners to avoid a splitting failure. These values are characteristic of a product and are given in approvals or technical data sheets of the manufacturers. In 1987, in order to improve the design methods, the general knowledge and the awareness of the engineering profession in this area, the formation of Task Group III/5 (TG III/5) with members from academia, practice and producers from Asia, Europe and North America was authorized by the Comité Euro-International du Béton (CEB, now fib). One of the TG III/5's first major tasks was providing test data to support the author in the construction of a data base of European fastener tests at the University of Stuttgart. Until 1991, the group produced a state-of-the-art report on fastenings to concrete and masonry, first published as CEB Bulletins 206 and 207. A revised hardcover edition was published in 1994 [5]. Therein the revised safety concept for the design of fastenings based on partial safety factors was introduced to Europe.
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In the new safety concept it has to be shown that the value of the design actions Sd does not exceed the value of the design resistance Rd. (1)
Sd < Rd Sd Rd
= =
value of design action value of design resistance
The partial safety factors for the actions depend on the type of loading and shall be calculated according to Eurocode 2 or Eurocode 3. The partial safety factors for the resistances cover steel failure, concrete cone failure, splitting failure and pull-out failure. Furthermore, the partial safety factor γ2, which indicates the sensitivity of a fastening system to installation inaccuracy, was introduced. It is determined as part of the proof testing in so-called suitability tests and may not be changed because it describes a characteristic of the fastening system. The partial safety factors can be found in the relevant approvals. In 1993, stimulated by these results, DIBt (Deutsches Institut für Bautechnik) replaced the traditional κ-method with the new CC-method and the new safety concept for postinstalled mechanical fasteners [12]. Cracked concrete still was assumed the normal state of the base material. In 1995 in Germany the first approvals based on this new design concept were released for headed studs and mechanical post-installed fasteners suitable for applications in cracked concrete. Compared to 1985, with regard to tensile loading nothing has changed. However, now the admissible shear load in cracked concrete C20/25 is 14,9 kN (compare to 6 kN in 1985). At the same time throughout Europe harmonized test regimes were developed to create data necessary to fit the new design concept and to prequalify the products for safety relevant applications. In 1995, the CEB TG III/5 published a comprehensive design method for cast-in-place headed anchors and mechanical post-installed fasteners in concrete based on the CC-method in CEB Bulletin No. 226, released as a revised hardcover edition in 1997 [13]. This approach to the design of mechanical anchors forms the basis for current design codes in Europe and the United States. It was adopted by EOTA in ETAG 001, Appendix C [14] in 1997. According to ETAG the design resistance is based on the performance of a specific product demonstrated in prequalification tests following the ETAG directive [14]. Corresponding to the type and number of tests, three different design methods are proposed. The relation between the design methods and the required tests is given in Table 1. The design method to be applied is given in the relevant European Technical Approval (ETA) of the product concerned. In design method A the characteristic resistance is calculated for all load directions and failure modes. It must be shown that Equation (1) is satisfied for all loading directions
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(tension, shear, combined tension and shear), as well as all failure modes (steel failure, pull-out failure and concrete failure). To design the anchorage the loads acting on each anchor shall be calculated, taking into account partial safety factors.
Table 1: Design methods and required tests according to ETAG [14] Design method
cracked and noncracked concrete
A
x x
non-cracked concrete only
characteristic resistance for C 20/25 only
x x x
B
x x
x x
x x x x
C
C 20/25 to C 50/60 x
x x
x x
x x x x
x x
tests according ETAG Annex B, Option 1 2 7 8 3 4 9 10 5 6 11 12
Design method B is based on a simplified approach in which the design value of the characteristic resistance is considered to be independent of the loading direction and the mode of failure. In the case of anchor groups, the design is performed for the most highly stressed anchor. Design method C is based on a simplified approach in which only one value for the design resistance FRd is given, independent of loading direction and mode of failure. The actual spacing and edge distance must be equal to or larger than the characteristic values given in the relevant ETA specifications. With this combination of testing guidelines and design models EOTA was able to publish approvals for mechanical fasteners that are valid in the whole European community. This means that for a product with an ETA there are uniform technical data for Europe. This is a significant improvement from the old situation, where different national approvals and manufacturers' recommendations showed different technical data and fields of application for the same product. Furthermore, it is now easier to compare similar products. Trade barriers have been removed and since establishment of the first ETA in 1998, engineers can now design with fastenings almost without problems Europe wide. Today about 30 ETAs for different types of mechanical post-installed fasteners exist.
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In accordance with European agreement after a transition period of 33 months after the publication of an ETAG , national approvals in the areas covered by an ETAG, are not allowed. For the first ETAGs the transition period takes longer i.e. for the ETAGs P.1 to P. 4 the deadline is June 2002. Since the establishment of the new design recommendations for mechanical anchors, in the mid 1990's the efforts of the CEB TG III/5 have been directed to channel bars and adhesive anchors. Channel bar and adhesive anchor design is still based mainly on knowledge from the 1980's. It is performed according to national regulations and recommendations of the manufacturers. It is hoped that design methods compatible with the CC-method can be formulated for these systems as well in the future. Work in this direction have already begun. It is under discussion in the now fib Task Group and is expected to be finalized within the next year. In 2000, the new Working Group of CEN/TC250/SC2 'Design of Fastenings' was given the task of coming up with a new Eurocode covering 'Design of Fastenings for Use in Concrete'. The Working Group plans to include the existing design provisions for mechanical anchors and the soon to be completed design provisions for adhesive anchors and channel bars under static and fatigue loading [15]. Earthquake loading will not be covered in this document due to lack of published research. A key element in the design philosophy will be that fasteners and fastening systems must be prequalified using performance criteria described in ETAG, stated by a European Technical Approval (ETA) or relevant Eurocode (EN).
6. Conclusion The first documentation of the use of fastenings to concrete was provided by Vitruvius over 2000 years ago. Up until the mid 20th Century, engineers were still designing fastening systems according to experience and gut feeling – often with huge safety factors thrown in for good measure. This situation changed dramatically with the development of hammer-drill tools and innovative post-installed fastening systems. The urgent need for the detailed understanding of the working principles of fasteners increased. In the last two decades very comprehensive research programs were undertaken to consolidate existing knowledge and significantly extend the general knowledge in the field of fastening technology. The efforts allowed the design of fastenings to be based on physical understanding. This allowed for the development of universal design models and their international application. Optimal utilization of anchor capacity in all applications under static loading using castin headed studs and mechanical metal anchors is possible by the existing CC-method. More recently, research efforts have been directed towards the design of grouted and
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bonded (adhesive) anchors. A design method compatible with the CC-method can be formulated for these systems and is under consideration in Europe. Additionally, the design of cast-in-place channel bars following the principles of the CC-method, has been undertaken and is nearly finalized. The design of anchors for earthquake loading continues to be a focus of research and will hopefully be addressed in future codes. It is known that the load-bearing behavior of fasteners can be enhanced by properly detailed local reinforcement. Such enhancement can be included in future design provisions a s well as the resistance of fasteners under seismic load. To conclude, today fastening systems are reliable, economical and satisfy many needs in construction practice. However, it is important to keep in mind that even the most expensive fastenings form a nearly negligible part of the total cost of a building, and a failure can damage property and endanger lives. Connections - their accurate design and correct application - are vital to the performance of the building!
7. Acknowledgements The author wishes to express special thanks to Dr. Schätzle (fischerwerke), Dr. Arndt and Dr. Pusill-Wachtsmuth (Hilti), Mr. Tschositsch (Unibautechnik) as well as Mr. Frischmann and Mr. Zimmermann (UPAT) who provided brochures, technical data and product information that were needed to give a historical background. Special thanks are also accorded to Matthew Hoehler who spent many hours in reviewing the paper.
8. References 1.
2. 3. 4. 5. 6. 7.
Fuchs, W., Eligehausen, R., and Breen, J.E., Concrete Capacity Design (CCD) Approach for Fastening to Concrete. ACI Structural Journal, 92(1), Jan.-Feb., 1995, pp. 73-93. Marsh, P., Fixings, Fasteners and Adhesives, Site Practice Series, Construction Press, London, New York, 1984. Maass, G., Bauwerksdübel, Werner-Verlag, Düsseldorf, 1987. Eligehausen, R., Pusill-Wachtsmuth, P., Stand der Befestigungstechnik im Stahlbetonbau. IVBH Bericht S-19/82, IVBH-Periodica 1/1982, Februar 1982. Comité Euro-International du Béton. Fastenings to Concrete and Masonry Structures – State of the Art Report. Thomas Telford Services Ltd., London, 1994. Eligehausen, R., Design of Fastenings with Steel Anchors – Future Concept. Betonwerk + Fertigteiltechnik, 5(88), pp. 88-100. Eligehausen, R., Fuchs, W., and Mayer, B., Load Bearing Behavior of Anchor Fastenings in Tension. Betonwerk + Fertigteiltechnik, 12(87), pp. 826-832, and 1/88, pp. 29-35.
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8.
9. 10. 11.
12. 13. 14.
15.
Eligehausen, R., and Fuchs, W., Load Bearing Behavior of Anchor Fastenings under Shear, Combined Tension and Shear or Flexural Loadings. Betonwerk + Fertigteiltechnik, 2(88), pp. 48-56. Cannon, R.W., Burdette, E.G., Funk, R.R., Anchorage to Concrete, Tennessee Valley Authority, Knoxville, Dec. 1975. ACI 349-76, Code Requirements for Nuclear Safety Related Concrete Structures, American Concrete Institute, Detroit, 1976. Fuchs, W., Entwicklung eines Vorschlags für die Bemessung von Befestigungen (Development of a Proposal for the Design of Fastenings to Concrete), Report to the DFG, Deutsche Forschungsgemeinschaft, Bonn, February 1991. Deutsches Institut für Bautechnik (DIBt), Bemessungsverfahren für Dübel zur Verankerung in Beton, DIBt, Berlin, 1993. Comité Euro-International du Béton. Design of Fastenings to Concrete. Thomas Telford Services Ltd., London, 1997. European Organisation for Technical Approvals (EOTA), ETAG, Guideline for European Technical Approval of Metal Anchors for Use in Concrete, P. 1: Anchors in General, P. 2: Torque-controlled Expansion Anchors, P. 3: Undercut Anchors, P. 4: Deformation-controlled Expansion Anchors, P. 5: Bonded Anchors, Annex A: Details of Tests, Annex B: Tests for Admissible Service Conditions – Detailed Information, Annex C: Design Methods for Anchorages, European Organisation for Technical Approvals, Brussels, 1997-2001. CEN/TC 250/SC/WG 2 'Design of Fastenings', Design of Fastenings for Use in Concrete, 1st Draft, Brussels, 2001.
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PROBABILISTIC CALIBRATION OF DESIGN METHODS Richard E. Klingner Dept. of Civil Engineering, The University of Texas at Austin, USA
Abstract In this paper, basic steps in the probabilistic calibration of design methods are identified. These include identification and evaluation of test data; comparison of design models with test data; evaluation of safety in the context of an overall design approach; and final development of code language. Challenges to the success of each step are described, and means of overcoming those challenges are suggested. Finally, calibration is shown to be an ongoing process, one of whose benefits is to suggest areas in which additional research would be particularly cost-effective.
1. Introduction This Symposium, had it been held a decade earlier, would have been quite different. At that time, many of the world’s researchers on anchor behavior were divided into two camps, which, if not opposing, certainly had different perspectives on how to design anchorage to concrete. Those different perspectives had been developed by technical committees of the Comité Euro-International du Beton in Europe, and the American Concrete Institute in the USA. In Europe, a broad-based and reasonably coordinated technical community, tied on many levels to the University of Stuttgart, was convinced of the reality of cracked concrete, and of the need to address concrete cracking in anchorage design. They were equally convinced of the potential weaknesses of traditional design methods for anchors, and of the need to develop and adopt new design methods. In the USA, an equally broad-based but much less coordinated technical community was beginning to examine these same issues. Instead of a single Eurocode, though, we had a bewildering array of manufacturers’ recommendations, consensus resource documents,
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and model codes, which agreed with each other only on the broadest issues, and were sometimes in direct conflict. The past 10 years have witnessed a remarkable convergence of technical understanding among Europe, the USA, and other countries around the world with respect to design of anchorage to concrete. Most modern design provisions for anchors admit the possibility of cracked concrete, and require that anchor designs have reasonably consistent levels of safety. In a most important sense, this convergence is the result of tremendous work by individuals who believed that a connection to concrete should behave in the same manner whether it is designed and built (for example) in Austin, Texas, or in Stuttgart, Germany. Several key steps in that convergence depended on the successful probabilistic calibration of design methods. That is the subject of this paper.
1. Basic Steps in the Probabilistic Calibration of Design Methods The probabilistic calibration of design methods can be discussed in terms of the following steps: o o o o
identification and evaluation of test data; comparison of design models with test data; evaluation of safety in the context of an overall design approach; and final development of code language.
In the remainder of this paper, each step is described, and is illustrated by specific examples from technical committee work in the anchorage area over the past decade. Challenges to the success of each step are described, and means of overcoming those challenges are suggested, again with reference to one specific example: tensile breakout capacity.
2. Background for Specific Examples Design codes are not intended to predict behavior. Rather, they are intended to enable practicing engineers to produce designs that are sufficiently safe. Nevertheless, if design codes are to be more than empirical expressions of what has worked before, their design equations must be linked to engineering mechanics and physical reality. The first linkage occurs through rational design models; the second, through comparison with test data. Let us first discuss design models, using the specific example of tensile breakout capacity. A decade ago, one particular area of controversy existed with respect to predicting the tensile breakout capacity of anchors in concrete. Many designers in the USA and elsewhere used the 45-Degree Cone Method, a traditional way of computing that capacity. A growing number of designers in Europe used what has now evolved into the CC Method.
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The 45-Degree Cone Method assumes that a constant tensile stress of 4 f c′ acts on the projected area of a 45-degree cone radiating towards the free surface from the bearing edge of the anchor (Figure 1). T
2hef+dh
45º
dh
Figure 1
Tensile breakout cone as idealized by 45-degree Cone Method
For a single tensile anchor far from edges, the mean cone breakout capacity is determined by:
(
To = 0.96 f c′ π hef2 1 + d h hef where: To f c′ dh hef
= = = =
)
N
(1)
tensile breakout capacity (kN); specified concrete compressive cylinder strength (MPa); diameter of anchor head (mm); and effective embedment (mm).
Breakout capacity is reduced by edges or adjacent anchors as a function of the reduction in area of the projection of the breakout cone on the free surface. The CC Method [1] computes the mean concrete breakout capacity of a single tensile anchor far from edges as:
To = k fc′ hef1.5
(3)
where: To = tensile breakout capacity (kN); k = constant; equal to 13.48 for expansion and sleeve anchors, 15 for undercut and headed anchors, in SI units; f′c = specified concrete compressive strength (6 in. × 12 in. cylinder) (MPa);
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hef = effective embedment depth (mm). In the CC Method, the breakout body is in effect idealized as a pyramid with an inclination of about 35 degrees between the failure surface and the concrete member surface (Figure 2). Breakout capacity is reduced by edges or adjacent anchors as a function of the reduction in area of the projection of the breakout pyramid on the free surface. Other modification factors are used as well. 3hef 3hef
h
ef
35º
Figure 2
Tensile breakout body as idealized by CC Method
3. Identification and Evaluation of Test Data A decade ago, technical discussion of the relative merits of the 45-Degree Cone Method and the CC Method for predicting tensile breakout was complicated by the fact that there was no consensus database of test results that could be used as a standard. Proponents of each method referred to separate sets of test data. To cut through that Gordian knot, Dr. Werner Fuchs, during a stay as a Visiting Researcher at The University of Texas at Austin, began to assemble such a database. He identified original test reports from all over the world; he placed each tensile test in a common framework of units (both US customary and SI); and most important, he began the process of evaluating each test result to distinguish those tests governed by steel failure, from those governed by pullout, and from those governed by concrete breakout. His original work was done in DOS. Since then, the database that he began has been converted into Excel, has been expanded to include many more tests, and has been even more extensively studied [2, 3, 4]. It is in the public domain, and is maintained by ACI Committee 349 (Subcommittee 3) and ACI Committee 355. The database for tensile breakout behavior in uncracked concrete under static load now numbers almost 1600 tests, partitioned into shallow and deep embedment, absence or presence of edge effects, and absence or presence of adjacent anchors. For cracked
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concrete, dynamic loading, or combinations of these, statistically significant number of tests (for example, 50 to 200) are available in several categories.
4. Comparison of Design Models with Test Data The next step is to evaluate each design model with respect to the consensus database of tensile breakout results. In the case of models for predicting tensile breakout capacity, the required steps are as follows: 1) For each failure mode, ratios of tested capacity to that predicted by the design provisions are computed. The ratios are plotted as a function of embedment depth. 2) The resulting plots are evaluated, using the criteria that an ideal design method should have: a) no systematic error (that is, no variation in ratios with changes in embedment depth); b) high precision (that is, little scatter of data); and c) appropriate conservatism, achieved by a combination of normalizing criteria for the design equation (mean versus lower fractile), load factors, and φ-factors. Examples of those plots are given in Figure 3 and Figure 4, for single tensile anchors with shallower embedments, for the CC Method and the 45-Degree Cone method respectively. Both methods have been normalized so that they predict approximately the mean capacity from test results. The implications of this normalization are discussed in more detail later in this paper. Comparison of those figures shows that the CC Method has little systematic error (that is, almost zero slope), high precision (that is, relatively low dispersion), and appropriate conservatism (mean values close to unity for this normalization). In contrast, the 45-Degree Cone Method, while at least as conservative, has high systematic error and lower precision.
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RATIOS OF OBSERVED TO PREDICTED CAPACITIES, CC METHOD, SHALLOWER EMBEDMENTS 3.5 y = 0.0009x + 0.9097
Mean = 0.981 COV = 0.197
3
(Nobs/Npre)
2.5 2 1.5 1 0.5 0 0
50
100
150
200
Effective Embedment, mm
Figure 3
Ratios of observed to predicted tensile breakout capacities, CC Method, single anchors with shallow embedment RATIOS OF OBSERVED TO PREDICTED CAPACITIES, 45-DEGREE CONE METHOD, SHALLOWER EMBEDMENTS, NO EDGE EFFECTS
3.5 3
Mean = 1.356 COV = 0.266
(Nobs/Npre)
2.5 2 1.5 1 0.5
y = -0.0059x + 1.8074 0 0
50
100
150
200
Effective Embedment, mm
Figure 4
Ratios of observed to predicted concrete tensile breakout capacities, 45Degree Cone Method, single anchors with shallow embedment
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Plots such as these immediately indicate how to improve a given design method. Downward-trending systematic error, as in the case of the 45-Degree Cone Method, indicates that as embedments increase, the ratios of observed to predicted capacity tend to decrease. This means that as embedments increase, predicted capacities are too high, and it implies that the exponent of the embedment (equal to 2.0 in the case of the 45Degree Cone Method) should be reduced to a value between 1.5 and 1.6.
5. Evaluation of Safety in the Context of an Overall Design Approach The next step is to compare the safety that will result from the use of different design models, in the context of a particular overall design approach. For example, as in the work of Farrow et al. [2, 3] and Shirvani [4], using each tensile breakout method, and a probabilistic analysis based on the design framework of ACI 349-90 Appendix B [5], the probabilities of failure under known loads, and the probabilities of brittle failure independent of load, are evaluated for each method. Any probabilistic evaluation of safety faces several daunting challenges: o o
many design professionals are suspicious of probabilities; and many design professionals are unfamiliar with probabilistic tools.
For example, referring to Figure 3 and Figure 4, many design professionals, while recognizing that the 45-Degree Cone Method has greater dispersion than the CC Method for shallow embedments, would intuitively think that this greater dispersion would be compensated for by the former’s higher ratios of observed to predicted capacity, leading to approximately equivalent levels of safety for each method. This in fact is not the case. In spite of the higher conservatism of the 45-Degree Cone Method, its greater dispersion makes it less safe than the CC Method. Experience has demonstrated that while very few technical committee members (including this author) have the formal mathematical background to compute probabilities of failure in closed form, most feel reasonably comfortable with approximating probabilities of failure by Monte Carlo analysis, for which tools such as Schneider [6] are readily available and reasonably user-friendly. Monte Carlo analysis has the additional advantage of being practical when a design method involves complex logic with many possible branches. Using an assumed statistical distribution of loads, and known distributions of the ratios between observed and predicted strengths as governed by steel yield and fracture, and by tensile breakout, it is possible within the context of a given overall design approach, such as that of ACI 349-90 [5], to predict the probabilities of failure under given loads, or the probabilities of brittle failure independent of loads. Results of typical statistical analyses for known loads are summarized in Table 1. Higher values of β indicate lower probabilities of failure. The table shows that in most anchor categories, anchors
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designed using the 45-Degree Cone Method to predict concrete breakout capacity, have a much higher probability of failure than if the CC Method were used. This is particularly evident for anchors with edge and group effects. Table 2 shows corresponding probabilities of brittle failure independent of load. These probabilities are essentially the probability of brittle failure if the load increases beyond the value used in design. For design against earthquakes or loads that are similarly difficult to predict, it is important to reduce the probability of brittle failure (“capacity design”). The 45-Degree Cone Method has much higher probabilities of brittle failure, than the CC Method. Table 1
Probability of failure under known loads for different categories of tensile anchors, ductile design approach, static loading, uncracked concrete CC METHOD ANCHOR CATEGORY
single anchors, shallower embedments single anchors, deeper embedments single anchors, shallower embedments, edge effects single anchors, deeper embedments, edge effects 2- and 4-anchor groups, shallower anchors, no edge effects 4-anchor groups, deeper embedments, no edge effects
45-DEG CONE METHOD Probability β of Failure 8.56E-04 3.14 1.99E-03 2.88
Probability of Failure 5.46E-05 1.39E-05
3.87 4.19
1.92E-03
2.89
1.00E-03
3.09
1.70E-06
4.65
9.87E-04
3.09
2.23E-05
4.08
1.79E-03
2.91
5.23E-04
3.28
5.08E-04
3.29
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β
Table 2
Probabilities of brittle failure independent of load for different categories of tensile anchors, ductile design approach, static loading, uncracked concrete CC METHOD ANCHOR CATEGORY
Probability of Brittle Failure single anchors, shallower embedments 0.178 single anchors, deeper embedments 0.088 single anchors, shallower embedments, 0.206 edge effects single anchors, deeper embedments, 0.0405 edge effects 2- and 4-anchor groups, shallower 0.107 anchors, no edge effects 4-anchor groups, deeper embedments, 0.0621 no edge effects
β
0.922 1.36 0.821
45-DEG CONE METHOD Probability β of Brittle Failure 0.066 1.51 0.369 0.335 0.198 0.848
1.75
0.717
0.573
1.24
0.125
1.15
1.54
0.273
0.603
6. Final Development of Code Language Once a design method has been agreed upon, it is necessary to decide how that method should be expressed in code language. The following questions are relevant: o o
How should the design method be normalized? How should appropriate load factors and understrength factors be derived?
Design methods can be normalized so that they predict either mean values, or some lower fractile (such as 5%). Provided that ratios of observed to predicted capacities are reasonably consistent from case to case, either normalization technique can produce equivalent levels of safety. Nevertheless, because the scatter of observed to predicted capacities varies from case to case, it is probably preferable to normalize design methods to a lower fractile of the expected capacity. It is simple to convert design models normalized on mean values, to models normalized on lower fractiles. For example, if a 5% fractile value is about 75% of the mean for the tensile breakout database, then design methods normalized to mean values can simply be multiplied by 0.75 to give the corresponding design methods normalized to 5% fractiles. For example, the leading coefficient k in the CC Method (normalized to mean values) for tensile breakout is 15 for cast-in-place and undercut anchors. If it is desired to normalize to the 5% fractile of test results, then the leading coefficient k would be 15 multiplied by that same factor of 0.75, or 11.25.
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Probabilities of failure such as those presented in Table 1 depend on the load and understrength factors used in the overall design framework. To keep the probability of failure the same, if the load factor is increased by 10%, the understrength factor should be decreased by 10%, without any need to run additional probabilistic studies. In most cases, load factors are prescribed uniformly for all materials, and are beyond the control of those developing anchor design provisions. In such cases, it is necessary to arrive at suitable understrength factors by trial and error. In some cases, understrength factors will be constrained by practical limitations, such as being less than unity, or less than that corresponding so some other failure mode. If both load factors and understrength factors are constrained, the only possible adjustments may be in the fractile against which the design method is normalized. Finally, it is necessary to modify design methods to account for effects such as dynamic loading and cracked concrete. Modification factors for such cases are most appropriately arrived at by comparing the results of tests in which everything is held constant, except for the loading rate, or the presence of cracks.
7. Summary, Conclusions and Recommendations In this paper, essential steps in the probabilistic calibration of design methods have been identified, and examples of how challenges to those steps were successfully overcome, with reference to the particular issue of methods for predicting tensile breakout capacity. Those steps, and the methodology behind them, need to be checked against new data and new design criteria. Finally, while more research is not always needed, the methodology outlined here can be used to indicate areas in which additional research information would be particularly cost-effective.
8. References 1.
Fuchs, W., Eligehausen and R. and Breen, J. E., “Concrete Capacity Design (CCD) Approach for Fastening to Concrete”, ACI Structural Journal, Vol. 92, No. 1, January-February, 1995, pp. 73-94.
2.
Farrow, C. Ben and Klingner, R. E., “Tensile Capacity of Anchors with Partial or Overlapping Failure Surfaces: Evaluation of Existing Formulas on an LRFD Basis,” ACI Structures Journal, Vol. 92, No. 6, November-December 1995, pp. 698710.
3.
Farrow, C. Ben, Frigui, Imed and Klingner, R. E., “Tensile Capacity of Single Anchors in Concrete: Evaluation of Existing Formulas on an LRFD Basis,” ACI Structures Journal, Vol. 93, No. 1, January-February 1996.
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4.
Shirvani, Mansour, “Behavior of Tensile Anchors in Concrete: Statistical Analysis and Design Recommendations,” M.S. Thesis, The University of Texas at Austin, May 1998.
5.
ACI Committee 349, “Code Requirements for Nuclear Safety Related Concrete Structures,” American Concrete Institute, Detroit, 1990.
6.
Schneider, Jörg, “VaP version 1.6,” Institute of Structural Engineering, Zurich, Switzerland.
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CURRENT STATUS OF POST-INSTALLED ANCHOR APPLICATION IN JAPAN Reiji Tanaka, Faculty of Eng., Tohoku Institute of Technology, Japan
Abstract Currently about 450 million pcs. of post-installed anchors are being used annually in Japan. This report introduces the outline where and how these post-installed anchors are utilized. Japan Construction Anchor Association (JCAA) is now producing an approval system and design guide of post-installed anchors. This outline is also presented. This report aims for the comprehensive study on current status and overall picture in the near future concerning post-installed anchor application in Japan.
1. Post-installed Anchor Products Construction Anchor Association
Approval
Project
by
Japan
Japan Construction Anchor Association (JCAA) is preparing for the approval of post-installed anchors. Target products are confined to ones manufactured or sold exclusively by JCAA members. Foreign products sold by JCAA members are qualified to get approval. The initial application was accepted in January, 2001. 1.1 Product approval procedure Product approval procedure is shown in the flow chart of Table 1. 1.2 Approval Committee Approval Committee members are composed of more than 10 experts. Present chairman is Prof. Reiji Tanaka, Tohoku Institute of Technology.
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1.3 Overall plan of product approval Followings are the outline of product approval project. Applicants Application Application receipt Receipt judgement
Notification of acceptance
Approval
Approval committee
Decision Yes/No
Notification of Yes/No
To sign the agreement
Issue of certificate
Renewal Table 1 Procedure of product approval
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a) Target products All products which applicants wish to apply. But the secretariat will check in advance whether these products are qualified for JCAA approval. z Post-installed anchors consist of metal anchors, bonded anchors and other anchor group. z Applicants can freely select which category their products belong to. z Basically every product can be acceptable by establishing the category of other anchor group and also their criteria can be specified by self-declaration. z But at least they should have shape and form of post-installed anchors. b) Approved products 1) Approved products consist of standard type and special type. Special type is composed of Type 1 and Type 2. Standard type Approved products Type 1 Special type Type 2 The structure of approved products is shown below for metal anchor, bonded anchor and other anchor group respectively. z
Metal anchors Standard type Approved products
Type 1 Special type Type 2
z
Bonded anchors Standard type Approved products
Type 1 Special type Type 2
z
Other anchor group Type 1 Approved products
Special type Type 2
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2) Standard type Similar to JIS standard, acceptance criteria is already available and only those that pass this criteria can be approved. Standard type has the self-regulatory feature, and has an advantage of clear quality contents for the public such as JIS standard. Also users receive the merit of exchangeability of products. This type is very important in order to show the consensus of JCAA to the public society. Some standard testing methods are available to confirm the performance in the acceptance criteria. Approval shall be given to depending on the experimental results of those testing methods. 3) Special type It is also necessary to cope with the technical development and originality of each manufacturer. The acceptance criteria of those products are self-declared by applicants. After the reliability of the self declared contents has been confirmed, approval will be granted. Though the contents of evaluation items are self-declared, the evaluation process is the same as standard type, and therefore the approval level is never damaged. Plenty of products are considered in special type, and they are classified into type 1 and type 2. It is up to the applicant to which category he wish to apply. The evaluation items should include specific ones in addition to the standard type items. These specific items are also self-declared. Type 1 is supposed to those anchors designed by the JCAA Design Guide. On the other hand, type 2 is supposed to be designed in very simple form or used without any engineering approach. Its evaluation items and evaluation methods are self-declared. For example, evaluation items can be several ones like shape, material quality, strength, etc. But the minimum information for anchor performance is necessary. Though the quantity of evaluation items may be small. their contents are carefully investigated like standard type and therefore the approval level is never damaged. As for specific evaluation items for special type, some standard testing methods will become necessary. At this time nobody knows which specific items will appear in the future, and we can not prepare all standard testing methods. But for the time being we estimate following ones: cyclic loading test (tension and shear), crack test(tension and shear), thermal effect test for bonded anchors. The name of above mentioned “standard testing method” is tentative. When some new specific items appear, we will have to consider additional standard testing methods to cope with them. For both metal anchors and bonded anchors, the next table is applied for standard type as well as specific type. For other anchor group, the rule of special type is applied.
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Standard type Evaluation item 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
approval standard
Approval standard is available
Special type Type 1 Type 2 Evaluation approval Evaluation approval item standard item standard 1 ** 2 ** Self3 ** declaration 4 ** 5 6 Self7 declaration 8 9 10 11 12 13 14 15 Specific items Selfdeclaration
z
Quality level of standard type and special type (Type 1 , Type 2) is as follows. Special type 1 > Standard type > Special type 2 z Specific items are declared by applicants. Foe example, we consider strength effect, rigidity effect, cyclic loading effect, crack effect, and thermal effect as specific items for the time being. z Evaluation items 1 through 15 of special type 1 are same as standard type. But the approval standard of special type is self-declared. z The evaluation items of special type 2 shall be selected from the counterparts of standard type 1 through 15 and self-declared. Approval standard is also self-declared. z Those anchors designed by JCAA Design Guide should belong to the category of at least standard type 4) Evaluation items and acceptance criteria Product approval is evaluated by next items. Evaluation items for metal anchors and bonded anchors are shown in Fig.2 and Fig.3 respectively.
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Table 2 Approval items of metal anchors Approval items
1) Shape, size and tolerance of anchor parts. 2) Material of parts. 3) Strength of parts 4) Hardness and ductility of parts 5) Thread class, appearance and surface finish 2 Subjects concerning quality 6) Shape, size and tolerance before and after “set” condition. and performance of anchor 7) Drill bit diameter, drilling depth and tolerance products. 8) Product strength 9) Hardness and ductility of products 10)Base material type 11)Scope of base material design strength 12)Tensile resistance 13)Tensile rigidity 14)Shear resistance 15)Shear rigidity Table 3 Approval items of bonded anchors 1
Subjects concerning quality and performance of anchor parts.
1
Subjects concerning quality and performance of anchor parts.
2
Subjects concerning quality and performance of anchor products.
Approval items
1) Shape, size and tolerance of capsule 2) Material and strength of adhesive 3) Property of adhesive 4) Type, shape and appearance of anchor bolts 5) Material and surface finish of anchor bolts 6) Strength and thread class of anchor bolts 7) Drill bit size and tolerance 8) Drilling depth and tolerance 9) Base material type 10)Scope of design strength of base material 11)Environmental conditions 12)Tensile resistance 13)Tensile rigidity 14)Shear resistance 15)Shear rigidity
For the evaluation of approval items in Table2 and Table3, the acceptance criteria on quality/performance are given in Table4 and Table5.
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Table 4 Quality/performance criteria of metal anchors Criteria 1 Shape, size and tolerance of anchor parts. Criteria 2 Material of parts. Criteria 3 Nominal yield strength and tensile strength of parts Criteria 4 Hardness and ductility of parts Criteria 5 Thread class, appearance and surface finish Criteria 6 Shape, size and tolerance before and after “set” condition Criteria 7 Drill bit diameter and drilling depth Criteria 8 Product material: nominal yield strength, tensile strength Criteria 9 Product material: Hardness, ductility Criteria 10 Base material type Criteria 11 Scope of design strength of base material Criteria 12 Tensile resistance Criteria 13 Tensile rigidity Criteria 14 Shear strength Criteria 15 Shear rigidity Table 5 Quality/performance criteria of bonded anchors Criteria 1 Shape, size and tolerance of capsule. Criteria 2 Material and strength of adhesive. Criteria 3 Mechanical property of adhesive Criteria 4 Type, shape and appearance of anchor bolts Criteria 5 Material and surface finish of anchor bolt Criteria 6 Strength and thread class of anchor bolts Criteria 7 Drill bit diameter and drilling depth Criteria 8 Drilling depth and tolerance Criteria 9 Base material type Criteria 10 Scope of design strength of base material Criteria 11 Environmental condition Criteria 12 Tensile resistance Criteria 13 Tensile rigidity Criteria 14 Shear strength Criteria 15 Shear rigidity 2.JCAA “Post-installed Anchor Design Guide” JCAA is now working on their original “Post-installed Anchor Design Guide (draft)”. Its working activities are nearly finished. Design Committee consists of eight members with chairman Prof. Reiji Tanaka, Tohoku Institute of Technology. I will give just the content of this guide below.
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Post-installed Anchor Design Guide and its Commentary (Draft) Contents 1. General rules 1.1 Scope of application 1.2 Post-installed anchors 1.3 Base material 1.4 Operation of post-installed anchors 1.5 Terminology 2. Design of post-installed anchors 2.1 Security of structural performance 2.2 Safety factor 2.3 Characteristic values of materials 2.4 Design load and design deformation 2.5 Design resistance and design deformation limit 2.6 Serviceability limit state design 2.7 Ultimate limit state design 3. Resistance and rigidity formula 3.1 Resistance and rigidity formula of metal anchors 3.2 Resistance and rigidity formula of bonded anchors 4. Structural specification Design example 1 Design example 2 Design example 3 Design example 4 Design example 5 Design example 6 Design example 6 Design example 7
Equipments fixed on floors (Underground) Equipments fixed on floors (High importance case) Equipments fixed on floors (Rooftop) Suspension Sign board (fixed on wall) Metal handrail Seismic reinforcing (added shear wall) Deformation design
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DESIGN METHOD FOR SPLITTING FAILURE MODE OF FASTENINGS Jörg Asmus*, Rolf Eligehausen** *Ingenieurbüro Eligehausen und Sippel, Stuttgart, Germany **Institute of Construction Materials, University of Stuttgart, Germany
Abstract The failure of a fastening is often caused by a rupture of steel, anchor pullout or by a concrete-cone failure. In the past these failure modes have been intensively investigated and the associated failure loads can be calculated with sufficient accuracy [1]. For the failure mode splitting there exists no general equation to calculate the failure load. Therefore, theoretical and experimental investigations have been performed [2]. Splitting of a concrete member can be expected if the member dimensions are relatively small or in large concrete specimens if the fasteners are installed near to an edge or corner. The splitting failure load depends on dimensions and on material properties of the concrete member. Moreover, the design and load-bearing area of the fastener influence the failure load as well. In the present paper the results of experimental and numerical investigations in case of splitting are discussed and a design method to calculate the splitting failure load is proposed. Details of the design method are given to illustrate how installation parameters (dimension of concrete member and material properties) and the type of the fastener (headed anchor and undercut anchor) influence the splitting resistance.
1. Introduction For fastenings loaded under tension concrete-cone failure, bursting failure, steel failure or pull-out failure are the most common failure modes (Fig. 1a-d). For these failure modes design methods are available [1]. However, fastenings in concrete can also fail by splitting (Fig. 1e). The corresponding failure load may be smaller than the concrete cone failure load. Therefore, the failure mode splitting has to be considered in the design of fastenings. The mechanism of splitting failure is not well understood and the ultimate load associated with it is not easily predictable. Currently splitting is prevented in Technical Approvals by prescribing minimum edge distances and spacing. These parameters have
80
to be determined in tests. However, to design safer and more economical fastenings for any geometry a realistic design method which accounts for splitting failure is needed.
a) concrete-cone failure
b) bursting failure
c) steel failure
d) pull-out failure
e) splitting failure
Fig. 1 Failure modes of fastening systems Splitting is especially relevant for anchor systems which transfer loads by high local stresses into the base material. These stresses are present for systems with mechanical interlock as well as for expansion systems. Therefore, a design method for the failure mode splitting valid for headed anchors, undercut anchors and torque controlled expansion anchors has been proposed [2]. In this paper the design model for headed anchors and undercut anchors is presented (Fig. 2). A1
F
αΗead
Drilling pin a) Mechanical interlock b) Headed anchor c) Undercut anchor Fig. 2 Fastening systems with load-transfer mechanism mechanical interlock
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2. Splitting failure mechanism 2.1. Numerical investigations To study the splitting failure mechanism numerical non-linear calculations using a realistic material model for concrete have been performed. In a three-dimensional (3D) finite element analysis the splitting of a concrete block caused by a concentrated internal pressure has been investigated. The results show that the ultimate pressure at splitting failure depends mainly on the size and geometry of the specimen as well as on the size of the load-bearing area. When the structure geometry and the load-bearing area are scaled proportionally, the ultimate load increases approximately proportionally as well, i.e. no significant size effect on the splitting failure load is observed. However, if the structure size is scaled proportionally but the size of the load-bearing area is kept constant, there is a strong size effect on the ultimate load. The reason is the localisation of damage and consequently a decrease of the peak resistance by an increase of the size. The numerical results are in good agreement with the experimental observations [2] as well as with theoretical and experimental studies for concrete members loaded by locally applied compressive forces [2]. The numerical investigations are explained in detail in [12]. 2.2. Model When modeling the splitting failure mode it must be taken into account that anchors transfer high loads on a relatively small area compared to the size of the concrete member. The concentrated load causes highly concentrated stresses which are several times higher than the uniaxial compressive strength. In literature several cases have been studied in which small areas are loaded by concentrated compression forces [4], [5], [6]. On the basis of theoretical and experimental investigations the pressure σu under the loaded area A1 is assumed to be proportional to the square root of the ratio between loaded area Ao and load transfer area A1 σu ∼ (Ao/A1)0,5. The investigations in [10] show that the square root relationship is valid for a range of Ao/A1 ≤ 950 which covers the range valid for fasteners. Assuming the tensile capacity of concrete as proportional to fcc0,5 the following equation for splitting resistance is recommended in [10]: Nu,sp = 4,65 ⋅ A10,5 ⋅ Ao0,5 ⋅ fcc0,5
(1)
When loading a small concrete area on the surface of a concrete member by a rigid disk the typical failure mechanism shown in Fig. 3a) is observed. First, a local failure on the concrete surface occurs, which is associated with radial cracking and spalling around the disk. If the ratio A1/Ao is high below the disk a sheared compressed cone with an angle between 25° to 40° is observed. Fig. 3a) shows a typical schematic cross section of a concrete specimen loaded by a stiff disk. With increasing load splitting failure may occur due to the wedging action.
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In case of headed or undercut anchors the concrete around the load bearing area is confined. Therefore no spalling is possible. As shown in numerical investigations [12] the loading zone is high compressed in all directions. Under the compressed volume zone high tensile strains localize in the radial as well as in the splitting direction and failure is caused by splitting. The failure mechanism is very similar to the failure mechanism shown in Fig. 3a). Therefore in principle, Equation (1) is also valid for headed anchors. However, certain modifications must be taken into account. While the loaded area Ao can easily be calculated the definition of the area A1 needs some considerations (see section 3.1).
Fastening by mechanical interlock
Loading plate member surface
h LE
h LE
αB
sheared compressed concrete
αB
Concrete member Sheared compressed concrete
a) Partial loading on a concrete surface
b) Loading by a headed anchor in a concrete member
Fig. 3 Load-transfer mechanism Based on the Mohr-Coulomb-law and a friction angle of concrete φ of about 36° [11] an angle of the compressed cone αB = 27° is determined [2]. This angle, α deduced by theoretical considerations, φ N agrees well with angles observed in α tension pull-out tests with headed anchors RES F [8]. In tension tests with headed anchors a shearing of the concrete in front of the R (α+φ) anchor head with an angle of about 25° is observed. Because the sheared compressed F Fig. 4 Forces in the load bearing area of cone in front of a headed anchor has angle αB = 27°, a similar behavior for headed a headed anchor anchors with a head angle (see Fig. 2b) between αHead= 27° to 90° is to be expected. For a head angle αB < 27° the splitting and bursting forces increase significantly. Therefore, the higher splitting forces of fasteners with mechanical interlock with a head angle αB < 27° have to be taken into account when calculating the splitting failure load. From the mechanical model shown in Fig. 4 a factor kα is introduced in Equation (2) to consider a head angle αB < 27°. z
SP
83
3. Calculation of the Average Failure Load for Splitting 3.1. General In [2] it is shown that a substitution of the loaded area Ao by the fracture area Acrack is needed. The fracture area depends on member size and edge distance. The fracture area for anchors installed in the middle of a narrow concrete member is defined by the member width b and the member height h. Numerical and experimental investigations with anchors installed in a large specimen near the corner or edge the typical splitting failure mode as shown in Fig. 5b is observed. The splitting crack appears at a specific angle β to the edge. In Fig. 6 the angles as observed in tests are plotted as a function of the edge distance. Besides the results of tension pull-out tests also results of tests with a shear load to the edge [7] are evaluated in Fig. 6. The test results can be approximated by Equation (6), which is represented by the line in Fig. 6. A similar result have been found for fasteners at the corner Equation (7). Equation (6) and (7) are valid for an edge distance c ≥ 40 mm. Furthermore, the splitting area must be restricted to a member height h ≤ 2hef (hef = embedment depth) because the concrete at a distance larger than hef is not stressed significantly [2]. Therefore, the member height in the calculation is limited by h ≤ 2hef (compare Equations (4) and (5)). Equations (2) to (7) give the average splitting failure load of a single fastener with mechanical interlock. In [2] equations for calculating the failure load of double and quadruple fastenings are given. Furthermore, an equation valid for torque controlled expansion anchor is proposed as well. Nu,sp = 4,65 ⋅ kα ⋅ A10,5 ⋅ Acrack0,5 ⋅ fcc0,5 kα = 0,51⋅tan (αB + 36°) = 1 fastening
for αHead < 27° for αHead ≥ 27°
(3)
member h
fracture area Acrack
h
fracture area Acrack
c3
bb
(2)
c1
c1
a)
c2
Fastener installed in the middle of b) Fastener installed at the edge or a narrow concrete member corner (5) h ≤ 2 hef ACrack = rCrack ⋅ h h ≤ 2 hef (4) ACrack = b ⋅ h Fig. 5 Failure area in a concrete member loaded by a fastener
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Angle of crack ß [°]
60
50
40
30
20
ß
ß
c1
rcrack/2
10
0 0
50
100
150
200
250
Edge distance [mm] h = 120 mm h = 240 mm Shear load to edge (scatter range)
Fig. 6
h = 160 mm tension, Blow-out sin (21 + 0,15c)
Splitting of a single fastener located at the edge; angle of crack as a function of the edge distance
rcrack,edge =
2 ⋅ c1 sin (21 + 0,15 ⋅ c1 )
(c1 ≤ 40 mm: r = 4,4c; c1 ≥ 160 mm: r = 2,8c)
(6)
2 ⋅ c1 sin (61 − 0,1 ⋅ c1 )
(c1 ≤ 40 mm: r = 2,4c; c1 ≥ 160 mm: r = 2,8c)
(7)
rcrack,corner =
3.2. Undercut Anchors Headed anchors are cast-in-place systems, while undercut anchors are systems installed in hardened concrete (post-installed systems). Undercut anchors transfer tension loads to the concrete primarily through mechanical interlock. Nevertheless, there are some differences between headed anchors and undercut anchors. Fig. 7 shows details of the load-bearing area of an undercut anchor. The annular gap between the anchor sleeve and the wall of the drilled hole and gaps between the elements of the expansion sleeve reduce the load-bearing area. Furthermore, with some types of undercut anchors with increasing tension load the cone is drawn further into the expansion sleeves. Due to this follow-up expansion the expansion forces are increased. Furthermore, the concrete surrounding an undercut anchor is affected by the drilling process. The aggregate granules may split when drilling the hole or when generating the undercut.
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To consider these differences to headed anchors for the calculation of the splitting failure load of undercut anchors a factor kp is introduced in Equation (2): Nu,sp,undercutanchor
= kP ⋅ Nu,sp
(8)
hLE Drilling pin
kP ≤ 1 product factor
Undercut elements
The factor kp is product dependent. For headed anchors it is kp = 1.0. For undercut anchor it must be evaluated by tests. For typical undercut anchors values kp = 0.8 to 1.0 have been found.
Sleeve Space Threaded rod Load bearing area b d1
d2
Fig. 7
Expansion zone of an undercut anchor
4. Comparison with experimental data To evaluate the proposed design method, numerous tests with undercut anchors (see Fig. 2c) were carried out. In these tests several influencing factors were investigated. According to Equation (2) the splitting failure load of systems with mechanical interlock depends on the member width or edge distance, member height and other parameters of the fastening system (embedment depth hef, load-bearing area A1). Fig. 8 a) to d) shows the ratio of the measured and calculated splitting failure load in narrow concrete member (compare Fig. 5a) plotted as a function of edge distance (c = b/2), member height, embedment depth and load-bearing area. The splitting failure load is calculated with a factor kp = 1, i.e. for a headed anchor. The head angle of the undercut anchor is 18°. An optimal agreement between measured and calculated splitting failure loads corresponds to Fu,test/Fu,calc = 1. The comparison shows a good agreement between the proposed formula and the experimental data. Furthermore, a histogram for the ratio of measured to calculated splitting failure loads is shown in Fig. 9. The diagram is based on the results of 164 tests with single fasteners in narrow concrete members. The coefficient of variation is approximately 20%. The scatter is not significantly larger than that of the measured concrete tensile strength. The design formula visualises the effect of influencing parameters and it predicts the splitting failure load obtained in the experiments with sufficient accuracy.
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Nu,s p,tes t/Nu,s p,calculation
2,00 1,80 1,60 1,40 1,20 1,00 0,80 0,60 0,40 0,20 0,00 0
100
200
300 400 Edge dis tance [cm]
500
0
100
200
300
500
2,00 Nu,s p,tes t/Nu,s p,calculation
1,80 1,60 1,40 1,20 1,00 0,80 0,60 0,40 0,20 0,00 400
M ember height h [cm] 2,00
Nu,s p,tes t/Nu,s p,calculation
1,80 1,60 1,40 1,20 1,00 0,80 0,60 0,40 0,20 0,00 0
50
100
150 Embedment depth h ef [mm]
0
100
200 300 Load-bearing area A 1 [mm²]
200
2,00
Nu,s p,tes t/Nu,s p,calculation
1,80
Fig. 8
1,60 1,40 1,20 1,00 0,80 0,60 0,40 0,20 0,00 400
Single fastenings with undercut anchors in narrow members; Ratio of the measured to the calculated splitting failure load as a function of (1 = optimal agreement): a) edge distance with c = b/2 b) member height c) embedment depth c) load-bearing area
87
50
n = 164 x = 1,08 v = 21,6 %
45 40 35
Number
30 25 20 15 10 5 0 0,0
0,5
1,0
1,5
2,0
Splitting failure load Test/Calculation
Fig. 9
Comparison of measured to calculated splitting failure loads; Single fastenings (undercut anchors) in narrow concrete members
In [2] more details are given related to the influence of the bending and the spacing of multiple fastenings on the splitting failure load. Furthermore, a design method for calculating the splitting failure load of torque controlled expansion anchors is proposed as well.
5. Summary Splitting of concrete occurs when the dimensions of the structural member are too small or the anchors are located too close to the edge or are spaced too closely. The failure load is normally less than in the case of concrete cone failure. Therefore, the failure mode splitting has to be considered in the design of fastenings. In the present paper the results of experimental and numerical investigations are discussed and a design method to calculate the splitting failure load is proposed. Details of the design method are discussed to illustrate how installation parameters (dimension of concrete member; material properties) and type of fastener (headed anchors or undercut anchors) influence the splitting failure load. To demonstrate the validity of the proposed design method, numerous tests with undercut anchors were performed. The calculated and experimentally obtained failure loads agree with sufficient accuracy.
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6. References [1]
[2] [3]
[4]
[5]
[6] [7] [8]
[9]
[10]
[11] [12]
[13]
European Organisation for Technical Approvals (EOTA) (1994): Guideline for European Technical Approval of Anchors (Metal Anchors) for Use in Concrete, Final Draft, Sept. 1994. Asmus, J., „Bemessung von zugbeanspruchten Befestigungen bei der Versagensart Spalten des Betons”, Dissertation, Universität Stuttgart, 1999. Eligehausen, R.; Mallee, R.: Befestigungstechnik im Beton- und Mauerwerksbau, Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH, Berlin, 2000. Lächler, W.: „Beitrag zum Problem der Teilflächenpressung bei Beton am Beispiel der Pfahlkopfanschlüsse.“, Dissertation, Institut für für Grundbau und Bodenmechanik der Universität Stuttgart, 1977. Spieth, H.P: Das Verhalten von Beton unter hoher örtlicher Pressung und Teilbelastung unter besonderer Berücksichtigung von Spannbetonverankerungen. Dissertation TH Stuttgart, 1959. Niyogi, S. K.: The Bearing Strength of Concrete-Geometric Variations; ASCE, Journal of the Structural Division No. 99, July 1973. Fuchs, W.: Tragverhalten von Befestigungen unter Querlast in ungerissenem Beton, Deutscher Ausschuß für Stahlbeton, Heft 424, Beuth-Verlag, 1992. Furche, J.: Zum Trag- und Verschiebungsverhalten von Kopfbolzen bei zentrischem Zug, Dissertation, Institut für Werkstoffe im Bauwesen der Universität Stuttgart, 1994. Furche, J.; Eligehausen, R.: „Lateral Blow-Out Failure of Headed Studs Near a Free Edge“, In: Senkiw, G. A.; Lancelot, H. B. (Herausgeber), SP-130, Anchors in Concrete, Design and Behaviour. American Concrete Institute, Detroit, 1991, S. 235 - 252. Lieberum, K.-H.: Das Tragverhalten von Beton bei extremer Teilflächenbelastung. Dissertation an der Technischen Hochschule Darmstadt, 1978. Szabo, G.: Über die Berechnung der Bruchlast örtlich belasteter Stahlbetonkörper, Betonstein-Zeitung, Heft 2/1963. Asmus, J.; Ozbolt, J.: Numerical and experimental investigations of the failure mode splitting of fastenings, Symposium on connections between steel and concrete, University Stuttgart 2001 Furche, J.: „Spalten des Ankergrundes Beton infolge zentrisch belasteter formschlüssiger Befestigungsmittel“; Nachtrag zur Diplomarbeit Bohner (1988), Bericht Nr. 9/7 - 88/20, Institut für Werkstoffe im Bauwesen der Universität Stuttgart, 1988.
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BEHAVIOUR AND DESIGN OF FASTENINGS OF SHEAR LUGS IN CONCRETE Harald Michler, Manfred Curbach Dresden University of Technology, Germany
Abstract Research on special structures with shear lugs to transmit high values of shear load to fixed ground has been carried out. An additional loading with normal force and bending moment is possible, but the shear load will be the main loading. In this case the base will be concrete and the fitting will be made of steel. The fixing is built into the green concrete. The advantage of the fittings with shear lug is reasonable in the splitting of the load transfer. The special components of the load especially the shear load is transmitted by highly specialized structural parts. The behaviour and capacity of these structures will be shown.
1. Introduction An experimental and theoretical analysis of the bearing behaviour of complex shear loaded fixtures with shear lugs has been carried out at Dresden University of Technology, which was supported by the DFG. As part of the working group ”Design of Fastenings in Concrete (Design Guide of fib)”, fastenings are examined for the transfer of great surface parallel shear loads into the concrete structure [1] [2] [3]. The experiments discussed later are an extension of work done at the Bechtel Power Corporation in Ann Arbor, Michigan and at the former Institute of Reinforced Concrete in Dresden. The earlier experiments in Dresden are the basis for this examination [4] [5]. The analysed units are different from systems based on friction or prestressed units. And they do not need any normal pressure, which is a usual feature of a steel pillar feet. The analysis has turned the attention to a major shear force load combined with small normal forces either in tension or compression and also a bending moment or not. The basic idea of the new components is the construction from highly sophisticated and specialised modules.
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The fixings mentioned can be used F for any kind of concentrated load fixture transmission or assembly joints M fitting between structural concrete (steel) V components, steel/wooden structures or other concrete elements loaded base plate parallel to the surface. Possible fields abutting of application of the new components padding will be all cases that match to the face principle of corbel load introduction. tie bar shear lug The strengthening of existing = round bolt concrete structures using additional headed Ø14 steel structures, fixing facade anchor bolt elements on the main construction Figure 1 Schema of fixing, main parts part or supporting girders using a corbel may be some examples for future applications. As shown in Figure 1, the component always consists of three main parts: the base plate, the shear lug and the tie bar. The base plate parallel to the surface is the interconnection between the load and the actual anchoring components, the shear lug and the tie bar. The design of the shear lug is supposed to deliver an optimal transmission of the shear force into the concrete component and the tie bar is designed only for the transfer of tension forces. Because the shear lug has a rectangular cross section with flat surfaces, the load transmission is more effective than the load transmission of the tie bar. Even it is possible to easily built a stress distribution at fixing systems much greater cross section than the circular cross • bending stiff • rigid joint section of a traditional anchor bolt of shear lug round anchor bolt. So the tie h e bar has only been a b considered as transmission of tension forces either from R2 h e external load or resulting from the eccentricity of the shear force V (see Figure 2). Normal compression forces R1 are transmitted directly R1 using the base plate. For this loading no further special cross section cross section elements are needed. So the of anchor bolt: of shear lug: specified construction is most ideal for great shear Figure 2 Comparison of stress distribution, anchor forces in combination with bolt and lug
V
l/2
V
l/2
91
lower normal forces or bending moments. A design concept for this shear anchorage will be presented here. The concept is based on numerous tests, and a numerical description will be discussed. The resistance will be explained in dependence on different stiffness conditions, especially the geometry and material of the lug, various depths of embedment of the lug and the tie bar, different strength of the concrete ground and, of course, different load combinations. In addition to the failure modes and the capacity, the ductility of the construction will be described.
F M
V eV
eS
RS
eD
RA
eA/2
eA/2
FA
RD shear lug
Figure 3
Forces at the fixture
2. Testing The tests have been carried out at the OTTO MOHR LABORATORY at the INSTITUTE OF STRUCTURES AND MATERIALS IN DRESDEN. The fittings are designed in the style of experiments carried out before. But, the double symmetric design of these former experiments is given up for the benefit of a directional layout. In this manner the individual elements can be specialized more consequently. In Figure 1, a schematic profile view is presented. It is easy to see that the shear force V is only suitable in one direction, according to the design. Consequently there is only one headed anchor bolt placed behind the shear lug, the tie bar. Its task is to take the tension part from the equilibrium moment and introduce it into the anchor ground. In front of the lug a weaker pressure-anchor is placed. Between these elements the shear lug itself is placed. It serves to transfer the shear load to the concrete base. The shear lug is supported by the base plate. The front end face of this base plate also transfers a part of the shear load to the ground. The experiments are designed to make the concrete failure in front of the lug decisive. A possible breaking of the tie bar bolt due to shear load is prevented by padding the bolt shaft directly below the base plate. By this coating, the concrete in this area is not connected to the tie bar shaft and no shear load can be transmitted. This will be the theory until there is a moving of approximately 2 mm. Therefore, the tie bar is only loaded by a tensile normal force, according to plan. There are three mechanisms which may lead to a breakdown of these fittings. These are: 1) concrete failure; shear failure of the concrete part in front of the lug and/or the base plate, or rather crushing 2) steel failure of the shear lug, shear failure or plastification and rotation 3) breaking down of the tie bar a) concrete cone failure or pull-out failure b) steel failure
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The concrete failure aspect should be examined mainly. A failure according to 2) and 3) is not planned, however, it represents important limiting conditions for failures according to 1). This mutual susceptibility can be shown if we look at the reaction forces RD, see Figure 3. The quantity of RD represents the main part of the shear force. But the eccentricity, say eD, of it sets the loading of the shear lug by the bending moment and of Figure 4 Fixings with rigid block lugs course the load of the tie bar FA according to the equilibrium moment. But this eccentricity itself is influenced by the vertical movement of the tie bar – theory of 2nd order. RD is based on the multiaxial compressive stress in front of the shear lug, and this stress itself is dependent on the tie bar extension. The whole tests are divided into three parts, to investigate the essential experimental parameters. The mean parameters are: concrete strength, lug stiffness, anchoring depth of the lug and the tie bar, and of course the load carrying capacity of the tie bar. Its influence on the shear load capacity of the shear lug will also be of interest. Figure 4 shows the fittings of a series of experiments of the 1st group. We see the stiff box lugs, composed from two channel sections, with stepping of 0 cm, 4 cm and 8 cm anchoring depth. By the first group the influence of the concrete strength is investigated, also the lug stiffness and the anchoring depth of the lug are varied. The lug stiffness is achieved by two different lug designs. On the one hand, flat lugs made from steel plates - 2 cm thickness. They will be called soft lugs. On the other hand, inflexible box lugs composed from two welded channel sections, which are the stiff ones. The cell composed from them is filled by concrete, too. All these lugs are tested with anchoring depths of 4 cm and 8 cm. So the building relevant sizes are covered. In each series fittings also are tested without lugs at all, so the anchoring depth will be 0 cm. In this case only the base plate will transmit the shear load to the ground. The tie bars are varying at 20 and 30 cm. Hereby the swapping stress state in front of the shear lug is tested. It is influenced by the volume belonging to the pull-out failure of the tie bar, and the stress in front of the shear lug itself. In the second group, the concrete strength is then held unchangeable and the load combination is varied. Only the soft flat-sheet lugs are applied with 4 and 8 cm anchoring depth. Besides an additional eccentricity of the shear force V, an unchangeable tensile or compression normal force F is applied. The tie bar anchoring depth itself is unchangeably 30 cm. In the third group, the experimental body is changed, first the location of the base plate is bonded in the concrete and, second on top of the concrete. Only soft 4 cm and 8 cm lugs are used. The solid experimental body, measuring 120·120·90 cm, of the first two groups is changed in the last group. Here a narrow rectangular reinforced column measuring
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45·45 cm is used. The effect of a placing of the fittings close to the edge should be examined hereby, and of course the influence of reinforcement. All experiments are designed to expect a failure of the concrete in front of the load transmitting faces. Only if higher strength classes of concrete and the stiff box lug are used, pull-out-failure or steel failure of the tie bar is to be expected.
3. Crushing mechanics and behaviours
V
v5 v4 v3
F
The failure case ”exhaustion of lug load-carrying v 1 v2 v6 v7 w4 capacity” is used for the assessment of lug effects and ability. This failure is characterized by w6 shearing a wedge-shaped concrete volume in front of the base plate, in general (Vks failure). With beginning loss of the pressure transmitting in front of the base plate the shear force itself is V 3 increasingly relocated to the shear lug and finally onto the bolt of the tie bar itself. This will 1 2 4 6 7 happen if the bolt will crush onto the concrete face after the padded path around the tie bar is used. The ability of the tie bar to pick up these 5 additional loads and to transmit them to the concrete decides whether it comes to an immediate Figure 5 Measuring points with breaking of fixing or a stable balance can still shift direction appear in the deformed state in spite of damage. The exact description and explanation of the damage process is of decisive importance. From the first crack to the crack propagation and the final crushing down, the whole procedure of damage is to be observed to do a valid description of the cause to fracture and the evaluation of a calculation model. Special attention must be given to the special cause that will release the final breaking down. The failure of the concrete can be traced back to four basic cases. These can occur both in a pure form and in combination: a) Loss of the stress transmission in front of the base plate by shearing a wedge sized concrete volume in front of the base plate face or damage of concrete in this area. The shear force is shifted onto the shear lug and possibly the anchor bolt of the tie bar. b) Shearing of an wedge sized concrete volume according to a) with immediately following breaking down of the tie bar near the base plate due to combined tensile shear load. c) Tie bar outbreak due to the load attacking at the tie bar head, with an outbreak of a cone behind the base plate. (pull-out failure) d) Complete destruction of the experimental concrete body. Cracking starting at the shear lug will reach up to the component edges. A more detailed description of these basic cases is done in [8] [9] and [10].
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4. Structural behaviour and load-bearing capacity
total failure load V [kN]
Figure 6 presents a first view of all achieved ultimate loads. All experiments are plotted on one graph and the load is shown over the concrete compressive strength. It should be noted that all tested parameters are shown. Therefore the achieved loads need some comments, because different load applications, different forms of fittings and, of course, reasons of crushing are presented. Obviously the three classes of concrete compressive strength can be recognized clearly. Please note the fittings have two different shear transfer faces with quite a varying bearing behaviour. The base plate, embedded in the concrete, which will transmit important parts of the shear loading into the concrete at its front face. But only 2 cm are embedded in the concrete, and the result is an edge compression. The free surface does not allow the concrete to establish a multiaxial compressive state of stress, in the sense of partial load pressure. And the shear lug itself that transmits decisive parts of the shear load V. The concrete body in front of this shear lug is enclosed in concrete and steel. On the top it is protected by the lateral cantilever of the base plate and all the rest is enclosed in concrete, too. So the differB15 B25 B45 -> concrete strength ent conditions make it clear 0 cm 4 cm flat 4 cm box -> lug anchoring that the failure mechanism 8 cm flat 8 cm box depth and sort for the final crushing canD, e = 0 cm Z, e = 0 cm -> additional load . D, e = 10 cm Z, e = 10 cm e = 10 cm tension/compression not automatically be the same for the experiments V eccentricity F bewehrt, bewehrt without lugs and for the mit Stirn ohne Stirn e experiments with lugs present. 1200 Consequently, the consideration of a summary lug face AC [8], cannot allow a 1000 general estimation of ultimate load. Also it is not 800 possible to transfer the results to a more general layout of fittings. So the 600 failure of the base plate end face (Vks) is to view separately from the total failure 400 (Vges). Here Vks designates the shear load step that 200 brings the breaking out of the concrete in front of the 20 25 30 35 40 45 50 55 base plate front side. Vges f c [N/mm²] whereas is the maximum shear load achieved in the Figure 6 Total failure load of all tests experiment.
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4.1.
Concrete failure in front of the base plate, Vks e 1000 The dependence of concrete failure on the existing uniaxil or multiaxial stress 800 state is confirmed by the experiments. In certain 600 experiments, the concrete in front of the base plate is crushed and is shifted out without dowel 400 4 cm rigid dowel without a total failure oc4 cm soft dowel curring. Even this case of 8 cm rigid dowel 8 cm soft dowel 200 events often is difficult to e = 10 cm compressiv F discover in the load-distensile F placement diagrams be0 cause there is no sudden 100 300 500 700 900 relocation of the load failure load V ks [kN] transmitted in the base plate contact surface to the lug Figure 7 Possible increasing of load Vks to Vges surface. This failure load Vks due to concrete failure in front of the base plate only indicates that the complete shear load V is now transferred by the shear lug itself. It is still possible to increase the load after the concrete destruction on the end face of the base plate. This is shown by Figure 7. For the experiments without special shear lugs (black points), the load must be relocated to the tie bar if the Vks-failure occurs. The bolt of the tie bar will now act as a dowel and will be shear loaded, like the lug. It looks similar in the experiments with flat sheet lugs (triangles). The load increasing ability is smaller in the case of the experiments with 4 cm lugs and greater in the case of the experiments with 8 cm lugs. For the experiments with the stiff block lugs the load is not increased after the Vks-failure has occurred. In this case the load due to the Vks-failure is greater than or equal to the load of final breaking, but this will happen on a quite higher load step. The same also occurs in all experiments with enlarged eccentric load attack eV, and in experiments with additional tensile normal force. Merely in the case of the experiments with pressing normal force an appreciable load increase can be found in turn.
V
increase of load Vks to Vges [kN]
F
4.2. Concrete failure in front of the lug – final failure Vges The concrete failure in front of the base plate brings a clear announcement of the breaking, but it will not automatically introduce it. Regardless of whether it is a question of block or flat lugs, in the fracture state the experiments show a concrete stress of 4.5 to 6.0 times fc for all the 4 cm lugs. The adequate values of the 8 cm lugs then range between 2.5 and 4.0 times fc, where the values of the block lugs fall out down. However,
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F-compression
load V [kN]
load V [kN]
for these block lugs no concrete failure is the final reason for breaking down. If the theoretical anchoring depth of all flat 8 cm lugs is reduced to 6 cm in general, the values will join the values of the F=0 4 cm lugs, too. By a pure F-tension shear load all the 4 cm lugs alone (flat and block) 0,2 0,6 1,0 1,4 1,8 give a concrete ultimate displacement v 4 [mm] stress of 5.2·fc. An additional pressure load increases this value to 800 7.1·fc, an additional tensile F-compression 700 normal force will reduce 600 the value to 4.1·fc. A 500 similar behaviour is to be 400 observed for an additional 300 eccentric load 200 F=0 introduction. A look at the 100 F-tension displacement values v4 and 0 w4 at the fracture state will show that an additional -0,2 0,2 0,6 1,0 1,4 1,8 normal force increases the displacement w 4 [mm] displacement considerably F v4 during failure. An Figure 8 Behaviour with tension w4 additional eccentric load and compression introduction with normal V force or without normal hD = 4/8 force then leads to lower values of the displacement value of w4 in the fracture state. Looking at the load displacements in Figure 8, the displacements v4 und w4 show the behaviour as it is described above. Figure 8 shows the displacements for 4 cm and 8 cm flat lugs without additional eccentric load introduction. The grouping of the lines is to be seen clearly. For an additional compressive normal load we get a very stiff behaviour, and the 8 cm lugs do not behave differently to the 4 cm lugs. The behaviour of both is much stiffer than in the case of pure shear load or shear load with additional tensile normal force. These experiments also react far more brittle than those with additional eccentricity of the load introduction. Arriving the maximal load the deformation will increase. Of course the load will go down hereby due to decreasing oil pressure, and the fitting in general is cut by shear force at the tie bar bolt.
800 700 600 500 400 300 200 100 0 -0,2
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This is the reaction to fact that the concrete also has broken down in front of the lug. And the steel fitting glides up, on a wedgeshaped body of concrete that was formed in the corner between the base plate and the lug front face. Finally tests with additional tensile normal force show a much more brittle behaviour with a more sudden breaking down. Again, in principle it is not important whether 4 cm- or 8 cm flat lugs are used. Only the ultimate load is higher in the case of the latter. However, the principle of failure is not changed at all. It can be seen that the additional pressing normal force constitutes a kind of initial preloading on the tie bar. The preloading will help the tie bar and is to be directly subtracted from the rest of the tie bar load. The additional tensile normal load then is a preloading with additional load. Especially noteworthy is that the load displacement lines for v4 are identical for all of the experiments with compressive normal force without additional eccentric load. Here all the lugs with 4 cm and 8 cm act quite identically at any rate up to Vks-failure. However, the fact must be considered that the experiments with compressing and compressing eccentric load show a considerably more good-natured post-break behaviour than the experiments with tension and tensioneccentric load. This will effect the dimensioning of this fittings, by the possible choice of permissible stresses in front of the shear lugs. There will be a necessary differentiation according to load combinations, especially load combinations with tension. 4.3. Other failure modes Steel failure in the lug can occur in two variants. On the one hand, the lug can be cut by shear load in the place of the maximal stress. Both will happen as reaction to the situation of the concrete stresses in front of the lug. The type of distribution of these concrete stresses over the lug height is to be assumed here. These cannot be measured in the experiments and is examined by means of an FEM-model. The tie bar works like a normal force loaded headed anchor bolt, and will crash like that. (steel failure, concrete cone failure or pull-out failure.
5. Model of design Finally, a simple model of dimensioning for these fittings should be presented. This must consider the three basic failure mechanisms separately (See Testing) Even if the different failure mechanism must not be considered completely independent, it is helpful for the checking process to do this. Within the framework of a simple and presumably rough dimensioning it is precise enough to isolate the failure mechanisms and to estimate deformations not at all. The key to the numerical dimensioning of the fittings is the concrete failure in front of the lug and/or the load transmitting face of the base plate. The knowledge of the resulting forces RS and RD will develop the loading of the tie bar, and all forces that will be transmitted in the fitting are known (see Figure 3). To know the location of the forces always a constant stress is assumed in front of the load transmitting surfaces. As shown, a concrete failure in front of the base plate can be distinguished clearly from a total failure. Furthermore, the dimensioning equations will be given for both, a permissible stress σm,AC and a permissible stress σm,AD. The stress of σm,AC will be combined with the available summary lug face AC, and no concrete out-
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break in front of the base plate is to be expected. On the other hand, the pure lug face AD may be applied to the stress of σm,AD. This is the part of lug face in front of which a multiaxial stress state may develop. The load step of VAC may be considered by a concrete breakout in front of the base plate, but it will not matter. This will occur if the value VAD is greater than the value VAC. The consideration of these two values will also offer the possibility to dimension fittings without a base plate embedded in the concrete, too. 5.1. General verification equation With consideration of all available experiments, the equations (1) can be developed. Hereby hD is replaced, so it is more easy to handle the equation. The value hD is to be calculated directly from the total shear load and the permissible stress σm, because the stress σm does not depend on hD furthermore. Also reprocessing of e'V (e'V is the value from the test protocols) to eV is done.
σm, AC fC
σm, AD fC
F − 0,005 ∗ eV − 0,002 ∗ fC FA F = 9,175 − 2,270 ∗ − 0,0150 ∗ eV − 0,100 ∗ fC FA
= 2,475 − 0,570 ∗
a) (1) b)
Units [N] and [mm]; eV ≥ 25 mm FA = FuE = 15,5 ∗ hr1,5 ∗ β w [N]
(2)
A post processing of the experiments based on these relationships gives a good agreement with the experimental values. Naturally, for the experiments without lug only Vksfailure can be calculated. Here the final failure is characterized by a bolt shear fracture of the tie bar, and the yielding mechanisms can be found in the literature due to headed tie bars [6], [7]. For each of AC and AD, the possible value of shear load is calculated, and of course the depended value of FA, the normal force at the tie bar. The greater value indicates the permissible shear load Vges and indicates simultaneously whether a concrete outbreak is possible in front of the base plate or not. Of course, the tie bar has to be able to serve the dependent value of FA. Otherwise the permissible shear load is to be reduced. It should be noted that the tie bar can break down with a steel failure or a pull-out failure. In practice, the tie bar will be a headed bolt, and so the load carrying capacity is known (see equation (2)). In this equation the value of hr gives the anchoring depth of the tie bar. The tie bar diameter has no effect on the concrete-pull-out loading.
5.2. Model For dimensioning the fittings, the following model can be used. This model is used to get the test results by calculation and therefore it works with mean values. It is valid to all fittings which strongly separate shear load transmission from normal force transmission. Even the normal force component of the balance moment is served by the separate tie
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bar. Using equation (1) to get the absorbable mean concrete compressive stress, the experimental total failure loads are reached sufficiently precise. Only the 8 cm lugs show a greater deviation in the results. This behaviour can be traced back to the approximation of the model itself. Naturally the effects on deformation will not allow a rectangular stress distribution in front of the lug over the hole anchoring depth. The effects of this state of affairs are more closely described in [11]and would go beyond the scope of this simple model. In detail, the procedure has to be carried out as shown in Figure 9: On the basis of the input variables, the absorbable mean concrete compressive stresses in front of the lug are determined. From these stresses the absorbable shear load is to be calculated. This total load is based, on the one hand, on the summary lug face area AC, and, on the other hand, on the pure lug face area AD. Notice that area AD will be only that contact surface which can develop a multiaxial stress status in front of itself. The bigger value of these two approaches indicates the absorbable shear load level - henceforth called V. If the shear load VAC is less than the shear load VAD, it is to be expected that the concrete will break out in front of the linked base plate, but still there will be a reserve available up to the total shear failure load given: searched: that will be V = VAD. The planned use and the secushear load V eccentricity eQ [mm] rity concept will decide normal force N [N] whether V as working AC tie bar load capacity F [N] A load may be exceeded or concrete strength fc [N/mm²] not. The form and stiffness of the lugs are still unimportant in this step. permissible stress / load Furthermore, the failure σm,AC -> tolerable VAC = σm,AC × AC of the single components is tested and they will be σm,AD -> tolerable VAD = σm,AD × AD dimensioned or the absorbable shear load V is load carrying fitness for use to be reduced to the capacity weakest part. In this step VAC ≥ VAD sudden crash it will be practically choultimate load VAC < VAD concrete breaks out in sen by which component tol VAC front of the linked base the final failure will be max =V tol VAD plate, but still load inintroduced. It is adviscrease to VAD possible able, to prove the tie bar first. Its load will be clearly given by the exdimensioning / verification ternal loading and the at the fixture (local) rectangular stress distribution in front of the base plate and the shear lug. Figure 9 Schema of verification The tie bar is to be veri-
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fied with respect to steel failure as well as to concrete outbreak. At last the lug itself should be proved. The proofing is to be done in a separate manner for a shear failure, and bending failure that will result in plastic flow with rotation. The last one is not to be allowed, because no deformations are expected in this model. In this form the proving has the advantage that not a reduced anchoring depth of the shear lug has to be used. As a result, the shear load component in the lug is reduced by static system alternations and the applied concrete compressive stress state will remain unchangeable. Using this lug dimensioning model will result in great deformations of the fitting, and therefore the concrete will break in front of the base plate. In the case of very big values of lug anchoring depth combined with a very small value of the lug bending stiffness this dimensioning model should not be used because it does not consider the real deformations in the fitting. So the local load introduction is done. Of course, a secure load transmission to the supports is to be ensured, too. The investigation of a possible punching of the fitting is also to be made. This case is not so erroneous at mass components with low reinforcement. The test with stiff lugs and high values of concrete strength does show this.
Bibliographic references [1] Fastenings to Reinforced Concrete and Masonry Structures, State-of-the-Art Report, Part I and Part II, CEB-Bulletin d’Information Nr. 206/7, Lausanne 1991 [2] Fastenings to Concrete and Masonry Structures, State-of-the-Art Report, CEBBulletin d’Information Nr. 216, Lausanne 1994 [3] Design of Fastenings in Concrete, Draft CEB Guide Part 1 to 3; Fastenings to Seismic Retrofitting, State-of-the-Art Report on Design and Application, CEB-Bulletin d’Information Nr. 226, Lausanne 1995 [4] Rotz, J.V.; Reifschneider, M: Combined Axial and Shear Load Capacity of Steel Embedments in Concrete, Report Bechtel Power Corporation, 1991 [5] Körner, C; Schweigel, P: Nachweis der Betontragfähigkeit im Verankerungsbereich von Stahleinbauteilen, Betontechnik H. 1, 1986 [6] Rehm, G.; Eligehausen, R.; Mallée, R.: Befestigungstechnik, published in Betonkalender 1988, (Teil II-D, 609-753; 1997) and other following [7] Eligehausen, R. and other; Tragverhalten von Kopfbolzenverankerungen bei zentrischer Zugbeanspruchungen, Bauingenieur 67 (1992) pp.183-196 [8] Körner, C.: Verankerung schwerer Lasten mit Schubdübeln, 34. Forschungskolloquium des DAfStb am 9./10. Oktober 1997 an der TU Dresden [9] Curbach, M.; Körner, C.; Michler, H.: Tragfähigkeit von Befestigungen mit Schubdübeln im Betonbau zur Übertragung großer Schubkräfte. Abschlussberichtzum Forschungsvorhaben DFG Cu-37/3-1, TU Dresden, Institut für Tragwerke und Baustoffe, Lehrstuhl für Massivbau, Dresden 2001 [10] Michler, H: Load Capacity of shear loaded anchorages. International PHD Symposium in Civil Engineering, Wien 2000 [11] Michler, H: Dissertation, Lehrstuhl für Massivbau, TU Dresden (in progress)
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SAFETY RELEVANT ASPECTS FOR TORQUE CONTROLLED EXPANSION ANCHORS Helmut Gassner, Erich Wisser Hilti AG, Schaan, Liechtenstein
Abstract For an assessment of expansion anchors, it is necessary to know, which parameters have to be considered. To investigate safety relevant aspects for Torque Controlled Expansion Anchors fife different types of anchors have been tested. The products were examined onto appearance, behaviour at setting and under static loading in tension and shear direction. The tests have been shown, that a lot of parameters have to be considered to compare the behaviour of different anchors, especially under difficult conditions on construction site. In addition to the ultimate pull-out and shear load, the setting procedure and the tightening torque moment are very important parameters.
1. Introduction To investigate safety relevant aspects for Torque Controlled Expansion Anchors fife different types of anchors have been tested. The dimensions and embedment depth are nearly identical. The products were examined onto appearance, behaviour at setting and under static loading in tension and shear direction. Basic data for concrete capacity C25/30 and drill hole were evaluated. All anchors of same size were set with same embedment depth obeying the setting instructions of the respective manual.
2. Test Setup Static pull-out test All pull-out tests were carried out with a testing system of 250 kN maximum load and a
102
chosen displacement speed of 6 mm/min. The tests were performed with and without tightening torque moments to check the reliability at wrong application. Static shear tests The shear tests were carried out with a servohydraulic test cylinder of an nominal capacity of 250 kN. The displacement speed of the piston was 16 mm/min. Clamping of gaps between concrete and attaching part Often only after installing the torque moment there is realized that the attaching part shows a gap to the substrate. So in the test a steel padding of 6 mm was placed between concrete surface and loading plate. The full torque moment was installed, then released and the padding removed. If after installing the torque moment again the loading plate could be clamped onto concrete surface, the clamping test was assessed positive. With the Anchor Type E one test was performed only with a low torque moment. Then the pads were taken out and the full torque moment applied for simulating a flexible footing.
Load F [kN]
3. Behavior under Tensile and Shear 70 A; M12 with Md A; M12 without Md B; M12 with Md B; M12 without Md C; M12 with Md C; M12 without Md D; 5/8" with Md * D; 5/8" without Md * E; M12 with Md E; M12 without Md
60
50
40
30
20
10
0 0
5
10
15
Fig. 1 Load Displacement behaviour - Pull-Out Tests
103
20
25 30 Displacement s [mm]
In Figure 1 the results at static pull-out tests for all anchor types are shown, black curves with tightening torque moment, red curves without. All tested samples of Anchor Type A were conform to the anticipated behaviour. The follow-up expansion worked well. At pull-out test the very small scattering in the load displacement behaviour up to ultimate load is significant. But the clamping force of the attaching part is comparatively low with 15 kN. Also in shear the system works as requested. With high ductility the ultimate shear load is achieved at a displacement of about 28 mm. The claming function is ensured up to a gap of 8 mm. The results at static pull-out test of Anchor Type B shows, that at in minimum two of five anchors the expansion sleeve cracked radially and moved onto the upper cone. This causes a high number of turnings for the torque moment. So the conversion of torque to pre-load is undefined and within a wide variation of deviation. At prescribed torque moment pre-stressing forces twice of Anchor Type A were achieved. At the static pullout tests the system acted brittle and without any follow-up expansion effect. At four of five anchors the cones were pulled through. The concrete failed but no concrete cone broke out. The average ultimate load was only at 63% of the Anchor Type A value. In shear the system works - due to the failure mode bending-tension of bolt - ductile but the maximum loads were achieved after already 5-12 mm displacement (Anchor Type A only after 28 mm). For the Anchor Type C, the transmission of the torque moment varied in a wide range as with Anchor Type B. To the customer this generates a dubious feeling. However prestressing forces of 120 to 200 % of the Anchor Type A values are realised. The loaddisplacement behaviour, the ultimate loads and the failure mode were equal to that of the Anchor Type A. Nevertheless at the pullout test without a torque moment the tested anchors failed without increasing of load. Also in shear loading the ductility of the tested Anchor Type C is about 30% below the ductility of the Anchor Type A. The average of the ultimate shear capacity is 18% less however with small standard deviation - below the Anchor Type A value. The results at static pull-out of Anchor Type D are described as follow. A high number of strokes was needed for setting the anchor. At two of five anchors the plastic ring broke so that the expansion sleeve did not touch the cone. At the attempt to install the torque moment the screw got stuck at the front of the slotted and compressed cone and the cone was not pulled into the expansion sleeve. In the drill hole the cone turned through. One of these two anchors was pulled out with only 4 kN ultimate load. The average ultimate load of the other anchors for pull-out amounted only 69% of the Anchor Type A value. Without torque moment both tested anchors were pulled out without load.
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The tested Anchor Type D System works very unsafe concerning the setting and pull-out behaviour. In shear the ductility of this anchor is comparable to Anchor Type A. The ultimate force is 17% below the Anchor Type A value because of the thin rolled sheet sleeve. The expansion cone of Anchor Type E differs from all other tested anchors in the twofold expansion angle. First an angle of 7º and 6 mm long followed by an angle of 15º and 7 mm long. At Anchor Type A the angle is 8º with a length of 12 mm. This may cause the high pre-stressing force, more than twice that of Anchor Type A. Sleeve and washer are equal to Type A parts. The torque moment was reached only after 4 1/2 to 6 turnings because 5 mm displacement are necessary that the front of the sleeve contacts the cone. Ultimate tensile load and its variation are equal to Anchor A. The follow-up expansion works well also the plastic deformation of the expansion sleeve to a tulip shape. Also without a torque moment the safety of this anchor at tensile loads is given. The shear capacity of Anchor Type E makes 73% of Type A value. But the threaded rod version of Type E has 27% reduced stress area. The ductility is much lower as with anchor A. The dimensions of the sleeve are equal to Anchor A.
4. Rest Results at Cclamping of Gaps At Anchor Type E the functions of the plastic collapsible section are integrated into the expansion sleeve made of sheet metal. These consist of 3 folded expansion parts of 1.2 mm thickness. The rips as crumble zone should prevent internal pretension when a gap between concrete surface and attaching part has to be closed. The thickness of the sleeve is 20% less than that of Anchor Type A. To assess the function of gap clamping two tests were performed. At the first one the total torque moment was installed using steel pads between concrete surface and attaching part, then released and the pads were removed. Now no clamping of attaching parts to concrete surface could be achieved with torque moment. At the second test after a small torque moment the pads were removed and the torque moment was increased to the prescribed value now producing a clamping force. The drilled out anchors show the insufficient function of the crumble zone. To get more information for the functioning at “gap clamping” a more detailed examination is proposed.
5. Setting Behavior In Table 1 is shown a synopsis of test results to setting behaviour. Most of anchors needs 1 to 2 hammer strokes for setting into the drill hole, but Anchor Type D significantly more. The mounting overhead can be made without falling out of the anchors and the antirotation device works at all anchors, too.
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The clamping test with a gap of 6mm worked more or less at all anchors. At Anchor Type B broke the expansion sleeve and was pushed over the conic part. At Anchor Type C the plastic section collapsed as defined, at Anchor D as undefined. Anchor Type E managed the clamping test only at facilitated conditions. The tightening with torque moment occurred at Anchor Type A with only 1 1/2 to 1 3/4 turns. The others partially needed much more turns as you see in the table. All anchors could be removed flush to the concrete surface.
type of anchor
number of mounting strokes at with 500g overhead hammer
antirotation device
clamping test (6 mm gap)
o.k. o.k., expansion sleeve broken o.k., defined collapse of plastic section o.k., undefined collapse of plastic section o.k., only at facilitated conditions
A B
1 2
o.k. o.k.
o.k. o.k.
C
1
o.k.
o.k.
D
12-17
o.k.
o.k.
E
2-3
o.k.
o.k.
needed removable turns for flush to the tightening concrete with torque surface moment 1 ½ -1 3/4 o.k. o.k. 4 ½ -10 1¾-4
o.k.
2-2½
o.k.
4½-6
o.k.
Table 1 setting behaviour
6. Behavior at Loading In the synopsis of test results to the behaviour at loading it is recognisable that the prestressing force of Anchor B, C and E is distinctly higher than at Anchor Type A. The pre-stressing force of Anchor Type D varies between 0 and 14 kN. The ultimate load at static pull-out of Type C is the highest one with the smallest standard deviation, followed by Anchor A. The follow-up expansion did not work at all anchors of Anchor Type B, 3 of 5 anchors of Anchor Type D.
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type of pre-stressing ultimate pull- follow-up ultimate pull-out ultimate shear anchor force out load, expansion load without load, standard standard tightening torque deviation, n=4 deviation, n=5 moment, n=2 A ~ 15 kN Fu,m = 61,9 kN o.k. Fu,m = 55,2 kN Vu,m = 100,6 kN v = 9,1 % Fu,m = 57,3 kN with v = 8,8 % follow-up expansion B ~ 32 - 40 kN Fu,m = 39,4 kN no follow- Fu,m = 37,0 kN Vu,m = 87,2 kN v = 11,6 % up Fu,m = 38,0 kN with v = 1,4 % expansion follow-up expansion C ~ 20 - 30 kN Fu,m = 63,9 kN o.k. Fu,m = 0,8 kN Vu,m = 82,3 kN v = 4,2 % Fu,m = 1,1 kN pull v = 3,2 % out by hand D ~ 0 - 14 kN Fu,m = 42,6 kN 3 of 5 Vu,m = 83,2 kN Fu,m = 2,0 kN v = 16,6 % without Fu,m = 2,0 kN no v = 4,6 % follow-up follow-up expansion expansion E ~ 35 - 40 kN Fu,m = 60,3 kN o.k. Fu,m = 45,4 kN Vu,m = 73,7 kN v = 9,3 % Fu,m = 59,6 kN with v = 1,3 % follow-up expansion Table 2 load behaviour The pull-out test without tightening torque moment simulates, that because of confined place a tightening with full torque moment is not or only partially possible. Here Anchor Type A, B and E demonstrated follow-up expansion and high pull-out forces. Anchor Type C and D exhibited no follow-up expansion and therefore low loads. The ultimate static shear load of Anchor A was the highest, this time followed by Type B.
7. Conclusion The tests of different expansion anchors demonstrates, that the Anchor Type A impresses with the clear and save function of the plastic collapsible section. The system is well calculable because of the small standard deviation of the results. All components are optimally adjusted to the setting procedure, pull-out and shear load. It has been shown, that a lot of parameters have to be considered to compare the behaviour of different anchors, especially under difficult conditions on construction site.
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STUDY ON STANDARD TEST METHODS FOR POSTINSTALLED ANCHORS Yoji Hosokawa*, Katuhiko Nakano**, Yoshiki Oohaga***, Shigeru Usami****, Kiyoshi Imai***** * Technical Development Group, Maeda Corporation, Japan ** Institute for Structural Concrete, Science University of Tokyo, Japan *** Institute for Structural Concrete, Tohoku Institute of Technology, Japan **** Institute for Structural Engineering, Kajima Corporation, Japan ***** Institute for Post-Installed Anchor, KFC Corporation, Japan
Abstract The present paper reports the test methods and test results of Bonded anchors and Metal Anchors. So far, in Japan, Post-installed Anchors cannot be used for a newly-built building, but can be used to reinforce an existing building for earthquake resistance strengthening. There for, standards test methods are important to meet the requirement of appraisal system.
1. Introduction About 4 hundred millions of Post-installed Anchors are used for fitting up machineries and reinforcing earthquake resistant structures. In common, the performances of Post-installed Anchors are determined by the makers, and there is not a unified standard to evaluate the performances of such anchors. In order to guarantee the quality and performances of Post-installed Anchors, Japan Construction Anchor Association makes an Approval System for the technical appraisals. The present paper reports the standard mechanical test methods, by which the necessary data of strength and stiffness are determined for the Approval of Post-installed Anchors. So far, three test methods were developed, which are the Set test, Tensile strength test and Shear test. The Set test is a performance test for a constructed anchor, in which strength test for the base material and adhesive strength is necessary for metal anchors and bonded anchors respectively. While, the Tensile test and Shear test are carried out by measuring the strengths and displacements due to tension and shear forces act on test anchors, which was supposed that the test anchors were constructed anchors fixed in concrete.
108
2. Set Test Method 2.1 Set test for metal anchors 2.1.1 Introduction In common, Metal anchors are cold formed, and the properties of its material are changed during the products process. Stress concentration always happens at the expansion head of an anchor, due to the beating and pressing during construction. So, it is very important for the quality control to confirm the performance and its quality by the Set test before the products leave the factory. 2.1.2 Method of the Set test The Testing equipment is Fig. 2.1 shown in Fig. 2.1. The equipment is composed by Reaction plate, Oil jack and Deflection Transducer. The test anchors are Nail-in, Internal cone, Out Cone, the diameter of the test anchor is M10—M20. 150
2.1.3 Test results Fig. 2.2 shows the loaddisplacement curve of the tests. The displacement
No1M10 No2M10 No3M12 No4M12 No5M20 No6M20 No7M20
125
Tensile Load (KN)
The test anchor is set between a tension rod and a jig fixed onto the equipment, and then the jack applies the tension force on to the set. Just like the real construction, the jig is filled with nonshrink mortar (compressive strength: 30N/mm2). The jig is made by steel, and its inner shape is a cone.
M20 100 M12
75
P M10
50
l
δ2
l=50mm δ = (δ 1 +δ 2 ) / 2
25
0 0
δ1
2.5
5
7.5
10
12.5
15
Displacement (mm) Fig. Fig.2.2 Relationship of Tensile Load and Displacement (Outer Cone Type Anchor)
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measuring points are 50mm and 100mm below the concrete surface for Out Cone and Nail-in type respectively. The broken locations are at the thread part for the cone anchor and Internal cone, minimum section or thread part for Nail-in type. 2.2 Set test for Bonded Anchor 2.2.1 Introduction By the Set test for bonded anchor, we measured the limited value of the bond strength of the anchors, and make a standard value for quality control of bonded anchors. Hence, the bonding surface of the anchor should be very homogenous. Steel jig and mortar filled steel jig are discussed, and then mortar filled steel jig are selected as a part of the testing equipment. Event for the test using old resin, we have not found the influence of aggregate in the steel jig. 2.2.2 The test method Fig. 2.3 shows the testing equipment and the jig. The jig is a steel pipe (89.1mm in diameter and 80mm in length) filled with non-shrink mortar. The test anchor is a bolt of M16 hammered into a bored hole in the jig. In such a bonding strength test, the object anchor was set on the tension rod, and tensile force was applied with a speed of 20N/mm2 per second by the oil jack till the anchor was pulled out of the jig. 3. The Tension test method 3.1 Introduction For this test, there is not a specification for the shape of the loading equipment. But, we set the inner dimension of the reaction plate food as shown in Table 3.1, considering the support position of the reaction plates have influence on the measures results of tension Fig. 2.3 performance of the anchor.
110
Table 3.1 Minimum Inner dimension of the reaction plate Broken Type of the anchors Metal anchors Cone broken type 3.5 h Not cone broken type 2.0 h
Bonded Anchors 2.0 h 1.5 h
Fig. 3.1 3.2 Testing equipment Fig.3.1 shows the testing equipment and its Deflection Transducer. There is not a specification for the dimension of the concrete object. We used common concrete, and its minimum thickness is double of the insert depth of the anchor in the concrete body, or the biggest value of the double of the insert depth and the depth plus 10cm (same as the Shear test). The tolerance of the load cell is less than 1.5%, and the maximum tension load acted on the load cell is 1/20 (5%) of its capability. The tolerance of the Deflection Transducer is less than 0.02mm. As showing in Fig. 3.1, three Deflection Transducers were set around the test anchor, which are 15mm from the concrete surface. The reference fix points are in a distance from the anchor, double of the insert depth of the anchor in the concrete body, and are set at the top and lateral surfaces where the influence due to the bending displacement of concrete can be considered as small enough.
111
3.3 The Test method For this test, a pre-load acted on the test anchor was introduced. The value of the pre-load is 5% of the maximum of a presumed load and smaller than 2.0KN. The load was acted at a loading speed smaller than 20N/mm2 per second. The measuring of load and displacements were continued till the anchor was broken. 3.4 Confirm the Test method In the present paper, the influence of pre-load and loading speed were discussed based on the tests for checking the validity of the test methods. Table 3.2 shows the types of the anchors and the out line of the test anchors. Table 3.2 Outline of Test Anchors Effective Effective Minimum Embedded Bolt Horizontal Calculated Embedded Anchor Type Nominal Diameter Section Length Length Project Aria Strength Ac (cm) Tc(kN) Diameter de (mm) (mm2) h (mm) Le(mm) Nail-in 16.0 119 60 44.0 82.9 130 Ｍ 16 Metal Internal Cone 20.0 127 60 40.0 75.4 119 Ｍ 16 Anchor Outer Cone 21.4 157 63 41.6 82.3 129 Ｍ 16 Type Hard Sleeve 21.7 157 60 38.3 72.2 114 Ｍ 16 Bonded Vinyl 16.0 157 125 109.0 427.8 506 Ｍ 16 Anchor Urethane Calculated Strength with Shear Cone Failure・ Tc=√ óB・ Ac（ Metal Type） ・ Tc=0.75√ ó B・ Ac（ Bonded Type） Here, óB： Concrete Strength at Test（ 26N/mm2） Ac： Effective Horizontal Project Aria（ c㎡） Le： Effective Embedded Length（ cm） ＝h－de
The pre-load was applied with 3 load levels, which were a determined load level, 0% and 200% of the determined load level. And then, 3 loading speeds were used, which were a determined speed, 50% and 150% of the determined speed. The tests were carried out with an anchor hammered into concrete block (110cm
180cm
30cm, Fc = 21N/mm2) and set onto the testing equipment . 3.4.1 Influence of pre-load Fig. 3.2 shows the relationship between the pre-load and the capability. In this diagram, the average value of 3 test pieces with different levels is shown as folded line. The influence of pre-load is obvious for anchors of Hard Sleeve, and there is not obvious influence for other types of anchors.
112
4. Shear test 4.1 Introduction For this test, we set the test anchor at a certain distance from the concrete edge, so that the edge part the concrete would not break.
80 Hard Sleeve Type 60 40 80 Outer Cone Type Maxuium Load (KN)
3.4.2 Influence of loading speed Fig 3.3 shows that the capability increased proportionally to the loading speed for a bonded anchor. But, a little influence of loading speed was measured for Nail-in anchors, and almost no influence was measured for other types of anchors.
40
40 20
0 (0%)
1.96 3.92 (Stndard) (200%) Pre-force of Bolt Pre-load of Bolt (KN)(KN)
Fig. Pre-force Fig. 3.2 Relationship relationship ofofPre-load and Maximum Strength And Maximum strength 120 100 Maxuium Load (KN)
Tests were carried out for different types of anchors, with different lengths of setting-plate, and different material of shearing surfaces. The anchor types used for the tests are Internal cone, Hard Sleeve, Out Cone, Nail-in and bonded anchors. Lengths of setting-plate are 7.5 and 15.0 times of the diameter of the anchor. The Pre-load are shown in Table 4.1. The shearing surface is thin steel sheet, and Teflon sheet.
40 60 Internal Cone Type
20 60 Nail-in Type
4.2 The testing equipment Fig. 4.1 shows the loading equipment. The loading equipment is composed with a setting-plate for supplying shear forces onto the anchor, a tension rod, an oil jack and a load cell. 4.3 Tests for confirming the equipment The tests were carried out by the equipment shown in Fig. 4.1, with different lengths of setting-plate and shearing surface, different levels of pre-load and different types of anchors. The concrete strength used for the tests is Fc = 32.7KN/mm2, and the diameter of the anchor is 16mm.
60
Bonded Anchor Type
80 80 60
Hard Sleeve Type
40 60 40 20
Nail-in Type 9.8 19.6 29.4 (50%) (Upper Limit of Stndard) (150%) 2 Loading Speed N/mm ( N/mm2/sec /sec ) )
Fig. 3.3 Relationship of Loading Speed and Maximum Strength
113
Reaction Frame H-200x200
Teflon sheet Reaction Frame Tension Rod Setting Plate
Swivel Load Cell Jack
S p ec ime n Anchor Plate
M1 6 A n ch o r Reaction Pedestal
Spring Fastening Anchor Bolt
Fig.4.1 Equipment of Shear Laoding Test Table 4.1 indicates the types of anchors and other items for the test. In the test procedure, the concrete close to the anchor was broke first by its bearing stress, and then the anchor broke lately, which is the common phenomenon of the tests.
Table4.1 List of Shear Tsets Table Se tting P late To r que B o undary C o nditio n Le ngth Anc ho r Type N o n 120 240 ・ ・ SS T mm mm 0 kN N o te 1 N o te 2 SS +T M A1 ～ 4 M A1 M A2 M A3 M A4 ○ ○ M A5 ～ 8 M A5 M A6 M A7 M A8 ○ ○ H ar d Sle e ve M A9 ～ 1 2 M A9 M A1 0 M A1 1 M A1 2 ○ ○ M A1 3 ～ 1 6 M A1 3 M A1 4 M A1 5 M A1 6 ○ ○ M B1～ 2 O ute r Co ne M B1 M B2 ○ ○ M C1 Inte rnal C o ne ○ ○ ○ M D1 N ail-in ○ ○ ○ B o nde d Anc ho r B A1 ～ 3 B A1 B A2 ,3 ○ ○ N o te 1 : To rque= M in. ［ 6 0 % o f Yie ld Stre ngth, 4 0 % o f Shear-C o rn failure Stre ngth, 4 0 % o f B o nd Stre ngth ］ , The To rque is c o ntro lle d by the 0 .2 to rque c o e f fic ie nt. H ar d Slee ve : To r que Value 2 3 5 N ･ m m (Axis fo rc e 7 .3 5 K N ) O ute r Co ne : To rque Value 2 2 5 N ･ m m (Axis fo rc e 7 .0 5 K N ) Bo nde d Anco r: To rque Value 2 2 5 N ･ m m (Axle Fo rc e 7 .0 5 K N ) BA2 : To rque Value 6 5 6 N ･ m m (Axle Fo rc e 2 0 .4 8 K N ) B A3 N o te 2 : Bo undary C o nditio n: N o n-she e t SS is Ste el She e t. T is Te flo n She e t. Metal Anchor
Spe cim e n N am e
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60
Shear Load Q (KN)
50
MA2-2(Steel Sheet)
MA1-1(Non-Sheet)
40 30 20 MA4-2(Steel + Teflon Sheet)
10 0 -2
MA3-2(Teflon Sheet)
0
2
4
6
8
10
Shear Deflectionδ (mm) Fig. Fig.4.2 Relationship Example of Shear Load and Displacement (Boundary Condition)
[1] Influence of concrete surface situation and setting-plate: The test anchor is Hard Sleeve, and take setting-plate (120mm in length) and 4 types of concrete surface situation as the items of the test. The test result are shown in Fig.4.2. The concrete surface situation (1) Bare concrete surface (2) Concrete surface covered by steel sheet (3) Concrete surface covered by Teflon sheet of 2mm in thickness (4) The composing of (2) and (3) Fig. 4.2 shows the difference of stiffness and capability depend on the situation of the concrete surface. Fig. 4.3 shows the result with different lengths of setting-plate, and that the capability and stiffness are increased with the increasing of the setting-plate lengths. [2] The influence of the pre-load Fig 4.4 shows the displacement-strength cure of Hard Sleeve due to torques of “0” and 235N･mm respectively. By this diagram, we found that there was not influence of the torque.
115
60
MA1-1(120mm)
MA9-3(240mm)
Shear Load Q (KN)
50 40 30 20
MA1-1(240mm)
10
MA3-2(120mm)
0 -2
0
2
4
6
8
10
Shear Deflectionδ (mm) Fig. Fig.4.3 Relationship Example of Shear Load and Displacement (Setting Plate Length)
60
Shear Load Q (KN)
50
M A 7-2 (3 .5K N )
40 30 20 M A 3-2(A xis For c e 0K N )
10 0 -2
0
2
4
6
8
10
Sh ear D e flection δ (m m ) Fig. F ig.4.4 R elations hip E xa m ple of S hear Loa d a nd D is pla cem e nt (A xis Fo rc e)
Fig. 4.5 shows the test results of bonded anchor, which is a comparison between three torques, “0”, 225N･mm and 656N･mm. The maximum of stiffness increased with the increasing of the pre-load.
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60 BA2-1(3.5KN)
Shear Load Q (KN)
50 40
BA1-1(0 KN)
30 20
BA3-1(10.3KN)
10 0 -2
0
2
4
6
8
10
Shear Deflectionδ (mm) Fig. 4.5 Relationship Example of Shear Load and Displacement Fig. (Axis Force)
5. Conclusion 1. 2. 3. 4.
We demonstrated that it is possible to confirm the performances of metal anchors and bonded anchors by set test method before the products leave the factories. For the tension tests, the influence of pre-load is very small besides the test for Hard Sleeve anchors. Besides the Nail-in anchors, almost no influence of loading speed on the capability was found. Henceforth, we will study the in situ test methods for the anchors.
Acknowledgement I am grateful to Dr. R. Tanaka (Tohoku Institute of Technology), Dr. Y. Matsuzaki (Science University of Tokyo) and JCAA for their good cooperation throughout the research. And then, I would like to thank Dr. Pei Shan Chen (Meada Co.) for his help with composing this paper.
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STATIC BEHAVIOR OF ANCHORS UNDER COMBINATIONS OF TENSION AND SHEAR LOADING Dieter Lotze*, Richard E. Klingner** and Herman L. Graves, III*** *Director of Research, Halfen GmbH & Co., Wiernsheim, Germany. Former, The University of Texas at Austin. **Phil M. Ferguson, The University of Texas at Austin, Texas, USA ***Office of Nuclear Regulatory Research, US Nuclear Regulatory Commission, Washington, DC, USA.
Abstract Under the sponsorship of the US Nuclear Regulatory Commission, a research program was carried out on the dynamic behavior of anchors (fasteners) to concrete. This paper deals with the static behavior of single and multiple undercut and sleeve anchors, placed in uncracked concrete and loaded by combinations of tension and shear. The results are used to draw conclusions regarding force and displacement interaction diagrams for single anchors, and regarding the applicability of elastic and plastic theory to the design of multiple-anchor connections to concrete.
1. Introduction Under the sponsorship of the US Nuclear Regulatory Commission, a research program has recently been completed, whose objective was to obtain technical information to determine how the seismic behavior and strength of anchors (cast-in-place, expansion, and undercut) and their supporting concrete differ from the static behavior. The research program comprised four tasks: 1) 2) 3) 4)
Static and Dynamic Behavior of Single Tensile Anchors (250 tests); Static and Dynamic Behavior of Multiple Tensile Anchors (179 tests); Static and Dynamic Behavior of Near-Edge Anchors (150 tests); and Static and Dynamic Behavior of Multiple-Anchor Connections (16 tests).
This paper deals with part of Task 2, concerning the static behavior of single and multiple undercut and sleeve anchors, placed in uncracked concrete and loaded by combinations of tension and shear. The results are used to draw conclusions regarding force and displacement interaction diagrams for single anchors, and regarding the applicability of elastic and plastic theory to the design of multiple-anchor connections to concrete.
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2. Background The behavior of anchors (fasteners) to concrete is discussed at length in Reference 1. The work of Fuchs [2] provides some useful information regarding shear behavior. As discussed in Reference 3, mean concrete breakout capacity in tension or shear is well predicted by the CC Method. Tensile capacity as governed by steel failure is given by the product of the ultimate tensile strength and the cross-sectional area of the anchor shank. For a uniform cross-section, the ratio of shear to tensile capacity is about 0.6 [4]. If the anchor sleeve goes through the baseplate, steel capacity in shear is increased, by an amount that depends on the degree of interaction between the anchor shank and sleeve, and the material of each component. Figure 1 shows different models for the interaction of tension and shear capacities. 1.2 1 Elliptical (5/3)
N/No
0.8 0.6
Tri-linear
0.4
Linear
0.2 0 0
0.2
0.4
0.6
0.8
1
1.2
V/Vo
Figure 1
Tension – shear force interaction for anchors
For failure by steel fracture, an elliptical interaction is used: p
p
N V + = 1 N 0 V0
(1)
The exponent p varies between 5/3 [5] and 2.0 [6]. For failure by concrete breakout, Johnson and Lew [7] propose a linear interaction as a lower bound (Figure 1). Bode and Roik [8] propose a tri-linear interaction (Equations 2a through 2c):
N = 1 N0
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(2a)
V = 1 V0 N V + = 1 N 0 V0
(2b)
(2c)
The elliptical interaction of Equation 2 has been proposed for concrete failure as well, using an exponent p equal to 4/3 [9], 5/3 [4], or 2.0 [6]. Displacement interaction has not been widely investigated [10], and is in theory not required for the elastic design procedure, in which no redistribution of anchor forces is assumed. If redistribution of anchor forces is assumed, as in the plastic design approach, then knowledge of displacement interaction is necessary.
3. Anchors, Test Setups and Procedures Based on surveys of existing anchors in nuclear applications, tests described here involved one undercut anchor (“UC1”) and a heavy-duty, sleeve-type, single-cone expansion anchor (“Sleeve Anchor”). Based on current use in nuclear applications, it was decided to test anchors ranging in diameter from 3/8 to 1 in. (9.2 to 25.4 mm), with emphasis on the 3/4 in. (19.1 mm) diameter. The Sleeve Anchor tested throughout this study is a single-cone, sleeve-type expansion anchor with follow-up expansion capability, shown in Figure 2. expansion sleeve structurally funished surface cone
D
lef
Figure 2
D2
plastic crushable leg
D1
spacer sleeve
lc
Key dimensions of Sleeve Anchor
The Undercut Anchor 1 (UC1) opens conventionally, and is shown in Figure 3.
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extension sleeve
expansion sleeve
D
lef
Figure 3
D2
cone
D1
threaded shank
lc
Key dimensions of Undercut Anchor 1
Embedment depths in Task 2 were varied according to whether steel failure or concrete breakout failure was desired. The embedments used are described when each set of test results is discussed. The target concrete compressive strength for this testing program was 4700 lb/in.2 (32.4 MPa), with a permissible tolerance of ±500 lb/in.2 (±3.45 MPa) at the time of testing. For these tests, a porous limestone aggregate was used. The typical test specimen was a concrete block 39.5 in. (1 m) wide, 24 in. (0.6 m) deep, and 87.5 in. (2.2 m) long. Seven #6 (32 mm) longitudinal reinforcing bars were placed in the middle of each block to provide safety when the block was moved. This reinforcement was placed at the mid-height of the block to permit testing anchors on both the top and bottom surfaces, while precluding interference with anchor behavior. Four lifting loops were located at the mid-height of the blocks, permitting transport by overhead crane. For loading anchors under combinations of tension and shear, the test setup consisted of a structural steel framework holding a center-hole actuator at a variable angle (Figure 4). Load was applied through a special loading shoe, shown in Figure 5. For eccentric shear tests on two-anchor attachments, the loading fixture consisted of a special baseplate with two high-strength steel inserts, two tension rods, and two compression bars (Figure 6). The inside thickness of these inserts was counter-bored to 3/4 in. (19 mm), the same as the diameter of the anchor bolts. The diameter of the baseplate holes was 13/16 in. (20.6 mm). The overall test setup is shown in Figure 7.
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actuator angle varies
steel frame
anchor
Figure 4
Test setup for anchors loaded at different orientations hole for mounting pin
30 deg
60 deg welded side plate baseplate screwed-in insert made of high-strength steel
Figure 5
Special loading shoe for tests at different orientations
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External Load Strain Gages
Compression Bars
Tension Rods
Inserts Strain Gages 5 deg Plan view of base plate Elevation
Figure 6
Loading fixture for eccentric shear tests on two-anchor attachments
Loading Attachment
Load DCDT Cell
Hydraulic Actuator
Clamping Beams Concrete Specimen
Restraint Tubes
Rollers Reaction Frame
Additional W12 Beams
Figure 7
--- Lab Floor ---
Tie-Down Rods On Floor
Setup for eccentric shear tests on two-anchor attachments
The axial force and bending moment in the baseplate were calculated from strain measurements from two sets of three strain gauges each, evenly spaced on the top and bottom of the center section of the baseplate. Based on the geometry of the loading apparatus, the force in the tension rods is 1.2 times the external shear load, and the tension force on the back anchor can be calculated by equilibrium of moments about the center of the baseplate. The shear force on the back anchor equals the measured tension force in the baseplate. External load on the connection was measured with a load cell, using a spherical bearing to eliminate error due to angular deviation. The tension forces
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on each anchor were measured with force washers placed between the normal washers and the baseplate. Baseplate slip was measured with a potentiometer placed against the back of the baseplate. The horizontal displacement of the loaded point 12 in. (305 mm) from the surface was also measured. The vertical displacement of the baseplate, δv, was measured at the centerline of the baseplate. Rotation of the attachment was calculated from the difference between the transverse displacements measured at the level of the baseplate and at 12 in. (305 mm) above the concrete surface.
4. Test Results Results for Single Anchors Loaded at Different Orientations (Series 2.3 and 2.4) Figure 8 shows the mean force interaction diagrams for Sleeve and Expansion anchors in Series 2.3 [11]. In that series, anchor failure was intended to be governed by yield and fracture of anchor steel, so deep embedments were used. Interaction of Load, Series 23 140
Series 23H64, Exp. = 1.8 Series 23M53 / 54, Exp. = 1.8
Vertical Load Component [ kN ]
120
Series 23M74 / 23H74, Exp. = 1.8 Series 23M34, Exp. = 1.67
100 80 60 40 20 0 0
50
100
150
200
Horizontal Load Component [ kN ]
Figure 8
Interaction curves for actions (Test Series 2.3, [11])
Mean displacement interaction curves for all sub-series in Series 2.3 and 2.4 are compared in Figure 9. That figure shows large displacements in Series 23M53 under tension, approaching the values achieved in higher strength concrete with increased load angle or increased shear. It also shows good agreement between the values for UC1 and the Sleeve Anchor. Differences are evident, however, due to installation method (through-sleeve versus flush-sleeve). Under pure tension, displacements are identical. Under oblique loading, anchors installed with flush sleeves generated smaller shell-
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shaped concrete spalling in the loading direction in front of anchors, than did otherwise identical anchors with through sleeves. For this reason, they failed under shear and oblique tension by shear fracture of the anchor shank at a comparatively small shearing deformation. With lower concrete strength, larger displacements were achieved at maximum load under tension. These approach the displacements in higher-strength concrete with increasing shear. Tests with 3/8 in. anchors showed smaller displacements, and no concrete spalling in front of the anchors under shear and oblique tension.
Vertical Displacement at Maximum Load (mm)
45 23H64, EAII, M16, flush-sleeve installation 23H74, EAII, M16, through-sleeve installation 23M54, UC1, 5/8 in., flush-sleeve installation 23M74, UC1, 5/8 in., through-sleeve installation 23M53, UC1, 5/8 in., flush-sleeve installation 23M34, UC1, 3/8 in., flush-sleeve installation
40 35 30 25 20 15 10 5 0 0
5
10
15
20
25
30
Horizontal Displacement at Maximum Load (mm)
Figure 9
Interaction curves for displacements (Series 2.3 and 2.4, [11])
Discussion of Results for Eccentric Shear Loading on Two-Anchor Attachments Despite the differences in gaps between anchors and baseplates among specimens, failure loads showed only slight scatter. In contrast, considerable scatter was observed in displacements, without any obvious correlation with the measured gaps. The gaps, however, did significantly affect the failure mode. In tests with an eccentricity of 18 in. (457 mm), failure always occurred by fracture at the outermost tension anchor. In tests with an eccentricity of 12 in. (305 mm) the shear anchors also fractured. The tension anchor fractured only with maximum gaps of the shear anchors. Normal force and bending moment in the baseplate were calculated from the results of the strain measurement. Strains are approximately constant over the width of the baseplate, due to its configuration. The bending moments and axial forces in the baseplate can be calculated from those strains. Axial force in the baseplate (equal to the
125
shear in the tension anchor) increases with the applied load. After the gap at the shear anchor is overcome, this increase slows, and the axial force even decreases near ultimate. When the shear anchor fractures, the axial normal force increases abruptly, because the applied shear must then be resisted entirely by the tension anchor. The hogging bending moment in the baseplate (tensile stresses on top) decreases with increasing external load, changing finally to a reversed moment caused by a combination of the diagonal compression (at the height of the axis of the shear anchor) and the support reaction from the concrete (at the compression edge of the baseplate). The fracture of the shear anchors causes an additional negative moment from the additional normal force of the tension anchor, applied eccentrically to the bottom edge of the baseplate. Observed versus Predicted Capacities for Two-Anchor Attachments with Eccentric Shear Loading The loading eccentricity used for these attachments was such that the tension anchors were required to resist combined shear and tension. Under these conditions, their load capacity could be limited either by load, or by deformation. Ratios of observed capacities to those predicted by elastic theory ranged from 0.954 to 1.154. Ratios of observed capacities to those predicted by plastic theory [4] ranged from 0.892 to 1.05.
5. Conclusions Tests on Single Anchors Loaded at Different Orientations 1) Force interaction is well described by an elliptical interaction relationship (Equation 1), with an exponent of 1.67 to 1.80 for steel failure and 1.6 for concrete breakout. 2) The displacement interaction diagram for steel fracture is bulb-shaped; that is, the shearing displacement at failure under oblique tension is larger than under pure shear. This is due to larger spalling under oblique tension in the direction of the shear, in front of the anchor. 3) Failure by steel fracture and ductile behavior of the steel of anchor shank do not by themselves guarantee ductile connection behavior. Brittle fracture of the anchor shank can still occur. Low steel strength, small anchor diameters, flush-sleeve installation, and high-strength concrete lead to small deformation capacity, particularly if shear dominates. 4) Ductile fractures will be achieved, in principle, if the maximum possible steel strength of the anchor is reached. Therefore, connections with large edge distance, high-strength yet ductile steels, and through-sleeve installation (sleeve extending to the top surface of baseplate) are recommended. Eccentric Shear Tests on Two-Anchor Connections 1) For large eccentricity in shear (capacity governed by fracture of the tension anchor), plastic theory accurately predicts connection behavior and capacity.
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2) At lower eccentricities of applied shear, the bulb-shaped interaction curve for displacements causes a failure transition from the tension anchor to the shear anchor. At this point both shear anchors and tension anchors are fully utilized, and the assumptions of plastic theory agree with the actual behavior of the connection. 3) At still lower eccentricities of applied shear, the transverse displacement of the tension anchor cannot exceed the transverse displacement of the shear anchor. For that reason, the tension anchors of a multiple-anchor connection cannot reach the fracture states in the “belly” of the displacement interaction curve. Contrary to the assumptions of plastic theory, this causes the strength of the tension anchor to be under-utilized at small loading eccentricities. Depending on how pronounced the “belly” of the interaction curve is, the calculated capacity of the group can be considerably overestimated by plastic theory, or even by elastic theory. Lotze [11] proposes that this problem be corrected by assuming an even distribution of shear to all anchors.
6. Acknowledgment and Disclaimer This paper presents partial results of a research program supported by the U.S. Nuclear Regulatory Commission (NRC) (NUREG/CR-5434, “Anchor Bolt Behavior and Strength during Earthquakes”). The technical contact is Herman L Graves, III, whose support is gratefully acknowledged. The conclusions in this paper are those of the authors only, and are not NRC policy or recommendations.
7. References 1.
CEB, “Fastenings to Reinforced Concrete and Masonry Structures: State-of-the-Art Report, Part 1,” Euro-International Concrete Committee (CEB), August 1991.
2.
Fuchs, W., “Tragverhalten von Befestigungen unter Querlast in ungerissenem Beton,” Dissertation, Universität Stuttgart, 1990.
3.
Fuchs, W., Eligehausen and R. and Breen, J. E., “Concrete Capacity Design (CCD) Approach for Fastening to Concrete,” ACI Structural Journal, Vol. 92, No. 1, January-February, 1995, pp. 73-94.
4.
Cook, R. A. and Klingner, R. E. “Ductile Multiple-Anchor Steel-to-Concrete Connections,” Journal of Structural Engineering, Vol. 118, No. 6, June 1992, pp. 1645-1665.
5.
McMackin, P. J., Slutter, R. G. and Fishere, J. W., “Headed Steel Anchor under Combined Loading,” Engineering Journal, AISC, Vol. 10, No. 2, April, 1973.
6.
Shaikh, A. and Whayong, Y., “In-place Strength of Welded Headed Studs,” Journal of the Prestressed Concrete Institute, 1985 pp. 56-81.
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7.
Johnson, M. and Lew, H., “Experimental Study of Post-Installed Anchors under Combined Shear and Tension Loading,” Anchorage to Concrete, SP-103, American Concrete Institute, Detroit, Michigan, 1987.
8.
Bode, H. and Roik, K., “Headed Studs Embedded in Concrete and Loaded in Tension,” Anchorage to Concrete, SP-103, American Concrete Institute, Detroit, Michigan, 1987, pp. 61-88.
9.
PCI Design Handbook - Precast and Prestressed Concrete, 3rd Edition, Prestressed Concrete Institute, Chicago, 1985.
10. Dieterle, H., Bozenhardt, A., Hirth, W. and Opitz V., “ Tragverhalten von nicht generell zugzonentauglichen Dübeln, Teil 4: Verhalten im unbewegten Parallelriß unter Schrägzugbelastung,” Bericht Nr. 1/45 - 89/19, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 1989. 11. Lotze, D. and Klingner, R. E., “Behavior of Multiple-Anchor Connections to Concrete From the Perspective of Plastic Theory,” PMFSEL Report No. 96-4, The University of Texas at Austin, March 1997.
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IMPROVED STRUCTURAL MODEL FOR CHANNEL BARS WITH MORE THAN 2 ANCHORS Josef Kraus, Joško Ožbolt, Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract At present, no model is available to describe concrete failure of channel bars with several anchor distances and for the general position of tensile loads. To examine this problem, an Finite Element-analysis of channel bars (profil 50/30) with several anchor distances has been carried out with various load positionings. Based on the results of the numerical study, a new design model for channel bars with more than two anchors, is proposed.
1. Introduction In current engineering practice, no design code for fastening elements exists. Consequently, the conditions for the use of channel bars are controlled by general building authority approvals. In these approvals, the limit values of the edge distances in concrete elements, the application of loads and the minimal member sizes are recommended. The regulations do not offer a possibility for a general design of channel bars. They reflect a structural framework of demands, which limit the variability of possible applications and often leads to not very efficient and economical solutions. Therefore, there is an obvious need for design rules, which should account for the specific geometrical and loading conditions. These rules have to assure safer and more economical fastenings. With channel bars there are principal two different kinds of failure modes: (1) concrete failure and (2) steel failure. The steel failure is to a large extent clarified. However, to better understand the concrete failure mechanism of channel bars with 3 or more anchors, additional investigations are needed. Therefore, a new model should be developed, in which the critical anchor is obtained on a system of a single-span beams. So, the influence on the single anchors can be determined and compared with the characteristical resistance of the considered anchor. The resistance of the anchor is calculated
129
based on the concept of the influencing area. Depending on the system, loads can be transferred from the considered anchor, due to the stiffness and degree of constraint of the channel, to the neighbour anchor with respecting their loading condition. For better understanding the failure of channel bars, Finite Element studies have been carried out. The analysis is useful to predict the structural behaviour of channel bars with any loading conditions (e.g. load distribution on the anchors, influenced area of each anchor). Based on the results of the parametric study, a new design model for channel bars with more than two anchors is proposed.
2. Channel Bars In engineering practice channel bars are used for fastening of facing masonry, at the mounting of claddings, for fastening of pipe systems, for the ground fastening engines and other applications.
Figure 2.1: Channel bar with bolt anchors Channel bars are made in cold-rolled or hot-rolled U-shaped steel. They are filled up with foaming agent, fixed in the formwork and casted into concrete. After removing the formwork and the foaming agent the construction members can be fixed with special hammer- or by hook bolts.
Figure 2.2: Hook bolt with channel bar The advantage of this method for fixing is, that the point of loading in direction of the channel bar, must not been known before. Consequently the system is very flexible. The
130
disadvantage of the system is, that the insertion of the channel bar has to be planned exactly. The screw can freely be moved along the channel bar and the load can be so transmitted to the channel bar. At the lower side of the channel bar headed studs are welded and they are responsible for the transmission of the load into the concrete. Several versions are available: welded I-shaped anchors clench anchors swaged headed studs The single bolts are connected by the U-shaped profile. The anchor rail itself cannot transfer loads into the concrete. The load can only be transferred to concrete by the anchors. A general topic to be discussed is, how the geometrical parameters and position of load influence the structural behaviour. The main parameters are the spacing of the anchors, the edge distance, the position of the load, the angle of load, the embedment depth and the size of the channel bar.
3. Concrete failure 3.1 Design method (CCD-method) When the steel strength is high enough, most fasteners lead under axial tension load to a concrete cone failure of a specimen. The inclination of the cone surface is between 30° and 40° measured to the direction of load. With increasing embedment depth the inclination of angle increases up to approximately 45°. The tensile resistance under the load is distributed differentially over the concrete cone. At the point of origin of the concrete cone, directly at the head of the anchor, the tensile strains are maximal and they decrease by reaching the surface of concrete. Based on a number of tests, the failure load of headed studs with large edge distances and large spacing of the anchors, can be calculated as:
N 0u ,c = 15,5 ⋅ h 1ef,5 ⋅ β w
(1)
with: hef = embedment depth [mm] βw = concrete compressive strength [N/mm2] The resistance calculated by equation (1) can only be achieved, if there is a sufficient concrete surface for each fastener. If the fastener is put close to the edge of the structural member or if a neighbour fastener is too close, the cones are overlapping. The characteristic spacing for an anchor group is s = 3 ⋅ hef. To transfere the maximum load of a fastener, the minimum edge distance must be at least 1,5 ⋅ hef. To estimate the concrete capacity of anchor groups and fastenings close to the edge of the building component, the mentioned influences are considered in the CCD-Method (Concrete Capacity De-
131
sign). In this method, the concrete cone is idealized as a rectangular projection of the concrete cone, on the concrete surface. By groups of anchors within the CCD-Method it is assumed that the anchor plate is sufficient stiff, to distribute the loads uniformly on all anchors. The group effect is taken into account by the formula.
N u ,c = with: Ac,n0
A c,N A
0 c,N
⋅ ψ s, N ⋅ N u0 , c
(2)
projected area of each single fastener with large edge distance and spacing. The concrete cone is idealized as a pyramide with the height hef and a length of the basis scr,n = 3 ⋅ hef .
Ac,n
actual projected area of the concrete cone on the concrete surface. The limits of the area are the overlapping of the single cones of the next fasteners and the edges.
ψs,n
= 0,7 + 0,3 ⋅ c/ccr,N edge distances c of a fastener; ccr,N edge distances required, to guarantee that a complete concrete cone can be developed, and so the tension of equation (1) with ccr,N = 1,5 ⋅ hef can be transmitted.
Nu,c0
resistance of a single anchor (1)
The ratio Ac,n/A0c,n considers the geometrical influence of the edge and further fasteners next to the calculated fastening group. An additional reduction of the concrete capacity is given by the factor ψs,n. It considers the disturbance of the radial-symmetric stress distribution. For fastenings without edge influence (c ≥ 1,5 hef) the factor is ψs,n = 1,0. This means that there is no disturbing influence of the radial-symmetric stress distribution. 3.2 Application of the CCD-method for channel bars By the calculation of the capacity of the anchor ground with a channel bar it is assumed, that by designing of each single anchor the design rules of headed studs can be used [1]. According to the method, the capacity of the anchor ground of channel bars with more than 2 anchors with any positions of single loads, is designed as follows. Each span of the channel bar can be considered as a single span beam (Figure 3.1).
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s
s
s
s
Figure 3.1: Channel bar as a system of single span beams The model should be used for spacings s of the anchors. The resistance is for each anchor calculated with respect of the actual influencing area i.e. according to (2). Ac,N 3 hef
s/2 + 1,5 hef
s
s
s
s/2 + 1,5 hef
Figure 3.2: Determination of the characteristical anchor resistances with respect of the influencing area. The above model is for channel bar only realisable, if the bar is stiff or the spacing of anchors relatively small. Therefore the model need to be improved.
4. Modelling of a specimen with channel bar 4.1 General To better understand the failure of channel bars a FE-analysis with the program MASA has been carried out. The FE-program MASA has been developed at the Institute of Construction Materials, University of Stuttgart and is aimed to be used for three dimensional linear and non-linear analysis structures of quasi-brittle materials, especially of concrete. The concrete is discretisized with 8-node solid elements. The channel bar is also discretisized by volume elements with steel material parameters. To discretisize the contact between channel bar and concrete, special contact elements are used which transfer only compressive forces. The load is applied incrementally by displacement control. For the graphical analysis mesh generation and analysis of the results, the pre- and postprocessor FEMAP® is used. Former investigations showed, that the symmetric part of the specimen can be used (Figure 4.1) to reduce the number of elements, what leads to a shorter calculation time.
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modelled area
Figure 4.1: Channel bar with 5 anchors and the modelled area 4.2 Modelling The concrete and steel are modelled separately. The mesh of the concrete and the steel elements has to be similar, to be able to connect both. Figure 4.2 shows a concrete member with the size length 1800 mm, edge distance c = 75 mm and spacing of the anchors of s = 300 mm with using the double symmetrie of the system. In the concrete member an acavity for the channel bar of the profile 50/30 with 5 anchors can be seen. The steel is although modelled with 5 anchors, the elementation is similar to the concrete.
position of load
Z Y X
Figure 4.2: Specimen for 5 anchors (¼ of the specimen)
Figure 4.3: FE-model of a channel bar profile 50/30 with 5 anchors (¼ of the bar)
The load is applicated in direction of the z-axis and it’s position is at the top of the channel. The load, which is applied as a displacement onto the channel bar, is first transferred to the anchors. From the anchors the tensile force is transferred into the concrete. The transmission occurs at the head of the anchor, where the elements of steel and concrete are connected to each other.
load transfer nodes (channel bar - concrete) Z
Figure 4.4: Back view of a channel bar with bolt and the load transfer nodes
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The rest of the nodes of the bolt are not connected to the concrete. They have a distance of 0,1 mm to the concrete nodes. To avoid load transfer, the vertical nodes of the channel bar, are also at the distance of 0,1 mm measured from the surface of the concrete member. Under load the channel lifts from the concrete surface. At some positions between channel bar and concrete, pressure caused by bending of the channel, can be transferred. To model the real contact between channel bar and concrete, special contact elements are used. The mesh of these elements is similar to the concrete and channel elements. The tensile stress which can be transferred from steel to concrete is very low (tensile strength of interface elements is close to zero). The thickness of the contact elements is 2 mm.
Figure 4.5: Contact between steel and concrete concrete channel bar
Z
contact elements
Y X
anchor
Figure 4.6: FE-model of a specimen
5. Numerical investigations of channel bars with 5 anchors 5.1 General The aim of the calculations is, to investigate the concrete failure of a channel bar for different loading positions. Totally predict 22 Finite-Element-Calculations with spacings of the anchors of s = 100 mm and s = 300 mm are carried out. The profile 50/30 (width, height of the channel) with an embedment depth of hef = 85 mm was analysed. The diameter of the bolt was d1 = 16 mm, the diameter of the head of the bolt was d2 = 24 mm. The protrusion of the channel in direction of the channel length was u = 300 mm. With the chosen protrusion of the channel, the corner influence should be avoided. At the calculations with a spacing of the anchors of s = 300 mm ≥ 3 ⋅ hef = 255 mm, there is no interaction between the anchors to be expected. At a spacing of s = 100 mm = 1,18 ⋅ hef there is a strong influence between the anchors,
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with respect to the transmission of load. In all calculations the edge distance on both sides was choosed c2 = c3 = 75 mm. The concrete properties are summarised in table 1. Concrete compressive strength Fc,cube200 [N/mm²] 29,4
Concrete compressive strength Fc,cylinder [N/mm²] 25,0
Concrete tensile strength ft [N/mm²]
Fracture energy GF
E-Modulus
[N/mm]
[N/mm²]
2,0
0,08
28000
Table 1: Concrete parameters The material model of the steel of the channel bar is supposed as linear elastic with an E-modulus of 210000 N/mm². I.e. in all cases concrete failure causes the system failure. The load on the channel bar is always symmetric to the middle anchor with 2 single loads (Figure 5.1). The distance of the single load to the middle anchor is signed with x. The position of load was varied between x = 0 mm (over the middle anchor A) and x = 100 mm respectively x = 300 mm (over the anchor B). x
C (le.)
B (le.)
s
s
x
A
B (ri.) s
C (ri.)
s
Figure 5.1: Designation of the anchors The supports in z-direction were placed at the concrete surface. The displacement was applied incrementally on the channel bar. The increment size was 0,05 mm. 5.2 Results of the calculations for spacing s = 300 mm Different load positions are investigated for a spacing of the anchors of s = 300 mm, and the maximum loads of the anchors are compared with each other. The anchor load B is shown only once, but it actually acts 2 times in the system, caused by the symmetry. The difference between the sum of the anchor loads and the system load, is a result of the minimum tensile capacity of the contact elements. Figures 5.2a and b show crack development at the maximum load of the first broken anchor. The failure is caused by a horizontal crack to the edge of the concrete member. As can be seen from the crack development for load position x = 0 mm, only the middle anchor A is activated. For load position x = 200 mm both anchors (A and B) are activated.
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0.01 0.00833 0.00667 0.005 0.00333 0.00167 0. Z
Z
Y
Y
X Output Set: MASA3 A10073 Contour: Avrg.Ez stra.
X Output Set: MASA3 A1096 Contour: Avrg.Ez stra.
Figure 5.2a: Cracks pattern, x = 0 mm
Figure 5.2b: Cracks pattern, x = 200 mm
40
40
35
35
Anchor load A, B [kN]
Anchor load A, B [kN]
In the Figures 5.3a and b the load distribution on the single anchors is shown. At load position x = 0 mm only anchor A is activated, then at about 75 % of the maximal anchor load, the anchors B are also activated. The load of the anchors B can nearly be neglected. The system failure is caused by failure of anchor A. In comparison with load position x = 200 mm from the beginning, the middle anchor A and the anchors B are activated. At maximum load of the system the anchors A and B take up almost the same load. The failure of the system is caused by concrete failure of the anchors A and B (ri./ le.).
30 25 20 anchor load A anchor load B
15 10
30 25 20 15 anchor load A anchor load B
10 5
5
0
0 0
10
20
30
40
50
0
60
Figure 5.3a: Anchor loads, x = 0 mm
20
40
60
80
100
120
140
Systemload [kN]
Systemload [kN]
Figure 5.3b: Anchor loads, x = 200 mm
Figure 5.4 shows, that by loading above position x = 0 mm the ultimate load of the system is nearly the same, as the ultimate load of a single anchor. Load position x = 200 mm shows, that the systemload is 3-times the load of the anchor acting at x = 0 mm. At the load positions from x = 0 mm to x = 50 mm the middle anchor carries about 97 % of the total load. The neighbour anchors get only 3 % of the total load. Beginning at position x = 150 mm the load in the system is better distributed. The anchors B take up at load position x = 150 mm 63,5 % of the maximum load and the middle anchor only 36,5 %. This tendency maintains up to load position x = 200 mm. At position x = 200 mm the anchors A and B are activated at the same size. From load position x = 200 mm on, activation of anchor A is decreasing. As a result between x = 200 mm and 300 mm the
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systemload becomes lower. 140
Systemload [kN]
120 100 80 systemload anchor load A anchor load B
60 40 20 0 0
50
100
150
200
250
300
350
Distance of loading point from middle anchor [mm]
Figure 5.4: Anchor loads and maximum load for different load positions At position x = 300 mm the systemload is 2 times higher than the load from position x = 0 mm. The results show, that for s = 300 mm when load is applied directly over an anchor, only that anchor can be activated. Generally can be seen, that the maximum anchor load of a single anchor is reached at 32 kN. This gives a maximal (optional) resistance if all anchors are directly loaded. This shows a good agreement between the calculated loads and the CCD-method. The analysis shows, that for s = 300 mm there is no interaction between the anchors. The results are in good agreement with the CCDmethod (34 kN), only if the load is applied directly over the anchor. 5.3 Results of the calculations for spacing s = 100 mm The representation of the results of the calculations with different load positions and spacing of the anchors of s = 100 mm is corresponding to section 5.2. The Figures 5.5a and b show crack development at the maximum. The maximum load is controlled by a horizontal crack in direction to the edge of the concrete member and a connecting crack between the heads of the anchors. From the crack development it can be seen, that at load position x = 0 mm the anchors A and B are activated and for the load position x = 75 mm the anchor C is activated as well. After peek load the anchors will break by concrete cone failure.
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0.01 0.00833 0.00667 0.005 0.00333 0.00167 0. Z
Z
Y
Y
X Output Set: MASA3 C7055 Contour: Avrg.Ez stra.
X Output Set: MASA3 C1053 Contour: Avrg.Ez stra.
Figure 5.5a: Crack pattern, x = 0 mm
Figure 5.5b: Crack pattern, x = 75 mm
In the Figures 5.6a and b the load distribution of the individual anchors is shown. At load position x = 0 mm anchor A carries the highest part of the acting load. In comparison with the channel bar with large spacing of the anchors the anchors B and C are activated as well (see Figure 5.3). Up to 50 % of the maximum load the activation of anchor B and C is nearly the same. From 50 % of the maximum load anchor B is activated more strongly. The system failure is caused by concrete failure of the anchors A and B. Compared with the load position x = 75 mm, both anchors A and B are activated from beginning of loading. At maximum load the loads are nearly the same. The anchor C is activated from beginning of loading as well. Extremely strong is the activation close by the maximum of the system load. The failure is caused by concrete failure of all 5 anchors. 40
Anchor load A, B, C [kN]
Anchor load A, B, C [kN]
40
anchor load A anchor load B anchor load C
30
20
10
0
30
anchor load A anchor load B anchor load C
20
10
0 0
10
20
30
40
50
60
0
Systemload [kN]
Figure 5.6a: Anchor loads, x = 0 mm
10
20
30
40
50
60
70
80
Systemload [kN]
Figure 5.6b: Anchor loads, x = 75 mm
Figure 5.7 shows, that for s = 100 mm the influence of the position of the load on the maximum load of the system is not so strong as for s = 300 mm. Nevertheless, the maximum load is growing up in dependence on the load position from x = 0 mm to x = 100 mm. At the load position x = 62,5 mm the ratio of activation of the anchors A and B is the same. From load position x = 62,5 mm to x = 100 mm anchor C is better activated. In the CCD-method mutual influence of the anchors by spacing of s = 100 mm with an embedment depth of hef = 85 mm is taken to account on the failure of a single anchor. In
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the FE-analyses the same influence can be seen. Especially it is shown in the activation of the single anchors at different load positions. Up to position x = 50 mm 3 anchors will break out, over x = 50 mm 5 anchors will break out. Generally it is shown, that the highest loaded single anchor has a failure load of about 20 kN. At load position x = 0 mm the failure load of anchor A is about 25 kN. This could be restored, because activated area of anchor A is low influenced by the anchors B and C. An indication therefore is the lower anchor load of the anchors B and C, compared with all other load positions at maximum load. 120
Systemload [KN]
100
80
60 systemload anchor load A
40
anchor load B anchor load C
20
0 0
10
20
30
40
50
60
70
80
90
100
Distance of loading point from middle anchor [mm]
Figure 5.7: Anchor loads and maximum load for different load positions By designing anchor groups using the CCD-Method it is assumed, that the anchor plate, which connects the anchors is sufficiently stiff. Figure 5.7 shows, that the anchors close to the loading point (anchor B and A) are both activated almost the same. However the ratio of activation of anchor C is lower than for the anchors A and B. Obviously by small spacing of the anchors, the CCD-method can be used only conditional, since the load distribution on all anchors is not the same.
6. Conclusions Presently no model is available to describe concrete failure of channel bars with more than two anchors and for different positions of loads. To investigate this problem a FEanalysis of channel bars (profil 50/30) with several anchor distances and for different load positions has been carried out. The results of the calculations are compared with the CCD-method for fasteners. By designing anchor groups with the CCD-method it is assumed, that the anchor plate which connects the anchors, is sufficiently stiff. Consequently, according to the model the load is uniformly distributed over all anchors. The numerical analyse shows, that for small spacing of the anchors, the channel bar can be viewed approximately as a stiff. Therefore the CCD-method can be used. However,
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the results show, that for large spacing of the anchors, it is reasonable to assume the channel bar as a system of single span beams. Therefore, in the new model for design of channel bars the critical anchor is obtained on a system of single span beams. The resistance of each anchor is calculated based on a concept of the influencing area. The cases studied in the present numerical investigations are two extreme cases. To formulate a more general design model, which should account for the transition from the approach with the stiff channel bar (CCD-method) to the system of a single span beams, further numerical and experimental work is needed.
7. Acknowledgements This work was supported by the following companies: Halfen and Deutsche Kahneisen. The support is very much appreciated.
8. References [1] Wohlfahrt, R.: Tragverhalten von Ankerschienen ohne Rückhängebewehrung, Stuttgart: Institut für Werkstoffe im Bauwesen, Mitteilung 1996(4). [2] Ozbolt, J.: „MASA- Macoscopic Space Analysis“, Stuttgart: Institut für Werkstoffe im Bauwesen, Internal report 1999. [3] Halfen GmbH & Co. KG: Zulassungsbescheid Halfen-Ankerschiene HTA (Z-21.434), Berlin: Deutsches Institut für Bautechnik (1998).
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ANCHORS IN LOW AND HIGH STRENGTH CONCRETE Jakob Kunz*, Yasutoshi Yamamoto**, Mario Berra***, Pietro Bianchi* *Hilti AG, Corporate Research, Liechtenstein **Shibaura Institute, Tokyo, Japan ***Enel.Hydro, Milan, Italy
Abstract Standard anchor design rules apply to normal strength concrete in a range of about 20 to 50 MPa compressive strength. However, we often encounter low strength concrete when retrofitting old buildings. On the other hand, the evolution in concrete technology leads to always higher compressive strengths in new concrete construction. A research commissioned by Hilti Corporate Research and carried out under the direction of Professor Yamamoto at Shibaura Institute of Technology in Japan investigated the transfer capability of anchors by conducting a systematic series of more than 500 shear and tension tests in low strength concrete. The behavior of anchors in high strength concrete has been investigated in the European project ANCHR. This paper puts together comparable results from both research programs and draws conclusions for the design of anchorage in low and high strength concrete. This leads to the conclusion that standard design rules can be applied for shear transmission, but that for tension load, the concrete strength has to be taken into account as proposed by structural concrete codes when designing anchorage for concrete capacity in low or high strength concrete.
1. Introduction Standard anchor design rules apply to normal strength concrete in a range of about 20 to 50 MPa compressive strength. The failure of the concrete capacity is usually associated with the concrete strength to the power of 0.5. Thus the concrete capacity design method (CCD, [1], [2]) gives the concrete cone failure caused by an anchor as:
N u ,m = k ⋅ hef1.5 ⋅ f c
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(1) with: Nu,m k hef fc
mean ultimate concrete cone pullout load [N] constant, =13.5 for metal anchors; =15.5 for headed studs and some undercut anchors [-] effective embedment depth [mm] concrete compressive strength [MPa]
and for shear loads:
Vc ,u ,m
hef = 0.9 ⋅ d ⋅ d
with: Vc,u,m d c Vs,u,m
0.2
⋅ c1.5 ⋅ f c ≤ Vs ,u ,m
(2)
ultimate load for concrete cone failure in shear [N] anchor diameter [mm] distance from axis of anchor to concrete edge [mm] maximum shear load for steel failure [N]
The value of the concrete compressive strength to the power of 0.5 is to represent the concrete tensile strength. This results in a good representation of the cone pullout strength for concrete strengths from 20 to 50 MPa. However, Neville [3] suggests, that probably the best fit to represent tensile strength of concrete ft is
f t ≅ 0.3 ⋅ f c2 / 3
(3)
In fact, Eurocode 2 [4] also uses this formula. In this study, tests for concrete failure with compressive strengths below and above the range of 20 to 50 MPa have been compared to both representations of the concrete tensile strength. The tests in low strength concrete have been taken from a research program carried out at the Shibaura institute of Technology, Tokyo under the direction of Professor Y. Yamamoto and the tests in high strength concrete are taken from the Brite-Euram Project ANCHR which investigated the anchor behavior in normal and high strength concrete under static load and under high strain rates. Another set of tests with undercut anchors in normal strength concrete from the Hilti testing laboratory is considered as well.
2. Tensile Load Capacity of Undercut Systems The tensile load capacity was evaluated with headed studs and undercut anchors. A total of 97 tests representing concrete compressive strengths from 5 to 120 MPa has been analyzed. The embedment depths range from 36mm to 135mm. The measured failure loads Fu,test have been “normalized” to an embedment depth of 100mm. Since the ultimate load depends on the embedment depth hef to the power of 1.5 (1), the normalized ultimate load Fu,norm is obtained as:
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Fu ,norm
100 = Fu ,test ⋅ h ef
1.5
(4)
Figure 1 shows the normalized measured ultimate loads with two calculated curves. The first curve represents formula (1), where the factor k for the considered sample was 17.2. Thus, curve (1) represents the dependence of the ultimate load on the square root of the concrete compressive. The second curve represents formula (5), i.e. the dependence of the ultimate load on the concrete strength to the power of 2/3.
N u ,m = 10.3 ⋅ hef1.5 ⋅ β w2 / 3
(5)
conrete cone failure load [kN]
350 300 250
formula (1) formula (5) tests Shibaura tests ENEL tests Hilti
200 150 100 failure loads normalized for hef = 100mm
50 0 0
20
40
60
80
100
120
140
concrete strength [N/mm2]
Figure 1: Tests with undercutting systems Figure 1 clearly shows that both formulae yield the same results with compressive strengths in the range of 20 to 50 MPa, but that for lower and especially for higher compressive strengths the differences are considerable. For low strength concrete, the test results are lower than the results of both formulae, but formula (5) is somewhat closer than formula (1). For a compressive strength of 120 MPa, formula (1) clearly underestimates the test results, while formula (5) gives a good prediction of the average test result. A thorough analysis of the test data has shown, that the quality of a predictive formula can be further increased by taking into account the undercutting area A.
N u ,m = 8.1 ⋅ (hef + 0.9 ⋅ A0.5 ) ⋅ f c2 / 3 1.5
(6)
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with: A undercutting area projected to a plane perpendicular to the axis of the anchor The ratio of measured to predicted ultimate load has been evaluated for all 97 tests with formulae (1), (5) and (6). The coefficient of variation obtained with the prediction formula (1) is 17.7% which corresponds to the values given in [1]. Considering formula (5), the coefficient of variation is reduced to 13.1% and with formula (6) even to 11.6%.
3. Tensile Load Capacity of Adhesive Bonded Systems a) Bond Strength As shown earlier[5], [6], the pullout resistance of bonded anchorage systems is mainly dependent on the product specific bond strength τb and the anchor surface. The influence of the compressive strength of the concrete depends on the product. In the considered tests, the dependence varied from none to proportional to the square root of the concrete compressive strength.
N u ,m ,b
f = τ b ⋅ φ ⋅ π ⋅ hef ⋅ c f c ,ref
n
(7)
with: Nu,m,b mean ultimate maximum load for pullout failure [N] τb product specific bond strength [MPa] φ diameter of anchor [mm] fc,ref reference concrete strength, corresponds to tb [MPa] n product dependent exponent, 0.0 < n < 0.5 This statement has been confirmed by both presented test series in low and in high strength concrete. b) Splitting Bond Failure If the anchor is set near the edge and therefore the concrete cover is small, the bond strength τb may not be reached before splitting of the concrete cover. Splitting failure has been tested in normal and high strength concrete. Cylindrical concrete specimens with a diameter of 100mm. High strength reinforcement bars with a diameter of 20mm were pulled out of the concrete cylinders. Thus the concrete cover around the reinforcement bars was 40mm or 2 times the bar diameter. From the measured maximum loads, the splitting bond stress τu,sp was evaluated by dividing the maximum load by the anchor surface, i.e:
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τ u ,sp =
Fu ,m
(8)
φ ⋅ π ⋅ hef
Figure 2 shows the splitting bond stresses evaluated from tests with cast-in and with post-installed bars against the concrete strength. Two curves show the best fit equations for predictions supposing that the splitting bond stress is proportional to the concrete strength to the power of 0.5, or to the power of 2/3, respectively.
splitting bond stress [MPa]
curve1 : τ u ,sp = 1.69 ⋅ f c0.5 ;
curve 2 : τ u ,sp = 0.81 ⋅ f c2 / 3
40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0
(9)
curve 1 curve 2 tests postinstalled tests cast in place
0
100
200
300
concrete strength [MPa] Figure 2: splitting bond tests with bonded systems The comparison of tests and prediction (figure 2) shows that the assumption that the splitting failure is proportional to the concrete strength to the power of 2/3 (curve 2) gives better results for very high and very low concrete strengths. When comparing the ratios of measured to predicted values, curve 1 yields a coefficient of variation of 38% while curve 2 yields a coefficient of variation of 29% for the considered sample of 30 tests. Nevertheless these results must be considered as preliminary, since the coefficient of variation is rather high in both cases.
4. Shear Load Capacity without Edge Influence in Low Strength Concrete In the test program at Shibaura Institute of Technology the shear capacity of single anchors and of groups of 3 anchors has been measured in low strength concrete specimens. The concrete base material was cast as 1.2m long concrete blocks with compressive strengths of 5 to 15 MPa. Monotonic shear loading tests on post-installed reinforcement bars were conducted in order to measure strength, displacement and failure modes that are basic characteristics of post-installed anchors.
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The number of cracks in the base material (existing member) decreased, as the concrete strength increased, since the mode of failure shifted from concrete bearing pressure to steel shear failure. Structural concrete design codes show how to calculate the strength of shear bolts. Eurocode 4 proposes the following formulae for the characteristic resistance PRk (sect. 6.3.2.1 [7]):
PRk = 0.8 f u
steel shear failure: concrete bearing pressure:
E cm = 9500( f ck + 8)
1/ 3
(E
π ⋅d 2
(10)
4 2 PRk = 0.29d f ck ⋅ Ecm cm
, f ck [kN / mm 2 ], EC2, sect. 3.1.2.5.2 )
(11)
normalized shear strength 2 2 Fu/(n*d ) [kN/mm ]
ultimate strength of steel with: fu fck characteristic compressive strength of concrete Ecm Young’s modulus of concrete 0.35
d16, single
0.3
d19, single
0.25 d22, single
0.2 0.15
d19, group
0.1 d22, group 0.05 0 0
5
10
15
concrete strength [N/mm2]
20
calculated steel failure calculated concrete failure
Figure 3: Shear tests Figure 3 shows the test results and the expected failure loads according to Eurocode 4, where the normalized shear strength is the shear strength divided by the diameter squared of the anchor rods, d2, and the number of anchors in a group, n. The diagram shows, that single anchors with small diameters perform in a clear concrete bearing failure, while anchors with bigger diameters in groups tend more to steel failure. In any case it seems advisable to design shear connections in low strength concrete for concrete bearing pressure.
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5. Conclusions All tests presented in this paper show the concrete capacity limit. For anchor pullout tests with concrete cone failure, the results have been compared to the concrete capacity design method and it has been confirmed that this method gives a good prediction for the ultimate resistance in normal strength concrete, but that in low and high strength concrete, the resistance should rather be estimated as proportional to the concrete strength to the power of 2/3. Bonded anchor systems with small concrete cover tend to reach their ultimate load when splitting of the concrete cover occurs. This is again reached with the concrete tensile capacity. For this case the considered tests also suggest to predict the failure load as proportional to the concrete compressive strength to the power of 2/3 if a wide range of concrete strengths is considered. Additional prediction accuracy can be obtained if the undercutting area of the anchorage system is taken into account. The last section has shown that the shear capacity of anchors without influence of concrete edges can be estimated with the formulae from Eurocode 4 with good precision. Thus, the investigations summarized in this paper suggest that the concrete capacity method is a good predictions of the failure loads in normal strength concrete, but that a more realistic model for the concrete tensile strength should be taken into account if a wide range of concrete strengths is considered.
6. Open Questions The investigations shown here compare fiber reinforced high strength concrete to normal and low strength concrete without fiber reinforcement. This has been done under the assumption that fibers are generally contained in high strength concrete in order to achieve a minimum ductility. Thus, simply saying “concrete” may mean fiber reinforced for high strengths and not reinforced with fibers for medium and low strengths. Nevertheless, it should be stated that by definition fiber reinforced concrete is a material different from normal concrete. The relations found in this research apply to the two different materials as they are generally used. In order to establish clear relationships for the two different materials (fiber reinforced concrete and concrete not reinforced with fibers) further research is required.
Acknowledgement The project ANCHR was sponsored by the BRITE-EURAM research framework 7. The authors would like to thank for the support.
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References 1.
2. 3. 4. 5.
6.
7.
Eligehausen, Mallée, Rehm: Befestigungstechnik. Sonderdruck aus dem Betonkalender 1997. Ernst & Sohn, Verlag für Architektur und technische Wissenschaften, Berlin 1997. Fuchs, W., Eligehausen, R., Breen, J. E.: Concrete Capacity Design Approach for Fastening to Concrete. ACI Structural Journal, January-February 1995. Neville, A.M.: Properties of Concrete. Pearson Education Limited. Essex, England, 1995. Eurocode 2: Design of Concrete Structures. Cook, R. A., Kunz J., Fuchs W., Konz C.: Behavior and Design of Single Adhesive Anchors under Tensile Load in Uncracked Concrete. ACI Structural Journal, V. 95, No. 1, January-February 1998. Kunz, J., Cook R. A., Fuchs W., Spieth H.: Tragverhalten und Bemessung von chemischen Befestigungen. Beton- und Stahlbetonbau 93 (1998), Hefte 1 und 2. Ernst und Sohn, Berlin. Eurocode 4: Design of Mixed Structures in Steel and Concrete.
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DEVELOPMENT OF COMMON UNIFORM REGULATIONS IN EUROPE FOR THE ASSESSMENT OF METAL ANCHORS Klaus Laternser Deutsches Institut für Bautechnik, Germany
Abstract The different national regulations in force in Europe in the field of metal anchors lead to the development of a first European UEAtc Directive for the assessment of anchors in 1986 by means of which common principles of testing and a mutual recognition of test results were achieved. On the basis of this Directive the EOTA (European Organisation for Technical Approval) has elaborated comprehensive compulsory "Guidelines for European Technical Approval of Metal Anchors for Use in Concrete". These Guidelines endorsed in 1997 by the European Commission resulted in the issue of a great number of European Technical Approvals (ETAs) for metal anchors.
1. Introduction During the past 30 years the use of metal anchors for anchorage in drilled holes of concrete elements has tremendously fast increased worldwide. This required regulations for the determination and evaluation of the properties and efficiency of anchors as well as for the installation of anchors. Differing national regulations in various European countries by agréments, technical approvals or standards led, at the beginning of the 80s, to a first European harmonization for the testing of metal anchors. Upon completion of uniform and binding regulations in Europe through guidelines for the European Technical Approval for metal anchors for use in concrete circa 30 European Technical Approvals could be granted up to now for metal anchors.
150
2. National regulations in Europe The first national approvals for metal anchors in Germany were granted in 1975. The anchors concerned were torque-controlled expansion anchors (sleeve type) and deformation-controlled expansion anchors (drop-in anchors). Four years later approvals were granted for expansion anchors for use in cracked concrete and bonded anchors. At present there are a great number of German technical approvals in force for different systems of metal anchors. In other European countries such as France, United Kingdom, Sweden and The Netherlands also agréments were granted and/or standards for testing of anchors were elaborated as well. As agreed with the European Commission national regulations shall be withdrawn and replaced, after a transitional period, by European Technical Approvals as soon as EOTA Guidelines for European Technical Approvals are available. For expansion anchors and undercut anchors this transitional period will end in mid-2002.
3. UEAtc regulations 3.1 General The UEAtc – Union Européenne pour l'Agrément technique dans la Construction European Union of Agrément - joins national institutes, centres and organisations of Europe, which deal with the establishment of common guides and the elaboration of technical agréments in building, with the objective to reduce costs and time required for the different approval procedures in the European area and to simplify the mutual recognition of agréments. 3.2 UEAtc Directives In December 1986 a first European regulation, the "UEAtc Technical Directive for the Assessment of Anchors Bolts" [1] was published. This Directive contained, in addition to terminology and general requirements, details on the determination of characteristics, advice for the evaluation of the test results, information on the quality control and conditions for the use of the anchors. It applied only to anchorages realised in the compressive zone of the concrete and not to anchorages in or in the vicinity of cracks. However, a uniform evaluation of the test results and a common safety concept could then not yet be established in a binding way. For anchorages realised in the compressive zone of concrete, however, the main first objectives, i.e. common principles for testing in all UEAtc countries and mutual recognition of test results, had been achieved. 3.3 UEAtc Technical Guides As an extension of the UEAtc Directive, the Institut für Bautechnik proposed in 1987 to set up a "Test programme for suitability tests and approval tests for anchors to be used in the tension zone of concrete".
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For the design of reinforced concrete structures the tensile zone of concrete is assumed to be cracked, since concrete has a low tensile strength which may already be utilised by inherent stresses and restraint of imposed deformations not taken into account. Additionally, there are locally increased tensile stresses in the anchorage zone due to splitting forces resulting from the installation and loading of the anchor. After agreement on the question of whether cracked and non-cracked concrete can be distinguished in practice, the scope of the new document was defined as applying to anchors - for use in cracked and non-cracked concrete, and - for use in non-cracked concrete only. The UEAtc Technical Guide [2] completed in 1992 includes the testing of torquecontrolled expansion metal anchors, the design of anchorages in concrete and details on the anchor installation. Of central importance are the good functioning tests. They are intended to establish the fitness of the anchor system for the intended use and to detect any poor performance, e.g. installation safety under normal site conditions, performance in different concrete strengths or under repeated and sustained loading.
4. EOTA The European Organisation for Technical Approvals (EOTA) [3] consists at present of 29 Member Bodies from 17 European countries, which were nominated and authorised to issue European Technical Approvals (ETAs). EOTA was created in the framework of the implementation of the Construction Products Directive [4] for the harmonization of construction products in the European Union. EOTA has the task to monitor the elaboration of Guidelines for European Technical Approval and to coordinate all activities in connection with the granting of ETAs. ETA-Guidelines (ETAGs) are elaborated for a certain product area within working groups and project teams. The elaboration is based on a mandate issued by the European Commission and on an approved work programme. In the field of anchors there is a total of four mandates issued by the European Commission for the elaboration of Guidelines for European Technical Approval: − Metal Anchors for Use in Concrete − Metal Anchors for Lightweight Systems − Plastic Anchors for Use in Concrete and Masonry − Injection Anchors for Use in Masonry. For all four anchor sectors EOTA has placed the elaboration under the chairmanship of the writer, thus ensuring a uniform assessment concept for the different anchor types. The convenorship and the secretariat for the four working groups are held by the Deutsches Institut für Bautechnik [5]. The European manufacturers of anchors, represented by their association CEO (Comité Européen de l'Outillage - European Tool Committee), are essentially involved in the elaboration of the Guidelines.
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5. ETAG 001 5.1 General The Guideline for European Technical Approval of Metal Anchors for Use in Concrete [6] was adopted in 1997 as the very first ETAG: ETAG 001. It consists of a general part for all types of metal anchors and of five further parts applying to - torque-controlled expansion anchors - undercut anchors - deformation-controlled expansion anchors - bonded anchors, and - anchors for lightweight systems. Part 1 includes the requirements and assessment methods for all metal anchors, whereas the subsequent parts contain additional and/or deviating requirements and assessment methods; they shall be used only in connection with Part 1. The Guideline includes three Annexes: - Details of tests - Tests for admissible service conditions – Detailed information - Design methods for anchorages. Parts 1 to 3 and Annexes A, B and C were published in 1997, Part 4 for deformationcontrolled expansion anchors was published in 1999. Part 5 for bonded anchors has been completed and will probably be published after its adoption in this year. Part 6 for anchors for use in redundant systems is presently in preparation and is envisaged to be completed next year. 5.2 Scope The Guideline applies to metal anchors placed into drilled holes in concrete and anchored by expansion, undercutting or bonding. The Guideline covers the assessment of metal anchors when their use shall fulfil the Essential Requirements 1 and 4 of the CPD and when failure of anchorages made with these products would compromise the stability of the works, cause risk to human life and/or lead to considerable economic consequences. The anchor has to be made of carbon steel, stainless steel or malleable cast iron. In the case of bonded anchors the mortar may be made of resin, cement or a combination of both. The minimum thread size of the anchor is 6 mm, the anchorage depth shall be not less than 40 mm. Anchors for use in lightweight systems shall have a diameter of at least 5 mm and an anchorage depth of 30 mm. The concrete member in which anchors are installed shall be made of normal weight concrete between strength classes C 20/25 and C 50/60. Part 6 covers also other strength classes and other types of concrete, e.g. lightweight aggregate concrete and aerated concrete.
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The Guideline applies to anchors subject to static or quasi-static actions in tension, shear or combined tension and shear or bending, and only applications are covered, where the concrete members in which the anchors are embedded are also subject to static or quasi static actions. The use categories are defined for use in cracked and non-cracked concrete or noncracked concrete only. The durability categories for use in structures subject to dry, internal conditions and/or in structures subject to other environmental conditions; e.g. external atmospheric exposure or exposure in permanently damp internal conditions. 5.3 Verification methods The assessment of anchors is based on the following tests: - tests for confirming their suitability - tests for evaluating the admissible service conditions - tests for checking durability. The tests for suitability are of decisive importance for the assessment of the anchors and are required for the following reasons: - The anchors must not be too sensitive to deviations from the installation instructions of the manufacturer, which might occur during installation. These may include • cleaning of the drilled hole • application of a torque moment higher or smaller than required • degree of expansion in the case of undercut anchors and deformation-controlled expansion anchors • mixing of mortar in the case of bonded anchors • striking of reinforcement during drilling. - The anchors must not be too sensitive to deviations from the concrete characteristics (e.g. concrete strength, cracks, opening and closing of cracks). - Due to drilled hole tolerances and wear of the drilling machine the load resistance of the anchor can be adversely affected. - The anchors must properly function even under sustained loads and repeated loads of varying size. However, gross errors are not covered by the ETAG 001 and should be avoided by proper training of installers and supervision on site. For these suitability tests it is accepted that there is a limited reduction of the load resistance of the anchor compared to the test results for the determination of the admissible service conditions. The different behaviour is assessed by using reduction factors and an installation safety factor of the anchor system as a function of the test results. The extent of the tests for determining the admissible service conditions depends of the field of use chosen by the manufacturer for the anchors. For this purpose the options given in Table 1 are included in the Guideline, which cover the use of anchors in
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cracked and non-cracked concrete and in non-cracked concrete only, the characteristic load resistance FRk as a function of the concrete strength class and load direction and the characteristic load resistance respectively as a uniform value for all concrete strength classes ≥ C 20/25 and/or for all load directions. There are further options for the characteristic spacing of the anchors scr and the characteristic distance between anchor and member edge ccr and for the minimum distances smin and cmin respectively. Characteristic distances are values at which the characteristic (i.e. the full) load resistance of the anchor in the event of concrete failure is achieved. The minimum distances are the minimum admissible values. Where when using the anchors spacing and edge distance respectively are smaller than the determined characteristic values – e.g. in the case of anchor groups and/or anchors near the edge – the characteristic load resistance of the anchors shall be reduced by applying one of the design methods given in Annex C. The tests for checking durability concern mainly the resistance to corrosion, the durability of coatings and the problem of jamming in the case of stainless steel. Table 1: Options Option Cracked Non- C20/25 C20/25 FRk to cracked only No one and C50/60 value nonconcrete cracked only concrete
1 2 3 4 5 6 7 8 9 10 11 12
x x x x x x
x x x x x x x x x x x x
x x x x
ccr
scr
cmin
smin
x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x
x x x x
x x x x x x
x x
FRk function of direction
x x x x
Design method according to Annex C
A B C
x x x x
x x x x
A B C
5.4 Assessment of the anchors The characteristic load resistance of the anchor is determined on the basis of statistical methods as 5% fractile of the ultimate loads measured in a test series for a confidence level of 90%. The load/displacement curves shall show a steady increase. A reduction in load and/or a horizontal or near-horizontal part in the curve caused by uncontrolled slip
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of the anchor is not acceptable up to a defined load. Furthermore, the scatter of the ultimate loads and of the load/displacement curves is limited. 5.5 Annexes Annex A includes details of tests, such as test samples, test members, anchor installation, test and measurement equipment, test procedure and test report. Annex B contains detailed information on the type and number of tests for admissible service conditions. The number of tests is dependent on the option chosen by the manufacturer and on the current experience available on the loadbearing behaviour of the anchors. The equations given for ultimate loads for single anchors are based on current test experience. If the behaviour of the anchors falls within the current range of test experience, a reduced test programme may be carried out. Where test results are available from the manufacturer, these results - with the exception of the suitability tests - can be taken into account thus reducing the number of the tests. Annex C describes the three design methods for anchors for use in concrete. The design of the anchorages (e.g. anchor groups, influence of concrete member edges or corners) is based on the characteristic value of the load resistance given in the relevant ETA for the anchor concerned.
6. ETAs Based on the ETAG 001 the first two European Technical Approvals were granted by Deutsches Institut für Bautechnik in February 1998. By that the first European technical specifications were available being automatically valid in all European countries; they were actually the first construction products bearing the CE marking at all. The anchors concerned are torque-controlled expansion anchors of sizes M8 to M24 made of galvanized steel and stainless steel. They were tested and evaluated under Option 1, the most extensive scope of application for use in cracked and non-cracked concrete fixed in the ETAG 001. They were followed by ETAs for undercut anchors of sizes M6 to M16, made of galvanized steel and stainless steel for use in cracked and non-cracked concrete under Option 1. Until the beginning of 2001 altogether circa 30 ETAs for metal anchors were granted by 5 different European approval bodies for 12 manufacturers in all. They were mainly expansion anchors made of galvanized steel or stainless steel which were evaluated and approved for different fields of application (cracked and non-cracked concrete or non-cracked concrete only).
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7. Prospects The adoption of ETAG 001 for Metal anchors for use in concrete has opened the possibility to grant European Technical Approvals which are automatically in force in all European countries and which are thus the basis for placing the first CE-marked construction products on the European market. The fact that so far a large number of European Technical Approvals have been granted by different European approval bodies is evidence for the broad acceptance of the Guideline.
References [1] UEAtc Directive for Assessment of Anchor Bolts, UEAtc - European Union of Agrément / Union Européenne pour l'Agrément Technique dans la Construction, M.O.A.T. N° 42:1986, December 1986 [2] UEAtc Technical Guide on anchors for use in cracked and non-cracked concrete, UEAtc - European Union of Agrément / Union Européenne pour l'Agrément Technique dans la Construction, M.O.A.T. N° 49:1992, June 1992 [3] European Organisation for Technical Approvals - EOTA: www.eota.be [4] Council Directive of 21 December 1988 on the approximation of laws, regulations and administrative provisions of the Member States relating to construction products (CPD), Official Journal of the European Communities N° L 40/12 of 11 February 1989 [5] Deutsches Institut für Bautechnik: www.dibt.de [6] Guideline for European Technical Approval of Metal Anchors for Use in Concrete - ETAG 001, EOTA
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BEHAVIOR OF MULTIPLE-ANCHOR FASTENINGS SUBJECTED TO COMBINED TENSION/SHEAR LOADS AND BENDING MOMENT Longfei Li*, Rolf Eligehausen** *MKT Metall-Kunststoff-Technik GmbH & Co. KG, Germany ** Institute of Construction Materials, University of Stuttgart, Germany
Abstract Multiple-anchor fastenings are commonly used to connect steel superstructures with concrete foundations both in highway and building constructions. A plastic design method may be used for multiple-anchor fastenings, if full redistribution of forces between anchors is possible. An analytical model was set up for exploring the behavior of multiple-anchor fastenings under combined tension/shear loads and bending moment. The correctness of the model was examined by comparisons between calculated and test results. A number of parametric studies was carried out with the analytical model. Based on the results of this study it will be discussed whether a plastic design method can be applied for typical post-installed metal anchors.
1. Introduction In building and bridge constructions the loads acting on the superstructures are frequently transferred by multiple-anchor fastenings through the steel columns to concrete foundations. The ultimate loading capacity of the multiple-anchor fastenings can be increased by using ductile anchors if the anchors are decisive for the load capacity of the multiple-anchor fastenings. The behavior of ductile multiple-anchor steel to concrete connections was investigated in several tests /1/. A systematic parametric study was carried out for ductile multiple-anchor fastenings subjected to bending moment /2/. However, the results of this studies may not be valid for typical post-installed metal-anchors. Therefor an analytical model was set up in order to simulate realistically the load-bearing and deformation behavior of multiple-anchor fastenings under combined tension/shear loads
158
and bending moment /3/. The ultimate load capacity of multiple-anchor fastenings may be predicted with the analytical model which was verified by comparison with experimental results. A number of parametric studies was carried out with the analytical model. Based on the results of this study it will be discussed whether a plastic design method can be applied for typical post-installed metal anchors.
2. Description of the analytical model 2.1 Basic assumptions The following assumptions were made for a numerical simulation of the behavior of a multiple-anchor fastening shown in Fig. 2.1: 1) 2) 3) 4)
Monotonically increasing load P with a constant angle α between oblique tension load P and vertical axis and a constant load eccentricity e. Rigid baseplate (The minor deformations of the baseplate are neglected). Constant coefficient of friction between baseplate and concrete. The load-displacement curves of individual anchors subjected to oblique tension (combined tension and shear loads) are known (e.g. determined by tests).
Fig. 2.1 Multiple-anchor fastening subjected to combined tension and shear load and bending moment ( N=P⋅cos α, V=P⋅sin α and M=P⋅e⋅sin α) 2.2 Material laws The load-displacement behavior of individual anchors subjected to combined tension and shear loads can be simulated by two families of curves with different load angles β based on the oblique loading tests /3,4/ (Fig. 2.2). For a mathematical description of the loaddisplacement relationships the curves are divided into four parts (Fig. 2.3), a plateau with zero stress representing the slip of the beseplate due to a gap between anchor and fixture, a non-linear ascending part approximated by the function σ=σ1⋅(δ/δ1)γ, a linear ascending part which simulates steel yielding or anchor pullout and a descending line which simulates steel
159
or concrete failure of the fastening. The tension and shear stresses are plotted against anchor tension and shear displacements respectively (Figs 2.2 and 2.3).
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a) Normal stress-displacement b) Shear stress-displacement Fig. 2.2 Normal and shear component of the stress-displacement relationships
Fig. 2.3 Idealization of the load-displacement curve by mathematical functions For the load-displacement behavior of the concrete under local high compressive stresses which occur at the compressed side of the fixture a linear and dimensionless stress-displacement relationship was assumed in the analytical model based on theoretical /3/ and test results /5/ (Fig. 2.4). The coefficient B may be determined by tests. The diameter d was calculated back from the compressed area A.
σ
fc
= B⋅
s d
161
(2.1)
d=
4⋅ A
π
≈ 1.13 ⋅ A
(2.2)
Stress σ d d d d d
for model
fc= 39 N/mm2
Relative penetration s/d [/]
Fig. 2.4 Load-displacement behavior of concrete under local high compressive stress in accordance with /5/ 2.3 Constitutive equations and their numerical solution For the multiple-anchor fastening shown in Fig. 2.5a we have the equilibrium and compatibility conditions shown in Fig. 2.5b,c with three degrees of freedom.
Fig. 2.5 Multiple-anchor fastening with equilibrium and compatibility conditions
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If the normal displacement on the baseplate is entered as x1, the shear displacement as x2 and the anchor plate rotation as x3, the following three equations of equilibrium are obtained:
∑N =0
N( x1 , x 2 , x 3 ) = 0
∑V = 0 ∑M = 0
V( x1 , x 2 , x 3 ) = 0 N( x1 , x 2 , x 3 ) = 0
(2.3)
The modified Newtonian method of iteration was used to solve the nonlinear equation system /6/. (k +1)
x
= x(k) - ω ⋅ [F ′(x )(k) ] -1 ⋅ F(x )(k) k = 0,1,2, ⋅ ⋅ ⋅
(2.4)
wherein:
x1 x = x 2 x 3
N( x1 , x 2 , x3 ) F(x) = V( x1 , x 2 , x3 ) M( x , x , x ) 1 2 3
∂N ∂ x1 ∂V F ′(x) = ∂ x1 ∂M ∂ x1
∂N ∂ x2 ∂V ∂ x2 ∂M ∂ x2
∂N ∂ x3 ω1 ∂V ω = ω 2 ∂ x3 ω 3 ∂M ∂ x3
(2.5)
(2.6)
with, for example:
∂N N( x1 + ∆ x1 , x 2 , x3 ) - N( x1 , x 2 , x3 ) = ∂ x1 ∆ x1
(2.7)
By an appropriate selection of the iteration constant ωk and ∆xi, the conditions of equilibrium with permissible tolerances ξN ≤ 1 N, ξV ≤ 1 N and ξM ≤ 10 Nmm, for one load step can be obtained after 5 to 10 iteration steps with a computer program /10/. In the computer program the anchor forces under combined tension and shear forces are determined by linear interpolation with the two families of the stress-displacement curves /3/. The calculation can be controlled by either the load, the normal displacement, the shear displacement or the rotation of the baseplate of the multiple-anchor fastening /3,10/.
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The calculated results can be visualized by a plot program so that the correctness of the calculated results can be quickly checked graphically /10/.
3. Verification of the analytical model by tests The M1 series of tests conducted in /1/ was calculated with the analytical model. Fig. 3.1 shows the dimensions of the multiple-anchor fastenings used for the tests. Failure was caused by steel rupture.
Fig. 3.1 Dimensions of the multiple-anchor steel to concrete connections using undercut anchors, Tests /1/ (1 inch = 25.4 mm) The load displacement-relationship of the anchor subjected to a centric tensile load was taken from the tests /7/, whereas the families of load-displacement curves of the anchor subjected to oblique tension were taken from the tests conducted in /4/. The tension/shear interaction of the anchor was calculated with the equation /9/:
(
N Nu
k
) +(
V Vu
k
) =1
(3.1)
with k = 2.0 and Vu = 0.6⋅Nu. The coefficient B (see equation 2.1) and the coefficient of friction µ were entered into the calculation with values of 0.00015 and 0.4.
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Figs. 3.2 to 3.4 show comparisons between the calculated peak loads and the measured values as a function of the eccentricity e. In Fig. 3.5 the calculated maximum anchor displacements are compared with the test results. In Fig. 3.5 the diagonal line corresponds to a complete agreement between tests and calculation. The calculated peak loads correspond well with the measured values. Some of the calculated normal and shear displacements are too high and some too small. This is probably caused by the inaccuracy of the assumed loaddisplacement curves.
Fig. 3.2 Comparison between calculated and measured peak loads for test series 2M1
Fig. 3.3 Comparison between calculated and measured peak loads for test series 4M1
Fig. 3.4 Comparison between calculated and measured peak loads for test series 6M1
Fig. 3.5 Comparison between calculated and measured maximum anchor displacements
More calculations were carried out with the computer program to simulate the behavior of multiple steel-to-concrete connections tested in /11/. The calculated results agreed well with the experimental values.
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4. Parametric Studies 4.1 General In case of combined tension and shear forces on an anchor the tensile loading capacity depends on the shear component of the load on the anchor (Equ. 3.1). If multiple-anchor fastening is subjected to combined tension and shear loads and bending moment, each row of anchors is loaded differently, depending on its geometrical and displacement conditions. In the following sections, the different stresses of the anchor rows are explained in detail by means of simulations for multiple-anchor fastenings. Fig. 4.1 shows the dimensions of the multiple-anchor fastening which was used for the simulation. The stress-displacement relationships of the anchor subjected to an oblique tension force were evaluated according to /4/ and /8/. The interaction was calculated according to Equ. (3.1) with k = 2.0 /9/.
Fig. 4.1 Dimensions of the multiple-anchor fastening for the parametric study 4.2 Influence of load eccentricity and load angle Fig. 4.2 shows the ultimate tension component of the ultimate load as a function of the shear component of the investigated multiple-anchor fastenings at different load eccentricities e. It can be seen that at e=0 the ultimate load of the fastening is exactly determined by the load interaction diagram of the individual anchors. At e≥76 mm (3 in), the ultimate tension and shear loads on the fastening have an approximately linear load interaction. Figs. 4.3 and 4.4 show the stress paths and the load-stress curves of different anchor rows at e=76 mm and α=75°. It is clearly visible that the anchors in different rows are stressed differently in normal and shear direction.
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Fig. 4.2 Tension and shear load interaction diagram at ultimate loads of the fastenings, under centric tension failure is caused by concrete breakout
Fig. 4.3 Stress paths of the anchors at α=75° (e=76 mm or 3 in)
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Fig. 4.4 Anchor stresses as a function of the load at α=75° (e=76 mm)
4.3 Influence of anchor ductility With the theory of elasticity, it is assumed that all anchors behave elastically and have a constant stiffness both in normal and shear direction. The ultimate load capacity of a multiple-anchor fastening is achieved when one anchor row has reached its oblique tension strength. With the theory of plasticity, it is assumed that the anchors are sufficiently ductile, so that full anchors in the tension zone of a multiple-anchor fastening can fully activate their oblique tension strength /3/. The conditions of the compatibility are neglected. Fig. 4.5 shows the ultimate loads on the fastening as a function of load eccentricity e. It was assumed that under tension and shear loads failure occurs by steel rupture. The calculation was done for different theories. It can be seen that the ultimate loads calculated on the basis of the actual material behavior correspond well with the values determined according to the theory of plasticity. This can be attributed to the ductile load-displacement curves used which allow a full redistribution of forces between anchors in the tension zone. The ultimate loads calculated according to the theory of elasticity are conservative, especially if the friction between baseplate and concrete is neglected. The contribution of friction on the ultimate load decreases with increasing eccentricity, because the shear load is reduced with increasing load eccentricity.
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Fig. 4.5 Comparison of ultimate loads on the fastening according to different theories (ductile anchor behavior)
5. Conclusions The behavior of multiple-anchor fastenings is determined by the load-deformation behavior of the individual fastening elements of the group. The load-displacement behavior is determined by the type of anchor and the failure model under tension and shear load. To determine the behavior of multiple anchor fastenings under arbitrary loading an analytical model is proposed. This model can be used to determine under which conditions a plastic analysis of a fastening is justified. The model shows that a plastic analysis is sufficient accurate if the anchors show a ductile steel failure.
6. Bibliography /1/
Cook, R.A.; Klingner, R.E.: Behavior and design of ductile multiple-anchor steelto-concrete connections. Research Report 11263, Center for Transportation Research, University of Texas at Austin, March 1989
/2/
Balogh, T.; Eligehausen, R.; Klingner, R.E.: Parametric studies on the ductility of anchor groups. Institut für Werkstoffe im Bauwesen, University of Stuttgart, December 1992
169
/3/
Li, L.; Eligehausen, R.: Loadbearing Behavior of Multiple-Anchor Fastenings Subjected to Combined Tension/Shear and Bending Moment. Institut für Werkstoffe im Bauwesen, University of Stuttgart, 1994
/4/
Bozenhardt, A.; Hirth, W.; Opitz, V,: Dieterle, H.: Tragverhalten von nicht generell zugzonentauglichen Dübeln. Teil 4: Verhalten im unbewegten Parallelriß (∆w=0.4 mm) unter Schrägzugbelastung. Institut für Werkstoffe im Bauwesen, University of Stuttgart, February 1990.
/5/
Lieberum, K.-H.: Lokal hohe Pressungen - Einfluß der Betonzusammensetzung und der Belastungsgeometrie auf das Last-Verformungsverhalten. Darmstädter Massivbau-Seminar, Vol. 5, Verankerungen in Beton. TH Darmstadt, 1990
/6/
Tönig, W.: Numerische Mathematik für Ingenieure und Physiker. Band I: Numerische Methode der Algebra. Springer-Verlag, Berlin, Heidelberg, New York, 1979
/7/
Collins, D.M.; Cook, R.A.; Klingner, R.E.: Load-Deflection Behavior of Cast-inPlace and Retrofit Anchors Subjected to Static, Fatigue, and Impact Tensile Loads. Research Report 1126-1, Center for Transportation Research, University of Texas at Austin, February 1989
/8/
Furche, J.: Zum Trag- und Verschiebungsverhalten von formschlüssigen Befestigungsmitteln bei zentrischem Zug. Dissertation, University of Stuttgart, May 1992
/9/
Rehm, G.; Eligehausen, R.; Mallee, R.: Befestigungstechnik. Betonkalender 1992, Berlin 1992
/10/
Li, L.: BDA: Programm zur Berechnung des Trag- und Verformungsverhaltens von Gruppenbefestigungen unter kombinierter Schrägzugund Momentenbeanspruchung. -Programmbeschreibung-. Institut für Werkstoffe im Bauwesen der Universität Stuttgart, 1994
/11/
Lotze, D.: Bemessung von Gruppenbefestigungen nach der Plastizitätstheorie. Forschungsvorhaben Nr. Lo 561/1-1 der Deutschen Forschungsgemeinschaft (DFG), 1996
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LOAD BEARING CAPACITY OF TORQUE-CONTROLLED EXPANSION ANCHORS Longfei Li MKT Metall-Kunststoff-Technik GmbH & Co. KG, Germany
Abstract The load bearing capacity of the torque-controlled expansion anchors depends on the internal and the external friction of the anchor. Especially for the re-expandable torquecontrolled expansion anchors which are suitable for use in cracked and non-cracked concrete, the coefficient of the internal friction must lie within a certain range, so that the anchors re-expand reliably and then resist the external loads efficiently. Unfortunately the coefficient of the internal friction can vary significantly depending on the materials as well as the speed of movement of friction surfaces. A test method to determine the internal and external frictional coefficient was introduced. The load bearing capacity of the torque-controlled expansion anchors was analyzed with the different values of the internal frictional coefficient.
1.
Introduction
Torque-controlled expansion anchors are widely used as post-installed systems to fix structural elements. Because of its simplicity of manufacture and easy installation they are often selected for anchoring of facades and banisters /1/. Torque-controlled expansion anchors are anchored in drilled holes by forced expansion which is achieved by a torque acting on the screw or thread. A tensile force applied to the anchor is transferred to the concrete by friction and some keying between expanded sleeve and the concrete. With increasing tensile load the anchor must expand reliably, so that it transfers the load to concrete safely. The safety of functioning as well as the load bearing capacity of the anchor depends on the internal (expansion sleeve/cone) and external (expansion sleeve/concrete) frictions. Higher external friction may be achieved by manufacture or by more tightening of the anchor
170
during installation. The internal friction is the main problem which must be solved during the development of new expansion anchors, especially for expansion anchors made of stainless steel. In this paper it was investigated to enlighten the bond friction between expansion sleeve and cone. The load bearing capacity of expansion anchors was estimated using the value of internal frictional coefficient with which the anchor expand reliably.
2.
General basis
2.1
Conditions for reliable functioning of expansion anchor
The torque-controlled expansion anchors installed in drilled holes can only resist the tension load efficiently, if the expand-condition (2.1) is fulfilled /2/. (2.1) δ c>α +δ i Where δc is the external frictional angle, α is the expansion angle of cone and δi is the internal frictional angle (fig. 2.1). Fig. 2.1 gives the details about the relationships between the expansion pressure fexp, expansion force Fexp and the splitting force Fspl.
Expansion force : F exp = ∫ f exp dϕ Splitti ng force : F spl = ∫ f exp sin ϕ dϕ Fig. 2.1 Internal forces of expansion anchor
171
2.2
Ultimate load of re-expandable expansion anchors
The load bearing capacity of expansion anchors with the failure type concrete-cone failure and steel failure are given in /3/. The concrete break-out load for an individual anchor in cracked concrete is reduced by approximately 40% in relation to the failure load in uncracked concrete. However, expansion anchors which are suitable for use in cracked and uncracked concrete have often the failure type pull-through because of the relative low internal frictional coefficient. The failure load can only be estimated by actual internal friction behavior of the anchor. According to the mathematical relations from fig. 2.1 and /3,4/ the failure load with the failure type pull-through can be calculated by equation (2.2) (fig. 2.2).
F u,m = F exp ,1 tan ( α + δ i ) + F exp ,2 tan δ i
(2.2)
Fig. 2.2 Expansion forces of the anchor
2.3
Test method to determine the internal and external frictional coefficient
The internal and external frictional coefficient of expansion anchors can be measured by means of FEP II – tests /2/(FEP II: replaced function test). For example, from the test results in fig. 2.3 an internal frictional angle of 7.1° is calculated by actual construction of MKT BZ M8 A4 at the tensile force of 5 kN.
172
Fig. 2.4 shows a test result for measuring the internal and external frictional coefficient. From these test results, the following important information can be determined about the anchor: 1. The value at point a determines the internal frictional coefficient at point a’ of the anchor. 2. The value at point b determines the external frictional coefficient of the anchor. 3. The distance between point a and b reflects the safety of the functioning.
Fig. 2.3 Example of test results from FEP II test /7/
Fig. 2.4 Example of test results to determine the internal and external frictional coeficient
173
/7/
2.4
Scatter of internal frictions
The coefficient of steel-to-steel frictions scatter very differently depending on the contact surfaces. For example, the roughness and hardness of the steel have a large effect on friction. Generally there is always an internal bond friction which makes re-expansion of the anchor less reliable. Fig. 2.5 shows a test result of a steel expansion anchor in which the coefficient of friction increases 18% after 10 minutes of installation.
Fig. 2.5 Bond friction between expansion sleeve and cone /7/ However, there was no internal bond friction observed with the MKT BZ A4 expansion anchor in which a special synthetic hose is installed between the expansion sleeve and the cone (fig. 2.6).
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Fig. 2.6 Behavior of internal friction of MKT BZ M12 A4 /7/
2.5
Verification of the calculation assumptions for ultimate load
The ultimate loads with the failure type pull-through are calculated according to equation (2.2) by a numeric program /5/. A parabolic relative stress-displacement relationship of concrete is assumed on the basis of test results from /6/. Fig. 2.7 shows the 18 calculated ultimate loads compared with the values of average ultimate loads of five tests each /7,8/ in which the internal frictional angle was determined by FEP II tests /7/. The diagonal line shows the absolut agreement between calculation and test. The calculated ultimate loads agree well with the mean value of failure loads from tests.
Fig. 2.7 Comparisons of calculated ultimate loads with those from test /7,8/
3.
Load bearing capacity of re-expandable expansion anchors
The ultimate loads of torque-controlled expansion anchors which are suitable for use in cracked and uncracked concrete were calculated by the numerical program /5/ according to equation (2.2). The following assumptions were made in the calculation: 1. The 5%-fractile of external frictional coefficient is equal to 0.45. µc,5%=0.45,
i.e. δc,5%=24.3°
2. The internal frictional coefficient scatters 20% with the normal distribution at n=∞. i.e. δi,m = 0.75 δi,95%
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According to equation (2.1) results in following re-expand condition: δi,m < 0.75 (24.3°-α) Fig. 2.8 shows the calculated ultimate loads with different expansion angles of cone in uncracked concrete. The loading capacity decreases with increasing expansion angle, because the expansion force Fexp, 1 (fig.2.1) decreases propotionatly. Fig. 2.9 shows the estimated load bearing capacity of expansion bolt anchors of sizes from M8 to M16 with α=11°.
Fig. 2.8 Mean value of failure loads depending on the expansion angle of cone
Fig. 2.9 Load bearing capacity of bolt anchors (α=11°, δi,m=10°)
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4.
Conclusions
The reliability of functioning as well as the load bearing capacity of torque-controlled expansion anchors depends on the internal and external frictions of the anchor. The coefficient of the internal and external frictions of the anchor can be measured exactly by FEP II tests. The loading capacity of expansion anchors in uncracked concrete was analyzed by a numerical program which was verified by tests. In accordance with the analysis the newly developed MKT stainless steel bolt anchors BZ A4 /1/ have achieved the optimum load bearing capacity.
5.
References
1.
European Technical Approval ETA-99/0010, MKT Bolzenanker A4, Torquecontrolled expansion anchor made of stainless steel of sizes M8, M10, M12 and M16 for use in concrete. Berlin, September 1999
2.
Mayer, B.: Funktionsersatzprüfungen für die Beurteilung der Eignung von kraftkontrolliert spreizenden Dübel. Dissertation of University Stuttgart, 1990
3.
Eligehausen, R.; Mallée, R.: Befestigungstechnik im Beton- und Mauerwerkbau. Verlag Ernst & Sohn, Berlin, 2000
4.
Lehmann, R.: Tragverhalten von Metallspreizdübeln im ungerissenen und gerissenen Beton bei der Versagensart Herausziehen. Dissertation of University Stuttgart, 1994
5.
Li. L.: Programm zur Berechnung der Durchzuglast von kraftkontrolliert Metallspreizdübeln.- Programmbeschreibung -. MKT Metall-Kunststoff-Technik GmbH & Co. KG, Weilerbach 2001, in preparation
6.
Lieberum, K.-H.: Das Tragverhalten von Beton Teilflächenbelastung. Dissertation of TH Darmstadt, 1987
7.
MKT test documents: FEP II – test with BZ A4 M8 to M12; Pull-out test with MKT Bolzenanker B M20. MKT report-No. BAB 01/2000, Weilerbach 2000.
8.
Eligehausen, R.; Asmus, J.: Evaluation report for the assessment of the torque controlled bolt anchor MKT Z A4 M8 to M16 for anchoring in concrete in accordance with the ”Gudeline for European Technical Approval”, Option 1, Stuttgart, July 1999
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bei
extremer
BEHAVIOUR AND DESIGN OF ANCHORS CLOSE TO AN EDGE UNDER TORSION R. Mallée Fischerwerke, Germany
Abstract In order to investigate the behaviour of anchor groups close to an edge under torsion tests with pairs of injection anchors M12 parallel to a free structural component edge were carried out. The tests indicate that the anchor with the lowest loadbearing capacity is decisive for the capacity of the group. Based on these results a design method for anchor groups close to an edge under torsion is proposed.
1. Introduction Anchors close to an edge under shear load fail due to concrete edge failure. Their loadbearing capacity can be calculated in accordance with the Concrete-CapacityMethod (CC-Method) /1,2/ taking into account all influencing parameters such as concrete strength, stiffness of the anchor, axial and edge spacings, dimensions of the structural component, angle between load and free edge and eccentricity of the load. The influence of the eccentricity is considered by a reduction factor ψec,V, which depends upon the distance eV between the shear load and the centre of gravity of the anchors. With groups of anchors parallel to the free edge the factor ψec,V may only be used, if all anchors of the group are loaded in the same direction (eV ≤ st/2, with st = spacing between the outermost anchors of the group). No assumption is available if the load direction within the group changes, e.g. with a group of two anchors under torsion, when one anchor is loaded perpendicular towards and the other away from the free edge. Based upon experimental research this paper outlines a proposal for the design of anchor groups close to an edge under torsion.
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2. Behaviour of anchors close to an edge under shear load Anchors close to an edge of a structural component may fail in consequence of concrete edge failure before the anchor’s steel capacity is exhausted. The angle between the failure crack and the edge is approximately 35° and the depth of the failure body on the side face of the structural component is about 1.5 times the edge distance of the anchor (Figure 1a) /1/. If a pair of anchors with an axial spacing s ≤ 3 ⋅ c1 (with c1 = edge distance) is installed close to an edge the concrete break-out bodies of the anchors can not develop completely, i.e. the bodies of adjacent anchors overlap each other (Figure 1b). This leads to a reduction of the surface of the break-out body and consequently to a reduction of the failure load.
a)
b)
Figure 1: Concrete edge failure a) Break-out body of a single anchor close to a free edge b) Break-out body of a pair of anchors close to a free edge If an eccentric load acts on a group the anchors are loaded to a different extent. An example is given in Figure 2a. It may be assumed that failure occurs when the most stressed anchor of the group fails. The effect of the eccentricity may be taken into account in analogy with /3/ by means of a reduction factor ψec,V.
ψ ec ,V =
1 1 + 2 ⋅ eV /( 3 ⋅ c1 )
(1)
Equation (1) is only valid if all anchors of the group are loaded either towards the edge or away from the edge. With acting torsion moments the load direction alters within a group. Figure 2b shows an example. Provided that the anchor loaded away from the edge has no effect on the behaviour of the anchor which is loaded perpendicular towards the free edge, it may again be assumed that the most stressed anchor is decisive for the loadbearing capacity of the group. Four test series with both, single anchors as well as pairs of anchors were carried out in order to investigate whether the two anchors of the groups influence each other. The test results are described in the following chapter.
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V
MT
a)
b)
Figure 2: Pair of anchors close to a free edge a) Anchors loaded by shear forces with the same direction b) Anchors loaded by shear forces with different directions
3. Test results Figure 3 shows the test set-up. A concrete block was introduced into a steel frame and fixed at the corners on four supports (steel plates or wedges). Two injection anchors M12 were installed with a specific edge V distance. The spacings between the anchors and the supports were sufficient to allow an Hydraulic press Concrete block unrestricted concrete edge failure. Shear forces were applied to the anchors by means of hydraulic presses in such a way that both anchors were loaded to the same extent, one perpendicular towards the edge and the other away from the edge. Thus a torsion moment was simulated. The loads were applied displacement controlled (5 mm / minute). V
Steel frame
Support
V
Figure 3: Test set-up
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The concrete had a compressive strength of fcc = 36.1 N/mm2 (measured on cubes 200 x 200 x 200 mm3). To reduce a possible influence of stresses due to shrinkage of the concrete, relatively old (564 days) concrete blocks were used. In order to allow small edge distances injection anchors were used which do not create expansion forces during installation. A shear load perpendicular to the axis of an anchor creates compressive stresses in the concrete in the area of the mouth of the drilled hole. The resultant of these stresses (compare Figure 4, force A1 for anchor No. 1 and A2 for anchor No. 2) and the shear force due to the torsion moment have the same direction. For conditions of equilibrium compressive stresses occur close to the end of the anchor on the opposing side of the shear load. The resultants of these stresses are shown in Figure 4 (force B1 for anchor No. 1 and B2 for anchor No. 2). It may be assumed that the probability that the forces A1 and B2 or A2 and B1 respectively affect each other increases with decreasing axial spacing and embedment depth of the anchors. Anchor No.1 Anchor No.2 Mt
A1
A2 B1
Figure 4: Pair of anchors under torsion: reaction forces in the concrete
B2
To investigate whether this has an influence, tests were carried out with two different embedment depths (hef = 50 mm and hef = 100 mm). This corresponds to a ratio of embedment depth and anchor diameter of 3.6 and 7.2 respectively. The axial spacings were varied between s = 50 mm and s = 200 mm. The edge distance was kept constant (c1 = 60 mm). For comparison two series of single anchors loaded perpendicularly towards the free edge were tested (series A and C). The test parameters and results are given in Table 1.
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Table 1: Test parameters and results Test Type Embedment Test series of fixing depth hef No. [mm] A
Single
50
B
Pair
50
C
Single
100
D
Pair
100
Axial spacing s [mm]
Ultimate load Vu [kN]
Mean ultimate load [kN]
0
14.9 14.7 14.9 12.0 15.6 13.4 12.7 13.4 12.5 15.1 16.9 18.1 21.2 19.3 19.3 17.6 14.7 18.3 20.0 21.0 16.6 18.1 16.1 19.3 21.0
14.8 (v = 0.8%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
50
150
0
50
100
150
200
13.7 (v = 13.3%) 12.9 (v = 3.7%) 17.8 (v = 14.4%)
18.7 (v = 5.2%) 17.7 (v = 15.3%) 18.6 (v = 12.0%) 18.8 (v = 13.2%)
The tests were stopped as soon as the anchor loaded perpendicularly towards the free edge failed in consequence of concrete edge failure. In the tests with small axial spacings (s = 50 mm) a failure crack was observed running from the anchor loaded towards the edge to the opposing side of the load of the second anchor (Figure 5a). With increasing axial spacing an independent break-out body developed (Figure 5b).
a)
b)
Figure 5: Failure cracks, hef = 100mm, a) spacing s = 50mm, b) spacing s = 100mm
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4. Evaluation of the test results In /4/ the following equation for the mean concrete edge failure load of single anchors loaded perpendicularly towards a free edge is given:
(
Vu = d nom ⋅ f cc ⋅ hef / d nom with:
dnom: fcc: hef: c1:
)
0.2
⋅ c11.5 / 1000 [kN]
(2)
anchor diameter [mm] concrete cube compressive strength [N/mm2] embedment depth [mm] distance to the free edge [mm]
Equation (2) gives calculated failure loads for the tested single anchors of Vu = 13.5 kN (hef = 50 mm) and Vu = 15.5 kN (hef = 100 mm) which are approximately 9% and 13% lower than the mean measured values (test series A and C). A reason for this may be assumed in the relatively high age of the concrete blocks. The older the concrete, the lower the stresses due to shrinkage which normally affect the loadbearing capacity at concrete edge failure. Figures 6 and 7 show the measured ultimate loads as a function of the axial spacing s. Figure 6 is valid for anchors with an embedment depth of hef = 50 mm and Figure 7 for hef = 100 mm. The results of the tests with single anchors are plotted at a spacing s = 0.
Figure 6: Ultimate shear load Vu of pairs of anchors as a function of the axial spacing s, embedment depth hef = 50 mm
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Figure 7: Ultimate shear load Vu of pairs of anchors as a function of the axial spacing s, embedment depth hef = 100 mm The failure loads of the anchors loaded perpendicularly towards the free edge and the ultimate loads of the single anchors are in the same range of scatter. It is obvious that the anchors of the group do not affected each other. A statistical analysis of all test gives the following results: hef = 50 mm: number of tests n: mean ultimate load Vu: standard deviation: s: coefficient of variation v:
9 13.8 kN 1.27 kN 9.2 %
hef = 100 mm: number of tests n: mean ultimate load Vu: standard deviation: s: coefficient of variation v:
16 18.3 kN 2.04 kN 11.1 %
5. Conclusion The test results indicate that with a pair of anchors parallel to a free edge under torsion the anchor with the lowest loadbearing capacity is decisive for the capacity of the group. The following proofs are required for the design: V Sd( 1 ) ≤ V Rk( 1,)c / γ Mc
(3a)
/ γ Mc
(3b)
V
(2) Sd
≤V
(2) Rk ,c
with: V Sd( 1 ) : design action of the shear load of anchor No. 1 V Sd( 2 ) : design action of the shear load of anchor No. 2
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V Rk( 1,)c : design resistance at concrete edge failure for anchor No. 1 V Rk( 2,c) : design resistance at concrete edge failure for anchor No. 2
γ Mc : partial safety factor for concrete edge failure The corresponding characteristic resistance at concrete edge failure may be calculated using the following equation /5/ : V Rk( 1,,c2 ) = V Rko ,c ⋅
Ac ,V Aco,V
⋅ψ s ,V ⋅ψ h ,V ⋅ψ α ,V ⋅ψ ucr ,V
(4)
For details regarding the parameters of equation (4) compare /5/. The anchor with the lowest ratio of design action and design resistance is decisive. This proposal is valid for anchors with a ratio of embedment depth and anchor diameter hef / dnom ≥ 4 and for axial spacings s ≥ 50 mm. For lower ratios and spacings further research is necessary.
6. References 1.
Fuchs, W.; Eligehausen, R. (1995): Das CC-Verfahren für die Berechnung der Betonausbruchlast von Verankerungen. Beton- und Stahlbetonbau, 1995, Heft 1, S. 6-9, Heft 2, S. 38-44, Heft 3, S. 73-76.
2.
Fuchs, W.; Eligehausen, R.; Breen, J.E. (1995): Concrete Capacity Design (CCD) Approach for Fastenings to Concrete. ACI Structural Journal, Vol. 92 (1995), No. 1, p. 73-94.
3.
Riemann, H. (1985): Das „erweiterte κ-Verfahren“ für Befestigungsmittel, Bemessung an Beispielen von Kopfbolzenverankerungen. Betonwerk + Fertigteil-Technik, 1985, Heft 12, S. 808-815.
4.
Comité Euro-International du Béton (CEB) (1994): Fastenings to Concrete and Masonry Structures. Bulletin d’Information No. 216, Lausanne, published by Thomas Telford, London, 1994.
5.
European Organisation for Technical Approvals (EOTA) (1994): Guideline for European Technical Approval of Anchors (Metal Anchors) for Use in Concrete. Final Draft, Sept. 1994.
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FIXINGS WITH ANCHORS: CONCERNING RELEVANT BASE PLATE THICKNESS R. Mallée, F. Burkhardt Fischerwerke, Germany
Abstract Based upon international guidelines, with groups of anchors the anchor forces are calculated in accordance with the theory of elasticity under the assumption that the steel plate of the attachment has a sufficient stiffness. No detailed information is given in the guidelines how to determine this stiffness. Based on tests and on non-linear Finite Element calculations taking into account realistic assumptions for the load displacement behaviour of anchors it is investigated which stiffness is needed to meet the requirements of the theory of elasticity.
1. Introduction Anchors to be used in the countries of the European Community will need an European Technical Approval. The necessary tests to gain an approval are laid down in guidelines /1/. Special attention is drawn on the proper functioning of the anchors in cracked and non-cracked concrete taking into account the influence of parameters which are unavoidable on site, such as tolerances of the drill hole diameter, the intensity of cleaning of the holes as well as tolerances of the applied torque with torque controlled expansion anchors or the amount of expansion energy with displacement controlled expansion anchors. These relatively high requirements are responsible for the development of high quality post-installed anchors which allow to apply high loads to reinforced concrete structures. It is obvious that high loads require a proper design of the fixings in accordance with good engineering judgement. Design concepts are available which consider all influencing parameters such as direction of the load (tension, shear, combined tension and shear), axial spacings to adjacent anchors, the anchor’s edge spacings and the condition of the base material (cracked or non-cracked) /1,2/.
186
If bending moments act on a group of anchors special consideration must be given to the determination of the anchor forces. In accordance with the design guidelines the anchor forces of a group shall be calculated under the assumptions of the theory of elasticity. One of these assumptions is that the anchor plate does not deform under the design loads. I.e. a sufficient stiffness of the steel plate is required but no detailed information is given in the guidelines how to determine this stiffness. This paper outlines an appropriate proposal which is based upon theoretical and experimental research.
2. Anchor forces 2.1 Theory of elasticity According to the theory of elasticity the following assumptions are made: - The anchor plate does not deform under the design actions. The stiffness of all anchors of a group is equal and corresponds to the modulus of elasticity of the steel. In the zone of compression under the steel plate the anchors do not contribute to the transmission of the normal forces. The assumption that the steel plate does not deform under the design actions corresponds to the Bernoulli hypothesis of reinforced concrete. The anchor forces are calculated like the forces in the reinforcement. This is strictly speaking applicable only for rebars in concrete. Post-installed anchors show an elastic deformation between the area of undercut or expansion and the surface of the attachment. Additional displacement is caused by the elastic / plastic deformation of the highly stressed concrete. The displacement gives rise to a rotation of the steel plate and thus to a reduction of the compression zone under the plate and to an increase of the effective internal lever arm between the anchor forces and the compression force in the concrete. Thus assuming a stiff steel plate and neglecting the anchor’s displacement leads to more conservative results. According to the theory of elasticity the stresses in the state of serviceability are proportional to the strains. The anchor forces depend on the ratio of the modulus of elasticity of steel and concrete and can be calculated from the equilibrium of the forces and moments. 2.2 Finite element analysis The assumptions of the theory of elasticity allow an easy calculation of the anchor forces. Nevertheless it must be pointed out that some simplifications are made. It is assumed that the concrete stresses below the plate increase linearly from the neutral axis to the compressed edge of the plate. In reality even small deformations of the plate cause a redistribution of the stresses which leads to a reduction of the stresses below the corners of the plate. The forces and the bending moments are transferred to the steel plate by a profile which is normally not considered when calculating the anchor forces.
187
Finite Element analysis show peaks of bending stresses in the steel plate close to the corners of the profile which may lead to a limited plastic deformation of the plate and again may cause a redistribution of the concrete stresses. And last but not least the displacement of the anchors has a positive influence on the internal lever arm between the anchor forces and the concrete compressive force. To consider the influence of the parameters mentioned above non-linear Finite Element calculations were performed using the program Ansys. The base material was idealized by three dimensional elements where the concrete was supported on two lower edges. For the steel plate and for the profile welded to the plate three dimensional shell elements were used. Contact elements were placed between concrete and steel which allow to transmit compression but no tensile forces. Thus the steel plate is in contact with the concrete only where compressive stresses occur. The tensioned anchors were idealized using non-linear spring elements. The behaviour of these elements corresponds to the load displacement behaviour of the anchors. Anchors in the zone of compression below the steel plate are not considered. Using this Finite Element approach groups with four anchors loaded by a tensile force and both, uni-axial as well as bi-axial bending moments were investigated. For confirmation test were performed. The validity of the theoretical approach may be assumed if the calculated anchor forces correspond to the measured values. The results of this comparison will be discussed in Section 4.
3. Steel plate thickness In actual computer programs for the design of anchors (e.g. /3/), the thickness of the steel plate is determined based on results of linear Finite Element calculations. On the one hand Finite Element analysis allows to determine the bending moments in the steel plate considering all influencing parameters such as size and thickness of the plate, size and position of the profile, type of loading (compression or tension load, uni-axial or bi-axial bending moments) as well as size and load displacement behaviour of the anchors. On the other hand a time-consuming non-linear approach is required if the entire system including the concrete and the contact between steel plate and base material is idealized. To simplify matters it is therefore proposed to support the steel plate on the welded profile and to apply the anchor and concrete forces as external loads. The advantage of using this is a reduced time for calculation for this linear approach instead of a more complex non-linear method. This however does not consider the influence of anchor displacement. The Finite Element analysis shows peaks of bending moments occurring in the corners of the welded profile (compare Fig. 1a), the size of which depends upon the size of the finite elements.
188
In the case of the design of the steel plate these moment peaks are not decisive, as in the relative small area of the peaks a plastic deformation of the steel without any large deformation of the plate itself can occur. For this reason it is proposed to use a mean value of the moment, calculated over the length 2 times the steel plate thickness t plus the profile’s wall thickness s (compare Fig. 1b) rather than the moment peak. The thickness of the plate may then be calculated from a bending proof using the mean bending moment and the characteristic steel strength. 2 t+s
s
s
a) b) Figure 1: Calculation of the mean bending moment in the steel plate a) Distribution of the bending moment b) Mean bending moment
4. Test results In order to assess the results of the non-linear Finite Element analysis (Section 2.2) and the proposal for the calculation of the anchor plate thickness (Section 3) 7 tests were performed (compare table 1). Square and rectangular shaped steel plates were tested, the dimensions of which are given in Figures 2a and 2b. 440
240 200
400
440
400
189
b)
560
500
a) Figure 2: Dimensions of the tested steel plates a) Square shaped steel plates b) Rectangular shaped steel plates
The load was applied by a straight (uni-axial bending) or L-shaped steel beam (bi-axial bending) (Fig. 3). The test set-up allowed tension loads, compression loads could not be applied. The steel plate thickness of the square and the rectangular plate were 20 mm and 25 mm respectively and thus smaller than the theoretical values in accordance with Section 3 (27 mm and 26 mm respectively). The concrete had a cube strength of fcc,200 = 32.4 to 40.0 N/mm2. In 6 of the 7 tests a thin layer of levelling mortar was placed between plate and concrete to ensure a close contact to the concrete over the entire area of the steel plate. In one test the plate was placed directly on the concrete. a) The anchors (Zykon undercut anchors FZA 14 x 60 M10) were set and prestressed with the required torque. The torque was reduced to null after 10 minutes and subsequently the anchors were tightened again by hand without any tool. In one test, the torque was not reduced to determine the influence of the higher anchor stiffness. The anchor forces were measured using a load cell with an accuracy of ± 0.5 %. b) Figure 3: Test setup a) Uni-axial bending b) Bi-axial bending Table 1: Test parameters Test No. Figure No.
1 2 3 4 5 6 7
2a
Bending
Levelling mortar
uni-axial
y n y y y y y
2b 2a
bi-axial
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Thickness of steel plate [mm] 20
25 20
Anchor force F [kN] 45 test No. 3 40 35 FEM (test No. 3) 30 test No. 1+2 25 FEM (test No. 1) 20 15 10 5 0 0 5 10 15
20
25
30 35 Tension load [kN]
Figure 4: Measured anchor force as a function of the applied tensin load (square shaped plate, uni-axial bending) Figure 4 shows the measured anchor forces as a function of the applied tension load for the tests with square steel plates (test no. 1 to 3) in comparison with the values found in the Finite Element analysis. The tests with non-prestressed anchors show a linear relationship between tension load and anchor force. It is obvious that the stiffness of the anchor plate was sufficient. The plate deformations are small and the influence of a nonlinearity may be neglected. The difference between the measured anchor forces and the Finite Element values are negligible. A prestressing force due to the applied tightening torque changes the behavior of an anchor. With no external load applied the anchor forces correspond to the prestressing force. Relatively low loads cause only a small increase in anchor force because the stiffness of the base material is significantly higher than the one of the anchors. With further increasing loads the anchor forces increase proportional to the tensile load and in the ultimate limit state correspond to the forces found in tests without prestressing. Again a good correspondence between measured and Finite Element values was found. Figure 5 shows the results found in tests with rectangular steel plates (test no. 4 and 5). The anchor forces are proportional to the external load and slightly lower than the values found in the Finite Element analysis. It may be assumed that the plate thickness is sufficient, no significant deformation of the plate occurred.
191
Anchor force F [kN] 40 35 test No. 4 test No. 5 FEM
30 25 20 15 10 5 0 0
5
10
15
20
25
30 35 40 Tension load [kN]
Figure 5: Measured anchor force as a function of the applied tensin load (rectangular shaped plate, uni-axial bending) Test no. 6 and 7 were performed under bi-axial bending. Figure 6 shows the test results. The measured forces in the most stressed anchor are slightly lower than the Finite Element values. Anchor force F [kN] 40 35 test FEM
30 25 20 15 10 5 0 0
2,5
5
7,5
10
12,5
15
17,5
20
22,5
25
Tension load [kN]
Figure 6: Measured anchor force as a function of the applied tensin load (square shaped plate, bi-axial bending)
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Based upon the test results and upon the comparison of measured and calculated values it may be assumed that the Finite Element model is suitable to describe the real behaviour of anchor groups under tension load and uni-axial or bi-axial bending with sufficient accuracy.
5. Parameter studies Parameter studies were performed using the Finite Element model described in Section 2.2. The studies cover both, square as well as rectangular steel plates. The plates were fixed to the concrete by 4 Zykon undercut anchors FZA 18 x 80 M12 with axial spacings of sx = sy = 200 mm (square plates) and sx = 200 mm, sy = 500 mm (rectangular plates). Compression or tensile forces and uni-axial or bi-axial bending moments were applied using hollow profiles. The sizes of the profiles were varied. The ratio of the profile height or width and the corresponding axial spacing was chosen to k = 0.4 and k = 0.8. Additionally the ratio of the bending moments My / Mx and the eccentricity of the external load (e = Mx / N) were varied. The parameters are given in Table 2. Table 2: Parameters of the Finite Element analysis Series No. sx / s y sx sy
1 2 3 4 5 6 7 8
[-] 1.0
[mm] 200
[mm] 200
0.4
200
500
k
My / Mx
[-] 0.4 0.8 0.4 0.8 0.4 0.8 0.4 0.8
[-] 0.0 0.0 1.0 1.0 0.0 0.0 0.4 0.4
In order to reduce the number of calculations only the combination of normal force and bending moment giving the maximum permissible load in accordance with the European Technical Approval was investigated (Fperm = 12.3 kN). Non-cracked concrete was chosen because the permissible load and thus the load on the steel plate is higher than in cracked concrete. The corresponding displacement of the anchor was found from tests to ∆ = 0.3 mm. The thickness of the steel plate was calculated in accordance with Section 3. Figures 7 and 8 show the results found with square steel plates (series no. 1 to 4). Figure 7 is valid for uni-axial and figure 8 for bi-axial bending. The figures show the ratio of the anchor force according to the Finite Element analysis and the force according to the theory of elasticity as a function of the eccentricity of the external load. The results according to the theory of elasticity are slightly conservative.
193
Figure 7: Ratio of anchor forces according Figure 8: Ratio of anchor forces according to Finite Element analysis and to Finite Element analysis and to theory of elasticity as a to theory of elasticity as a function of the eccentricty function of the eccentricty (square shaped plate, uni-axial (square shaped plate, bi-axial bending) bending) Figures 9 and 10 show the results found with rectangular steel plates. The ratio of the anchor force according to the Finite Element analysis and the force according to the theory of elasticity is equal or slightly larger than 1. The difference between the anchor forces according to the Finite Element analysis and those found under the assumptions of the theory of elasticity is rather small (< 5 %) and may be neglected.
Figure 9: Ratio of anchor forces according Figure 10: to Finite Element analysis and to theory of elasticity as a function of the eccentricty (rectangular shaped plate, uniaxial bending)
194
Ratio of anchor forces according to Finite Element analysis and to theory of elasticity as a function of the eccentricty (rectangular shaped plate, biaxial bending)
In a further series the influence of the anchor displacement was investigated. A rectangular steel plate was chosen loaded by an uni-axial bending moment. The displacement varied between ∆ = 0 mm and ∆ = 0.6 mm. Figure 11 shows the results. A slight influence of the displacement was observed. The calculated anchor force decreases with increasing displacement because the displacement gives rise to a rotation of the steel plate and thus to a reduction of the compression zone under the plate and to an increase of the effective internal lever arm between the anchor forces and the compression force in the concrete.
Figure 11: Anchor force according to Finite Element analysis as a function of the anchor displacement
6. Conclusion In actual computer programs for the design of anchors, the thickness of the steel plate is determined based on results of linear Finite Element calculations. A comparison with test results and with the results of non-linear Finite Element analysis taking into account realistic assumptions for the load displacement behaviour of the anchors shows that this thickness is sufficient to meet the requirements of the theory of elasicity. This is valid for plates under tension load and uni-axial or bi-axial bending. Further reaearch is necessary for plates under compression load.
7. References 1.
European Organisation for Technical Approvals (EOTA) (1994): Guideline for European Technical Approval of Anchors (Metal Anchors) for Use in Concrete. Final Draft, Sept. 1994.
2.
Deutsches Institut für Bautechnik (DIBt), Berlin (1993): Bemessungsverfahren für Dübel zur Verankerung im Beton (Design Concept for Anchors in Concrete). June 1993 (in German).
3.
fischer Fixing Systems: COMPUFIX, Program for the Design of Anchorages, Version 5.1, April 2001.
195
INSTALLATION VERIFICATION OF MECHANICAL AND ADHESIVE ANCHORS Lee Mattis CEL Consulting, Oakland, USA
Abstract In the United States building codes allow increased design loads for expansion anchors whose installation has been verified to be in accordance with the engineer's design and the manufacturer's recommendations. The verification process is called special inspection. Adhesive anchors require special inspection for all installations with no increase in design loads. This paper describes the background of the building code provisions and typical procedures used to verify proper installation of expansion and adhesive anchors in concrete.
1. Introduction Independent inspection of certain construction activities where unique expertise or additional assurance of quality is deemed necessary is mandated in the US building codes. This inspection is called "special inspection". Special inspection is continuous observation of these construction activities. Concrete placement, masonry construction, structural welding and high strength bolting are common special inspections. These inspections are in addition to the normal progress inspections performed by municipal building inspectors. Special inspection of expansion and adhesive anchors is specified by ICBO Evaluation Service, Inc. (ICBO ES) in evaluation reports for proprietary post-installed anchors. The basis for this is the building code requirement for special inspection of "Bolts installed in concrete" which permits higher design loads for cast-in-place anchor bolts when special inspection prior to and during the placement of concrete around the bolts is provided. The evaluation reports permit use of proprietary products such as post-installed concrete
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anchors as alternatives to the generic items such as cast-in-place anchors in the building code.
2. Qualification of Special Inspectors A special inspector is a specially qualified person with both inspection and practical experience in the construction operation requiring special inspection. The individual must submit his qualifications to the municipal building official for approval. Approval is sometimes done on a case by case, individual basis or is granted to local independent testing agencies who employ inspectors with the expertise. In many cases the approval is informal, based on previous experience with firms and individuals. Engineers may be qualified as special inspectors, however an engineering degree or license does not automatically qualify a person as a special inspector.
3. Employment of Special Inspectors The owner of the construction project or the engineer or architect of record acting as the owner’s agent must employ the special inspector. Although not explicitly stated in the building code, the wording is such that the contractor cannot employ the special inspector. This would be a conflict of interest and not in accordance with the intent of special inspection as an independent evaluation.
4. Duties and Responsibilities of Special Inspectors The special inspector observes the work for conformance with the approved design drawings, specifications and workmanship provisions of the building code, brings discrepancies to the immediate attention of the contractor and to the design authority and municipal building official if not corrected and submits periodic and final inspection reports to the municipal building official and project engineer or architect. The special inspector is considered an extension of the municipal building official's authority by virtue of the code requirements for progress inspections by the building official and special inspection. The City of Los Angeles formalizes the relationship with special inspectors in this regard, and they are called “deputy inspectors”.
5. Recognized Special Inspection Procedures 5.1. Expansion anchors When the design engineer specifies anchors installed with special inspection, ICBO ES evaluation reports permit use of twice the allowable tension loads than anchors installed without special inspection. To meet the requirements of continuous inspection, the special inspector must verify that the installation is in accordance with the requirements
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of the approved plans, evaluation report and manufacturer’s installation instructions. This means that the special inspector must be present during all anchor installation, verifying the location of the anchor including any edge distance and spacing requirements, drill bit type and size, hole depth, hole cleaning technique (if applicable), anchor type, size, embedment and installation procedure. Proof loading of anchors is frequently specified, however this alone is not recognized as meeting special inspection requirements. Periodic (non-continuous) special inspection may be performed if specified on the project plans and approved by the municipal building official as provided for in the building codes. A program of post-installation visual inspection for location, size and embedment combined with torque or tension proof load testing is used in California hospital construction and could be considered as acceptable periodic inspection in other construction. A detailed written procedure was developed by the author working with the State of California Office of Statewide Health Planning and Development (OSHPD), the state agency responsible for approving plans and observing construction, and has been in use for over ten years. The document is named Interpretation of Regulations IR 26-6. The procedure includes visual observation and proof loading or torque testing of the installed anchors and covers typical Wedge, Sleeve and Drop-In anchors. Torque testing is applicable for Wedge and Sleeve type anchors only. Torque test values found to be typical of installation torque recommendations for a majority of these anchors are specified. The torque test value must be achieved within one-half turn of the nut to account for torque relaxation. Torque testing is not applicable for Drop-In type anchors. Proof loading of a small percentage combined with verification of proper plug setting of a larger percentage is used for Drop-In anchors. Proof loading is applicable to all these anchor types. Proof load levels are high enough to detect improper installation but low enough to prevent any movement of a properly installed anchor. The acceptance criterion is that anchors must show no visible signs of movement during or after the proof loading. Test frequency is 50% for both torque and proof load testing. The basic philosophy of this procedure is to verify proper installation (setting) of the anchors which can be done after installation for these types of anchors. If the anchor is properly installed, it should perform in accordance with the manufacturer's load ratings. Design parameters such as size, quantity, location and embedment can be visually determined after installation. The ICBO ES requirement for a length identification symbol on the exposed ends of anchors recognized for multiple embedments makes it possible for the special inspector to determine the embedment of these anchors after installation.
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5.2. Adhesive anchors ICBO ES evaluation reports require special inspection for all installations. The special inspector must verify that the installation is in accordance with the requirements of the project plans, evaluation report and manufacturer’s instructions. This means verifying the location of the anchor, any edge distance and spacing requirements, drill bit type and size, hole depth, hole cleaning technique (very important), anchor type, size, embedment and installation procedure including adhesive expiration date and proper dispensing. Proof loading alone is not recognized as meeting special inspection requirements. While proof loading may be specified as a supplement, visual inspection of the anchor installation must still be provided since it is not possible to verify embedment and important installation procedures such as hole cleaning, mixing and adhesive dispensing after the anchors have been installed. Periodic special inspection is possible, however there are no established procedures like the OSHPD procedures for expansion anchors. A reasonable approach to periodic inspection for adhesive anchors is: • Initial inspection of installation of the first anchors • Proof loading to the lesser of 50% of expected adhesive ultimate bond strength or 80% of steel yield strength. Proof loading should be done after a minimum curing period specified by the manufacturer. Anchors should have no visible indications of movement during or after the application of the proof load. • For highly redundant applications such as rebar doweling for shotcrete or slab doweling, proof load a minimum random sampling of 5% of the anchors. The engineer or architect should consider higher sampling rates for installations with less redundancy or that are considered more critical. • Subsequent inspection of installation when there is an change of personnel performing the installation or use of a different product. The following is an example of a periodic inspection procedure used on an actual project: • Initial inspection is required for each different subcontractor. The inspector will verify location and configuration of the anchors based on the project plans including any edge distance and spacing requirements, drill bit type and size used, hole depth, hole cleaning technique, anchor type, size, embedment and installation procedure including adhesive expiration date and proper dispensing. • Subsequent inspection of installation will be required only when there is a change of personnel doing the installation. The general contractor shall call for such inspection
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in the event of such a change, defined as any one or more persons drilling, preparing holes or installing anchors. • Initial inspection and proof load testing are required for the following. Anchor type and location, (drawing detail reference), test frequency and tension proof loads for each condition are: #4 Rebar Dowels at shotcrete walls (7/S1.2) - 5%/9000 lbs #4 Rebar Dowels at lower level ramps (5/S1.1) - No testing #5 Rebar Dowels at roof infill (2/S1.3) - 10%/14,000 lbs 3/4" Epoxy Rods at steel moment frames (1-7/S5.1) - 5%/20,000 lbs 1" Epoxy Rods at steel moment frames (9/S5.1) - 5%/28,000 lbs 1-1/4" Epoxy Rods at steel moment frames (8/S5.1) - 1 at each frame/50,000 lbs • Test loads are based on either 80% of steel yield or 50% of expected ultimate adhesive bond tension capacity, whichever is less, to avoid permanent distress. Anchors shall have no visible indications of movement during or after the application of the proof load.
6. Equipment and Calibration 6.1. Hydraulic Systems Hollow core rams with pressure gages are used when proof loading is part of the special inspection procedures. Each combination of ram and gage must be calibrated together as a system in a testing machine or other device that is traceable to the National Institute of Standards and Technology (NIST). It is not acceptable to calibrate the gage alone and calculate the load by multiplying gage pressure time the ram area. When testing anchor to ultimate failure, the load reactions from the bridging system should be at least two times the anchor embedment away from the anchor when testing anchors to ultimate failure. However when using the OSHPD procedure, it is permissible to have the reactions close to the anchor as long as the fixtures do not restrict the anchor from pulling out. The reason for this is that only the anchor installation is being verified using a relatively low proof load.
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6.2. Torque Wrenches Torque wrenches are used when torque testing is part of the special inspection procedures. They must be calibrated by a standard traceable to NIST.
6.3. Other Torque bridges, levers and other custom devices must be carefully conceived and calibrated to insure that the required proof load is applied to the anchors. Torque bridges are particularly problematic since the calibration procedures in testing machines using rigid connections may not be valid for anchors that move when loaded (are less rigid than the calibration set up).
7. Conclusion Good workmanship is important to any construction activity and in particular to the installation of post-installed concrete anchors. Special inspection and related testing procedures are mandated in the United States to provide assurance that anchor installations are done properly and to promote good workmanship for proprietary concrete anchor systems.
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STEEL CAPACITY OF HEADED STUDS LOADED IN SHEAR Neal S. Anderson, Donald F. Meinheit Wiss, Janney, Elstner Associates, Inc., Northbrook, Illinois USA
Abstract The Precast/Prestressed Concrete Institute (PCI) sponsored a comprehensive research program to assess the shear capacity of headed stud group anchorages. This program was initiated in response to new provisions introduced into the ACI 318 Building Code. These new provisions are based on an extensive experimental database consisting mostly of post-installed anchor tests. Tests of headed stud anchorage groups loaded in shear, as used in precast construction, are not extensively reported in the literature. The test program, conducted by Wiss, Janney, Elstner Associates, Inc. (WJE), examined headed stud connections loaded toward a free edge (de3), loaded toward a free edge (de3) near a corner, loaded parallel to one free edge (de1), loaded parallel to two free edges (de1 and de2), loaded away from a free edge (de4), and in-the-field of a member, such that edge distance was not a factor. The information reported herein addresses one aspect of the overall test program, the steel capacity failure mode.
1. Introduction Headed stud anchorages are used throughout the concrete industry in both cast-in-place and precast construction. Welding studs to steel plates provides an economical structural connection by allowing larger variability in construction dimensions and tolerances. Commonly, studs in precast members are 75 to 200 mm long and found almost always in multi-stud group connections. The load capacities of these connection types are affected by stud spacings, edge distances, and member depth or thickness. This research work1 focused on anchorages and geometric conditions typically used in precast / prestressed members. The research concentrated on diameter, embedment depth, and number of welded headed studs on connection plate configurations commonly used in precast applications; the study excluded post-installed anchors.
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Figure 1: PCI notation for anchorage geometry.1 In the United States, headed stud anchorage design usually followed procedures set forth in the PCI Handbook 2 or the nuclear structures code of ACI Committee 349.3 The Concrete Capacity Design (CCD) approach for anchorage to concrete has recently been approved as Chapter 23 of the upcoming 2002 version of the ACI 318 Building Code.4, 5 The work reported herein summarizes stud anchorage behavior when the connection is loaded in shear away from a free edge and in-the-field. These two conditions cause the ultimate capacity to be dictated by the stud steel. Referring to Figure 1, the overall research program tested anchorages toward, parallel, and away from a free edge. Several test series were repeated in both 152 and 406-mm thick specimens to evaluate member thickness effects. This paper is limited to defining the stud steel capacity in shear.
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2. Literature Review 2.1 Push-off testing The welded, headed stud received research attention in the late 1950s and through the 1960s in concrete slab-steel beam composite construction.6-13 Testing to evaluate composite beam behavior utilized a push-off specimen, consisting of a wide flange beam section sandwiched between two concrete slabs. Headed studs were welded to both flanges of the beam in some prescribed spacing pattern and embedded into a thin concrete slab, representing the composite deck slab. Early push-off test results provide the design basis for headed stud groups loaded in pure shear. Push-off test failures were sometimes due to stud steel shear. The push-off specimen having one transverse stud row (one y-row) is viewed to be analogous to a headed stud anchorage located in-the-field of a member, away from all edge influences, and is relevant to this paper. When stud groups with multiple longitudinal rows were tested using the push-off specimen, the test results become more difficult to interpret because large y-spacings reduce anchor group efficiency due to shear lag effects; these tests were thus excluded from our analysis. Significant findings are summarized below. 2.2 Embedment depth and steel capacity The reviewed data indicates 1.0AsFut (see Eq. (1) notation) is a good predictor for a steel failure when the effective embedment depth / stud diameter (hef/d) exceeds about 4.5. This is slightly greater than the value of 4.2 identified by Driscoll and Slutter.12 A value reduced for tensile yield (Fy = 0.9 Fut), where Fy is the offset tensile yield stress, is not as good, although more conservative. Likewise, AsFut is a much better capacity predictor than using shear yield (Fvy = Fut von Mises-Hencky yield criteria.
3 ), where Fvy is the shear yield stress per the Huber-
Work performed by Ollgaard, Slutter, and Fisher13 at Lehigh University produced a longstanding prediction equation, independent of failure mode, basing individual stud strength on stud area, concrete compressive strength, and elastic modulus of the concrete. Studs with an hef/d of 3.26 and different types of lightweight and normalweight concrete were used. Failures were noted in both stud steel shear or by a concrete mechanism. Their final prediction equation used in composite beam design was: Q u = 0.5A s f 'c E c ≤ A s Fut
(1)
where: Qu = Nominal shear stud connector strength embedded in a solid concrete slab (N) As = Effective cross-sectional area of a stud anchor (mm2) f’c = Cylinder compressive strength of concrete (MPa) [ = 0.8 x cube strength (fcc) ] Ec = Modulus of elasticity of concrete (MPa) Fut = Ultimate tensile strength of the stud steel (MPa)
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When headed studs have hef/d < 4.5, a concrete pryout failure mechanism can occur. Pryout failure is a concrete breakout failure mode not associated with edge distance but a function of the headed stud “stiffness.” Eq. (1) predicts this failure mode well. 2.3 Lightweight aggregate concrete Our analysis of reported steel shear failures for headed studs embedded in lightweight concrete indicates test strengths less than a 1.0AsFut prediction. Lightweight aggregate concrete apparently provides an embedment environment whereby the stud induces greater concrete crushing, producing more stud bending deformation resulting in larger overall relative slip between the stud and concrete. The increased concrete deformation produces more bending in the stud and attachment weld, thereby making the failure mode appear to be one of combined shear and tension stress on the stud at the tension stressed region of the weld. In our analysis, this higher bending deformation combined with shear deformation reduces the headed stud capacity to a value lower than 1.0AsFut. 2.4 Connection plate thickness Minimum plate thickness research is limited to work by Goble at Case Western Reserve University, 10 where he focused on the minimum flange thickness required in light-gage steel in order to fully develop a welded stud connection. Goble determined the minimum flange thickness required must be greater than 0.37d to develop the stud weld. 2.5 Minimum slab thickness Steel stud failures in the push-off specimens were achieved in some relatively “thin” slabs ranging in thickness from 102 to 178 mm. We have concluded that slab thickness is not a variable influencing a stud steel shear failure.
3. Experimental Program 3.1 Background The literature search and analysis of existing headed stud and cast-in-place anchor bolt data was used to formulate an experimental program, conducted in the WJE structural laboratory. The program tested 312 plate configurations in shear and 16 push-off type specimens. The tests were typically conducted in slabs measuring 1.2 x 3.0 m, or 1.5 x 1.5 m with either a 152 or 406-mm thickness. Push-off specimen tests simulated shear loading conditions when an embedded anchor group is adjacent to two side edges. A total of 14 different combinations of plate size, stud spacing, stud embedment depth, and stud diameter were evaluated. Plate thickness and concrete compressive strength were not testing variables in the program. Headed stud diameters of 12.7 and 15.9 mm were tested in this program. Both tension and double shear guillotine tests were performed on the studs, “in-air,” in support of this work. Test specimen concrete was a commercially available 34.5 MPa, normal-weight concrete containing 19-mm limestone coarse aggregate. All slabs were cast with the anchorages
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on the bottom of the form to ensure good concrete consolidation around the studs. Reinforcement, used only in the 152-mm thick slabs for handling purposes, was placed as not to interfere with the stud anchorage plates or provide anchorage confinement. All slabs were tested flat (horizontal) on the laboratory test floor. A specially fabricated channel pulling test rig had a welded shoe plate, which reacted on the back edge of the stud anchorage plate. This loading scheme was used to practically eliminate the eccentricity from the shear tests, which theoretically was one-half the plate thickness or 6.4 mm. All slab shear tests were instrumented with a load cell and two linear variable displacement transformers (LVDTs). 3.2 Individual stud tests For design, it is convenient to base the headed stud capacity on the tensile yield or strength values and relate the steel shear capacity to a fraction of either value. Steels used for manufacturing headed studs do not generally exhibit well defined yield point values. The headed stud steel shear strength was thus correlated to the measured stud tensile strength properties. WJE independently measured the geometry and tested the physical characteristics for the various steel heats in the project stock. Four different stud length and diameter configurations were received, manufactured from six different steel wire heats. Headed studs were tested for their tensile and shear strength properties, “in air.” The test fixture was similar to that suggested in the American Welding Society (AWS) D1.1-2000 structural welding code.14 Double shear, guillotine tests were conducted on the middle third of the shank to determine the steel shear strength. A universal testing machine was adapted to tension test headed studs welded to a square plate. Tension test results for the various steel heats showed ultimate strengths of 536 to 563 MPa for the 12.7 mm diameter and 538 MPa for the 15.9 mm diameter studs. Each stud exhibited a roundhouse load-deformation curve, requiring the 0.2% offset determination of yield strength. The measured stud yield strength was approximately 80% of the tensile strength; the strength of each steel heat exceeded the AWS D1.1-2000 requirements shown below in Table 1. AWS Type B studs are headed, bent, or of other configuration. They are an essential component in composite beam design and construction, and constitute those most used in precast concrete construction. Table 1 – Minimum mechanical property requirements for headed studs (from AWS D1.1-200014) Property Tensile Strength ( min. ) Yield strength ( 0.2% offset ) Elongation ( min. % in 2 in. ) Reduction of area ( min. )
Type A 420 MPa 340 MPa 17% 50%
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Type B 450 MPa 350 MPa 20% 50%
The double shear, guillotine tests were conducted with a three plate fixture. Double shear tests showed ultimate strengths of 328 to 381 MPa for the 12.7-mm diameter and 352 MPa for the 15.9-mm diameter studs. These tests imply the shear strength would be about 65% of the tensile strength. Earlier reported push-off test results exhibited a shear strength that is better than what these “in-air” material test results imply. 3.2 Tests loading away from a free edge (de4) Shear load on anchorages directed away from a free edge is not commonly encountered in precast construction. However, special framing conditions may dictate use of this type of connection. In this study, 23 tests were conducted with the shear force directed away from the back free edge (refer to Figure 1). Two series had single studs and the third series had two headed studs oriented in one y-row. The two single stud anchorage series examined both 12.7 and 15.9 mm diameter studs. The two stud anchorage groups used 12.7-mm diameter studs, spaced 4.5d apart. All three series were tested in 406-mm thick specimens; hef/d for these tests were 5.34 and 5.93. For the 12.7-mm diameter single stud connection, five de4 distances (4d to 12d) were evaluated with two tests performed per edge distance. Eight tests failed due to steel stud failure, and two failed at the stud weld. After failure, only minor concrete damage was observed. Concrete crushing at the stud front was accompanied by hairline, transverse cracks (normal to the shear load) propagating 50 to 100 mm each side of the stud center. Seven tests were conducted with 15.9-mm diameter studs. Edge distances evaluated were 4d, 8d, and 12d, with three tests conducted at 4d. All tests failed in a steel shear mode, with no weld failures in this series. The two-stud anchorage tests used 12.7-mm diameter studs at nominal 4d, 8d, and 12d edge distances with six total tests. Two tests exhibited weld failures in one or both studs, while the other four tests failed by stud shearing through both stud shanks. From these tests, it was concluded that the de4 edge distance variable is not a factor causing concrete breakout of stud anchorages in shear. 3.3 Tests in-the-field Some anchorages used in precast concrete members are located at such large edge distances that all concrete breakout capacities exceed the capacity developed by the individual studs failing in steel shearing; these test series are classified as in-the-field tests. Six series were conducted to test two and four anchor connections, with an emphasis on evaluating x- and y-row spacing and embedment depth effects on capacity. These test series had 24 total tests in 406-mm thick test slab specimens using 12.7-mm diameter studs. The first two tests in a series used studs with an effective embedment depth (hef) of 67.7 mm; longer studs with hef = 124 mm were used for the second two tests. Based on the push-off testing review, steel stud failure can be achieved in relatively thin slabs. As such, we conclude slab thickness influence on the anchorage’s ability to develop steel failure was viewed to have little effect, especially with the 12.7-mm diameter studs used in this study.
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For the 24 tests conducted in the six in-the-field test series, the test-to-predicted steel stud shear capacities ranged from 0.90 to 1.05, using AsFut as the calculation basis. When the short and long stud results are compared for all series, there is no discernable difference in the ultimate steel shear capacity due to stud length. For the x- or yspacings investigated, 4.5d and 7.0d in different combinations and loading orientations, stud spacing did not have a significant effect on the ultimate shear strength.
4. Steel Failure Analysis 4.1 Data review and proposed design equation Testing has shown that the steel stud failure mode typically occurred for back edge (de4) and in-the-field tests performed in 406-mm thick slabs. In all cases, steel failures were marked by two failure modes: a ductile, shear yielding-type stud failure, accompanied by appreciable lateral deformation, or a stud weld failure at the plate interface. When the corresponding failure area on the concrete slab specimen was observed, the still embedded studs had elliptical-shaped fracture surfaces with the major axis parallel to the load direction. The concrete in front of the stud was locally crushed, due to stud shank bearing; this concrete crushing also created a void (pocket) behind the stud. The second steel failure type experienced was the weld of the stud to the plate. Varying degrees of weld region porosity, confined within the shank diameter, marked the weld fracture surface. Weld porosity often ranged from 25 to 75% of the shank area. In this test program, the stud failures due to welding were a random occurrence, attributed to weld machine malfunctions and operator error. The steel shear failure database from this program is based on the de4 and in-the-field testing, and other tests (de1 and de3 testing), where the distance to a free edge was large enough to transition from a concrete to steel stud failure. Anchorage capacity governed by steel stud shank failure can be predicted by the number of studs in the group (n) times the stud area (As) multiplied by the ultimate stud tensile strength (Fut). Stud weld failures, however occurred at steel shear stresses less than the ultimate tensile strength. When the weld failure data are omitted from the population, the WJE database represents stud steel shear failures only; the number of tests is 80 with an average test-to-predicted ratio of 1.00. The sample standard deviation is 0.07, thus indicating the relative tightness of the data. A frequency distribution is plotted to the left in Figure 2. Given that the steel stud shank shear failures can be used as a database, the characteristic strength equation from a 5% fractile analysis (κ factor = 1.957) when the actual ultimate tensile strength is known, becomes: Vsteel = 0.86 nAsFut
(using actual Fut)
(2)
However, actual tensile strength is generally not used in design. An analysis using the minimum design ultimate strength of 450 MPa from Table 1, shows the average test-to-
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25 Prediction with
Frequency (or Number of Occurances)
Design Tensile Strength (450 MPa) 20
Actual Tensile Strength Mean = 1.00
15 Mean = 1.21
10
Shear Prediction Equation: Vs = nAsFut 5
0 0.80
1.00
1.20
1.40
1.60
Test-to-Predicted Capacity
Figure 2: Frequency distribution plot of steel stud failures. predicted ratio is 1.21 with a standard deviation of 0.10; the coefficient of variation is 7.8%. The 5% fractile characteristic prediction equation thus becomes: Vsteel = 1.0 nAsFut
(using design minimum Fut)
(3)
From a probability standpoint, this indicates with 90% confidence that over 95% of the failure loads occur at a value represented by Eq. (3) above. Using the minimum design strength of 450 MPa and WJE data, no tests had test-to-predicted ratios less than 1.0. 4.2 Steel failure behavior The reason there is an apparent steel shear strength increase when the stud is embedded in normal-weight concrete, versus “in air” results, is related to stud weld metallurgy. In the stud welding process, the shielded arc weld melts the stud end creating a shallow weld pool beneath the stud. The stud gun then plunges the stud into the molten weld pool, holding the stud in position while the liquid metal solidifies. Although this process occurs very quickly, a heat-affected zone (HAZ) is created in the weldment. AWS defines the HAZ as that portion of the welded metal where the mechanical properties or microstructure have been influenced by the welding heat. The heat developed tends to heat-treat or temper the steel such that locally the steel’s strength and hardness will increase. This transformation hardening process is dependent on the initial material temperature after arcing, the cooling rate, and the final (ambient) temperature.15 Figure 3 shows a stud weld cross section submitted for metallurgical work, which had failed in a concrete breakout mode. The numbers represent locations where Rockwell B
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Hardness tests were performed; the locations are shown in scale. The Rockwell B Hardness values were then converted to ultimate steel tensile strength.16 Table 2 shows the approximate tensile strength is greater in the HAZ than the nominal stud shank strength. The stud typically sheared off above the weld flash region in the parent stud material, corresponding to hardness locations 2, 9, and 14 in Figure 3. Tensile testing of this stud heat revealed an average ultimate tensile strength (Fut) of 538 MPa; on a relative basis, the indicated strength in the weld area is between 40 to 130 MPa higher. Table 2 - Rockwell B Hardness readings. Test Points 1 2 / 14 3 4 5 6 / 16 7 8 9 / 17 10 / 15 11 12 13 / 18
Rockwell B Hardness 90.1 93.7 91.8 95.1 101.5 99.5 89.9 85.0 87.7 102.3 106.5 92.3 82.1
Converted Fut (MPa) 606.8 667.4 634.3 703.3 841.2 795.0 603.3 544.7 588.1 856.7 986.0 630.2 515.1
Figure 3: Stud weld cross-section.1
5. Summary
Well-embedded studs are recommended to have a minimum effective embedmentto-diameter ratio (hef/d) of 4.5 to achieve steel stud failure. The minimum stud hef/d used in this study was 5.30, but the literature review justified a smaller hef/d. For steel failure in headed stud anchorage groups, this study shows the shear failure load is best predicted using the ultimate stud tensile strength. In normal weight concrete, Eq. (3) is recommended as the steel prediction equation (Vs) for headed studs with hef/d > 4.5. For lightweight concrete, see Reference 1 for background. Headed studs with an hef/d less than 4.5 will likely cause a pry out failure mode. The design ultimate capacity will be less than that predicted by 1.0AsFut. Again, Reference 1 provides a proposed characteristic equation for short, “stocky” studs.
6. References 1.
Anderson, N. S. and Meinheit, D. F., “Design Criteria for Headed Stud Groups in Shear: Part 1 – Steel Capacity and Back Edge Effects,” PCI Journal, V. 45, No. 5, September/October 2000, pp. 46-75.
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2. 3.
4.
5.
6.
7.
8.
9.
10. 11. 12.
13.
14. 15. 16.
PCI Design Handbook, Fifth Edition (PCI MNL 120-99), Precast/Prestressed Concrete Institute, Chicago, Illinois, 1999. ACI Committee 349, "Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-97)," ACI Manual of Concrete Practice, Part 4, American Concrete Institute, Farmington Hills, MI, 2000. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACI 318R-99), American Concrete Institute, Farmington Hills, MI, 1999. Fuchs, W., Eligehausen, R., and Breen, J. E., "Concrete Capacity Design (CCD) Approach for Fastening to Concrete," ACI Structural Journal, V. 92, No. 1, January-February 1995, pp. 73-94. Viest, I. M., “Investigation of Stud Shear Connectors for Composite Concrete and Steel T-Beams,” Journal of the American Concrete Institute, V. 27, No. 8, April 1956, pp. 875-891. Baldwin, Jr., J. W., “Composite Bridge Stringers – Final Report,” Report 69-4, Missouri Cooperative Highway Research Program, Missouri State Highway Department and University of Missouri-Columbia, May 1970, 62 p. Buttry, K. E., “Behavior of Stud Shear Connectors in Lightweight and NormalWeight Concrete,” Report 68-6, Missouri Cooperative Highway Research Program, Missouri State Highway Department and University of Missouri-Columbia, August 1965, 45 p. Dallam, L. N., “Push-Out Tests of Stud and Channel Shear Connectors in NormalWeight and Lightweight Concrete Slabs,” Bulletin Series No. 66, Engineering Experiment Station, University of Missouri-Columbia, April 1968, 76 p. Goble, G. G., “Shear Strength of Thin Flange Composite Specimens,” Engineering Journal, AISC, V. 5, No. 2, April 1968, pp. 62-65. Chinn, J., “Pushout Tests on Lightweight Composite Slabs,” AISC Engineering Journal, V. 2 No. 4, October 1965, pp. 129-134. Driscoll, G. C. and Slutter, R. G., “Research on Composite Design at Lehigh University,” Proceedings, AISC National Engineering Conference (May 11-12, 1961), Minneapolis, MN, 1961, pp. 18-24. Ollgaard, J. G., Slutter, R. G., and Fisher, J. W., “Shear Strength of Stud Connectors in Lightweight and Normal-Weight Concrete,” AISC Engineering Journal, V. 8, No. 2, April 1971, pp. 55-64. AWS, Structural Welding Code – Steel, AWS D1.1:2000, 17th Edition, American Welding Society, Miami, FL, 2000. Linnert, G. E., Welding Metallurgy – Carbon and Alloy Steels, Volume I – Fundamentals, Fourth Edition, American Welding Society, Miami, FL, 1994. ASTM, Standard Hardness Conversion Tables for Metals (Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Rockwell Superficial Hardness, Knoop Hardness, and Scleroscope Hardness) (ASTM E140-97e2), V. 3.01, American Society for Testing and Materials, West Conshohocken, PA, 1999.
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THE ANALYSIS OF FASTENER STRENGTH USING THE LIMIT STATE APPROACH Jindrich J. Melcher, Marcela Karmazínová Inst. of Metal and Timber Structures, Brno University of Technology, Czech Republic
Abstract In this paper a brief information about the results and statistical analysis of experimental research program directed to investigation of actual behaviour of the torque-controlled expansion POLYMAT anchors will be presented. Especially the problems of failure mechanism, ultimate and design strength, the influence of edge distance and anchor diameter will be discussed. Based on the test results and theoretical approaches the design formulas have been verified.
1. Introduction The effectiveness and accurate placement together with the new easy techniques and technology are the most important advantages of the post-installed anchor systems increasingly used for the connection of other structural or constructional parts to hardened concrete and masonry supporting structures. In the new construction as well as in repair and strengthening works the anchor behaviour can be rather complicated considering the influence of concentrated loads, their different direction and especially the type of the failure mode depending on the way of the load transfer from anchor body into the concrete or masonry base. Thus the experimental verification together with statistical analysis of appropriate results should be an authority for the theoretical modeling and practical design procedures of the fastening systems. Recently a wide range of post-installed anchor systems have been developed. Wellknown producers in this area are HILTI, FISCHER, UPAT and SPIT, for example. The application of fastening systems to reinforced concrete and masonry, in general, is based on experimental and theoretical investigations and continuous work of international technical groups and committees - see [ 1 ], for example.
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In this paper a brief information about analysis of results of the experimental research program directed to problems of actual behaviour of torque-controlled expansion anchors produced in our country will be presented.
2. Basic information on experimental research program During 1998 - 2000 in the testing laboratory of the Institute of Metal and Timber Structures of the Civil Engineering Faculty at Brno University of Technology the experimental research program [ 2 ], [ 3 ] directed to the analysis of actual behaviour and design strength of expansion anchors to hardened concrete under tension loading has been conducted. The goal of this investigation was concentrated to the domestic torque-controlled fastenings of POLYMAT type and its comparison with results derived for other similar types of expansion anchors. Together 169 specimens under static action and 13 specimens under dynamic action have been tested. For the anchor bolts - see Fig. 1 - the steel grade of 5.6 and 8.8 (with nominal values of the bolt ultimate tensile strength fub = 500 MPa and fub = 800 MPa, respectively) and diameters of d = 8 mm, 12 mm and 16 mm have been used. The external diameter of anchor sleeve was D = 12 mm, 18 mm and 24 mm. The cube concrete strength of the specimen bodies was in the range of fcc = 22 MPa to fcc = 76 MPa. The effective anchor depth hef was in the range of 30 mm to 85 mm . Fig. 1 Expansion Anchor Scheme
3. Analysis of expansion anchor strength parameters In this paper the test results of specimens under static tension action will be discussed. During the test process the failure mechanism and ultimate tensile strength of the tested specimens have been verified. Depending on basic parameters of fastening arrangement different types of failure mode can be established. Especially the anchor depth and concrete strength together with the bolt dimension and its strength are for the anchor behaviour decisive. Also the size of the edge distance influences significantly the fastening strength. Mainly the concrete-cone failure occurred, in some cases also the anchor extraction has been found. For the anchors placed closely to the edge of the test body the edge break out failure was typical mode appropriate to ultimate strength. In the frame of the information presented here the results covering the set of concretecone failures and edge break out failures are presented (altogether 76 and 31 test,
213
respectively). In Fig. 2 some typical examples of corresponding failure modes are shown. Additionally in 31 cases the bolt extraction and also in 31 cases the simple bolt rupture occurred.
Fig. 2 Examples of concrete-cone failure mode For the elaboration of the test results the calculation models based on large sets of test results according to published results - see Ref. [ 1 ], for example - will be used. For subsequent analysis directed to characteristic and design values of fastener strength the procedure based on the specified European document [ 4 ], [ 5 ] for design assisted by testing can be used. Concrete-cone failure mode According to the so called ψ-method [ 1 ] the mean value of the fastener strength for concrete-cone failure mode can be expressed by the format of Nu,m = k1 . hef1,5 . fcc0,5 ,
(1)
where fcc is the cube concrete strength, hef is the effective anchor depth and k1 = 13,5 is a coefficient derived from tests. In [ 6 ], [ 2 ] the corresponding general expression is presented in the form of Nu,m = k2 . hef2 . fcc0,5 .
(2)
Based on the format of Eq. (1) and using the regression analysis of our test results the mean value of expansion anchor strength is given by Nu,m = 17 . hef1,5 . fcc0,5 and the appropriate value of characteristic strength is
214
(3)
Nu,k = 10 . hef1,5 . fcc0,5
.
(4)
Similarly for the format of Eq. (2) the corresponding mean and characteristic anchor strengths are , (5) Nu,m = 2,2 . hef2 . fcc0,5 Nu,k = 1,3 . hef2 . fcc0,5
(6)
150
Nu,test [kN]
Nu,test [kN]
150
.
100
50
100
50
0
0 0
50
100
0
150
50
Fig. 3 Relationship according to Eq. (3)
150
Fig. 4 Relationship according to Eq. (5)
20
Frequency [%]
20
Frequency [%]
100
Nu,m [k N]
Nu,m [k N]
15
10
5
15
10
5
2
1,7
1,4
1,1
0,8
2
1,7
1,4
1,1
0,8
0,5
0,2
0,5
0,2
0 0
Nu,test / Nu,m
Nu,test / Nu,m
Fig. 5 Distribution based on Eq. (3) Fig. 6 Distribution based on Eq. (5) In Fig. 3 and Fig. 4 the test results and regression relationship between experimental (Nu,test) and theoretical (Nu,m ) strength values according to Eq. (3) and Eq. (5) are
215
presented. The corresponding distributions for the ratio of Nu,test / Nu,m are shown in Fig. 5 and Fig. 6. Using the procedure for design assisted by testing [ 4 ] the corresponding formulas for design strength are (7)
NRd = 0,79 . hef2 . fcc0,5 , respectively.
(8)
100
100
80
80
60
60
Nu [kN]
Nu [kN]
and
NRd = 6,50 . hef1,5 . fcc0,5
40
40
20
20
0
0 0
20
40
60
80
0
100
20
40
60
80
100
h ef [m m ]
h ef [m m ] TESTS
TES TS
MEA N V A LUE ac . to ( 3)
MEA N V A L UE a c . to ( 5 )
CHA R. V A LUE ac . to ( 4)
CHA R. V A L UE a c . to ( 6 )
DESIGN V A LUE ac . to ( 7)
DES IG N V A L UE a c . to ( 8 )
Fig. 7
Fig. 8
The test results compared to the course of the mean, characteristic and design strengths are plotted as a function of effective anchor depth hef in Fig. 7 (for the relationships going out of the Eq. 3) and Fig. 8 (for the relationships going out of the Eq. 5). The values elaborated here are standardized for the concrete cube strength taken as fcc = 25 MPa. The influence of edge distance - edge break out failure mode
216
According to [ 1 ] for the anchor edge distance e ≥ 2 hef the concrete-cone failure mode is for the fastening strength decisive. Thus analyzing the influence of the edge distance the mean values of anchor strength according to Eq. (3) to the test results in the range of e ≤ 2 hef have been compared. The corresponding mean value of the strength of the anchor placed in the edge distance of "e" can be expressed by Nue,m = 0,5 (e / hef ) Nu,m .
(9)
Using the Eq. (5) the appropriate results are practically identical.
Nu,test / Nu,m
1,5
1
0,5
0 0,5
1
1,5
2
2,5
3
3,5
e / hef TESTS
Fig. 9
THEORY - MEAN VALUE ac.to (9)
The influence of the anchor edge distance
The corresponding characteristic values based on test results and Eq. (9) are given by Nue,k = 0,6 Nue,m .
(10)
The influence of anchor diameter The effective anchor depth is the decisive parameter for the value of fastening strength. Based on the analysis of test results also the influence of external sleeve diameter "D" can be verified.
217
2
Nu,test / N u,m
1,5
1
0,5
0 0,15
0,2
0,25
0,3
0,35
0,4
0,45
D / h ef TE S TS
Fig. 10
THE ORY - M E A N V A LUE ac .to (11)
Test elaboration based on Eq. (3)
2
Nu,test / N u,m
1,5
1
0,5
0 0,15
0,2
0,25
0,3
0,35
0,4
D / h ef TE S TS
THE ORY - M E A N V A LUE ac .to (12)
Fig. 11 Test elaboration based on Eq. (5)
218
0,45
Analyzing the relationship between the fastening strength and ratio of D / hef the main value of expansion anchor strength can be expressed by NuD,m = (0,80 + 0,62 D / hef ) . Nu,m
(11)
for Nu,m according to Eq. (3) and by NuD,m = (0,28 + 2,56 D / hef ) . Nu,m
(12)
for Nu,m according to Eq. (5) . The corresponding results plotted against the test strenth values are plotted in Fig. 10 and in Fig. 11.
4. Conclusions For the POLYMAT type of torque-controlled expansion anchors the analysis of basic strength parameters has been presented in consideration of experimental research program and corresponding theoretical models. The statistical elaboration of test results is based on limit state design approach and on procedures derived for design assisted by testing. Especially the anchor strength, the influence of edge distance and anchor sleeve diameter have been analyzed. Acknowledgements : This paper has been elaborated under gratefully acknowledged support of projects MSM 261100007 and GAČR reg. No. 103/00/0758.
References 1.
Eligehausen, R. (Editorial Chairman), 'Fastenings to Reinfoced Concrete and Masonry Structures', Bulletin d'information No. 206, CEB, Lausanne, 1991. 2. Karmazínová, M., 'Some Problems of Design of Expansion Anchors', Ph.D. Theses, Brno University of Technology, 1999. 3. Karmazínová,M.,'Loading Tests of Expansion Anchors', In: Proceedings of Seminar "Steel and Timber Structures - Brno '99", VUT - FAST, Brno, 1999, pp. 93 - 96. 4. ENV 1993-1-1:1992/A2:1998, Annex Z, 'Determination of Design Resistance from Tests', CEN, Brussels, 1998. 5. Karmazínová,M. - Melcher,J., 'To the Problem of Design Assisted by Testing', Proceedings of 19th Czech and Slovak Conference "Steel Structures and Bridges": held in Štrbské Pleso, C-PRESS Publisher, Košice, 2000, pp. 39 - 42. 6. VN 73 2615:1994, 'Directions for anchoring of steel structures', Firm Specification, VÍTKOVICE, 1994. 7. Karmazínová,M., 'To the Problem of Load-carrying Capacity of Expansion Anchors', In: Proceedings of the XI. International Conference of the Brno University of Technology, Part No. 7, VUT - FAST, Brno, 1999, pp. 91 - 94.
219
BEHAVIOR OF SHEAR ANCHORS IN CONCRETE: STATISTICAL ANALYSIS AND DESIGN RECOMMENDATIONS Hakki Muratli*, Richard E. Klingner**, and Herman L. Graves, III*** * Dallas, Texas, USA; former, The University of Texas at Austin, TX, USA. ** Dept. of Civil Engineering, The University of Texas at Austin, TX, USA. *** U.S. Nuclear Regulatory Commission, Washington, D.C., USA.
Abstract The overall objective of this paper is to evaluate three different procedures for predicting the concrete breakout capacity of shear anchors under static and dynamic loading, and in uncracked and cracked concrete. A data base for shear anchors was developed, evaluated, and placed in the public domain. Observed capacities of shear anchors failing by concrete breakout were compared with the predictions of three methods: the 45-Degree Cone Method; the CC Method, and a variation of the CC Method, obtained by regression analysis. Each predictive method was then evaluated using Monte Carlo analyses to predict the probability of failure by concrete breakout, using the design framework of ACI 349-90 [1].
1. Introduction The objective of this research was to provide the US Nuclear Regulatory Commission (NRC) with a comprehensive document that could be used to establish regulatory positions regarding fastening to concrete. Shear behavior of anchors under static and dynamic loading in uncracked and cracked concrete, and for cast-in-place, undercut, sleeve and expansion anchors, is evaluated using the design framework of ACI 349-90 [1], and three possible predictive equations for concrete breakout: 1) the CC Method; 2) the 45-Degree Cone Method; and 3) a variation on the CC Method, obtained by regression analysis. Available test data are evaluated and organized by failure mode, using descriptions and photographs presented by the original researchers. Each set of design provisions is evaluated [2] based on the criteria that:
220
1) An ideal design method should give ratios of observed to predicted capacity showing no systematic error (that is, no variation in ratios with changes in embedment depth), high precision (that is, little scatter of data). 2) An ideal design method should have acceptably low probabilities of failure in the overall design framework in which it is to be used.
2. Background General information on anchor types and behavior is given in CEB [3]. The most widely known procedures for predicting shear breakout capacity are the CC Method and the 45-Degree Cone Method, described here. A variation on the CC Method, obtained by regression analysis, is described later. Shear Breakout Capacity by Concrete Capacity Method (CC Method) The CC Method [4] computes mean shear breakout capacity as: 0.2
0.5 Vno = 13 (d o f c ) l c1.5 1 do
lb
(1a)
N
(1b)
0.2
0.5 Vno = 1.0 (d o f cc ) l c1.5 1 do
where: do = l = = = fc c1
outside diameter of anchor (in. in US units, mm in SI units); activated load-bearing length of anchors, ≤ 8do; hef for anchors with a constant overall stiffness; 2do for torque-controlled expansion anchors with spacing sleeve separated from the expansion sleeve; = specified compressive strength of concrete; and = edge distance in the direction of load.
The above formula is for the mean rather than 5% fractile concrete breakout capacity in uncracked concrete, and is valid for a member with a thickness of at least 1.4 hef. For anchors in a thin structural member, or a narrow member, or affected by adjacent anchors, breakout capacity must be reduced based on the idealized model of a halfpyramid measuring 1.5c1 by 3c1 (Figure 1).
221
35 º
35 º
c1
1.5c1
Figure 1
3c1
3c1
FromTest Results
Simplified Model
Idealized breakout model for a single shear anchor, CC Method
In such cases,
Vn =
Av ψ 4ψ 5ψ 6 Vno A vo
(2)
where: Av = actual projected area at the side of concrete member; Avo = projected area of one fastener in thick member without influence of spacing and member width, idealizing the shape of the projected fracture cone as a half-pyramid with side length of 1.5c1 and 3c1; ψ4 = modification factor for shear strength to account for fastener groups that are loaded eccentrically; ψ5 = modification factor to consider the disturbance of symmetric stress distribution caused by a corner; = 1, if c2 ≥ 1.5 c1 =
0.7 + 0.3
c2 , if c2 ≤ 1.5 c1; 1.5c1
where: c1 = edge distance in loading direction; = greater of (c2,max/1.5, h/1.5) for anchors in a thin and narrow member with c2,max < 1.5c1 and h < 1.5c1; where: h = thickness of concrete member; c2 = edge distance perpendicular to loading direction. ψ6 = modification factor for shear strength to account for absence or control of cracking.
222
Shear Breakout Capacity by 45-Degree Cone Method By the 45-Degree Cone Method, a tensile stress of 4 f c′ is assumed to act on the surface of a half-cone with an inclination of 45 degrees to the concrete surface (Figure 2).
45 º
Figure 2
Breakout body assumed by 45-Degree Cone Method
Equilibrium in the direction of the applied shear leads to:
Vno = 2π f c′ c12
lb
(3a)
Vno = 0.48 f c′ c12 N
(3b)
where c1 is the edge distance in loading direction. If the depth of the concrete member is smaller than the edge distance, or the spacing of anchors is smaller than 2c1, or the width of the concrete member is smaller than 2c1, the shear breakout capacity is modified as follows:
Vn =
Av Vno A vo
(4)
where: Av = actual projected area of semi-cone on the side of concrete member; Avo = projected area of one fastener in thick member without influence of spacing, and member width, idealizing the shape of projected fracture cone as a halfcone with a diameter of c1, so that AVo = (π/2) c12 (Figure 3).
223
2 πθ c AV = π − + sin θ 1 2 180
45 º
h c1
θ = 2 cos −1
h
Figure 3
Projected areas for shear anchors, 45-Degree Cone Method
Effects of Dynamic Shear Loading and Cracks on Shear Breakout Capacity In this research, predicted shear breakout capacities under static loading are proposed to be multiplied by a dynamic factor equal to 1.20 [5]. Predicted shear breakout capacities in uncracked concrete are proposed to be multiplied by a crack factor equal to 0.714 for cases involving cracked concrete.
3. Test data for shear anchors in concrete An extensive search was conducted for data on single and multiple shear anchors, with and without edge effects, group effects, or cracks, and including dynamic as well as static loading: a)
Only tests with concrete breakout failure were included.
b) Only tests on cast-in-place, expansion and undercut anchors were included. c)
Tests are from the US and Europe. Some static shear tests in uncracked concrete from Germany are not included, because the mean ratios of observed to predicted capacities were about 0.859, about 20% lower than the rest of the data in this category (1.075), and the coefficient of variation was about 0.4, much higher than for the rest of the data. This difference could be explained by unreported information on the thickness of the concrete specimens for those tests.
d) Tests were sorted according to type of loading (static or dynamic) and condition of concrete before the test (cracked or uncracked). Only limited tests were available with dynamic loading. e)
Most tests on multiple-anchor connections were excluded, because their resistance mechanisms and failure sequence are complex. Because it is normally not possible to measure the tensile and shear failure loads taken by each anchor, nor the friction between baseplate and concrete, it is difficult to decide how anchors share axial and shear load. As a consequence, it is difficult or impossible to distinguish those tests showing concrete breakout failure.
224
f)
The confining effect of baseplate and presence of reinforcement affect the type of failure and concrete breakout capacity. The compression on concrete from the baseplate around some anchors usually increases the concrete breakout capacity. In addition, reinforcement may also confine the concrete after cracking. Since these effects are not fully understood, tests with reinforcement in concrete were not included.
g) Out-of-plane eccentric loading is another factor that affects load-carrying mechanism and type of failure. The eccentricity changes the type and magnitude of the load taken by each anchor, and the friction between baseplate and concrete. Because these points are still under investigation, tests with out-of-plane eccentricity were not included. Shear Breakout Data for Single and Double Anchors in Uncracked Concrete under Static Loading Data in this category come from Klingner [6] (85 tests), Drillco [7] (5 tests), Hallowell [5] (5 tests), and Hilti1 (154 tests). Twenty-seven of these tests are in lightweight concrete, and the rest, in normal-weight concrete. The Klingner [6] and Hallowell [5] tests are on cast-in-place anchors; the Drillco [7] and Hilti1 tests are on undercut and expansion anchors respectively. Figure 4 shows the variation of ratio of observed to predicted capacity as a function of edge distance c1, based on the CC Method [4]. A linear regression is fitted to the data. In general, the ratio of observed to predicted capacity decreases with increasing edge distance. This systematic error suggests that the exponent applied to the edge distance c1 in the current equation is slightly high. The negative slope is also influenced by the low ratios for a few tests with edge distances greater than 250 mm.
225
Static Shear Loading - Single and Double Anchors Uncracked Concrete - CC Method 2.50 Mean= 1.075 COV = 0.215
Vobs/Vpred
2.00
y=-0.0006x+1.1606 1.50 1.00 0.50 0.00 0
50
100
150
200
250
300
350
Edge Distance (mm)
Figure 4
Ratios of observed to predicted concrete shear breakout capacities, uncracked concrete, CC Method
Figure 5 shows the same ratios for the 45-Degree Cone Method. Mean values in the two figures are almost the same, but the coefficient of variation is higher for the 45-Degree Cone Method. The negative slope of the best-fit line for the 45-Degree Cone Method is quite high, indicating significant systematic error. The outliers with mean values higher than 1.50 correspond to tests from Drillco [7], in which the tensile strength of concrete was higher than the value implied in the equations of the CC Method and the 45-Degree Cone Method. Similar information is presented in Reference 2 for dynamic loading, cracked concrete, and post-installed versus cast-in-place anchors.
226
Static Shear Loading - Single and Double Anchors Uncracked Concrete - 45-Degree Cone Method
Vobs/Vpred
3.00 2.50
Mean= 1.073 COV = 0.339
2.00
y=-0.003x+1.5111
1.50 1.00 0.50 0.00 0
50
100
150
200
250
300
350
Edge Distance (mm)
Figure 5
Ratios of observed to predicted concrete shear breakout capacities, uncracked concrete, 45-Degree Cone Method
Development of an Alternative Method based on Regression Analysis Because significant systematic error was observed in the preceding graphs of the ratios of observed to predicted shear breakout capacities as a function of edge distance, multivariate regression analysis was used with the data for single anchors in uncracked concrete, static loading, to attempt to improve the CC Method in this regard. Considering all data categories and slightly modifying the mathematically optimum values for design convenience, the following values were obtained for the parameters: α = 2.7; m1 = 0.1; m2 = 0.3; m3 = 0.5; and m4 = 1.4: Vno = 2.7 ⋅ l 0.1 ⋅ d o
0 .3
⋅ fcc
0.5
⋅ c1
1.4
(5)
There is little difference between the alternative method as optimized using regression analysis, and the CC Method, except with respect to the exponent of the edge distance, c1. The regression formula has significantly lower systematic error than the CC Method, suggesting that the CC Method’s exponent of 1.5 should be reduced to 1.4. Similar results are obtained for the other conditions discussed above.
4. Probabilities of failure associated with each breakout formula To evaluate the accuracy and suitability of the CC Method, the 45-Degree Cone Method and the alternative method as design approaches, the probabilities of concrete breakout failure under known loads and independent of load were computed. The probabilistic
227
evaluation is carried out assuming the ductile design framework and current load and understrength factors of ACI 349-90, Appendix B [1] (load factor = 1.7; φ = 0.85 for steel; φ = 0.65 for concrete). Assuming the exact forms of load and capacity distributions, the probabilities of failure are computed using FORM (First Order Reliability) analysis. These calculations are based on a normal distribution for all variables. The basic procedure is similar to that reported in Farrow [8, 9]. The results of these probabilistic analysis are presented in Table 1 and Table 2. Probabilities of failure are consistent with observations made earlier based on evaluation of ratios of observed to predicted shear breakout capacities. The CC Method, with acceptable mean ratios and low systematic error, has lower probabilities of failure under known loads, and lower probabilities of brittle failure independent of load, than the 45Degree Cone Method, when both are used in the ductile design framework of ACI 34990, Appendix B [1]. Table 1
Probabilities of failure under known loads for different categories of shear anchors, ductile design approach CC METHOD
ANCHOR CATEGORY single and double anchors, uncracked concrete, static shear loading single anchors, cracked concrete, static shear loading single anchors, uncracked concrete, dynamic shear loading single anchors, cracked concrete, dynamic shear loading
45-Degree CONE REGRESSION METHOD METHOD Probability Probability β β of Failure of Failure
Probability of Failure
β
2.665E-04
3.55
1.138E-02
2.28
1.56E-04
3.77
3.275E-04
3.48
3.885E-04
3.42
--
--
7.567E-05
5.10
7.554E-05
5.39
--
--
8.620E-05
4.25
9.130E-05
4.16
--
--
228
Table 2
Probabilities of brittle failure independent of load for different categories of shear anchors, ductile design approach CC METHOD
ANCHOR CATEGORY Probability of Brittle Failure single and double anchors, uncracked concrete, static 0.189 shear loading single anchors, cracked concrete, static shear 0.290 loading single anchors, uncracked concrete, dynamic shear 0.034 loading single anchors, cracked concrete, dynamic shear 0.011 loading
β
45-Degree CONE REGRESSION METHOD METHOD Probability Probability of Brittle of Brittle β β Failure Failure
0.88
0.270
0.61
0.271
0.61
0.55
0.402
0.25
--
--
1.83
0.003
2.70
--
--
2.29
0.023
2.00
--
--
5. Conclusions 1) The ductile design approach in the draft proposal for ACI 349 [1] (including the CC Method) is safe and efficient for shear fasteners in concrete. 2) The CC Method is more reliable than the 45-Degree Cone Method as a design tool for shear breakout. It can be safely used for design of cast-in-place and postinstalled anchors for edge distances up to 250 mm. 3) The systematic error of the CC Method for shear breakout could be decreased by changing the exponent of edge distance from 1.5 to 1.4. 4) For dynamic loading, the capacity of cast-in-place anchors increases by 20% compared to static loading. 6) The concrete breakout capacity of post-installed anchors is 10% lower than that of cast-in-place anchors. Therefore, predicted breakout capacity should be based on anchor type. This can be done by adjusting the mean normalization constant k to 0.97 for the basic uncracked concrete case for post-installed anchors.
229
6. Acknowledgement and disclaimer This paper presents partial results of a research program supported by U.S. Nuclear Regulatory Commission (NRC) under Contract No. NRC-04-96-059. The technical contact is Herman L. Graves, III. Any conclusions expressed in this paper are those of the authors, and are not to be considered NRC policy or recommendations.
7. References 1) ACI 349 1990, ”Code Requirements for Nuclear Safety Related Concrete Structures,” American Concrete Institute, Detroit, Michigan, 1990. 2) Muratli, Hakki, “Behavior of Shear Anchors in Concrete: Statistical Analysis and Design Recommendations,” M.S. Thesis, The University of Texas at Austin, May 1998. 3) Comite’ Euro-International du Beton, Fastening to Reinforced Concrete and Masonry Structures: State-of-the-Art-Report, bulletin D’Information Nos.206 and 207, August 1991. 4) Fuchs, Werner, Eligehausen, Rolf, and Breen, John E., “Concrete Capacity Design (CCD) Approach for Fastening to Concrete,” Journal of the American Concrete Institute, Vol. 92, No. 1, January-February 1995, pp. 73-94. 5) Hallowell, Jennifer, “Tensile and Shear Behavior of Anchors in Uncracked and Cracked Concrete Under Static and Dynamic Loading,” M.S. Thesis, The University of Texas at Austin, December 1996. 6) Klingner, R. E. and Mendonca, J. A., “Shear Capacity of Short Anchor Bolts and Welded Studs: A Literature Review,” Journal of the American Concrete Institute, Proceedings Vol. 79, No. 5, September-October 1982, pp. 339-349. 7) Arkansas Nuclear One Maxibolt Anchor Bolt Test Program, Entergy Operations, Inc. Arkansas Nuclear One Steam Electric Station, MCS Design, May 14, 1992. 8) Farrow, C. Ben and Klingner, R. E., “Tensile Capacity of Anchors with Partial or Overlapping Failure Surfaces: Evaluation of Existing Formulas on an LRFD Basis,” ACI Structures Journal, Vol. 92, No. 6, November-December 1995, pp. 698710. 9) Farrow, C. Ben, Frigui, Imed and Klingner, R. E., “Tensile Capacity of Single Anchors in Concrete: Evaluation of Existing Formulas on an LRFD Basis,” ACI Structures Journal, Vol. 93, No. 1, January-February 1996.
1
Personal communication, Peter Pusill-Wachtsmuth, Hilti AG, Schaan, Liechtenstein, 1997.
230
STUDY ON SHEAR TRANSFER OF JOINT STEEL BAR AND CONCRETE SHEAR KEY IN CONCRETE CONNECTIONS Katsuhiko Nakano* and Yasuhiro Matsuzaki* *Dept. of Architecture, Faculty of Engineering, Science University of Tokyo, Japan
Abstract Shear transfer across a definite interface must frequently be considered in the design of precast concrete connections. As the following various resistances in the effecting shear transfer strength are given: (1) Dowel action, (2) Shear-key, (3) Friction with axial force, (4) Adherence on the concrete surface. The purpose of this paper is to reveal the compound effects of the various resistance elements. Basic experiments on the interface shear transfer at the precast joint faces ware carried out. Ten panel type specimens with the same dimensions were tested. As a conclusion, the relation of the shear transfer mechanism and shear displacement behaviour in concrete connection is clarified. And the evaluation equation of the shear transfer strength with consideration to the shear displacement conformity is proposed.
1. Introduction General design method for the precast-concrete building structures has not yet established, especially for the details of connections. The behaviour of precast concrete structures subjected to earthquakes may be greatly influenced by the resistances of various elements within precast-concrete connections. The factors influencing shear transfer strength are considered as following: (1) Characteristics of the shear interface, (2) Characteristics of the reinforcement, (3) Mechanical properties of the concrete, (4) Direct stress acting parallel and transverse to the shear interface. The shear resistances in concrete connections are assumed as following: (1) Dowel action of joint bars, (2) Direct shear resistance of concrete shear-key, (3) Friction with axial compressive force, (4) Adherence of the concrete surface. The concrete shear-key, friction and adherence show brittle failure, and the shear dis-
231
placement is tiny. Maximum dowel strength is associated with a certain amount of shear displacement along the interface. In design of shear transfer elements, deformation characteristics are also very important as well as the strength. We are based on the stress transfer mechanism in concrete connections, and think that it is necessary to systematize the designing method by the theoretical model. This research aims at the following: (1) Extraction and modelling of the shear transfer elements in the concrete connection, (2) Proposal of the additional method of the various resistances satisfied with the condition of the shear displacement, (3) Verification by the structural experiment.
2. Test Program 2.1 Specimens The list of specimen parameters is shown in Table 1. And the dimensions of specimens are shown Fig. 1. The specimens used for investigation of the shear transfer mechanism consisted of two concrete blocks. The dimensions and reinforcement details of all the specimens were identical: the width of 900 mm, the height of 1400 mm, the thickness of 225 mm with an interface of 860 mm × 225 mm at the height of 700mm from the base. The following parameters are investigated: 1. The kind of shear resistance in concrete connections [friction with axial force, dowel bar, shear-key, and compound of various elements] 2. Direct force acting transverse to the concrete interface [N = 0, 1500, -220 kN]. Combinations of parameters for all 10 specimens are given in Table 1. The joint steel bars are used 2-D22 ( φ = 22 mm, deformed bar). Table 1 List of specimen parameters No. Axial force Shear resistance (kN) Friction Dowel Sear-key RF01 Variable*1 Yes No No RF02 0 No No Yes RF03 1500 Yes No Yes RF04 0 No Yes No RF05 1500 Yes Yes No RF06 -220 No Yes No RF07 Variable*2 Yes Yes*3 No RF08 0 No Yes Yes RF09 1500 Yes Yes Yes RF10 -220 No Yes Yes
400 Shear -key
300
Joint bar
300 400
90
*1) 250,500,750,1000,1250,1500,1750,2000kN *2) positive loading: -220kN, Negative loading: 100, 750, 1500kN *3) High yield stress of joint bars
30
30
Fig. 1 Dimensions of specimens
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The shear-key is used in the central part of a concrete interface, and the height is hck = 30 mm, the length is Lck = 240 mm and the width is tck = 225 mm. Since the form ratio of a shear-key ( hck / Lck ) is 1/8, the shear-key shows compressive failure mode. The lower part in the Fig. 1 was cast first using steel form at the interface. The upper part was five days after then. The steel form was removed before connecting two concrete blocks and the interface was filled with grease. Thus, adherence of concrete surfaces was eliminated and shear force could be transferred by means of dowel bars, concrete shear-key, and friction with the axial force. Mechanical properties of concrete and joint steel bar are shown in Table 2. Table 2 Mechanical properties of materials Steel bar Ec Concrete σB ( D22 ) (kN/mm2) (N/mm2) Upper 31.1 281 Normal Lower 66.7 350 High Average 48.9 316
σy (N/mm2) 380 735
Es (kN/mm2) 180 198
σu (N/mm2) 592 897
Shear displacement: δ sd= ( δ sd1+ δ sd2 )/2
Axial force
15 15
+Q
-Q
δ sd1
30 30
δ sd2 Loading Joint bar
Specimen Fig. 2 Loading Apparatus
30 15 15
Strain gauges
Fig. 3 Measuring devices for dowel bars
2.2 Testing Arrangements The concrete interfaces of specimens were subjected to cyclic shear forces and constant axial forces, using the loading apparatus shown in Fig. 2. The loading direction was reversed at the horizontal displacement amplitudes of 3, 6, 9 mm, which was measured at the height of 30 mm from the concrete interface. The location of displacement gauges and strain gauges of dowel bars are shown in Fig. 3.
3. Test Results 3.1 Friction with Axial force The typical hysteresis relation of the shear force (Q) of the friction with axial force and the shear displacement ( δ sd) are shown in Fig. 4, and the relation of the frictional shear
233
force (Qf) and the axial force (N) are shown in Fig. 5. RF01 has been carried out to investigate the relation of friction and compressive axial force. It was measured on the compressive axial force level of eight stages [N = 250, 500, 750, 1000, 1250, 1500, 1750, 2000 kN] using the same specimen. The friction with axial force can roughly be evaluated from the hysteresis loop as the following: (1) Qf can be estimated from the first positive maximum strengths of the specimens under different axial force levels, and the force is proportional to the axial force. (2) The friction with axial force under cyclic loading may be taken at the flat level in the reloading to the other direction until the original displacement. 3.2 Dowel Action The typical hysteresis relation of the shear force (Q) of a dowel action and the shear displacement ( δ sd) are shown in Fig. 6. RF04 was subjected to shear force and without axial force. Thus, the shear force could be transferred only by means of dowel action of the two deformed bars crossing the interface. The dowel action can roughly be evaluated from the hysteresis loop as the following: (1) Substantial stiffness decreases gradually. (2) The maximum shear displacement with cycling increases. (3) The pinching effect is very pronounced, and the area of hysteresis loops with cycling decreases. 300 200 100 0 -100 -200 -300
Q(kN)
RF01
200
N= 500kN
= 0.08
100
δsd(mm)
N= 1500kN
50
N(kN)
0
-12
-9
-6
-3
0
3
6
9
12
Fig. 4 Typical curves of mean values of Frictional force vs. Shear displacement 400 300 200 100 0 -100 -200 -300
Qf (kN) Friction coefficient
150
Q (kN)
RF04
calculation
1 mm
δsd (mm) -12
-9
-6
-3
0
3
6
9
12
Fig. 6 Typical curve of mean values of Dowel force vs. Shear displacement
0
500
1000
1500
2000
Fig. 5 Influence of Axial force on Frictional force 400 300 200 100 0 -100 -200 -300
RF02
calculation
Q (kN) 1 mm
δsd (mm) -12
-9
-6
-3
0
3
6
9
12
Fig. 7 Typical curve of mean values of Direct shear force of shear-key vs. Shear displacement
234
400 300 200 100 0 -100 -200 -300 -400
RF04+0.08N RF05
1 mm
δsd (mm) RF04+0.08N -12
200 100 0 -100 -200
calculation
Q (kN)
-9
RF06
-6
-3
0
3
-9
-6
-3
9
12
calculation
Q (kN) 1 mm
-12
6
0
3
δsd (mm) 6
9
12
800 700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 -600 -700
Q (kN) RF03
RF02+0.08N
1 mm
RF02+RF04 1 mm
calculation
δsd (mm) RF02+RF04
400 300 200 100 0 -100 -200 -300 -400
-9
-6
-3
0
3
6
9
12
calculation
Q (kN)
RF02+RF06 RF10
-9
-6
δsd (mm)
1 mm
RF02+RF06
-12
-3
-9
-6
-3
0
3
6
9
12
RF08
Q (kN)
-12
δsd (mm)
RF02+0.08N
-12 500 400 300 200 100 0 -100 -200 -300 -400 -500
calculation
0
3
6
9
1000 900 800 700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 -600 -700 -800 -900
Q (kN) RF02+RF04+0.08N
1 mm
calculation RF02+RF04+0.08N
δsd (mm) -12
12
RF09
-9
-6
-3
0
3
6
9
12
Fig. 8 Hysteresis curves of mean values of Total force (dowel resistance or the shearkey resistance with axial force) vs. Shear displacement 3.3 Direct Shear Resistance of Concrete Shear-key The typical hysteresis relation of the shear force (Q) of a shear-key resistance and the shear displacement ( δ sd) are shown in Fig. 7. RF02 subjected to shear force and without axial force. Thus, the shear force could be transferred only by means of shear-key resis-
235
tance. RF02 showed compressive failure of shear-key. The stiffness of the hysteresis loop is high and the displacement of that is tiny until compressive failure of shear-key. The resistance after compressive failure is keeping. 3.4 Compound effect of shear resistances with different hysteresises The hystereris relations between the shear force and the shear displacement are shown in Fig. 8. The relations of the total shear force and shear displacement are shown with dotted lines. The total shear force combines each shear resistance at the same shear displacement Combination of dowel and shear-key RF08 is the combination of the shear-key and dowel action. And the hysteresis loop of RF08 is the compound hysteresis loop (RF02+RF04) of the shear-key (RF02) and the dowel action (RF04) shown with the dotted line. RF08 and RF02 showed compressive failure of the shear-key in the first positive and negative loading. The positive and negative shear capacities of (RF02+ RF04) are almost equal to the capacity of RF08. The enveloped curves of hysteresis loops between RF08 and (RF02+RF04) show almost equal behaviour. However, the pinching effect of RF08 is pronounced, and decreases the area of histeresis loop with cycling. Combination of dowel and friction RF05 and RF06 are the combination of the dowel action and the friction with axial force. RF05 was subjected to compressive axial force +1500kN, and RF06 was subjected to tensile axial force –220kN. Therefore, although the friction occurs in the interface of RF05, the friction does not occur in the interface of RF06. The hysteresis loop of RF05 is the compound hysteresis loop (RF01+ RF04) of the dowel action (RF04) and the friction with axial force (RF01) shown with the dotted line. The hysterisis loops between RF05 and (RF01+ RF04) show almost equal behaviour. However, the shear displacement occurred suddenly in the first loading of RF05, and the shear force was larger to that of (RF01+RF04). Combination of shear-key and friction RF03 and RF10 are the combination of the shear-key and the friction with axial force. RF03 was subjected to compressive axial force +1500kN, and RF10 was subjected to tensile axial force –220kN. Therefore, although the friction occurs in the interface of RF03, the friction does not occur in the interface of RF10. The hysteresis loop of RF03 is the compound hysteresis loop (RF01+ RF02) of the shear-key (RF02) and the friction with axial force (RF01) shown with the dotted line. RF03 and RF10 showed compressive failure of the shear-key in the first positive and negative loading. The positive and negative shear capacities of (RF01+ RF02) are larger than the capacity of RF03 by about 80%.
4. Discussion 4.1 Strain distribution of Joint bars Strain distributions of RF04, RF05 and RF06 to investigate the dowel action at the same shear displacement ( δ sd = 0.5 , 1 mm ) are shown in Fig. 9. The configurations of the front reverse sides are symmetrical to the loading direction, and the shear force is resisted due to bending of the joint bars locally. Also, those configurations are equal re-
236
gardless of the axial force levels subjected, but the strain levels with tensile force are different. The characteristics of such a strain distribution are similarly observed in RF08, RF09 and RF10 to investigate the compound effects of dowel action and shear-key resistance. (mm)
yield strain= 2114
100 80 60 40 20 0 -20 -40 -60 -80 -100
-6
strain (×10 )
-4000 -2000
0
2000 4000 6000
(mm)
Ο :RF04 ∆ :RF05 ◊ :RF06
yield strain= 2114
100 80 60 40 20 0 -20 -40 -60 -80 -100
Upper Concrete Lower Concrete -6
strain (×10 )
-4000 -2000
0
2000 4000 6000
U δsd
Ul U M ma
Q
U lm
L lm L M max
L l0
Q
Anti-force of concrete
M oment curve
Shear displacement curve of Steel bar
L δsd
Fig. 10 Dowel mechanism
100 calculation 90 80 RF04 70 +Q=132 kN 60 δsd=0.51 mm 50 40 30 20 10 δ sd (mm) 0 -0.2
0
0.2
0.4
0.6
Depth of dowel bar (mm)
δ sd : shear displacement δ sd =L δ sd +U δ ｓｄ
Depth f dowel bar (mm)
Fig. 9 Strain disributions of specimens to investigate the dowel action calculation
100 90 80 70 60 50 40 30 20 10 0 -0.2
RF05 +Q=265 kN δsd=0.51 mm
δ sd (mm) 0
0.2
0.4
0.6
Fig.11 Shear displacement of dowel bar
4.2 dowel mechanism Referring to the dowel mechanism shown in Fig. 10. The external shear force tends to produce slippage along the interface. It is thought that the dowel bar is subjected to bending moment from concrete for the anti-force. The anti-force per this unit length is expressed with Eq. 1. It assumes that the anti-force coefficient is fixed in the depth of concrete, and the basic equation to calculate the bending displacement of the dowel bar will be given by the Eq. 2.
p s (x) = k c ⋅ B ⋅ y
(Eq. 1)
4
E s Is
d y + kc ⋅ B ⋅ y = 0 dx 4
(Eq. 2)
237
The variables are defined as: x : Depth of the dowel bar from the interface ( mm ), y : Horizontal displacement of the dowel bar in the depth x ( mm ), Es : Modulus of elasticity of the dowel bar ( N/mm2 ), Is : Geometrical moment of inertia ( mm4), ps(x) : Horizontal anti-force of the concrete in the depth x ( N/mm ), B : Diameter of the dowel bar ( mm ), kc : Coefficient of concrete ant-force ( N/m3 ) For the calculation of dowel strength, it is assumed that the dowel behaves like a horizontally loaded free-headed pile embedded in cohesive soil and that yielding of the bar and crushing of the concrete occur simultaneously. In the interface, the shear force of the opposite direction is loaded [ the absolute value ] mutually equally. Therefore, the dowel bar in depth 0 mm from the interface is subjected to a shear force (Q = -H ), and is not subjected to a bending moment ( M = 0 ). Moreover, when kc is assumed to be fixed, and a dowel bar is assumed to be an elastic material, and the theoretical solution of Eq. 2 is calculated, it can express with the following equations. H (Eq. 3) e −βx cos βx y= 3 2E s I s β H (Eq. 4) M = e −βx sin βx β
M max = −
π
π H −4 H e ⋅ sin = −0.3224 β β 4
(Eq. 5)
Where: k ⋅B , π 2π l m = , l0 = β=4 c 4β β 4E s I s Mmax : Maximum bending moment of the dowel bar (N • mm), lm : Depth of Mmax ( mm ), l0 : Depth of immobility In general, where the dowel is simultaneously subjected to a tensile stress σ s = α ⋅ σ y ( α ≤ 1.0 ), the plastic moment of the bar decreases.
M pl =
(
d3 ⋅ σy 1− α2
)
(Eq. 6)
6 Thus, the dowel strength is calculated by Eq. 7 ( Mmax = Mpl ). d3 ⋅ σy ⋅ 1− α2 2β ⋅ Q dwl = 6 0.3224
(
)
(Eq. 7)
Shear-displacement distributions of the dowel bars in the upper concrete of RF04 and RF05 are shown in Fig. 11. The calculations are integrated twice with the strain distributions shown in Fig.9. The calculations agree well with the measurements. Therefore, it is thought that the proposed dowel mechanism is appropriate.
238
4.3 Total method of various shearing resistance forces Monotonic hysterisis relations of per one dowel resistance (qdb) and shear displacement are shown in Fig. 12. The curves (RF04 and RF05) measured by the experiment are solid lines and the curve calculated from the Eq. 3 is shown by the dotted line. The dowel resistance of RF05 subtracts the calculated friction with axial force from the measured total shear force. The calculation evaluates the measurement of RF04 without axial force appropriate. The shear displacement of RF05 occurs suddenly, and the calculation evaluates the measurement of that a little more larger. This seems to be influenced by the adherence of concrete surface. Monotonic hysterisis relations of per one shear-key (qck) and shear displacement are shown in Fig.13. The shear-keys of RF03 and RF09 subtract the calculated frictions with axial force from the measured total shear forces, and also the shear-keys of RF08 and RF09 subtract the calculated dowel resistances from the measured total shear forces. The hysterisis curves of the shear-keys with the same axial force level show an almost equal. These figures lead to the following: (1) Total shear resistance can be evaluated as the sum total of each shear transfer element at the same shear displacement. (2) Dowel action is not influenced by compressive axial force. (3) Structural performance (resistance and stiffness) of shear-key increases by compressive axial force. 800
100
RF05: N=1500kN
qdb(kN)
qck(kN)
RF03:N=1500kN
600
75
RF09:N=1500kN
RF04: N=0kN
50
400
RF08: N=0
calu lat io n
200
25 δsd (mm) -0.5 0 -25
δsd (mm)
RF02: N=0
0
0 0.5
1
1.5
2
2.5
Fig. 12 Monotonic hysterisis curves of Dowel action
3
-0.5 0 -200
0.5
1
1.5
2
2.5
3
Fig. 13 Monotonic hysterisis curves of shear-key resistance
4.4 Evaluation equation of the shear resistance force in the interface Strength equations for design tools for shear transfer elements such as dowel action, shear-key, friction with axial force and adherence are given. In the design of shear transfer elements, deformation characteristics are also very important as well as the strength. An allowable limit of the shear displacement ( δ sd) should be proposed so that the effect of the shear displacement in concrete connections to structural response could be minimized during earthquake. We propose the limit of the shear displacement is 1 mm from the following: (1) The limit investigated by many structural experiments of BeamColumn-Joint, Column-to-Column Connection, Beam-to-Beam Connection, Beam-to-
239
Slab, Connection of a wall, etc. is 1 mm. (2) Experimental results in this research show the capacity of each shear transfer element is in full at the shear displacement 1 mm. We propose the strength equation (Qsr) for total shear resistance showing in Eq. 8. The total shear resistance (Qsr) is the sum total of the dowel bar (Qdwl), the shear-key (Qsky), the friction with compressive axial force (Qfrc), and the adherence (Qadh). However, the strength of dowel bar is the dowel resistance at shear displacement 1 mm. The shear resistance due to adherence is sometimes large to neglect. However the resistance is very sensible to the condition of the surface and subjects to change easily. Thus no value is shown for the strength due to adherence.
Q sr = Q dwl + Q sky + Q frc + (Q adh = 0) Q dwl = n s ⋅
(
d3 ⋅ σy ⋅ 1 − α2 6
)⋅
(Eq. 8)
2β , Q sky = n c ⋅ γ ⋅ A p ⋅ σ B , Q frc = µ ⋅ N 0.3224
Where
E δ k ⋅B , k c = κ ⋅ c ⋅ sd β=4 c 4E s I s Es 2 ns : Number of joint steel bars,
−
3
4 ⋅ σ B , δ sd = 1 mm α ⋅ σ y : Yield stress of joint steel bar with tensile axial force, Ec : Elastic modulus of concrete, κ : Configuration coefficient of stress-strain curve of concrete ( κ = 24 is recommended in this research ), nc : Number of shear-key, γ : Effective coefficient of axial force ( γ = 1 is recommended in this research ), Ap : Compressive Area of shear key (Ap= Wck × Hck, Wck : Width of shear-key, Hck : depth of sear-key ) σ B : Minimum compressive strength of concrete, µ : Coefficient friction ( µ = 0.08 is recommended in this research ), N : Axial force We have shown the shear transfer strengths calculated by Eq.8 for Fig. 6 – Fig.8. The measured strengths of specimens with shear-keys with axial force are larger than the calculated strengths by about 90 %, and the rate increases of the other specimens are about 30%. The evaluation equation should be investigated further in detail, although there is no problem for the design of concrete connections.
5. Conclusions Basic experiments with concrete connections were conducted on the shear transfer and the shear displacement behaviour in concrete connections under shear and axial force. The following conclusions may be drawn. (1) The shear transfer mechanism and shear displacement behaviour in concrete connections is clarified. And the shear transfer mechanism is verified by the structural experiments. (2) The shear transfer strength can be evaluated as the sum total of each shear transfer element at the same shear displacement. And the evaluation equation is proposed.
240
PERFORMANCE OF UNDERCUT ANCHORS IN COMPARISON TO CAST-IN-PLACE HEADED STUDS Peter Pusill-Wachtsmuth Hilti AG, Principality of Liechtenstein
Abstract Cast-in-place headed studs are world-wide used. In general there are no major concerns with their suitability and performance in concrete. In the meantime undercut anchors have been developed that show similar behaviour. In this paper only the performance under tension and shear is compared. It was not intended to discuss other differences such as costs, installation procedures or convenience in planning of an anchorage. The comparison shows that the performance characteristics of headed studs and undercut anchors are approximately the same. The main difference is the required member thickness. For the selected undercut system, HDA, it is shown that the required values of the approval document can be drastically reduced. So headed studs and the undercut anchors are comparable and competitive in their performance.
1. Introduction Cast-in-place headed studs welded to a fixture are used to transfer a local acting force into the concrete. The dimensions of the studs and the design methods may differ in national regulations and standards. In general the design engineer has no doubts of a proper performance of the anchorage. In recent years post-installed anchors have been developed, which are intended to be used for the same application as headed studs. To create confidence in this new technique, it was necessary to run an approval procedure according national or international codes or guidelines. The approval documents give performance characteristics of the product and give help for the design of an anchorage. In the following the main performance characteristics of headed studs and undercut anchors are compared. Also the technical requirements of anchor configurations and the dimensions of the base material are discussed. The design concept for both systems is relatively complex. The more complex the design concept the closer the calculation can be to the real behaviour of the anchors. The complexity makes it difficult to give a
241
complete overview. To avoid any unfair comparison the basis on which the results are obtained must be clearly shown. Otherwise it is very easy to show the benefits of one system and to show the weakness of the other. The comparison is made only on performance characteristics and on the design. This report does not cover any other characteristics of headed studs and undercut anchors, which give help for the decision whether to choose the one or the other system. These may be cost reasons for the product and for the installation. It also may be advantages of post-installation versus cast-in-place and vice versa. These and all other characteristics must be discussed separately.
2. Headed Studs The dimensions and tolerances of headed studs used for comparison with undercut anchors are standardised in ISO 13918 /1/. Also the material properties are given there. In general these studs fulfil the requirements of the design guide of CEB /2/. Only the thickness of the head is less than required, which is neglected in the following. Headed studs can be used without any prequalification tests if the proposed values for edge distance and spacing according to /2/ are accepted.
d1
d2
Fig. 1: Headed studs according to EN ISO 13918
D
hef
Table 1: Headed studs according EN ISO 13918 10 13 16 19 22 Diameter of the stud (d1) mm Diameter of the head (d2) mm 19 25 32 32 35 Anchorage depth (hef) available in different length
242
25 40
3. Undercut Anchor There are many undercut anchors on the market, which differ in the installation procedure, in dimensions and shape. The following comparison is based on one selected product, the Hilti HDA Anchor /3/. The comparison can be easily completed for other products. For the selected undercut anchor an European Technical Approval /3/ is available. So the anchor is prequalified according to the European rules. In the prequalification tests it is shown, that the anchor is not very sensitive to variations in installation compared to the written manufacturer’s instructions. Also the anchor is not sensitive to the largest crack width that may occur in reinforced concrete construction. In the prequlification tests it is shown that the anchor behaves properly under repeated loads and in concrete structures , where the crack width varies. It can be said, that a prequalified anchor will behave in a predictable and reliable manner. For applications according to the scope of the design guide /2/ there is no difference in reliability of headed studs or undercut anchors. Fig. 2: HDA Undercut anchor
Table 2: HDA Undercut anchor drill bit diameter anchorage length
(d0) (hef)
mm mm
M 10 20 100
M12 22 125
M 16 30 190
4. Performance under tension loading 4.1 Performance without edge and spacing effects The calculation of the performance of headed studs is based on Bulletin d’Information No. 226 of CEB, ‘Design of fastenings in concrete‘, 1995 /2/. For the undercut anchor the data are based on the European Technical Approval ETA-99/0009, ‘Hilti HDA Anchor‘, 1999 /3/. For headed studs all sizes according to /1/ are included, for the
243
undercut anchor only the size M 12. The anchorage depth hef = 125 mm is chosen for all anchors considered in this analysis. This can be easily completed for other sizes of the undercut anchor. Table 3 shows the resistance for the different failure modes under tension loading in C 20, when there are no edge or spacing effects. For steel failure the values for headed studs are based on the yield strength and for undercut anchors on the ultimate strength. Also, the partial safety factors differ. So only the design resistance is comparable. For all other failure modes the partial safety factors are the same. Steel failure is not decisive for the headed studs or for the undercut anchor. Pull-out failure and concrete cone failure are separated for cracked and for non-cracked concrete. For pull-out failure of headed studs the design has to be done for the ultimate limit state and for the serviceability limit state. In /2/ an admissible pressure under the head of the studs is given for the serviceability limit state. This value is converted to a characteristic action and to a design action by using the partial safety factor of 1.0. The design action is equal to the design resistance, so this value is given in the table. The equations to calculate concrete cone resistance differ in the k-factor for headed studs (9.0) and undercut anchors (7.5) in /2/. In the approval procedure of the undercut anchor it was possible to show that the factor for headed studs can also be used for this product. Table 3: Comparison of design resistance of headed studs and undercut anchors Headed studs according EN ISO 13918 d1 mm 10 13 16 19 22 25 hef mm 125 125 125 125 125 125 Steel failure NRd,s kN 22.9 38.7 58.6 82.7 110.9 143.2 cracked concrete Pull out failure NRd,p kN C 20 17.1 29.8 50.3 43.4 48.5 63.8 Pull out failure, serviceability limit state NRd,p kN C 20 10.2 17.9 30.2 26.0 29.1 38.3 Concrete cone failure NRd,c° kN C 20 31.3 31.3 31.3 31.3 31.3 31.3 non-cracked concrete Pull out failure NRd,p kN C 20 25.1 43.8 73.7 63.6 71.1 93.6 Pull out failure, serviceability limit state NRd,p kN C 20 16.4 28.7 48.3 41.7 46.6 61.3 Concrete cone failure NRd,c° kN C 20 43.8 43.8 43.8 43.8 43.8 43.8
HDA M 12 125 44.7
19.4 19.4 32.2
45.1 45.1 45.1
For the largest size of the headed studs, concrete cone design resistance is decisive in cracked concrete. For all other sizes it is the pull-out resistance in the serviceability limit state. Also, the pull-out design resistance is the smallest value for the undercut anchor.
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The resistance of HDA M 12 can be compared with a headed stud size between diameter 13 or 16 mm. For all the larger diameters the design resistance of headed suds is larger than for the undercut anchor M 12, because the bearing area significantly increases. In case of non-cracked concrete, cone failure is decisive for the undercut anchor and for one medium and the two largest sizes of the headed studs. The value for the design resistance is the same. The small deviation for headed studs in comparison to the undercut anchor are linked to the differently rounded values in the equation for the calculation of the concrete resistance. For the two smallest sizes and a medium size of the headed studs pull out is decisive. The resistance is smaller than for concrete cone failure and therefore smaller than for the undercut anchor. In summary it can be said that in general, pull-out resistance is decisive in cracked concrete. The undercut anchor has the same performance as a headed stud with a diameter of more than 13 mm and less than 16 mm. For non-cracked concrete the undercut anchor behaves like headed studs with a diameter of more than 13 mm, when pull-out is not decisive. 4.2 Influence of edge and spacing effects In Table 4 the relevant edge distance, spacing and minimum member thickness are given for headed studs and the undercut anchor. The values for edge distance and spacing (ccr,N and scr,N) necessary to develop the characteristic tension resistance of a single anchor without spacing and edge effects in the case of concrete cone failure are the same for headed studs and the undercut anchor. As shown in Table 3 the concrete cone resistance is also the same. In all configurations of anchor groups up to the lower limit of minimum edge distance and spacing (cmin and smin) the design resistance for concrete cone failure of headed studs and the undercut anchor is the same. The main difference are the values of cmin and smin , which are in general lower for headed studs. That means headed studs can be used with smaller edge distances and spacing compared to undercut anchors. (In this case the design resistance has to be calculated for local blow-out failure, which is not done in Table 3 and 4. For comparison it is not necessary here, because undercut anchors are not allowed to be used with these small edge distances). The reason for the difference in cmin and smin is, that headed studs are not torqued, when they are welded to a fixture. Undercut anchors are torqued after installation to clamp the fixture to the concrete. For splitting, the edge distance and spacing ccr,sp and scr,sp are the same as ccr,N and scr,N in case of undercut anchors. That means, splitting failure is not decisive and can be neglected in the design of anchorages. For headed studs the values of ccr,sp and scr,sp are given in /2/. They are on the safe side. Smaller values are possible if an adequate performance is shown by prequalification tests. The biggest advantage for headed studs is the minimum member thickness. It is required that hmin is in minimum the length of the headed stud embedded in concrete plus the required concrete cover for reinforcement according to the reinforced concrete standards.
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In Table 4 the minimum cover of 1.0 cm is chosen. For the undercut anchor the required minimum thickness is approximately 75% larger than for the headed studs according to /3/. The following section 5. is dealing with the minimum member thickness of undercut anchors, because the required values are a limitation for many applications. Table 4: Edge distance, spacing, member thickness of headed studs and undercut anchors Headed studs according EN ISO 13918 HDA M 12 d1 mm 10 13 16 19 22 25 hef mm 125 125 125 125 125 125 125 ccr,N mm 190 190 190 190 190 190 190 scr,N mm 375 375 375 375 375 375 375 cmin mm 30 39 48 57 66 75 100 smin mm 50 65 80 95 110 125 125 ccr,sp mm 250 250 250 250 250 250 190 scr,sp mm 500 500 500 500 500 500 375 hmin mm 142 143 143 145 145 147 250
5. Behaviour of undercut anchors in thin concrete members The minimum member thickness for all post-installed anchors in their approvals and also in /2/ is based on the assumption hmin = 2 hef (or larger than 100 mm). The limitation is necessary to avoid splitting failure during installation or under loading. Splitting mainly occurs when anchors are situated close to an edge. For post-installed anchors ccr,sp and cmin are checked in tests. For ccr,sp pullout tests in tension are required where the anchor is situated in the corner of a concrete member with c1 = c2 = ccr,sp and the member thickness is 2 hef. It is required that the failure load is approximately equal to the failure load of an anchor without any edge and spacing effects. For evaluation of cmin a double anchor group is placed parallel to the edge with cmin and smin. The member thickness is 2 hef. The anchors are either torqued or loaded up to failure, which in most cases is splitting of the concrete. For post-installed anchors, where a torque moment is required, the torque at failure must have a defined safety margin in comparison to the required installation torque. When the anchors are loaded in tension, the failure load must be compared to the failure load calculated according to the design concept in /2/ or Annex C of /5/. In general, design for splitting is only necessary, when it is shown that the concrete is not cracked in the anchoring area and the higher resistance is used in the calculation. As stated before the minimum member thickness is fixed because of splitting failure. At present the same member thickness is required for cracked concrete. Here splitting is not decisive (the concrete is already cracked), but even here hmin = 2 hef has to be used. Of course this is on the safe side. In general the rule does not limit the applications, because
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post-installed anchors are used with low anchorage depth. For undercut anchors, which can be compared with headed studs, the limitation is not acceptable. For an anchorage depth of 190 mm for the HDA M16 anchor, a member thickness of 380 mm is required. This is much more than usually available on a jobsite, especially for slabs and walls. Tests were performed with all sizes of the undercut anchor to assess reasonable member thickness, edge distance and spacing /4/. The test conditions met the requirements of the ETAG /5/. The minimum member thickness was chosen to avoid any damage at the opposite side of the concrete during drilling and setting. This was assessed for a member thickness equal to the anchorage depth plus two diameters of the drill bit. ccr,sp was chosen to be 1.5 hef and scr,sp to be 3 hef. These are the same values as for concrete cone failure, which ensures that splitting calculations in the design procedure are never decisive. cmin and smin were the same values as in the approval document. In a later step it seems to be possible to assess reduced values. But for now it was intended not to change too many parameters. Test parameters, results and evaluation are summarised in Table 5. In all cases, where only c1 and c2 are given, single anchor in the corner were loaded in tension. Where c1 and s are given, it was tension loading of a double anchor group parallel to the edge. The following failure modes were observed: splitting (Sp), concrete cone or edge failure (C) and steel failure (S). The evaluation is based on the fact that splitting is not decisive if the ultimate load in these tests is equal to or larger than the concrete cone resistance. The concrete cone resistance is calculated according to Equation (1), which is the basis for the evaluation of the characteristic resistance of the undercut anchor.
N u ,exp = 15.5
1000
⋅ f c ⋅ hef1.5
[kN]
Table 5: Test results of HDA undercut anchors in thin concrete members test HDA hef fc c1 c2 s h Fu fm Nu,exp Ac,N ψs,N kN M mm Mpa mm mm mm mm kN /A° 1.1 10 100 34.0 80 80 140 44.89 Sp 90.4 0.59 0.86 2 10 100 34.0 80 80 140 44.51 C 90.4 0.59 0.86 3 10 100 34.0 80 80 140 47.80 C 90.4 0.59 0.86 4 10 100 34.0 80 80 140 48.47 S 90.4 0.59 0.86 2.1 10 100 34.0 150 150 140 48.82 S 90.4 1.0 1.0 2 10 100 34.0 150 150 140 47.25 S 90.4 1.0 1.0 3 10 100 34.0 150 150 140 47.90 S 90.4 1.0 1.0 4 10 100 34.0 150 150 140 48.43 S 90.4 1.0 1.0 3.1 10 100 34.0 80 100 140 90.42 S 90.4 1.02 0.86 2 10 100 40.7 80 100 140 88.36 C 98.9 1.02 0.86 3 10 100 40.7 80 100 140 85.74 Sp 98.9 1.02 0.86
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(1)
Nu,m
xi,j
45.7 45.7 45.7 45.7 90.4 90.4 90.4 90.4 79.5 86.9 86.9
0.98 0.97 1.05 >1.06
>1.14 1.02 0.99
test HDA M 4.1 12 2 12 3 12 4 12 5.1 12 2 12 3 12 4 12 6.1 12 2 12 3 12 4 12 7.1 12 2 12 3 12 8.1 16 2 16 3 16 4 16 9.1 16 2 16 3 16 4 16 10.1 16 2 16 3 16 4 16 11.1 16 2 16 3 16
h hef fc c1 c2 s mm Mpa mm mm mm mm 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190
34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 34.2 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7 35.7
100 100 100 100 190 190 190 190 100 100 100 100 190 190 190 150 150 150 150 285 285 285 285 150 150 150 150 285 285 285
100 100 100 100 190 190 190 190 125 125 125 125 375 375 375 150 150 150 150 285 285 285 285 150 190 190 190 570 570 570
170 170 170 170 170 170 170 170 170 170 170 170 170 170 170 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
Fu kN 70.08 69.12 72.60 69.62 73.20 73.84 73.18 73.03 119.28 121.54 114.12 112.96 149.67 149.19 150.82 131.31 135.31 138.37 136.12 138.49 135.19 132.87 135.48 241.28 255.25 263.19 269.47 267.92 267.02 271.77
fm Nu,exp Ac,N kN /A° C 126.7 0.59 C 126.7 0.59 C 126.7 0.59 C 126.7 0.59 S 126.7 1.0 S 126.7 1.0 S 126.7 1.0 S 126.7 1.0 C 126.7 1.02 C 126.7 1.02 C 126.7 1.02 Sp 126.7 1.02 S 126.7 2.0 S 126.7 2.0 S 126.7 2.0 S 242.5 0.58 S 242.5 0.58 S 242.5 0.58 S 242.5 0.58 S 242.5 1.0 S 242.5 1.0 S 242.5 1.0 S 242.5 1.0 C 242.5 0.96 C 242.5 1.02 Sp 242.5 1.02 S 242.5 1.02 S 242.5 2.0 S 242.5 2.0 S 242.5 2.0
ψs,N Nu,m 0.86 0.86 0.86 0.86 1.0 1.0 1.0 1.0 0.86 0.86 0.86 0.86 1.0 1.0 1.0 0.86 0.86 0.86 0.86 1.0 1.0 1.0 1.0 0.86 0.86 0.86 0.86 1.0 1.0 1.0
64.0 64.0 64.0 64.0 126.7 126.7 126.7 126.7 111.4 111.4 111.4 111.4 253.4 253.4 253.4 121.2 121.2 121.2 121.2 242.5 242.5 242.5 242.5 200.6 211.7 211.7 211.7 485.1 485.1 485.1
xi,j 1.09 1.08 1.13 1.09
1.07 1.09 1.02 1.01
1.08 1.12 1.14 1.12
1.20 1.21 1.24 1.27
In most cases Nu,exp has to be multiplied by the influencing factors Ac,N/A° and ψs,N according to /2/ or Annex C of /5/.. These factors take into account small edge distances and small spacing. The result is the expected mean ultimate load of the anchor or the anchor group Nu,m. xi,j is the ratio of the measured failure load and the mean expected value for concrete cone failure. In cases where steel failure occurred the ratio was not calculated. The resistance for steel failure is lower than the concrete cone resistance. The
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ratio was calculated only in the two test series, where other failure modes were also observed. To show that the concrete cone resistance was reached in the tests the factor xi,j may scatter around the value of 1.0 with a coefficient of variation of 15%. Looking at the results it is obvious, that the requirement is fulfilled. In summary it can be said that even with the thin member thickness splitting is not decisive for HDA undercut anchors. All edge distances (ccr,N and cmin ) and spacing (scr,N and smin ) can be taken from the approval document for the calculation of the concrete cone resistance.
6. Performance under shear loading For steel failure under shear loading without lever arm the design resistance VRd,s of the undercut anchor M12 is 24 kN. This is in between a headed stud of 10 mm diameter (17.2 kN) and a diameter of 13 mm (29.1 kN), calculated according to /2/. For the calculation it has to be taken into account that the material properties of headed studs are lower than for the undercut anchor. This also influences the partial safety factor. On the other hand a better factor in the equation for VRd,s (0.75 instead of 0.6) can be used for headed studs, because the resistance to shear forces is positively influenced by the studwelding process. As a result headed studs and the undercut anchor show approximately the same design resistance, when the diameter of the stud and the bolt are the same. For shear load with lever arm the same rules apply to both anchors. For pry-out failure, the same rules also have to be used for undercut anchors and headed studs. The pry-out resistance is based on the concrete cone resistance under tension. Because the concrete cone resistance is the same, the design resistance under pry-out is the same. For concrete edge failure the design is based on the same equations and on the same partial safety factors. The only difference might be the fitting factor lf in the equation for VRk,c°. The value for lf is given in the approval document for the undercut anchor and is 70% of the anchorage depth for M10 and M 12 and 50% for M16. For headed studs the design guide /2/ does not mention any values for lf. So it is assumed that the designer will take lf = hef. In the equation for VRk,c° the factor lf is covered by (lf/dnom) to the power of 0.2. So the difference in VRk,c° for headed studs and the undercut anchor is relatively small. In summary it can be said, that under shear loads headed studs and undercut anchors follow the same equations of /2/ or /5/ Annex C, when calculating the design resistances. The differences are only linked to steel strength, diameter of the stud or bolt and to the stiffness of the anchor (lf/dnom). For the chosen undercut anchor the differences in the design resistances for the different failure modes compared to headed studs are small.
249
7. References 1.
ISO 13918, ‘Welding – Studs and ceramic ferrules for arc stud welding‘, 1998
2.
CEB Bulletin d’Information No. 226, ‘Design of fastenings in concrete‘, 1995
3.
European Technical Approval ETA-99/0009, ‘Hilti HDA Anchor‘, 1999
4.
Bautechnische Versuchsanstalt an der HTL Rankweil: ‘Prüfbericht über Zugversuche mit HDA-P M10, M 12 und M 16, ungerissener Beton C 20/25, Einzel- und Doppelbefestigungen in dünnen Platten‘ vom 30.3.2001 (only in German, not published)
5.
EOTA, ETAG No 001: ‘Guideline for European Technical Approval of Metal Anchors for Use in Concrete‘, Brussels 1997
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SHEAR ANCHORING IN CONCRETE CLOSE TO THE EDGE Norbert Randl* and Marcel John** *Hilti AG, Kaufering, Germany **Hilti AG, Schaan, Principality of Liechtenstein
Abstract Since design rules for post-installed anchors are usually based on investigations in unreinforced concrete, the design resistance of fixings set close to the concrete edge and loaded in shear towards the edge is low. It is therefore necessary to consider the effective strength of the reinforced concrete edge. This paper first demonstrates that the current methods to take into account the strength of the concrete edge are insufficient in many cases and proposes different edge strengthening methods based on extensive laboratory testing. Finally a Eurocode 2 compatible design formula for cast-in hairpin reinforcement is derived.
1. Introduction Limited space often requires the fixing of anchor plates like baseplates of steel columns, railings or lamp posts in the vicinity of the edge of the concrete foundation.Though in practice the concrete usually is reinforced, design rules for anchors are typically based on investigations in unreinforced concrete. The failure load of such fixings set close to the concrete edge and loaded in shear towards the edge is determined by a brittle concrete cone breaking out in front of the anchor. The shear resistance therefore reduces significantly with decreasing edge distance. If the edge distance is very small, splitting due to wedge forces must also be considered. Adhering to prescribed minimum edge distances will typically prevent this mode of failure. Fig. 1 Anchoring of guard rail
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Extensive testing has shown that standard slab lateral reinforcement is usually not sufficient to significantly increase the shear resistance of anchors loaded towards the edge. Higher shear resistance can be activated, for example, by using elongated holes in the anchorage base plate for the anchors situated closest to the edge or by externally reinforcing the edge. If no external reinforcement is to be applied, cast-in additional Ushaped reinforcement in the concrete has been shown to be a very effective method to strengthen the edge [1], [2]. For this strengthening method, a design formula based on the Eurocode safety concept as described in [3] has been derived from test results. This allows the design engineer to plan post-installed anchorages closer to the concrete edge, and with higher resistance than would be possible with standard anchor design concepts.
2. Unreinforced Concrete The analytical determination of the ultimate load capacity is difficult as it depends on the behaviour of concrete under multiaxial stresses and has to consider the scatter in local concrete strength, size effects etc. Most equations for the prediction of failure loads have therefore been derived empirically, taking into account the observations from tests and are available only for the case without any retaining hanger reinforcement. Based on regression analyses of 147 tests Eligehausen and Fuchs propose the following equation for the calculation of the average ultimate failure load in unreinforced uncracked concrete [4, 5]: h 0 ,5 ⋅ f cc0,5 ⋅ ef Vum ,c = k ⋅ d nom d nom
with: dnom hef c1 fcc k
0 ,2
(units: [N, mm])
⋅ c11,5
(1)
outside diameter of anchor anchorage depth [5] edge distance of anchor axis concrete cube strength constant factor (k = 1.0)
3. Effect of Standard Reinforcement A concrete plate with reinforcement bars parallel to the edge and with ties along the edge shall be considered as having standard reinforcement. Reinforced concrete is typically assumed to be cracked concrete. To account for the cracks, the load bearing capacity of uncracked concrete has to be multiplied by a global factor of 0.7 [5]. In the presence of minimum edge reinforcement, this reduction can be partially compensated for by a factor of 1.2 or 1.4, depending on the density of the edge reinforcement [6]. This is only a very rough approximation, and tests have shown that, for smaller anchor
252
diameters, it may even be unsafe. Small diameter anchors have a low bending resistance and introduce the load right at the top of the concrete surface. Thus, the failure cone is pushed over the edge reinforcement (Fig. 2) [7]. With greater anchor diameters the edge ≈ reinforcement may support the shear load more effectively because the anchor is able to introduce the load farther away from the concrete surface. Figures 3 and 4 show test results with edge reinforcement of diameters 6 – 12 mm and welded wire meshes. Especially the test results with M16 anchors are somewhat higher than those expected in ≈ unreinforced concrete, nevertheless the effect is rather negligible. Fig. 2: Small anchors with edge reinforcement Force Vu [kN] 70 60 50 40 Equ. (1) unreinforced series1 series2
30 20 10
Rk (steel failure)
0 0
25
50
75
100
125
150
175
200
c1 [mm]
Fig. 3 Tests with anchors HSL M12
Force Vu [kN] 120 100 80 60 Equ. (1) unreinforced series1 series2
40 20
series3 Rk (steel failure)
0 0
25
50
75
100
125
150
175
200
c1 [mm]
253
225
250
Fig. 4 Tests with anchors HSL M16
4. Subsequent Constructive Measures 4.1 External Edge Support column anchorage baseplate HSL
HSL HAS with HIT-HY 150 or HVU failure cone
Fig. 5 Scheme of back anchorage
Fig. 6 Shear support
A steel bar reinforces the concrete edge by anchoring the concrete edge behind the expected failure cone. The support steel bar is designed according to the rules of steel construction, assuming a uniformely distributed load. The anchorage is composed of bonded anchors reaching behind the expected failure cone (Fig. 5). The shear anchors (HSL) developed a very high resistance and typically failed by yielding of the steel rod in shear (Fig. 6). 4.2 Use of Elongated Holes in Anchorage Baseplate If the anchorage baseplate has two or more rows of anchors, the holes for the anchors closest to the edge should be elongated, directed towards the edge. Thus, these anchors do not take any shear loads. The anchors of the row farther away can activate a bigger failure cone and, therefore, a higher load capacity.
5. Cast-In Hairpin Reinforcement 5.1 Research program A comprehensive test program was carried out at the laboratories of Hilti AG [7] and the Institute for Concrete Construction at the University of Innsbruck [8] in order to quantify the effect of cast-in hairpin reinforcement and to develop corresponding design rules. The U-shaped hairpins were set with an inclination of 5°- 10°. The following parameters have been varied: hairpins: - diameter ds [mm]: 12, 16 - diameter of bend resp. distance e of hairpin legs: e = 88 - 134 mm - concrete cover to front side (csv = 10 - 30 mm) and top surface (cso = 7 - 33 mm) anchors: - anchor type: expansion anchors HSL, bonded anchors HVU - anchor diameter d [mm]: 12, 16, 20
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- edge distance c1: 55 - 150 mm - excentricity of anchor axis (in relation to axis of the hairpin) The concrete cube strength fcc was between 25 and 30 N/mm² for all tests. The loading was displacement controlled. A total of 62 tests with cast-in hairpin reinforcement and 14 tests without any reinforcement in the anchorage area were carried out. The load was introduced by a LINEAR POTENTIO M ETER steel plate parallel to the PTFE-LAYER concrete surface (Fig. 7). PTFE layers were put V ~10 30 c so between steel plate and c sv concrete in order to reduce friction. HAIRPIN ANCHO R BO LT
Fig. 7 Test setup 5.2 Test results: Failure usually occurs by formation of a failure cone followed by pullout or breakage of the anchor. Typically, the maximum load is reached, when the failure cone starts to break out. The cracks start from the anchor and run towards the edge. Their inclination to the concrete edge is 30° 45° . Generally, the angle becomes smaller towards the edge (Fig. 8). Fig. 8 Concrete cone failure of specimen 12.2 (Dowel HVU 16, hairpin ø16) Some tests showed a second increase of the load after displacements of 10mm and more: One reason is the tensile capacity of the deformed, inclinded anchor (kinking effect) and the second is that anchors set very close to the edge touched the hairpin reinforcement. Four tests with bonded anchors yielded in shear failure of the anchor without formation of a concrete cone (steel failure). These tests have not been considered in the development of the design recommendation for the resistance at the concrete edge. The tests confirm that cast-in hairpin reinforcement can significantly increase the loadbearing capacity. Moreover, the post peak load behaviour becomes much more ductile. The most significant increase of up to 200% is observed if the edge distance is very small (Fig. 9). Due to the reinforcement, the first cracks appear at about 50% higher loads than in unreinforced concrete.
255
Test no. 5.1 V [kN]
Test no. 5.2
V [kN]
HSL 12, c1 = 65 mm, hairpin ø12, cso=11mm
HSL 12, c1 = 65 mm, unreinforced
50
50
40,8 kN ∇
45
45
40
40
35
35
30
30
25
25 20 15
st ∇ 1 crack
20
12,9 kN ∇
15
10
10
5
5
0
0 0
2
4
6
8
10
12
14
16
18
20
0
s [mm]
2
4
6
8
10
12
14
16
18
20
s [mm]
Fig. 9 Load-displacement curves for specimens without and with hairpin reinforcement The parameter most strongly influencing the peak load is the distance of the hairpin reinforcement from the concrete surface (cso), especially with small reinforcement diameters and with anchors set very close to the edge. While the peak load can be increased by a factor of 3 with a concrete cover of 10mm for 12mm diameter hairpins, the influence of the same reinforcement with a cover of 30mm is scarcely observable. The tests also show that the peak load increases with the diameter of the cast-in reinforcement. However, this increase is not directly proportional to the increase of the steel area. The effect of the hairpin reinforcement is independent of the exact position of the anchor between its legs. 5.3 Theoretical considerations and prediction of failure load Anchors subjected to shear loads experience bending, shear and with increasing lateral displacement also axial stresses. Small loads are directly introduced from the shaft into the surface concrete. The load-displacement curve is steep and shows a linear-elastic behaviour. The transmission of the shear force from the anchor bolt to the concrete takes place within a depth measured from the surface of 1 to 2 times the dowel diameter [9,10]. A hanger reinforcement makes sense only in this area, because the resulting compression strut then finds a support. Due to the locally high pressure in front of the bolt, the surface concrete plasticizes under increasing load and flexural stresses are generated in the anchor shaft. For anchors situated near the edge this finally leads to the formation of a concrete failure cone. Some of the tests have also been analysed by means of a 3-dimensional finite element modelling using non-linear material laws and a smeared crack approach. The computer simulation confirmed that the failure is due to cracking and crushing of the concrete in front of the anchor. Provided that the anchor has sufficient embedment length, this leads to the development of a plastic hinge. The hinge is closer to the surface if the hanger reinforcement has less concrete cover and thus significantly reduces the lever arm of the anchor. Moreover the calculations demonstrated that the hairpins remain elastic until the peak load is reached. The increase of the ultimate load is not proportional to the steel area because the
256
centerpoint of the support for the compression strut moves down with increasing hairpin diameter at constant concrete cover. The results of the tests in unreinforced concrete correspond well to formula (1). The best agreement is reached with a factor k = 1,0, the coefficient of variation results in a rather low value of 14 %. The cast-in reinforcement delays the formation of cracks starting from the anchor as well as their propagation. The additional energy required for crack growth corresponds to the possible increase of the load bearing capacity. Therefore, it is best represented by an additional term to equation (1). The effectiveness of the hanger reinforcement is about inversely proportional to the concrete cover and decreases with increasing distance between the anchor and the hairpin reinforcement bend. Moreover, the anchor stiffness, characterized by dowel diameter and embedment depth, has an influence on the loadbearing behaviour. The combination of all relevant parameters with respect to their effects leads to the following approach for the prediction of the failure load: k
2 d nom (2) < Vum,s Vum = Vum,c + κ ⋅ A s,h ⋅ f y ,h ⋅ 1 − f 1 (l proj , c1 , h ef ) ⋅ k c d ⋅ + s 1 so with: κ ...... effectiveness factor taking into account that the c1 concrete will crush before the ultimate capacity csv of the hairpin is reached k1, 2 ... constants f1 ....... empirical function ds ..... nominal diameter of hairpin reinforcement e lproj hef .... anchorage length [5] dnom ... outside diameter of anchor lproj .... projective length: can be approximated in terms of the edge distance and the concrete cover ahead of the hairpin (Fig. 10): lproj ≈ 1,7 ⋅ (c1 - csv) ≤ e Fig. 10 Projective length As,h.... total cross section of both hairpin legs fy,h..... yield strength of hairpin steel
(
)
Steel failure due to a combination of shear and bending of the anchor shaft represents an upper bound on the shear capacity: Vum,s = α ⋅ As ⋅ fy with α ≈ 0,6 - 0,7 [5]. (AS = cross section and fy = yield strength of anchor) The formation of the concrete cone is considered as the failure criterion. This generally corresponds to the first peak load or the first horizontal branch of the load displacement curve. The systematic variation of the different parameters and the subsequent statistical evaluation finally leads to the following form of equation (2): Vum = Vum ,c + 0,4 ⋅ A s,h ⋅ f y ,h
l proj0,5 ⋅ c10,5 d nom ⋅ 1 − 0,5 ⋅ ⋅ h ef 1,2 ⋅ c so + d s
257
1,5
(3)
Fig. 11 shows the comparison of predicted and observed failure loads for undercut anchors type HSL in function of the edge distance c1. Considering all specimens with introduced hairpin reinforcement except for the 4 tests with early shear failure of the dowels the average ratio of actual to predicted failure load is 1.05. With a coefficient of variation of 19 % and a factor of correlation of 89%, the scatter zone is within acceptable limits (Fig. 12). HSL ø16 (Hairpin reinforcement ø12 and ø16) V [kN] 120
Eq. (1) (unreinforced)
110 100
Eq. (3), hairpin ø16, cso ≈ 9 mm Eq. (3), hairpin ø12, cso ≈ 11 mm Vks (steel failure)
90 80 70 60 50
HSL 16, hairpin ø16, cso ≈ 9 mm HSL 16, hairpin ø12, cso ≈ 11 mm unreinforced
40 30 20 10 0 50
70
90
110
130
150
170
190
210
Edge distance [mm]
Fig. 11 Predicted (calculated) and observed failure loads in function of c1 Vexp 120,0
[kN]
100,0 80,0 60,0 40,0
Vcalc =Vexp
20,0 0,0 0,0
20,0
40,0
60,0
80,0
100,0
120,0
Vcalc [kN]
258
Fig. 12 Comparison of calculated and experimental results
5.4 Design formula and recommendations for execution For practical design purposes the transition from mean ultimate loads to characteristic values (fractiles) is required. The characteristic resistance is derived as the 5%-fractile of the mean value of strength with a confidence level of 90%. Admitting a log-normal distribution, the statistical evaluation of the tests conducted in reinforced concrete yields a global reduction factor ψ = 0,72. This corresponds to the factor of ψ = 0,7 proposed by Eligehausen in [4] for unreinforced concrete. The material properties are also considered by their lower fractile; this additional safety will not be used in the design formula. The design resistance is derived in accordance with the safety concept of MC 90 [3] and Eurocode 2 by applying appropriate partial safety factors. In unreinforced, cracked concrete, the design resistance is the mean ultimate load multiplied by ψ = 0,7 for the statistical evaluation of the 5%-fractile [4], multiplied again by 0,7 accounting for the effect of cracks [4, 5] and divided by the partial safety factor γMc [6]:
VRd ,c =
1 γ Mc
0 ,5 h ef 0 ,5 ⋅ 0,5 ⋅ d nom ⋅ f ck ⋅ d nom
0 ,2
⋅ c11,5
(units: [N, mm])
(4)
with: fck ...... characteristic cylinder compressive strength of concrete γMc .... safety factor for system with normal installation safety: γMc = γ1⋅ γ2 = 1,8⋅1,2 = 2,2 [6]. According to equation (3) the shear load capacity with cast-in hairpin reinforcement becomes: 1,5 l proj 0,5 ⋅ c10,5 d nom 1 (5) ⋅ 0,3 ⋅ A s,h ⋅ f yk ,h ⋅ 1 − 0,5 ⋅ VRd = VRd ,c + ⋅ 1,2 ⋅ c so + d s γ Ms h ef (valid for fyk,h ≤ 600 N/mm², fck ≤ 40 N/mm², 4 dnom ≤ hef ≤ 8 dnom, dnom ≤ 25 mm) with: γMs = γ1⋅ γ2⋅ γ3 = 1,15 ⋅ 1,5 ⋅ 1,2 = 2,1 γ1 .... partial safety factor for steel in tension γ2 .... partial safety factor taking into account deviations in the height position of the reinforcement and uncertainties due to anchor installation γ3 .... partial safety factor accounting for scatter of failure loads and model uncertainties Eq. (5) is valid for single anchors and sufficient thickness of the concrete member (h > 1,5 c1) as well as an edge distance c2 perpendicular to the direction of the shear load measured from the axis of the anchor c2 > 1,5 c1. For execution special attention should be paid to the following aspects: The hairpin reinforcement should be anchored outside the assumed failure cone and consist of ribbed reinforcing bars with a diameter not larger than 16 mm. It should be
259
inclined with respect to the concrete cover. Thus the concrete cover of the hairpin legs is bigger than that of the bend, which improves the anchorage. Corrosion generally should not be relevant, since the baseplate of the fixed part is typically grouted over the bend of the hairpin reinforcement. If not, the reinforcement must be protected by galvanization, special coatings or the use of stainless steel. Sufficient bending radius will compensate for the positioning tolerances of the hairpin reinforcement and thus make sure that the anchors will be positioned within the hairpin.
6. Summary After reviewing some alternative methods to most effectively utilize the concrete edge strength, the reader has been presented with a formula to design anchors under shear loads when hairpin reinforcement is present in the concrete. This formula is compatible with modern design concepts and has been adapted to Eurocode 2. Moreover it has been shown, that global design concepts do not always clearly represent the complex situation near a concrete edge. Therefore it is strongly recommended to use engineering judgement and well based design concepts in the planning of safety relevant fixings near a concrete edge.
7. References 1. Paschen, H., and Schönhoff, Th., ‘Untersuchungen über in Beton eingelassene Scherbolzen aus Betonstahl’, Deutscher Ausschuß für Stahlbeton 346 (Wilhelm Ernst & Sohn, Berlin, 1983) 105-147. 2. Klingner, R., Mendonca, J., and Malik, J., ‘Effect of reinforcing details on the shear resistance of anchor bolts under reversed cyclic loading’, Journal of the American Concrete Institute 79 (1) (1982) 3-12. 3. Comité Euro-International du Béton, CEB-FIP Model Code 1990 (Thomas Telford, London, 1993) 437 pp. 4. Eligehausen, R., Mallée, R., Rehm, G., ‘Befestigungstechnik’, Betonkalender 1997, part 2, 609-753. 5. Comité Euro-International du Béton, ‘Fastenings to concrete and masonry structures’, Bulletín 216 (Thomas Telford, London, 1994) 249 pp. 6. Comité Euro-International du Béton, ‘Design of fastenings in concrete’, Bulletín 233 (Thomas Telford, London, 1997) 83 pp. 7. Hartmann, M., Silva, J., ‘Versuche zur Erhöhung der Tragfähigkeit von randnahen Ankern’ (HILTI AG Konzernforschung, Report No. A-IF6-8/97, 1999). 8. Fritsche, G., Wicke, M., ‘Versuche zur Prüfung von Metalldübeln’, Institut für Betonbau, Universität Innsbruck (Report No. 22, 1998). 9. Randl, N., Wicke, M., Schubübertragung zwischen Alt- und Neubeton, Beton- und Stahlbetonbau 95 (8) (2000) 461-473. 10. Randl, N., Untersuchungen zur Kraftübertragung zwischen Alt- und Neubeton bei unterschiedlichen Fugenrauhigkeiten, Doctoral thesis (Universität Innsbruck, 1997) 369 pp.
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BEHAVIOR OF TENSILE ANCHORS IN CONCRETE: STATISTICAL ANALYSIS AND DESIGN RECOMMENDATIONS Mansour Shirvani*, Richard E. Klingner**, and Herman L. Graves, III*** * Former, The University of Texas at Austin, USA. ** Dept. of Civil Engineering, The University of Texas at Austin, USA. *** U.S. Nuclear Regulatory Commission, Washington, D.C., USA.
Abstract The overall objective of this paper is to evaluate four different procedures for predicting the concrete breakout capacity of tensile anchors under static and dynamic loading, and in uncracked and cracked concrete. An existing public-domain data base of tensile anchors was evaluated and updated. Observed capacities of tensile anchors failing by concrete breakout were compared with the predictions of four methods: the 45-Degree Cone Method; the CC Method, and a variation on it; and a “Theoretical Method.” Each predictive method was then evaluated using Monte Carlo analyses to predict the probability of failure by concrete breakout, using the design framework of ACI 349-90, Appendix B “Steel Embedments.” [1]
1. Introduction The objective of this research was to provide the US Nuclear Regulatory Commission (NRC) with a comprehensive document that could be used to establish regulatory positions regarding fastening to concrete. Tensile behavior of anchors under static and dynamic loading in uncracked and cracked concrete, and for cast-in-place, undercut, sleeve and expansion anchors, is evaluated using the design framework of ACI 349-90, and four possible predictive equations for concrete breakout: 1) the 45-Degree Cone Method; 2) the Concrete Capacity Method (CC Method), and a variation on that method; and 3) a “Theoretical Method” related to the CC Method. Available test data are evaluated and organized by failure mode, using descriptions and photographs presented by the original researchers. Each set of design provisions is evaluated based on the following criteria [2]:
261
1) An ideal design method should give ratios of observed to predicted capacity showing no systematic error (that is, no variation in ratios with changes in embedment depth), high precision (that is, little scatter of data). 2) An ideal design method should have acceptably low probabilities of failure in the overall design framework in which it is to be used.
2. Test Data for Tensile Anchors in Concrete The public-domain data base used for this purpose is maintained by ACI Committees 349 and 355, and comes from many contributors, including Dr. Werner Fuchs (University of Stuttgart), Drilco Industries, Inc., Prof. Peter Carrato (Bucknell University), The University of Texas at Austin, Hilti AG, and various members of ACI Committees 349 and 355. The data base contains data for tensile breakout failures only.
3. Background General information on anchor types and behavior is given in CEB (1991) [3]. Essential information is summarized here. Tensile Breakout Capacity by 45-Degree Cone Method The 45-Degree Cone Method assumes that a constant tensile stress of 4 f c′ acts on the projected area of a 45-degree cone radiating towards the free surface from the bearing edge of the anchor (Figure 1). T
2hef+dh
45º
dh
Figure 1
Tensile breakout cone as idealized by 45-degree Cone Method
262
For a single tensile anchor far from edges, the cone breakout capacity is determined by:
(
To = 4 fc′ π hef2 1 + d h hef
(
)
To = 0.96 f c′ π hef2 1 + d h hef
)
lb
(1a)
N
(1b)
where: f c′ = specified concrete compressive cylinder strength (psi in US units, MPa in SI units); dh = diameter of anchor head (inch in US units, mm in SI units); and hef = effective embedment (inch in US units, mm in SI units). If the cone is affected by edges (c < hef) or by an adjacent concrete breakout cone, the breakout capacity is:
Tn =
AN To ANo
(2)
where: AN = actual projected area of failure cone or cones; ANo = projected area of a single cone unaffected by edges =
π hef2 (1 + d h hef ) .
Tensile Breakout Capacity by Concrete Capacity Method (CC Method) The CC Method [4] computes the concrete breakout capacity of a single tensile anchor far from edges as: (3) To = k fc′ hef1.5 where: To = tensile breakout capacity; k = constant; for anchors in uncracked concrete the mean values originally proposed based on previous tests are: 35 for expansion and sleeve anchors, 39 for undercut and headed anchors, in US units; or 13.48 for expansion and sleeve anchors, 15 for undercut and headed anchors, in SI units; f′c = specified concrete compressive strength (6 × 12 cylinder) (inch in US units, MPa in SI units.); hef = effective embedment depth (inch in US unit, MPa in SI unit). In the CC Method, the breakout body is idealized as a pyramid with an inclination of about 35 degrees between the failure surface and the concrete member surface (Figure 2).
263
As a result, the base of the pyramid measures 3hef by 3hef. If the failure pyramid is affected by edges or by other concrete pyramids, the concrete capacity is calculated according the following equation:
Tn =
AN ψ 2 Tno A No
(4)
where: ANo = projected area of a single anchor at the concrete surface without edge influences or adjacent-anchor effects, idealizing the failure cone as a pyramid with a base length of scr = 3hef (Ano = 9 hef2) (See Appendix A of Reference 2); AN = actual projected area at the concrete surface; 3hef 3hef
h
ef
35º
Figure 2
Tensile breakout body as idealized by CC Method
ψ2 = tuning factor to consider disturbance of the radially symmetric stress distribution caused by an edge, = 1, if c1 ≥ 1.5hef; = 0.7 + 0.3
c1 , if c1 ≤ 1.5hef; 1.5hef
where: c1 = edge distance to the nearest edge. Tensile Breakout Capacity by “Theoretical Method” The “Theoretical Method” is based on linear elastic fracture mechanics, including the size effect [5]. Tensile breakout capacity is:
264
Nn =
where : Nn fcc hef k
= = = =
k ⋅ f cc ⋅ h 2 ef hef 1 + 50
0.5
(5)
predicted concrete tensile breakout capacity (kN) actual tested strength of a 200-mm concrete cube (MPa) effective embedment (mm) 2.75 for undercut and cast-in-place anchors, and 2.5 for expansion and sleeve anchors.
Tensile Breakout Capacity by the Variation on the CC Method As a result of previous work in ACI Committees 318 and 349 (Subcommittee 3), it has been proposed to modify the CC Method slightly, changing the exponent of the embedment depth from 1.5 to 1.67 for effective embedments of 250 mm (9.84 in) or greater, and changing the leading coefficient appropriately. Effects of Dynamic Tensile Loading and Cracks on Tensile Breakout Capacity In this research, predicted tensile breakout capacities under static loading were multiplied by a dynamic factor equal to 1.25 for undercut, cast-in-place, and sleeve anchors, and equal to 1.0 for expansion anchors [6, 7, 8]. Capacities in uncracked concrete were multiplied by a crack factor equal to 0.9 for undercut and cast-in-place anchors, equal to 0.7 for sleeve and expansion anchors [5, 7, 8, 9].
4. Statistical Evaluation of Database (static, uncracked) The database for static testing on anchors in uncracked concrete comprises 1566 tests: a) Single tensile anchors, effective embedment ≤ 188 mm, no edge effects (1130 tests); b) Single tensile anchors, effective embedment > 188 mm, no edge effects (77 tests); c) Single tensile anchors, effective embedment ≤ 188 mm, edge effects (137 tests); d) Single tensile anchors, effective embedment > 188 mm, edge effects (33 tests); e) Tensile 2- and 4-anchor groups, effective embedment ≤ 188 mm, no edge effects (170 tests); and f) Tensile 4-anchor groups, effective embedment > 188 mm, no edge effects (19 tests). Means and coefficients of variation for ratios of observed to predicted capacity are shown in Table 1. All are for static loading in uncracked concrete.
265
Table 1
Mean and COV of ratios of observed to predicted capacity for each anchor category (static loading, uncracked concrete) CC METHOD
ANCHOR CATEGORY Single anchors, shallower embedments Single anchors, deeper embedments Single anchors, shallower embedments, edge effects Single anchors, deeper embedments, edge effects 2- and 4-anchor groups, shallower anchors, no edge effects 4-anchor groups, deeper embedments, no edge effects
45-DEG CONE METHOD Mean COV
THEORETICA L METHOD Mean COV
Mean
COV
0.981
0.197
1.356
0.266
0.999
0.231
1.110
0.189
0.867
0.257
0.929
0.192
1.032
0.271
1.024
0.252
1.054
0.286
1.203
0.173
0.675
0.210
1.014
0.244
1.081
0.192
1.188
0.331
1.057
0.225
1.336
0.254
0.930
0.229
1.133
0.252
Examination of Table 1 shows that the CC Method and the Theoretical Method usually are more accurate than the 45-Degree Cone Method (mean values closer to unity), and have less scatter (smaller COV). Since the 45-Degree Cone Method generally gave a higher COV than both the CC and Theoretical Methods, it was decided to exclude it for analysis of other cases.
5. Probabilities of Failure associated with each Breakout Formula Using the overall ratios of concrete breakout capacity, appropriately approximated by normal distributions (Appendix B of Reference 2), probabilities of failure were computed for an assumed statistical distribution of loads, and probabilities of brittle failure were computed independent of load, for single anchors designed according to each method for predicting concrete breakout capacity. This statistical evaluation was carried out using the Monte Carlo approach, and assuming the ductile design framework and the load and understrength factors of ACI 349-90, Appendix B [10, 11]. Probabilities of Failure under Known Loads, Static Loading, Uncracked Concrete Results of the statistical analyses are summarized in Table 2. Higher values of β indicate lower probabilities of failure.
266
Table 2
Probability of failure under known loads for different categories of tensile anchors, ductile design approach, static loading, uncracked concrete CC METHOD
ANCHOR CATEGORY single anchors, shallower embedments single anchors, deeper embedments single anchors, shallower embedments, edge effects single anchors, deeper embedments, edge effects 2- and 4-anchor groups, shallower anchors, no edge effects 4-anchor groups, deeper embedments, no edge effects
45-DEG CONE METHOD Probability β of Failure
THEORETICA L METHOD Probability β of Failure
Probability of Failure
β
5.46E-05
3.87
8.56E-04
3.14
1.57E-04
3.60
1.39E-05
4.19
1.99E-03
2.88
5.10E-05
3.89
1.92E-03
2.89
1.00E-03
3.09
2.92E-03
2.76
1.70E-06
4.65
9.87E-04
3.09
7.41E-04
3.18
2.23E-05
4.08
1.79E-03
2.91
2.53E-04
3.48
5.23E-04
3.28
5.08E-04
3.29
7.45E-04
3.18
Because the probability of failure associated with the 45-Degree Cone Method was consistently higher than that of the CC Method or the Theoretical Method, it is not investigated further here. Probabilities of Failure for Other Cases (Dynamic Loading, Cracked Concrete, or Both) For known loads, probabilities of failure with the CC Method and the Theoretical Method are given in Table 3. All results are for single anchors, shallow embedment, no edge effect). These results are somewhat different from those of Farrow et al. [10, 11], because the anchors were categorized differently in that work (edge distance / embedment, spacing / embedment), and because this work used a more extensive data base.
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Table 3
Probability of failure under known loads for different cases of tensile anchors, ductile design approach, Category One CC METHOD
ANCHOR CASE
THEORETICAL METHOD Probability β of Failure
Probability of Failure
β
2.94E-13
7.20
6.47E-15
7.70
9.78E-08
5.20
1.20E-08
5.58
2.10E-08
5.48
3.80E-08
5.38
1.60E-03
2.95
4.68E-04
3.31
1.58E-08
5.53
9.07E-10
6.01
3.62-06
4.49
3.02E-07
4.94
dynamic loading, uncracked concrete, cast-in-place and undercut dynamic loading, uncracked concrete, expansion and sleeve static loading, cracked concrete, cast-inplace and undercut static loading, cracked concrete, expansion and sleeve dynamic loading, cracked concrete, caste-in-in-place and undercut dynamic loading, cracked concrete, expansion and sleeve
Probabilities of Brittle Failure Independent of Load, Ductile Design Approach Probabilities of brittle failure independent of load are given in Table 4. Probabilities of Brittle Failure Independent of Load for Other Cases (Dynamic Loading, Cracked Concrete, or Both) Probabilities of brittle failure independent of load are given in Table 5.
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Table 4
Probabilities of brittle failure independent of load for different categories of tensile anchors, ductile design approach, Static, Uncracked CC METHOD
ANCHOR CATEGORY single anchors, shallower embedments single anchors, deeper embedments single anchors, shallower embedments, edge effects single anchors, deeper embedments, edge effects 2- and 4-anchor groups, shallower anchors, no edge effects 4-anchor groups, deeper embedments, no edge effects Table 5
45-DEG CONE METHOD
THEORETICAL METHOD
Probability of Brittle Failure
β
Probability of Brittle Failure
β
Probability of Brittle Failure
β
0.178
0.922
0.066
1.51
0.188
0.884
0.088
1.36
0.369
0.335
0.248
0.680
0.206
0.821
0.198
0.848
0.201
0.837
0.0405
1.75
0.717
0.573
0.200
0.841
0.107
1.24
0.125
1.15
0.152
1.03
0.0621
1.54
0.273
0.603
0.129
1.13
Probability of brittle failure independent of load for different cases of tensile anchors, ductile design approach, Category One CC METHOD ANCHOR CASE
dynamic loading, uncracked concrete, castin-place and undercut dynamic loading, uncracked concrete, expansion and sleeve static loading, cracked concrete, cast-inplace and undercut static loading, cracked concrete, expansion and sleeve dynamic loading, cracked concrete, castein-in-place and undercut dynamic loading, cracked concrete, expansion and sleeve
269
THEORETICAL METHOD Probability of Brittle β Failure
Probability of Brittle Failure
β
7.16E-02
1.46
1.03E-01
1.26
8.73E-02
1.36
8.15E-02
1.40
1.19E-01
1.18
1.33E-01
1.11
1.20E-01
1.17
1.19E-01
1.18
5.89E-02
1.56
6.61E-02
1.51
5.74E-02
1.61
1.67E-01
0.97
These probabilities of failure are independent of the assumed statistical distribution of the loads. The ductile failure criterion, which requires actual steel fracture before concrete breakout, is quite severe, and these computed probabilities of brittle failure are conservative (high). Results from Tables 4 and 5 imply that the CC Method generally gives lower probabilities of brittle failure than the 45-Degree Cone Method and the Theoretical Method. Probabilities of Failure for the Variation on the CC Method, Known Loads Probabilities of failure under known loads are presented in Table 6. The probabilities of failure are of course identical in Anchor Categories One, Three and Five, since the method is identical to the CC Method for shallower embedments, so the table includes only deep-embedment categories. Probabilities of failure are clearly higher for the variation in the CC Method. Table 6
Probability of failure under known loads for different categories of tensile anchors, ductile design approach, Static, Uncracked CC METHOD
ANCHOR CATEGORY
single anchors, deeper embedments single anchors, deeper embedments, edge effects 4-anchor groups, deeper embedments, no edge effects
β
VARIATION ON CC METHOD Probability β of Failure 4.89E-05 3.89
Probability of Failure 3.27E-05
4.51
1.70E-06
4.65
8.84E-08
5.01
5.36E-04
3.27
6.78E-04
3.14
6. Conclusions 1) The CC Method and the Theoretical Method have a generally lower probability of failure under known loads, than the 45-Degree Cone Method. These results are consistent with those of Farrow et al. [10, 11]. The lower probability of failure is particularly striking for deeper embedments. The CC Method has a generally lower probability of failure under known loads, than the Theoretical Method. 2) The CC Method has a generally lower probability of brittle failure independent of load, than the 45-Degree Cone Method and the Theoretical Method. 3) The Variation on the CC Method, which uses an exponent of (5/3) for the effective embedment at deeper embedments, has higher systematic error and higher probabilities of failure than the CC Method. It has no technical justification.
270
7. Acknowledgement and Disclaimer This paper presents partial results of a research program supported by U.S. Nuclear Regulatory Commission (NRC) under Contract No. NRC-04-96-059. The technical contact is Herman L. Graves, III. Any conclusions expressed in this paper are those of the authors, and are not to be considered NRC policy or recommendations.
8. References 1.
ACI Committee 349, “Code Requirements for Nuclear Safety Related Concrete Structures,” American Concrete Institute, Detroit, 1990.
2.
Shirvani, Mansour, “Behavior of Tensile Anchors in Concrete: Statistical Analysis and Design Recommendations,” M.S. Thesis, The University of Texas at Austin, May 1998.
3.
CEB, “Fastenings to Reinforced Concrete and Masonry Structures: State-of-Art Report, Part 1,” Euro-International-Concrete Committee (CEB), August 1991.
4.
Fuchs, W., Eligehausen and R. and Breen, J. E., “Concrete Capacity Design (CCD) Approach for Fastening to Concrete”, ACI Structural Journal, Vol. 92, No. 1, January-February, 1995, pp. 73-94.
5.
Eligehausen, R. and Ozbolt, J., “Influence of Crack Width on the Concrete Cone Failure Load,” Fracture Mechanics of Concrete Structures, Z. P. Bazant, ed., Elsevier Applied Science, 1992, pp. 876-881.
6.
Rodriguez, M., “Behavior of Anchors in Uncracked Concrete under Static and Dynamic Loading,” M.S. Thesis, The University of Texas at Austin, August 1995.
7.
Hallowell, J. M., “Tensile and Shear Behavior of Anchors in Uncracked and Cracked Concrete under Static and Dynamic Loading,” M.S. Thesis, The University of Texas at Austin, August 1996.
8.
Zhang, Y. “Dynamic Behavior of Multiple Anchor Connections,” Ph.D. Dissertation, The University of Texas at Austin, May 1997.
9.
Eligehausen, R. and Balogh, T., “Behavior of Fasteners Loaded in Tension in Cracked Reinforced Concrete,” ACI Structural Journal, Vol. 92, No. 3, May-June, 1995, pp. 365-379.
10. Farrow, C. Ben and Klingner, R. E., “Tensile Capacity of Anchors with Partial or Overlapping Failure Surfaces: Evaluation of Existing Formulas on an LRFD Basis,” ACI Structures Journal, Vol. 92, No. 6, November-December 1995, pp. 698710. 11. Farrow, C. Ben, Frigui, Imed and Klingner, R. E., “Tensile Capacity of Single Anchors in Concrete: Evaluation of Existing Formulas on an LRFD Basis,” ACI Structures Journal, Vol. 93, No. 1, January-February 1996.
271
PERFORMANCE OF SINGLE ANCHORS NEAR AN EDGE UNDER VARYING ANGLES OF LOADING Richard E. Wollmershauser, Ute Nestler, and Vincent Smith HILTI, Inc., USA
Abstract While the performance of anchors near an edge under shear loading perpendicular to the edge is well documented, especially under the concrete capacity design (CCD) method, virtually no published tests or reports are available to establish the influence concrete capacity of anchors at angles other than perpendicular. Single anchor tests on adhesive-bonded anchors have been performed at three edge distances and under angles of shear loading varying from 0 to 180 degrees from the perpendicular. Analysis is performed to develop influencing factors resulting from edge distances and angles of loading. A proposal is made for anchor influencing factors under these loading conditions for inclusion in the CCD method.
1. Introduction The concrete shear capacity of an anchor near the edge of a concrete element when the loading is perpendicular to the edge is well documented. However, the capacity when the angle of loading varies from perpendicular is not well known. This paper presents the results of tests of adhesive-bonded anchors at three edge distances with loading angles varying from perpendicular to the edge through 180 degrees. Finite element analysis has been performed to correlate with the results, as well as to investigate the capacity with very stiff anchor rods. Finally, a recommendation is made for an angle influencing factor to account for the effects of loading angle in shear.
272
2. Current State of Knowledge The CEB Design of Fastenings in Concrete1 provides the only known and widely available recommendation for the effect of loading angle on the shear capacity of an anchor near an edge and is based on very limited testing. It is assumed that there is no influence up to 55 degrees from the perpendicular toward the edge. The following is excerpted from ref. 1. The factor ψα,V takes into account the angle αV between the load applied, Vsd, and the direction perpendicular to the edge under consideration for the calculation of the concrete resistance of the concrete member (see Figure 1).
ψα,V = 1.0
ψα,V =
for 0° < αV < 55°
1 cos αV + 0.5 sin αV
for 55° < αV < 90°
ψα,V = 2.0
for 90° < αV < 180°
Fig. 1—Loading angle The above equations are known to be conservative.
3. Test Program with Adhesive-Bonded Anchors A test program was performed with 12 mm (1/2-inch) adhesive-bonded anchors using threaded rods meeting ASTM A193 B7 with fut = 862 MPa (125 ksi) and fy = 724 MPa (105 ksi). The concrete compressive strength was approximately B25 (3,200 psi). The embedment depth, hef, was 108 mm (4-1/4 in.), with hef/do = 8.5. Three edge distances, c, were tested, 38 mm (1-1/2 in.), 63.5 mm (2-1/2 in.), and 90 mm (3-1/2 in.). The angle of shear loading varied in 30-degree increments from perpendicular to the edge (0 degrees) to away from the edge (180-degrees from the edge). A Teflon® sheet was placed between the concrete and the shear loading plate. See Figures 2 and 3 for the load
273
application. All testing was in accordance with the requirements of ASTM E488-962. Figures 2 and 3 depict the typical test setups. The load was applied by pushing toward the free edge. Edges were prepared by saw cutting into the slab at a depth sufficient to not influence the test results.
Fig. 2—Overall test setup
Fig. 3—Detailed shear loading
4. Test Results Test results are given in Table 1 and Figure 4. Concrete edge breakout was the typical failure mode for all anchors loaded from 0o through 90o except at an edge distance of 90 mm, where the failure mode shifted to anchor steel. Beyond 90o the failure mode shifted to anchor steel. Figure 5 presents typical concrete edge breakout failure modes. Table 1—Shear test results Angle of loading (o)
1 2
c = 38 mm Vult (kN)
Adhesive-bonded anchors c = 63.5 mm
Failure mode2
Vult (kN)
Failure mode2
0 10 5B 18 5B 30 12 5B 20 5B 60 18 5B 32 5B 90 31 5B 45 5B 120 42 5B 52 4D/1B 150 51 5B 52 5D 180 47 4B/1D 52 5D not tested B = concrete failure, D = anchor steel failure
274
c = 90 mm Vult (kN)
Failure mode2
30 34 44 52 --1 --1 --1
5B 5B 5B 5D ----
60
Failure Load [kN]
50
40
90 mm
30
63.5 mm 20 38 mm 10
0 0
30
60
90
120
150
180
Angle [degrees]
Fig. 4—Shear capacity as a function of angle of loading
Fig. 5—Typical failure mode
5. Finite Element Analysis 5.1. The Model The Finite Element model of the numerical analysis is shown in Figure 6. It shows the anchor at an edge distance of 90 mm (3-½ inch). The adhesive ensuring the bonding between the anchor and concrete employs a mortar like behavior. A special material model describing this behavior is implemented in the Finite Element code. The same material model is used to describe the behavior of the concrete. It enables the observation of how cracks develop in the adhesive and concrete.
275
5.2. Crack Distribution Figure 7 shows the crack distribution when the load on the anchor is acting perpendicular to the edge. It can be seen that the cracks formed a cone like failure pattern towards the free edge. There is another crack zone forming parallel to the free edge.
Fig. 6— Finite element model
Legs of Cracked Concrete Cone
Perpendicular Load Direction Cracks perpendicular to Edge
Fig. 7—Crack distribution in concrete under load perpendicular to the edge The failure cone shape changes as the load direction changes from the perpendicular direction. The larger the load angle becomes the more the direction of the concrete failure cone turns accordingly, as illustrated by Figure 8. It shows the crack pattern with loads acting at angles of 30 and 60 degrees. At all angles less than 90 degrees the fastening fails due to concrete failure.
276
Notice that the perpendicular crack is fully developed at angles less than 90 degrees. At an angle of exactly 90 degrees it is still fully developed (see Figure 9).
60 degrees
30 degrees
Fig. 8—Crack distribution in concrete under loads acting at angles of 30 degrees and 60 degrees Load direction parallel to free Edge
Fig. 9—Crack distribution in concrete under load parallel to the edge If the load angle is greater than 90 degrees the cracks perpendicular to the free edge are not as fully developed than with smaller load angles. In fact, the anchor behavior is much like that of anchors without any edge influence (Figure 10). No breakage cone develops and the failure mode is steel failure. Anchors employing smaller edge distances behave similarly to the anchor at an edge distance of 90 mm. But the concrete failure occurs at smaller loads due to the fact that less amount of material resists the “crack growth”.
277
120 degrees
150 degrees 180 degrees
Fig. 10—Crack distribution in concrete under loads acting at angles of 120, 150 and 180 degrees 5.3. Failure Loads The failure loads from the simulation are shown in Table 2 and Figure 11. Table 2—Failure loads from simulation Edge distance (mm)
38
63.5
90
Angle of loading (o) 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180
Failure load (kN) 13 17 20 29 49 49 49 20 25 30 43 49 49 49 34 35 40 49 49 49 49
278
Failure load (lb) 3,000 3,900 4,600 6,500 11,000 11,000 11,000 4,500 5,600 6,700 9,600 11,000 11,000 11,000 7,700 7,800 9,000 11,000 11,000 11,000 11,000
Failure Load [kN]
60 50 40 30
90 mm 63.5 mm
20
38 mm
10 0 0
30
60
90
120
150
180
Angle [degrees] Fig. 11—Failure loads 5.4. „Perfect Steel“ Rods The simulation with an edge distance of 38 mm has also been done with anchor rods using higher strength steel. That was done to minimize the influence of steel strength on the failure load results. Figure 12 shows the results of those simulations: 100
Failure Load [kN]
90 80
'"Perfect' steel"
70
Yield Stress 724 MPa
60 50 40 30 20 10 0 0
30
60
90
120
150
180
Angle [degrees]
Fig. 12— Failure loads employing very stiff anchor rods
279
6. Proposed Equations There is no single equation that can describe the anchor behavior as a function of the angle of the applied load. The anchor behavior has been divided into two angle segments, from 0 to 90 degrees and for angles greater than 90 degrees. The two equations describing the anchor behavior have been obtained using regression analysis: 0° < αV < 90°
F = 0.0012* αV2 + 0.0549*αV + 13.656 (kN)
(Eq. 1)
90° < αV < 180°
F = -0.0052*αV2 + 2.0623*αV - 113.76 (kN)
(Eq. 2)
Figure 13 shows the equations compared with simulation.
100
Failure Load [kN]
90 80 70
Equations
60
'"Perfect' steel"
50 40 30 20 10 0 0
30
60
90
120
150
180
Angle [degrees] Fig. 13—Comparison of equations and simulation
7. Summary and Recommendations This paper has presented a limited test program of shear loading of anchors near the free edge at varying load angles. The suggested equations have been proposed to describe the behavior at angles from perpendicular to the free edge to 90 degrees and from 90 to 180 degrees. The equations have their limitations because they only describe the anchor behavior for a limited sample of anchors under a limited number of conditions. Further tests and simulations should be undertaken to investigate the sensitivity of the equation parameters towards variables such as anchor diameter, edge distance and concrete strength.
280
8.
References
1
Design of Fastenings in Concrete, Comite Euro-International du Beton (CEB), Thomas Telford Services Ltd., London, Jan. 1997. 2 “Standard Test Method for Strength of Anchors in Concrete and Masonry Elements, ASTM E488-96,” American Society for Testing and Materials, West Conshohocken, 1996.
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THE PREQUALIFICATION OF ANCHORS IN THE UNITED STATES OF AMERICA: PAST, PRESENT AND FUTURE Richard E. Wollmershauser HILTI, Inc., USA
Abstract Anchor prequalification in the United States for fastening to concrete is undergoing significant change in order to meet new requirements of ACI 318 Concrete Building Code. In the past and up to the present, there have been limited requirements under the ICBO Uniform Building Code that apply only to the western portion of the United States that use this code. Manufacturers have generally published data based on ASTM E 488 testing requirements or the ICBO ES Acceptance Criteria AC01 or AC58. Testing has been limited to uncracked concrete. These requirements are briefly reviewed ACI 318 has approved a code addition based on the Concrete Capacity Design Method to be included in the year 2002 version that requires mechanical anchor prequalification. ACI Committee 355 Anchorage to Concrete has developed and approved a prequalification standard, ACI 355.2, that meets the new code requirements and is closely harmonized with the European Technical Approval Guideline 001. These prequalification requirements are discussed. The future prequalification requirements of bonded anchors are also included.
1. Introduction The prequalification of post-installed anchors in the USA is currently on the midst of significant change from the past. The first anchor prequalification standard has been in use since July 1975, with others developed since then for adhesive-bonded anchors and unreinforced masonry applications. With the proposed adoption of design provisions for anchors in ACI 3181, significant developments are underway to enhance and harmonize anchor prequalification requirements. The key organizations are ACI2, ASTM3, and ICBO ES4.
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2. The Past 2.1 Mechanical Anchors In August 1975, The International Conference of Building Officials Research Committee, later to become ICBO Evaluation Services, Inc., adopted what is believed to be the first anchor prequalification standard in the USA, Standard for Testing Expansion Anchors in Concrete under the Uniform Building Code5. This standard, which was developed by the Expansion Anchor Manufacturers Institute, later became known as Acceptance Criteria 01 (AC01)6. It contained very limited testing requirements, but allowed for approvals in normal-weight and lightweight concrete. Included were tension and shear tests with sample sizes of three for each tested condition. Edge and spacing tests were optional, with unconservative default requirements if testing was not performed. Allowable stress design capacities were prescribed using a safety factor of eight without special inspection of anchor installation and four with special inspection. This standard was reissued in April 1986 to bring into compliance with then current references. Recognizing the limitations of the standard, a group of representatives from manufacturers and testing laboratories developed an improved version of AC01 based on the European UEAtc M.O.A.T. 49 document7, but with significant differences that preclude direct equivalence. This version of AC01 was adopted in July of 1991 by ICBO ES, Inc. and included definitions, more detailed requirements for concrete, added masonry as a base material, prescribed more detailed testing procedures in accordance with ASTM E 488-908, and allowed the calculation of allowable loads based on a 5 percent fractile probability method. Table 1 gives a brief listing of the tests of AC01. All tests are in uncracked concrete. But more importantly, it introduced the concept of proper functioning (suitability requirements) as well as service condition requirements. The suitability tests included sensitivity to drilled-hole diameters (larger and smaller) and reduced setting torque of 0.2 Tinst. Further enhancements in 1993, 1997 and 1999 added technical corrections, seismic testing methods for tension and shear (as a result of the January 17, 1994 Northridge earthquake) and displacement requirements. The service condition tests evaluated single anchor tension and shear performance, edge and spacing performance, performance under groups, and combined tension and shear loading. However, the approvals issued under this criteria have been limited to uncracked concrete, since the criteria contains no testing provisions to demonstrate performance in cracks. A similar acceptance criteria for undercut anchors is under preparation and should be adopted within 2001. 2.2 Adhesive-Bonded Anchors Adhesive-bonded anchors remained without any specific criteria until January 1995, when ICBO ES adopted AC589 as developed and recommended by a group of anchor
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manufacturers, later to become the Concrete Anchor Manufacturers Association10 (CAMA). This criterion used many of the tests from AC01, but deviated significantly in delineating suitability requirements in evaluating the performance of the many available Table 1—Tests Contained in AC01 Test Series Description of Tests
Test Parameters
Proper Functioning 1, 2 Tension tests, Tolerance on drilled hole 3 Tension tests, intensity of expansion
Large hole, small hole Reduced setting torque
Service Conditions – Tension 4, 5, 6 Tension tests, single anchors 7, 8, 9, 10 Establish critical and minimum edge distances 11, 12 Anchor group tests critical and minimum spacing Service Conditions – Shear 13 Single anchors 14, 15, 16, 17 Establish critical and minimum edge distances 18, 19 Group of two anchors, critical and minimum edge distance Service Conditions – Oblique Loading 20, 21 Single anchors, under combined shear and tension loading at critical edge distance Seismic Tests 22 Simulated seismic tension tests 23 Simulated seismic shear tests
Low-, medium-, and high-strength concrete Low-, and high-strength concrete Low-strength concrete
Low-strength concrete Low-, high-strength concrete Low-strength concrete with minimum spacing Low- and high-strength concrete
Mid-strength concrete Mid-strength concrete
adhesives. These suitability requirements included the following six requirements. For each of those not performed, specific restrictions were included in the evaluation report. • • • • • •
Fire resistance (optional) Creep under sustained loading (optional) In-service temperature (mandatory) Sensitivity to moisture in the drilled hole (optional) Freezing and thawing (optional) Seismic resistance (optional)
The service condition tests evaluated single anchor tension and shear performance, edge and spacing performance, performance under groups, and combined tension and shear loading. Again, the approvals issued under this criteria have been limited to uncracked concrete, since there have been no testing provisions to demonstrate performance in cracks. Technical enhancements were made in 1997, 1998, 1999, and 2000. Table 2 gives the specific tests of AC58, all being performed in uncracked concrete. 2.3 ACI and ASTM Activities In 1991, ACI Committee 318, voted to begin the preparation of design provisions for anchorage to concrete, based on the then newly developed Concrete Capacity Design (CCD) Method11. Committee 318 further requested that ASTM Subcommittee E 6.1312
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began work on a required testing program that would prequalify post-installed mechanical anchors in concrete, meeting the design requirements of the draft ACI anchorage provisions. The ASTM drafts were based on the work for mechanical anchors that had been developed in the UEAtc, and which was later transferred to EOTA and became ETAG 00113. Table 2—Tests Contained in AC58 Test Series Description of Tests
Test Parameters
Service Conditions – Tension 1, 2, 3 Single anchors 4, 5, 6, 7 Establish critical and minimum edge distances 8, 9 Group of two anchors, critical and minimum spacing 10, 11 Group of four anchors, critical and minimum spacing Service Conditions – Shear 12 Single anchors 13, 14 Establish critical and minimum edge distances Service Conditions – Oblique Loading 15 Single anchors, combined tension and shear loading at critical edge distance Suitability Requirements 16 Fire resistive 17 Creep 18 In-service temperature 19 Dampness 20 Freezing and thawing resistance 21, 22 Simulated seismic tension and shear tests
Low-, medium-, and high-strength concrete Low- and high-strength concrete Low-strength concrete Low-strength concrete
Low-strength concrete Low-strength concrete Low-strength concrete
3,000 psi concrete 3,000 psi concrete 3,000 psi concrete 3,000 psi concrete 4,500 psi concrete 3,000 psi concrete
Progress was slow in ASTM. Then in 1997, ACI Committees 318 and 355 recommended that ACI Committee 355 take over the preparation of the standard, so that the testing standard and the code provisions could be completed for the 1999 version of the ACI 318 Code. While many drafts and ballots were prepared by ACI 355, the deadline for inclusion into the 1999 version was missed. Committee 355 did complete work in early 2000, and an ACI provisional standard, ACI 355.2-0014 was approved in July 2000, to be required by reference in ACI 318-02.
3. The Present 3.1 Status as of Mid-2001 The most widely accepted anchor approvals in the United Stated currently are those issued by ICBO ES, as previously discussed. While they are issued for use under the Uniform Building Code, their applicability has been at times informally accepted for use under other building codes by design engineers because of their reliance on formally adopted acceptance criteria. The limitation of exclusion from use in tension zones limits their use. There is a growing understanding in the United Stated among designers,
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especially in higher seismic zones, that anchors need to be prequalified for use in concrete that is prone to cracking. Enter the newly developing ACI code and standard. 3.2 ACI Activities With the completion of balloting and approval of ACI 355.2-00, as a provisional standard, processing is continuing toward a full standard by conducting a 90-day public comment period, with resolution of comments expected in the fall of 2001. This standard covers only post-installed mechanical anchors, which include undercut, torquecontrolled expansion and displacement-controlled expansion anchors. This standard becomes effective when it is called into use under ACI 318-02 as implemented in the IBC 2003. Thus, for practical purposes, this new prequalification standard will only become effective with the adoption of the IBC 2003 by governmental jurisdictions in the year 2003 and after, unless adopted by an approval entity for use before then. 3.3 What is ACI 355.2-00? Simply stated, it is a post-installed mechanical anchor prequalification standard containing both test methods and acceptance criteria that apply to both compression and tension zones of concrete structures. It also contains a Commentary that provides explanations for many of the sections of the standard that need further clarification to be easily understood. It applies to undercut, torque-controlled, and deformation-controlled expansion anchors. A qualified and experienced testing laboratory under the direction of a registered professional engineer performs tests, and a report is issued if the anchor system meets all the requirements. Data for the anchor system is published and is used for design under ACI 318 Appendix D. No approval agency oversees or issues an evaluation report, which is a significant departure from current procedures. All of the included tests, with the exception of the seismic tests, are identical to those of the ETAG 001, Parts 1 through 4. While not all of the tests from the ETAG 001 were used, those that were included were written so that the test methods were essentially the same. Why? Because the design requirements that both ACI 355.2-00 and ETAG 001 are tested against are almost identical and are based on the CCD Method. ACI 318 Appendix D is generally the same as ETAG Part C. Let’s look at the specifics of ACI 355.2-00. ACI 355.2-00 provides for the prequalification of anchors in either uncracked concrete, or both uncracked and cracked concrete. Specific test programs are delineated for each, giving reference tests, reliability (suitability) tests, and service condition tests. Depending on the results of the reliability tests and their relationship to reference tests, an anchor category, 1, 2, or 3, is established that is used by ACI 318 Appendix D for establishing strength reduction factors (φ) applied to the resistance calculations. These tests are summarized in the following Table 3.
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All tests for uncracked concrete prequalification are performed in uncracked concrete, while most of the tests for prequalification for both uncracked and cracked concrete are performed in cracks, as shown below. As of the writing of this paper, no anchor systems have been tested and qualified according to ACI 355.2-00 in the United States due to the short time the standard has been available. Table 3—Anchor Prequalification Tests in ACI 355.2-00 Tests for uncracked concrete Reference Tests
Tests for uncracked and cracked concrete
1. Tension tests in low strength uncracked concrete 2. Tension tests in high strength uncracked concrete --
1. Tension tests in low strength uncracked concrete 2. Tension tests in high strength uncracked concrete 3. Tension tests in low strength concrete in 0.012 in. (0.3 mm) cracks 4. Tension tests in high strength concrete in 0.012 in. (0.3 mm) cracks
--
Reliability Tests 3. Tension tests for sensitivity to reduced installation effort in uncracked concrete 4. Tension tests for sensitivity to large drilled hole diameter 5. Tension tests for sensitivity to small drilled hole diameter 6. Tension test under repeated load application in uncracked concrete – 10,000 cycles
5. Tension tests for sensitivity to reduced installation effort in 0.012 in. (0.3 mm) cracks 6. Tension tests for sensitivity to crack width and large drilled hole diameter in 0.020 in. (0.5 mm) cracks 7. Tension tests for sensitivity to crack width and small drilled hole diameter in 0.020 in. (0.5 mm) cracks 8. Tension test in crack whose width is being cycled between 0.004 and 0.012 in. (0.1 and 0.3 mm)
Service-condition tests 7. Tension tests in corner to verify concrete capacity edge requirement of 1.5 hef in uncracked concrete 8. Minimum edge and spacing to preclude concrete splitting upon installation, uncracked concrete 9. Shear capacity of steel in uncracked concrete (can calculate for standard threaded sections) ---
9. Tension tests in corner to verify concrete capacity edge requirement of 1.5 hef in uncracked concrete 10. Minimum edge and spacing to preclude concrete splitting upon installation, uncracked concrete 11. Shear capacity of steel in uncracked concrete (can calculate for standard threaded sections) 12. Seismic tension tests in 0.020 in. (0.5 mm) cracks 13. Seismic shear tests in 0.020 in. (0.5 mm) cracks
3.4 ASTM Activities Since ACI 355.2-00 does not include adhesive-bonded anchors, a project has begun in ASTM Subcommittee E 6.13 to develop a companion standard for their prequalification. A task group has met twice and developed a list of tests that should be included. Thus, we move toward the future.
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4. The Future 4.1 ACI Activities In order to fully implemented ACI 355.2-00, Appendix D will undergo further processing to become part of ACI 318-02 by reference, and ACI 318-02 subsequently part of the IBC 2003 by reference. These activities have been set in motion and it is expected that within two years, there will be a nation-wide prequalification standard for mechanical anchors for both uncracked concrete and cracked and uncracked concrete. ACI 318 Subcommittee B15 has initiated the development of code provisions for the design of adhesive-bonded anchors, to be added in a future code revision (possibly 2005 or 2008). Testing has taken place at the University of Stuttgart and the University of Florida to support analyses leading to such design proposals. Design proposals have been proposed at a working level in fib SAG 416 and work continues to finalize specific design methods as an extension of the CCD Method. 4.2 ASTM Activities The ACI code provisions are expected to require a standard for the prequalification of adhesive-bonded anchors, similar to ACI 355.2-00 for mechanical anchors. This activity has been initiated in ASTM Subcommittee E6.13 by a joint ASTM-CAMA task group. A first draft is expected in late 2001 with adoption to follow in accordance with ASTM standards development procedures of balloting and development of consensus on a final document. The final adoption date will determine which ACI 318 code (2005, 2008 or later) will include adhesive-bonded anchors.
5. Summary In the past and continuing into the near future, the ICBO ES acceptance criteria for mechanical (AC01) and adhesive (AC58) anchors will remain the primary post-installed anchor prequalification methods in the United States. Because of changing code requirements in ACI and the IBC, it is expected that within 2 years ACI 355.2-00 will become the primary post-installed mechanical anchor prequalification standard for both cracked and uncracked concrete. For adhesive-bonded anchors, AC58 will remain the only functioning prequalification standard for adhesive-bonded anchors for the next several years, but with limitations to uncracked concrete zones. If parity is to be maintained with mechanical anchors, the issue of performance in cracked concrete will need to be addressed. Activities are under way to develop code provisions and an anchor prequalification standard for adhesive-bonded anchors, possibly covering the cracked concrete issue. However, it is expected to take several years before full implementation is achieved.
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6. References 1
ACI 318-99, “Building Code Requirements for Structural Concrete and Commentary (ACI 318-99/ACI 318R-99),” American Concrete Institute, Farmington Hills, 1999. 2 American Concrete Institute, Farmington Hills, Michigan. 3 American Society for Testing and Materials, West Conshohochen, Pennsylvania. 4 International Conference of Building Officials Evaluation Service, Inc., Whittier, California, USA. 5 “Uniform Building Code, 1997,” International Conference of Building Officials, Whittier. 6 “Acceptance Criteria for Expansion Anchors in Concrete and Masonry Elements, AC01,” ICBO Evaluation Service, Inc, Whittier, January 2001. 7 European Union of Agrément, “UEAtc Technical Guide on Anchors for Use in Cracked and Non-cracked Concrete, M.O.A.T. No. 49, 1992,” 8 “Standard Test Methods for Strength of Anchors in Concrete and Masonry,” ASTM E 488, American Society for Testing and Materials, West Conshohocken, PA. 9 “Acceptance Criteria for Adhesive Anchors in Concrete and Masonry Elements, AC58,” ICBO, Evaluation Services, Inc., Whittier, California, January 2001. 10 CAMA, Concrete Anchor Manufacturers Association, St. Charles, MO. 11 Fuchs, W., Eligehausen, R., and Breen, J., “Concrete Capacity Design (CCD) Approach for Fastenings to Concrete,” ACI Structural Journal, V. 92, No. 1, Jan.-Feb. 1995, pp. 73-94. 12 Subcommittee E 6.13 Performance of Connections in Building Construction, ASTM, West Conshohocken, Pennsylvania. 13 European Technical Approval Guideline 001, Edition 1997, European Organization for Technical Approvals, Brussels. 14 “Evaluating the Performance of Post-Installed Mechanical Fasteners in Concrete (ACI 355.2-00) and Commentary (ACI 355.2R-00),” July 7, 2000, ACI, Farmington Mills, Michigan. 15 ACI Subcommittee 318-B, Reinforcement and Development, American Concrete Institute, Farmington Hills, Michigan. 16 fib SAG 4, Fastenings to Structural Concrete and Masonry, Fedération Internationale du Béton, Lausanne.
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ON THE RATIO OF PLATE THICKNESS TO STUD DIAMETER FOR STEEL CONCRETE STUD SHEAR CONNECTORS Howard D Wright, Anwar Elbadawy, Roy Cairns University of Strathclyde, Glasgow, UK
Abstract Stud shear connection between concrete slabs and steel beams are common in composite construction. Current design guidance for slab to beam flange composite beams merely places a limit on steel plate thickness in relation to stud diameter. This paper shows the behaviour of the connection when studs are welded to relatively thin steel plates. Tests are currently made on Double skin composite (DSC) elements. DSC system comprises steel-concrete-steel sandwich elements that consist of a layer of un-reinforced concrete, sandwiched between two layers of thin steel plates. These in turn are connected to the concrete by welded shear stud connectors. Shear studs are used to transfer slip shear between the outer steel skins and concrete core. Four series of push-out tests are presented in this paper to investigate the behaviour of the shear studs when welded to thin steel plates. The plate thickness to stud diameter ratio was 1:3. Micro-concrete with maximum aggregate size smaller than 2.41 mm was used. The properties of the microconcrete are described. The micro-concrete core is pushed through the plates in direct shear in series 1,2 and 3 but in series 4 the compression force is applied to the steel plates simulating direct compression on this element. Failure modes are defined for each of the series of tests. The studies show that failure occurred by yielding for all shears stud connectors in series 1, 2 and 3 buckling failure of the steel plate in series four.
1. Introduction Stud shear connection between concrete slabs and steel beams is common in composite construction. It is normally assumed that the relatively complex behaviour of the connector under load is independent of the plate to which it is attached as long as the plate is of a certain thickness. The behaviour of the connection when studs are welded to relatively thin plates will be discussed in this paper. Double skin composite (DSC) elements, are basically steel-concrete-steel sandwich elements that consist of a layer of normally un-reinforced concrete, sandwiched between two layers of thin steel plates.
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These in turn are connected to the concrete by welded shear stud connectors. Several experimental and analytical studies have been carried out to understand the behaviour of the Double skin composite element (1,2,3,4). The main conclusion from these studies was that DSC elements could generally be designed in accordance with normal reinforced concrete practice but satisfying the following criteria; (a) Yielding of the tension steel plate. (b) Yielding or buckling of the compression plate. (c) Shear failure of the stud connectors. (d) Crushing of the concrete in compression. (e) Shear failure of the concrete. (f) Pull out failure of connectors. Of these, (b), (c), (e) and (f) are specific to DSC. Those criteria specific to DSC are influenced by the thickness of the steel plate, spacing of shear stud and the stud diameter. An experimental study on DSC elements has been reported in reference (5). This work is extended in this paper to include additional tests on plate buckling. The main aim is to investigate the behaviour of shear studs when welded to thin steel plates and the ratio of plate thickness to stud diameter. The experimental study involves push tests consisting of two thin steel plates connected together to a core of concrete by shear stud connectors. The plate thickness to stud diameter ratio was 1/3. The concrete core was pushed through the plates in direct shear in series 1, 2 and 3 and compression force applied to the steel plates in series 4, allowing the behaviour of the plate to stud connection to be observed without the need for full panel bending tests. In these tests it has been decided to investigate arrangements where the plate thickness to stud diameter is low.
2. Test program: Twelve model push-out tests were fabricated each consisting of two 2mm steel plates connected together by a 50mm thick core of concrete and shear stud connectors. Microconcrete was used the mix used being established by Hossain (6). Table (1) show the properties of the micro-concrete control mix. Table 1: Micro-concrete properties Cylinder Splitting Cube Strength fc' Strength fs Strength (N/mm2) fcu(N/mm2) (N/mm2) 28.0 19.55 1.13
Density γ (Kg/m3) 2400
Modulus of Rupture fb (N/mm2) 4.51
Ec (KN/mm2) 14.55
The twelve models are classified in four series and identified in the text as POT1 to POT12. A typical push-out test model is shown in the figure (1) and full details of each model are given in table (2).
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In summary: Four test series were carried out as follows: 1-Three models with three studs connectors in one column (1x3) with spacing 100mm. 2-Three models with six studs connectors in two-columns (2x3) with spacing 150mm in two directions. 3-Three models with six studs connectors in two-columns (2x3) with spacing 200mm in two directions. 4- Three models with six studs connectors in two-columns (2x3) with spacing 150mm in two directions and 5 mm reduce from top and bottom of the concrete core.
Elevation
Section
Figure 1: Geometry of Push-out test model Table 2: Detail models of push-out test No Stud Spacing End spacing mm Series Specimen Of Horizontal Vertical Top & Lift & Studs mm mm Bottom Right POT1 1x3 100 100 50 1 POT2 1x3 100 100 50 POT3 1x3 100 100 50 POT4 2x3 150 150 75 75 2 POT5 2x3 150 150 75 75 POT6 2x3 150 150 75 75 POT7 2x3 200 200 100 100 3 POT8 2x3 200 200 100 100 POT9 2x3 200 200 100 100 POT10 2x3 150 150 75 75 4 POT11 2x3 150 150 75 75 POT12 2x3 150 150 75 75 In series 1, 2 and 3, The perimeter of the plates was stiffened with additional steel frame members using a sufficient number of bolts. The models were tested by applying uniformly compressive force over the breadth of the top surface of micro-concrete core
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to push it through the plates in direct shear. But in series 4, the model was tested by applying uniformly compressive force over the breadth of the top surface of steel plates to push it around the concrete core. The steel plates in this series were constructed without a frame to observe the local buckling.
3. Material properties: The properties of all materials used in the push-out tests were determined as follows: 3.1 Steel plates: the properties of the steel plates were determined from tensile tests on random samples taken from each batch of steel. A summary of the steel plates tensile test results shown in the table (3). 3.2 Stud connectors: the properties of the stud connectors were determined from tensile tests on three specimens cut at random from the studs material. A summary of the studs' tensile test results shown in the table (4). 3.3 Micro-concrete: the micro-concrete consisted of Ordinary Portland Cement, seadredged sand of 2.41-mm maximum size. A summary of the results is given in table (1). The properties of micro-concrete in each individual series of models were determined from at lest three tests on 100-mm cubes and three tests of 200 mm long by 100-mm diameter cylinders (for split cylinder tensile test and crush cylinder test). A summary of the test results on micro-concrete is shown in the table (5). The models were cast vertically and in stages. The models were covered with polythene and the micro-concrete was then allowed to cure in air until testing commenced. Table 3: Steel plate properties Thickness 0.2%Proof stress (mm) (N/mm2)
Ultimate stress (N/mm2)
1.93 315 393 Table 4: Stud connector properties Diameter 0.2%Proof stress Ultimate stress (mm) (N/mm2) (N/mm2)
Es (KN/mm2) 195 Es (KN/mm2)
6.22 360 517 196 Table 5: Properties of micro-concrete in push-out test Cube Cylinder Splitting Series strength strength strength Remark (N/mm2) (N/mm2) (N/mm2) Series Series Series Series
1 2 3 4
25.33 24.33 29.75 N/A
20.31 18.72 22.73 N/A
2.53 1.69 1.85 N/A
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7 days 7 days 12-28 days N/A
4. Test procedure and instrumentation: 4.1 (series 1, 2 & 3) The compressive force was applied to the top of micro-concrete core of model by means of a 250 KN actuator using deflection control mode. Instrumentation of the model is shown in Figure (2). The movement of the microconcrete core relative to the steel plate was measured by two dial gauges, which were attached to concrete core at 5 cm from the bottom level of concrete core. One was attached on each face. The load slip values were simultaneously recorded and printed.
Figure 2: Model instrumentation
Figure 2: Model instrumentation 4.2 (series 4) The compressive force was applied to the top surface of the steel plates of model by means of a 250 KN actuator using deflection control mode. Five strain gauges were fixed to each steel plate between shear studs in the top half of the specimen. The load strain values were simultaneously recorded and printed.
5. Loading and test observation: At the start of each test the initial dial and strain gauges reading were recorded. The compressive force was applied to the model by increasing increment loads gradually until the failure load. The slip between steel plates and micro-concrete core was recorded at each increment load until end of the test. Figure (4) shows the typical load-slip relationship of the push-out tests for series 1, 2 and 3. Same procedures were used in series 4 and figure (5) shows the typical load-strain relationship. The observation on the tests is as follows: 5.1 Series 1 (Specimen POT1, POT2 and POT3) During the test cracking noises were heard at loads between 10-14 KN, 22-28 KN and 37-38 KN. All specimens cracked vertical in the middle of concrete core and separated through the studs. The specimens
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failed at a compressive load of 37.0 KN, 39.6 KN and 37.0 KN for specimen POT1, POT2 and POT3 respectively. In specimen POT1 it was noted that a part of concrete core touched one of the dial gauges following lateral movement. In specimen POT3 the micro-concrete core started cracking in the middle of concrete core from the top and separated through the studs in an inclined crack above the dial gauges. Stud yielding occurred in all the specimens. 5.2 Series 2 (Specimen POT4, POT5 and POT6) During the test cracking noises were heard at loads between 15-18 KN, 44-56 KN and 95-107 KN. All specimens were cracked vertical in the two lines in concrete core and separated through the studs. The specimens failed at a compressive load of 95.0 KN, 107.0 KN and 101.0 KN for specimen POT4, POT5 and POT6 respectively. Stud yielding failure occurred in all the specimens. Push-out Test 120
100
Loads KN
80
Series 1 60
Series 2 Series 3
40
20
0 -1
0
1
2
3
4
5
6
7
Slip mm
Figure 3: Typical load-slip of the push-out tests series 1, 2 and 3 Stress-Strain Relationship 70 60 D.G.1 D.G.2
50
D.G.3 D.G.4
Stress
40
D.G.5 D.G.6
30
D.G.7 D.G.8
20
D.G.9 D.G.10
10 0 -0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
Strain
Figure (4) Stress-Strain for specimen POT 11 in series 4
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5.3 Series 3 (Specimen POT7, POT8 and POT9) During the test low noises were heard throughout and a high cracking noise at failure. None of the specimens were found to have cracking in the concrete core. The specimens failed at a compressive load of 107.7 KN, 77.0 KN and 86.0 KN for specimen POT7, POT8 and POT9 respectively. Stud yielding failure occurred in all the specimens. This led to separation of the stud connectors from the steel plates. 5.4 Series 4 (Specimen POT10, POT11 and POT12) During the test low noises were heard throughout and a high buckling noise at failure. None of the specimens were found to have cracking in the concrete core. The specimens failed at a compressive load of 100.0 KN, 80.0 KN and 95.0 KN for specimen POT10, POT11 and POT12 respectively. Local buckling failure occurred in all specimens. Stud yielding occurred for most of the studs, connected with to the buckling steel plate.
6. Theoretical study The behaviour of the DSC system is reported in many studies. This paper concentrates on the behaviour of the shear studs when welded to thin steel plates. The arrangement and the properties of shear stud connectors could be carried out using BS 5950 pt 3(7) or EC 4(8). The following is a comparison between the these push-out tests and these Codes and other studies: 6.1 Stud/plate ratio: The BS 5950(7) put the limit of the ratio between shear stud diameter to steel plate thickness as not greater than 2.5 also EC 4(8) put the same ratio with stud diameter not a minimum criteria of the be less than steel plate thickness. Obeid (9) showed that the best ratio between stud diameter to steel plate thickness equal 3 this was derive from a study of 3, 4, 5, 6 and 8 mm shear studs connectors welded to thin steel plates. In this paper a value of 3 has been taken. 6.2 Steel plate buckling and shear studs spacing: The ratio of the centre to centre distance between stud shear connectors Sc to plate thickness tsc is limited in BS 5950(7) by the maximum spacing between stud being 600 mm or 4 times the concrete core thickness and the minimum spacing not be less than the 5 time the stud diameter. The limitation in EC 4(8) is stated as maximum stud spacing to plate thickness ratio of 40. Wright (10) showed that this ratio must not be less than 67.5 for stud layouts where platebuckling mode is likely and 40 for stud layouts where a column-buckling mode is likely. Wright (10) described a method of evaluated this ratio when the compression plate was in contact with a rigid medium (as in the case of DSC elements). The limit reduced to the 37.71 in plastic, 47.12 in compact and 51.91 in semi-compact case. In this paper this ratio is 50 in series 1, 75 in series 2 and 100 in series 3. During the tests in series 1, 2 and 3 the local buckling was not noted but this was due to the fact that these tests are in direct shear with no compression in the plates. But local bucking did occur in series 4 because the compression force was applied to the steel plates directly. Wright(11) showed local stability of plate by calculate the plate stiffness D = (t3De)/12 where De = E/(1-ν2)
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which is plate material stiffness. Wright (10) showed that the stress in these plates can calculated from this equation Sc/t = √(D π2/3σ). Table (6) show the stresses and the strain in the plates at the buckling for the specimens POT 10, POT 11 and POT 12. This table also shows the stresses calculated by used the material linearity (Hook’s law). By using these stresses the theoretical buckle ½ wave Stheory may be evaluated. This suggests a buckle spacing bigger than the actual spacing between the stud connectors Sc. This may be due to the fact that the stud connectors stretch allowing the wave buckling length to increase as shown in the figure (5). It should be noted that the direction of the load is not always perpendicular to the stud panel layout the yield lines may be diagonal to the edges. In this case the ratio must be checked with the diagonal spacing between shear studs.
Sc
Steel plate
Stheory
Shear stud Before buckling
After buckling
Figure (5) The spacing between shear stud Table 6: Comparison for the stresses and strain series 4 Specimen Experimental Analytical Averg. Strain Stress Stress Averg. N/mm2 Stress N/mm2 Stress POT10 66.7 0.00032 62.4 61.11 65.18 POT11 50.0 0.00029 56.5 N/mm2 0.00039 N/mm2 POT12 66.7 76.7
Spacing Sc Stheory mm mm 150 173.6 150 182.5 150 156.6
6.3 Shear stud connector capacity: Many previous studies (1,2,3,4) showed that the strength and stiffness of stud connectors in DSC elements is significantly less than determined from push-out shear tests. Therefore, the design resistances of studs attached to the compression and tension plates are limited in the some Codes and studies. In BS 5950(7), the capacities of shear connectors are taken as 80 % and 60 % from its characteristic resistance when attached to the compression and tension steel plates respectively. The values of the characteristic resistance of shear studs from 13 mm to 25 mm are tabulated. EC 4(8) limits the characteristic resistance by the lesser of: PRd=0.29αd2 (fckEc) 0.5 / γv or PRd=0.8fu πd2/4γv. Roberts(4) used the same equations. Wright (3) used similar equations but limits the design resistances of shear stud in the tension zone to 50 % of the characteristic resistance of shear studs. Obeid (9) showed that the characteristic resistance of 6-mm shear stud is 7.27 KN in tension and 6.3 KN in
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shear (experimental). In the tests reported in this paper the characteristic resistance of 6 mm shear stud is between 6.17 to 6.59 KN in series 1, 7.92 to 8.917 KN in series 2, 6.42 to 8.975 in series 3 and 6.67 to 8.33 KN in series 4.
Table 7: Comparison with various codes of practice and research studies Data BS 5950 EC 4 Previous Push-Out pt.3 Studies Test Stud/plate ratio Stud spacing Min. Max. Stud spacing/plate thickness Min. Max. Stud capacity
≤ 2.5
≤ 2.5 & tsc< d
3(Obeid)
30 mm 200 mm
11.41 mm 150 mm
40(Wright)
Sc>30 Sc≤200 Tabulated not given for 6 mm stud
≤ 40 37.71 (Wright) 4.67 KN (Concrete) 9.05 KN (Stud) 4.67 KN (Min)
4.67 KN (Roberts) 7.27 KN (Tension) 6.3 KN (Shear) (Obeid)
Remark
3 100 mm 150 mm 200 mm 50,75,100m m 70.71, 106.1, 141.4 mm 6.17-6.59 7.92-8.92 6.42-8.98 6.67-8.33 (KN)
Series 1 Series 2,4 Series 3 Longitudinal spacing Diagonal spacing Series 1 Series 2 Series 3 Series 4
Table 7 shows comparison between the results of push-out tests with the Codes and other research work.
7. Conclusions The aim of this paper has been to investigate the behaviour of the connection when studs are welded to relatively thin plates. Push-out tests have been used to establish the behaviour of this connection. The failure modes observed include yielding failure for shear stud connectors in all specimens, linear cracking for the concrete core in series 1&2 and yielding failure for all shear stud connectors and pull out for most in series 3. This for concentrated shear force on the connection of stud with the steel plate and increase the bond stresses between steel plates and large concrete core in series 3. Buckling failure in series 4.
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8. References: 1-Oduyemi T.O.S. & Wright H.D., An Experimental Investigation into the Behaviour of Double-Skin Sandwich Beams, Journal of Constructional Steel Research, Vol.14, pp.197-220, (1989) 2-Wright H.D., Oduyemi T.O.S. & Evans H.R., The Experimental Behaviour of Double Skin Composite Elements, Journal of Constructional Steel Research, Vol. 19, pp. 97110, (1991) 3-Wright H.D., Oduyemi T.O.S. & Evans H.R., The Design of Double Skin Composite Elements, Journal of Constructional Steel Research, Vol. 19, pp. 111-132 (1991) 4-Roberts T.M., Edwards D.N. & Narayanan R., Testing and Analysis of Steel-ConcreteSteel Sandwich Beams, Journal of Constructional Steel Research, Vol. 38, pp. 257-279, (1996) 5-Wright H.D., El-badawy A. & Cairns R., Shear Connection between Concrete and Thin Steel Plates in Double Skin Composite Construction, Third International Conference on Thin-Walled Structures, Cracow, Poland, 5-7 june 2001. 6-Hossain, K.M.A., In-plane shear behaviour of composite walling with profiled steel sheeting, Ph.D., (1995) 7-BS 5950 Part 3.1, The Structural Use of Steelwork in Building, Design in Composite Construction, Code of Practice for Design of Composite Beams, British Standards Institution, London, (1990) 8-European Committee for Standardisation (CEN), Eurocode 4 Part 1.1, Design of Composite Steel and Concrete Structures, General rules and rules for buildings, DD ENV 1-1 (1994) 9-Obeid G. A., Stud welding and its application to ceiling supports, M. Sc., Cardiff, University of Wales, (1986) 10-Wright H.D., Buckling of plates in contact with a rigid medium, Journal of the Institution of Structural Engineers, Vol. 71 No.12, pp. 209-215, (1993) 11-Wright H.D., Local stability of filled and encased steel sections, Journal of Structural Engineers, pp. 1382-1388, October (1995)
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INCORPORATION OF THE SIZE EFFECT AND OTHER FACTORS IN STRENGTH DESIGN OF CONCRETE FASTENINGS, IN THE CONTEXT OF THE CEB DESIGN GUIDE V.I. Yagust and D.Z. Yankelevsky National Building Research Institute, Technion-Israel Institute of Technology,Haifa, Israel
Abstract The paper shows that the method adopted in the CEB Design Guide (hereinafter "DG") [1] for strength design of fastening in concrete - overlooks a number of important factors. In strength design for cone failure or local blow-out failure of the concrete, in distinction to DG allowance should be made for the size effect which - as know - determines the transition from the pseudoplastic to the brittle mode with increase of the height of the failure cone. The errors resulting from this omission are estimated. Allowance is also obligatory for the critical stress intensity factor K1c , which should replace the square root of concrete compressive strength ( f c ) resorted to in DG. It is shown that use of the latter for different concretes also makes for errors. On the basis of experimental data, formulas incorporating the two factors were obtained for different element geometries - including the case ( not discussed in DG) of a flat element loaded in its plane of symmetry. The above circumstances should be taken into consideration in revising the Guide.
1. Introduction New design methods of anchoring in concrete using the CEB Design Guide [1] have replaced the old ones. The old estimation method of cone failure strength using the concrete tensile strength fct assumed in fact pseudoplastic failure (PPF). Yet it was found, that anchoring failure is attended by stable crack development [2,3,4]. Therefore, the new estimate is based on linear fracture mechanics (LEFM) by assuming brittle fracture and based on the fracture toughness KIC in the calculations. In fact, many experiments have shown that either one of the mentioned failure modes occurs, or an intermediate
300
mode, depending on the characteristic length D* in the problem, i.e. a size effect is present [5,6,7], on which the pseudoplastic failure mode changes smoothly to a brittle one as D increases. The size effect is neglected in the current DG [1] on the assumption that LEFM is applicable for all values of D; during which KIC is replaced by f c (up to a constant factor). The following discussion sheds light on the consequences of these assumptions.
2. Size effect considerations 2.1. It is well known [5,6,7] that the scopes of applicability of LEFM and of the PPF model depend on the types of problems and the material properties. In each cone failure or local blow-out failure problems these ranges are determined by the unique ratio between the crack length l at the moment of fracture (or the D dimension, which is related to l ) and the size of the fracture process zone (FPZ) behind the crack end. The limiting value d of the FPZ depending on the maximal aggregate dimension a, is evaluated in the Barenblatt-Dugdale-Panasyuk's fracture model [8,9,10] by the expression 2
π K d = IC ,
(1)
8 f ct
obtained for l » d and in the absence of a stress gradient in the crack continuation line caused by external loads acting out the crack [2,6]. The D/d ratio in a specific problem defines the application limit of the LEFM and PPF models for that problem. Therefore experimental data should be processed as a function of D/d. The obtained curves in dimensionless coordinates are independent on the maximal aggregate size a or other material properties. These results can also be obtained by direct application of the two-parametric Barenblatt-Dugdale-Panasyuk's fracture model [6]. 2.2. The test data on a cone failure problem under tension were processed as the function N N (a three-dimensional problem [2,3,11-20]) or (plane problem 1.5 K IC h ef K IC h ef0.5 h where the force N acts in the symmetry plane of a flat element with a thickness h [2,3,20]) of the ratio hef /d. It was found that for large values of this ratio the above functions are stationary (Fig.1a,2a). It therefore follows that the failure load N is proportional to K h ef1.5 or to K hef0.5h in the mentioned problems respectively, IC IC
*The characteristic length D here is either the anchorage depth hef in a cone failure problem under tension, or the distance c or c1 between the anchor and the edge of the concrete element in problems of a cone failure under shear or a local blow-out failure under tension respectively.
301
a
b
Fig.1. Experimental results and approximation of size effect on ratio N/(K1Chef1.5) (a) and N/(fcthef2) (b) for 3-dimensional elements
302
a
b
Fig.2. Experimental results and approximation of size on ratio N/(K1Chef0.5h) (a) and N/(fcthefh) (b) for 2-dimensional elements
303
LEFM can be applied, as was in fact done in the DG (with replacing KIC by
f c ).
However, when the hef/d ratio is lower than 0.6 to 1 (3-dimensional problem) or than 3 to 4 (plane problem), the values of these functions become lower, i.e. LEFM can not be applied and the value of N given by LEFM should be reduced. This circumstance was not taken into account in the DG, and the anchoring strength for low hef /d values, as determined according to the DG is higher than the one found in testing. The replacement of KIC by fct and d using equation (1) results in different expressions for hef /d the failure load as a function of fct, hef, h, hef /d, corresponding to the tests at any and resembling the expression for the Bazant's size effect [21]: 5.5 f ct hef2 (2) N= 0.5 1 − 0.5(hef / d ) + 2.05hef / d (three-dimensional problem, Fig.1b), 1.4 fct hef h (3) N= 0.5 1 − 0.3(hef / d ) + 0.49hef / d (plane problem, Fig.2b). When hef /d → 0, (2) and (3) give the pseudoplastic failure load for the considered problems as N = 5.5 f ct hef2 and N =1.4 fcthefh respectively. When hef /d → ∞, we obtain N for these problems at brittle failure as N = 2.4 K h ef1.5 IC and N = 1 .25 K h ef0.5 h respectively. IC It should be noted that the obtained curves are independent of the value of a or any other material properties. It is assumed that the washer diameter is much smaller than the depth of anchorage and may be neglected. 2.3. By a similar method for processing the test results, one can obtain formulae for the failure load in cone failure under shear loading for any value of c0/d (c0 = c - ds /d, ds is the anchor diameter). For example, in the three-dimensional case we have: 2.2 f ct c02 , (4) Q= 0.3 1 − 0.9(c0 / d ) + 2.82c0 / d in the plane case (the anchor is set along the width h of the concrete element) we have: 0.73 f ct hc0 (5) Q= 1 − 0.72(c0 / d ) + 0.64c0 / d 0.2
Figs. 2,4 in [20] show the test results and their approximations by formulae (4), (5) here. These expressions neglect the effect of the length of the shear force lever arm, since it is assumed that it is small compared to the anchor diameter. 2.4. The inclusion of different possible failure modes (mainly PPF and intermediate failure) is necessary for calculating the local blow-out failure load of concrete as well. For example, the corresponding formula (6) for a stretched anchor with a washer at its end in crack-free concrete is (Fig.3):
304
Nds0.25/(fctc1(dh+0.35a)1.25)
100
19(1-0.1(c1/d)0.4+0.5c1/d)0.5
10 0.1
1
10
c1/d
Fig.3. Experimental results and approximation of size effect in case of local blow-out failure in tension
19 f ct c1 (d h + 0.35a )
ds−0.25 , + 0.5c1 / d 1.25
N=
(6)
1 − 0.1(c1 / d ) where dh is the washer diameter, N is the axial tension force in the anchor [ 3 ]. 0.4
2.5. The considered types of loads and corresponding failures indicate the limited nature of the application ranges of the PPF and LEFM models. Neglect of the scale effect and consideration of all possible cases as the brittle case may introduce errors for small D/d that may make , for instance, in cone failure problems under tension to 40% and higher. As an example, let us consider an anchor with a washer at its end, which is fixed during placing concrete into plain crack-free concrete C20 with a = 20 mm. The distance between the anchor and the edge of the concrete element is assumed large. The characteristic resistance NRk,c of the stretched anchor on cone failure of the concrete needs be determined. The depth of anchorage is 20 or 4 cm in a three-dimensional problem and 80 or 10 cm in a plane problem (the anchor is set in the symmetry plane of a 10 cm thick concrete element). The data and calculated results for NRk,c are given in Table 1. The calculation was made according to formulae (2) and (3) (column 1). NRk,c was also calculated using LEFM by assuming its applicability for any anchorage depth (column 2). In Table 1 the characteristic values KICk and fctk for concrete, which are required for calculating NRk,c, are based on the variation coefficient of 0.18. The mean value of KIC for concrete with a = 20 mm was found by the empirical formula according to tests [2]:
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0.148 fc0.64 K IC = 2 − 0.00028 fc + 0.04 fc + 0.39 Here KIC is in MPa⋅m 0.5, fc in MPa.
fc ≤ 35 MPa
(7)
35 < fc ≤ 60 MPa
Table 1 a mm
K1Ck MPa.m0.5
fctk MPa
d cm
Dimension of problem 3-dimensional
20
0.61
1.3
8.6 2-dimensional
hef cm 20 4 80 4
NRk,c , kN 1 123.1 8.7 66 15.9
2 126.5 11.3 66.7 23.6
Diff. % 3 30 1 48
Table 1 clearly shows that for deep anchorage LEFM-based calculations approach those obtained from (2) and (3), and correspond to the experiments (Fig.1,2). However, for low-depth anchorage LEFM-based calculations overestimate the anchorage strength.
3. Replacement of the KIC value by
fc
3.1. Use of LEFM for calculating cone-failure strength (under tension and shear) and local blow-out failure strength (under tension) assumes that the failure load is proportional to the KIC of the anchoring concrete. KIC is replaces in the formulae of the DG [1] by f c and no by other material parameters. However, KIC is not proportional to
f c , as evident from (7), even for a constant maximal aggregate dimension a. In
addition, it is well known [2,22], that the value KIC is also dependent on a. Thus, for a = 20 mm KIC is found from (7), and for a = 5 mm from equation (8) [2]: K IC = 0.224 f c0.4
f c ≤ 60 MPa
(8)
0.5
Here KIC is in MPa⋅m , fc in MPa. The ratio between the KIC values for concrete of the same compression strength, but with aggregate of different maximal dimensions 20 mm and 5 mm, is not equal to 1 as differentiated from the DG, but may vary from 1.45 for C20 concrete to 1.55 for C50 concrete. The error introduced in the replacement of KIC by f c causes overestimation of the anchoring strength for a < 20 mm, since the formulae of the DG were determined in tests at a = 20 mm. In brittle failure (at high D/d) this overestimation may reach 50% when an aggregate with a maximal dimension of 5 mm is used for mixing of the concrete.
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3.2. As an example, let us consider an anchor with a washer at its end, fixed during placing concrete in a depth of 15 cm into a plain crack-free C40 concrete element. The edge of the element is far from the anchor. Let us find the characteristic resistance NRk,c for the stretched anchor in cone failure of the concrete when using an aggregate with a = 20 mm or with a = 5 mm. The data for the two types of concrete and the calculated results are given in Table 2. Table 2 a mm
K1Ck MPa.m0.5
fctk MPa
d cm
NRk,c KN
5
0.52
2.1
2.4
70.8
20
0.82
2.1
6.0
108.7
It is clear that the ratio between the characteristic cone failure resistances in the concrete with a = 20 mm and with a = 5 mm is in fact 1.53 (as opposed to 1 according to [1]).
4. Conclusions In revising the DG we consider it necessary to take the following circumstances into account: 1. To avoid errors, the characteristic anchoring resistance should be determined using the presented formulae, which correspond to the experiments and take into account of the size effect, i.e. of pseudoplastic, brittle and intermediate types of anchoring cone failure under tension and shear, as well as local blow-out failure under tension in relation to the value of D/d. 2. The proposed expressions also take into account of the influence of the value of the maximal aggregate dimension on the failure load value in brittle failure of the aboveenumerated modes. 3. The DG should also include the case of anchoring along the symmetry plane of a flat concrete element. 4. In order to refine the numeric coefficients in the proposed formulae, additional testing is needed for certain limiting values of D/d in addition to the existing data: a) axial tension (cone failure, plane problem, anchor in the symmetry plane of the flat element) - hef /d ≤ 0.8; b) axial tension (local blow-out failure) - c1/d ≥ 3; c) shear (cone failure, 3-dimensional problem) - c/d ≤ 0.2; d) shear (cone failure, plane problem, anchor along the width of the element) c/d ≤ 1.2. 5. Testing is also needed for the other cases not considered in the DG and in the paper (for example, the anchor under shear set in the symmetry plane of a flat concrete element).
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References 1. 2.
3.
4. 5.
6.
7. 8. 9. 10. 11.
12. 13. 14. 15.
16.
'Design of Fastenings in Concrete, Design Guide', ( CEB, 1997) 83. Yagust, V.I. 'Resistance to development of crack in concrete structures taking into account the influence of material macrostructure', D.Sc. thesis ( NIIZhB, Moscow, 1982 ) 24 ( in Russian ). Shapiro, G.I. and Yagust, V.I. 'Strength of plane concrete element under concentrated load, in 'Investigation of Bearing Concrete and Reinforced Concrete Structures of Multistory Precast Buildings', eds. G.N.Lvov and J.M. Strugatsky ( MNIITEP, Moscow, 1980 ) 74-111 (in Russian). 'Fastenings to Reinforced Concrete and Masonry Structures', Bulletin d'formation, N206 ( CEB, 1991) 486. Entov, V.M. and Yagust, V.I. , 'Experimental investigation of the laws governing qusi-static development of macrocracks in concrete', Mechanics Solids ( translation from Russian), 10 (4) (1975) 87-95. Yagust, V.I., 'Application of the model of Leonov-Panasuk-Dugdale for evaluation of crack development in concrete structures', in 'Strength Investigations of Bearing Structures of Multistory Precast Buildings', eds. G.N.Lvov and J.M.Strugatsky ( MNIITEP, Moscow, 1983 ) 66-84 ( in Russian ). Bazant, Z.P. and Planas J., 'Fracture and Size Effect in Concrete and Other Quasibrittle Materials, ( 1997) 597. Barenblatt, G.I., 'The mathematical theory of equilibrium cracks in brittle fracture', Advances in Appl. Mech., 7 (1962 ) 55-129. Dugdale, D.S., 'Yielding of steel sheets containing slits', J. of Mech. and Phys. of Solids, V.8 (1960) 100-108. Panasyuk,V.V., 'The Limit Equilibrium of the Brittle Solids with Cracks',(Kiev,1968) (in Russian ). Eligehausen, R. and Sawade, G., 'A fracture mechanics based description of the pull-out behavior of headed studs embedded in concrete', in 'Fracture Mechanics of Concrete Structures. From Theory to Application', ed. L. Elfgren (London, 1989) 281-299. Skramtaev,B.G. and Wolf,I.V. 'Control of the Concrete Strength', (Moscow, 1939) (in Russian). Kononov, I.A. 'The embedment depth determination', in 'Vibration Application in Building ', ed. I.J. Petrov (Moscow, 1962) 31-65 ( in Russian ). Sattler,K., 'Betractung über neuere Verdübelungen in Verbundbau', Der Bauingenieur, 37 (1) (1962)1-8 (in German). Lukojanov, U.N., 'The experimental study of behavior concrete in anchor fastenings ', in 'Design and Construction of Industrial Buildings and Constructions', ed. V.G. Desjatov (Moscow, 1964) 18-27 ( in Russian ). Nizhnikovsky,G.S., 'The new type of anchor bolt joining', 'Express Information', 149 (Moscow, 1964) ( in Russian ).
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17. Holmjansky,M.M., 'The Laying Details of Precast Reinforced Concrete Structure (Moscow, 1968) 208 ( in Russian). 18. Tchujko,P.A., 'The study of concrete strength by method of cone failure and shear failure', in 'The Interbranch Problems of Building. Home Experience', ed. D.A. Korshunov (CINIS, Moscow, 1972) (in Russian). 19. Zhao,G., 'Tragverhalten von randfernen Kopfbolzenverankerungen bei Betonbruch', in 'Deutscher Ausschuss für Stahlbeton, H.454 (1995) 98 (in German). 20. Yagust, V.I. and Yankelevsky, D.Z., 'Strength of a concrete element under the action of concentrated tensile or shear force', in 'Fracture Mechanics of Concrete Structure', V. 2, Proc. of the Sec. Intern. Conf. on Fracture Mechanics of Concrete Structures (FRAMCOS 2), Zurich, Switzerland, Juli 25-28,1995 (1995) 1361-1368. 21. Bazant, Z.P., 'Size effect of blunt fracture: concrete, rock, metal'. J. of Eng. Mech., 110 (4) (1984) 518-535. 22. 'CEB-FIP Model Code 1990', CEB, Bulletin d'information N203 (1991).
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CORROSION BEHAVIOR OF MATERIALS IN FIXING APPLICATIONS Norbert Arnold Fischerwerke, Artur Fischer GmbH & Co. KG, Waldachtal, Germany
Abstract To ensure the durability of fixing elements besides an appropriate design, the use of suitable materials must be considered. Due to economical reasons it is necessary to choose the material, which meets the specific needs of each application best. According to general experience increasing corrosive potentials of specific environments require materials of higher resistance to these conditions. This is normally associated with higher costs. According to increasing corrosion resistance, appropriate corrosion protection comprises zinc-based coatings for unalloyed steels, stainless steels and highly corrosion resistant special alloys. Comparative results of laboratory as well as outdoor exposure tests are presented and the application of these materials in approved fixing elements is discussed.
1. Introduction In most applications fixings are expected to function during the whole life time of the building. In Europe this means a period of 50 years. Due to the difficulties of predicting the corrosion behaviour of materials for 50 years in advance, one approach of achieving save fixing elements is to accept materials only, which show practically no interaction with the expected corrosive media. This is the case in Germany and the range of validity of the „European Technical Approval“ for anchors. As a consequence two main groups of base materials are created:
313
1. Low alloyed surface-protected steel for indoor applications, which needs a corrosion resistance (through non-permanent protective layers) mainly for storage, transportation and installation purposes. 2. Highly alloyed stainless steel (with permanent corrosion resistance) for environments with high corrosion potential. A second approach for outside applications is to use protective coatings, which proved to be durable through long-time experience under defined environmental conditions. The most widely used protection-systems of this type are thick layers of zinc on low alloyed steel.
2. Corrosion protection for fixings in building applications 2.1 Non-permanent protection Table 1 displays a summary of the most widely used non-permanent protection systems: Table 1. Non-permanent protective coatings Type Typical layer thickness [mm] Zinc, electro plated, blue passivated 5 – 15 Zinc, electro plated, yellow passivated 5 - 15 Zinc, organic binder (Dacromet 320) 1 – 3 Zinc, organic binder (Delta tone) 1–3 Zinc, hot dip galvanized 20 - 100 In the field of fixings, only hot dip galvanized steel is used for outside applications. Without further protection the other zinc-systems are used for indoor applications only. 2.2 Permanent corrosion resistance As fixing elements have to display their full performance during the whole lifetime of the building a reduction in the mechanical properties due to corrosion is not acceptable. This usually means that only stainless steels or even metalls with higher corrosion resistance (e. g. Ni- or Ti-alloys) are suitable for outside applications. The most widely used type of stainless steel belongs to the Cr/Ni-Type (e. g. 1.4301, BS 304) or the Cr/Ni/Mo-type (e. g. 1.4401, BS 316). Germany has probably the most detailed regulations for the use of stainless steels. The field of applications for these alloys is regulated by „Allgemeine bauaufsichtliche Zulassung“ 1) .
3. Corrosion behaviour of fixing elements To determine the long time corrosion behaviour of a protective coating several shorttime tests are common. None of these can give an exact forecast of the behaviour under the expected practical conditions. Nevertheless, testing different corrosive systems under
314
identical conditions can supply us with information about differences to expect in real life properties. 3.1 Corrosion behaviour of non-permanent protection-systems All coatings were tested in a salt spray box according to DIN 50 021. Anchor-bolts with a diameter of 12 mm and an app. length of 10 cm were used as test-specimens. The coatings were applied under industrial condition. The corrosion resistance of the various system was measured by determining the percentage of specimen-surface covered by red rust. Three test-series were conducted. The details are summarized in table 2. To determine the effect of mounting on the corrosion behaviour of the bolts, one series (3) was conducted, where the specimens were mounted, demounted (by splitting the concrete slab) and then exposed in the salt spray box. Table 2: Coatings tested according DIN 50 21. Series Specimen- Coating type No 1 1 none 1 2 Zinc, electro plated , yellow passivated 1 3 Zinc, electro plated, blue passivated 1 4 Dacromet ® 320 1 5 Delta Tone ® 2 6 Zinc, hot dip galvanized 2 7 Zinc, mechanically plated (McDermid) 2 8 Zinc, mechanically plated (sheradized acc. BS 4921) 2 9 Zinc, mechanically plated (sheradized acc. BS 4921 + passivation treatment) 3 10 Zinc, hot dip galvanized 3 11 Zinc, mechanically plated (McDermid) 3 12 Zinc, hot dip galvanized 3 a) 13 Zinc, hot dip galvanized, demounted 3 a) 14 Zinc, hot dip galvanized, demounted 3 a) 15 Zinc, hot dip galvanized, demounted
315
Thickness [µm] 5-7 5-7 1,2 - 2,2 1,0 - 2,2 40 - 50 40 - 50 30 - 40 30 - 40 55 - 60 55 - 60 50 - 55 55 - 60 55 - 60 50 - 55
The results of the corrosion-tests are displayed in the according figures 1 - 4. Figure 1: Test results of series 1
100
roh Red rust [%]
galvanisch verzinkt Delta Tone einfach 50
Delta Tone zweifach Dacromet gvz, blau
0 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Time [d]
Figure 2: Test results of series 2
Red rust [%]
100
6
7
8
9
50
0 3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Time [d]
316
19
20
21
22
23
24
25
26
27
28
29
Fig. 3: Test results of series 3
Red rest [%]
100
10 50
11 12
0 5
6
7
8
9
10
11
12
13
14
Time [d]
Figure 4 Test results of series 3 a) 100
Red rust [%]
13 14
50
15
0 6
7
8
9
10
11
12
13
Time [d]
317
14
15
16
17
18
3.2 Permanently corrosion-resistant fixing elements 3.2.1 Standard-Applications Outdoor exposures of different stainless steels for long periods proved that stainless steels of the Cr/Ni/Mo-type showed no substantial corrosion 2). As a consequence they are now the standard alloys for fixing elements in outdoor applications. 3.2.2 Highly corrosive enviroments Practical experience also showed that in certain applications, especially indoor swimming-pools and road-tunnels, failure of fixing elements could occur due to stress corrosion cracking. Under these conditions even some highly alloyed steels showed severe corrosion attack 5) (table 3). Table 3. Pitting corrosion of different stainless steels (depth in µm). Material-no. short-name (Werkstoff-Nr.)
Field research 4) Lab research 5) (2 years) (5.5 days)
1.4301 1.4401 (1.4571) 1.4462 1.4529 1.4565
50 55 30 0
X 5 CrNi 18 10 X 5 CrNiMo 17 12 2 X 2 CrNiMoN 22 5 3 X 1 NiCrMoCuN 25 20 6 X 3 CrNiMnMoNbN 23 17 5 3
55 43 27 0
As a consequence the stainless steel 1.4529 has become the standard-material for these applications
4. Application examples 4.1 Indoor applications Electro plated blue or yellow passivated zinc is usual. Other thin zinc protections layers are used in exceptions only (e. g. 6). 4.2 Outdoor applications 4.2.1 Facade fixings according to German approval In case of approved plastic anchors with a completley closed plug-sleeve, steelscrews protected by electro plated zinc in combination with an additional protections of the head of the screw by a thick protective coating is sufficient. 4.2.1.1 Facade fixings in aerated concrete Due to a lack of experience about corrosion effects in that material, screws protected by electro plated zinc in combination with the higher corrosionresistant yellow passivation (compared to the blue one) is mandatory.
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4.2.2 Standard atmospheres According to European guidelines for urban and industrial applications 1.4401 (1.4571) is suitable. 4.2.3 Road tunnels Typical examples are the „Engelberg-Tunnel“ (2.4 km long, opened in 2000) or the 4th tube of the „Elbtunnel“ (2,5 km long, opening planned for 2003) where all anchors used were made from 1.4529. 4.2.4 Extreme corrosion resistance Flue gas desulfuration is an example where even highly alloyed steels show strong corrosion. In this application titanium is the suitable material.
5.
References
1) Allgemeine bauaufsichtliche Zulassung Z-30.3-6, Deutsches Institut für Bautechnik. 2 ) Ergang, R., Rockel, M. B., Werkstoffe und Korrosion 26, 36 – 41 (1975) 3) Hütterer, H., Schadgaskorrosion von Werkstoffen in der Befestigungstechnik, Diplomarbeit, FH Konstanz 1994 4) Übeleis, A. Felder, G. Nock, R., Einflüsse von Schadstoffen auf die Beständigkeit metallischer Werkstoffe in exponierten Bauwerken, Vortrag anläßlich der 23. Jahrestagung der GUS, Finztal, 1994 5) Arnold, N. Gümpel, P. Heitz, T. W., Materials and Corrosion 50, 140 – 145 (1999) 6) Allgemeine bauaufsichtliche Zulassung Z-21.1-971, Deutsche Institut für Bautechnik
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BEHAVIOUR OF POST-INSTALLED ANCHORS IN CASE OF FIRE Konrad Bergmeister, Anton Rieder Institute of Structural Engineering, Vienna, Austria
Abstract Due to the loss of strength of concrete and steel at high temperatures the load capacity of anchors in case of fire is expected to be reduced. Especially in tunnels post-installed anchors are commonly used to fix heavy equipment like ventilators, which must not fall down and injure or even kill escaping people or firemen in case of an accident with releated break-out of fire. The failure mode of expansion or undercut anchors depends primarily on the embedment depth: for small embedment depths concrete spalling will be decisive, steel failure usually is the consequence of large embedment depths. Another important feature is the effect of cracked concrete (w = 0.3 mm). In an experimental setup in a real motorway tunnel the behaviour of expansion and bonded anchors is tested in cracked and uncracked concrete during a fire. For this purpose an axial load is applied and the temperature in different depths and the displacement of the anchors are measured continuosly.
1. Introduction The most important variable in questions of fire protection is the temperature propagation. Due to the fact that evolution of fire is a highly instationary process the temperature is a function of space and time. Theoretically it can be calculated by solution of the partial differential equation which describes the conservation of energy and in cartesian coordinates has the following form:
∂ ∂T ∂ ∂ ∂ ∂ ∂T λ + λ + λ + q = ρc ∂x ∂x ∂y ∂y ∂z ∂z ∂t
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(1)
λ
heat conductivity [W/(mK)]
ρ
density [kg/m3]
c
specific heat capacity [J/(kgK)]
q
heat source or heat sink [W/m3]
T
temperature [K]
t
time [sec]
The speed how fast the temperature rises in an element is governed by the temperature conductivity term λ/(ρc). The time and / or space dependance of all this parameters makes it impossible to give an analytical solution for eq. 1, therefore numeric nonlinear approximation procedures are necessary. One of the main problems in modelling material behaviour at high temperatures is the heat transfer from the fire szenario to the structural part because it strongly dependends on convection and ventilation conditions, surface roughness, geometry and temperature. For this purpose experimental data are non-available. It is of interest how the anchor influences the heat transfer in the concrete. Due to the high temperature conductivity of steel it is heated much faster then concrete and this affects the load capacity of the system steel to concrete. In case of fire following failure modes of post-installed anchors in tension can be observed: 1. Steel failure The yield strength of steel decreases with increasing temperature. This leads to a critical temperature Tcrit at a certain stress level. For a structural steel for example the residual strength at 500°C is about 60% of the strength at room temperature. 2. Pull-out failure Due to the opening of cracks in the concrete at high temperatures the friction between expansion sleeve and concrete and hence the ultimate load capacity decrease. For expansion and undercut anchors suitable in the cracked tensile concrete zone this effect should not appear. Bonded anchors usually exhibit failure of the chemical mortar at elevated temperatures. 3. Pull-through failure In case of poor concrete quality and / or opening of cracks the steel cone slides through the expansion sleeve without any concrete breakout. This is not only a consequence of high temperatures, but it can be observed also at room temperature and in cracked concrete.
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4. Concrete cone failure Concrete exhibits the quartz-inverison (α-quartz → β-quartz) at a temperature of 573°C and has to be evaluated as a completely destroyed zone. With increasing time this zone expands in the inside of the structural part and the anchor is pulled out with the concrete cone. For bonded anchors this failure mode can be observed only for small embedment depths. 5. Concrete spalling At moisture contents ≥ 2 mass-% explosive spalling can arise due to the expansion of water vapour in the pores: if the porosity is very low the vapour cannot expand and the tensile strenght of the concrete is exceeded. This effect can be favourished close to an anchor due to the higher heat input through the steel. For the evaluation of a structural part in case of fire the full developed burning is decisive. Reproducable laboratory fire tests are guaranteed by use of a standardized temperature vs. time curve (T-ISO 834) which can be described by following equation:
ϑ − ϑ0 = 345 lg(8t + 1)
(2)
whereas ϑ is the temperature at time t and ϑ0 is the temperature at the t = 0. During the fire test a constant axial load is applied on the anchor. By determining the time the anchor can bear the load it is possible to assign a fire resistance duration. However, in natural fires the temperature development can be quite different from the standardized curve described by eq. 2. For this purpose the thermic and mechanical behaviour of post-installed anchors in a natural fire has been investigated.
2. Experimental setup The experimental setup is shown in fig. 1. A kind of “minitunnel” is build up with two concrete walls (200x200x30 cm) on both sides and four slabs (80x80x30 cm) as ceiling, all of them of the strength class C50/60. The temperature evolution and distribution on the surface of the expansion anchors is measured by thermoelements of type K placed in a notch during the fire test (fig. 2). The isolation material is glass silk and resists a permanent temperature of 700°C. For the determination of the temperature in the chemical mortar of the bonded anchors there are used standard thread rods without fixing element and with a notch in axial direction. Bonded anchors and expansion anchors of different shape are installed in cracked and uncracked concrete (see table 1). Through a lever-arm a constant axial load (fig. 3) of 10 kN is applied on three bonded anchors of the shape M12 and the displacement of the anchors is measured through a hole from the back side of the slab via potentiometric displacement transducers (fig. 4).
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tfix
T4
T3
T2
T1
Fig. 1 and 2: Experimental setup and tempeature measurement anchor
Bonded M10
Bonded M12
Bonded M16
Expansion M8
Expansion M12
Expansion M16
material
1.4529
1.4529
1.4529
1.4401
1.4401
1.4401
Embedment depth [mm]
60
80
125
45
70
85
Torque [Nm]
20
40
50
20
60
110
Crack [mm]
0.3
0.3
0.3
0
0
0
Load [kN]
unloaded
axial 10 kN
unloaded
unloaded
unloaded
unloaded
tfix [mm]
20
30
35
30
30
25
width
Table 1: Tested anchors
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Fig. 3: Axial load
Fig. 4: Displacement transducer
3. Results 3.1 Temperature A typical evolution of temperature on the surface of an expansion anchor in different depths is shown in fig. 5. On the fixing element (25 mm) the temperature raises up to 800 °C and drops very fast due to the low heat capacity of the steel. The constant temperature level at 100 °C in 50 and 100 mm depth is caused by a phase change of the pore water. As expected, in the concrete the maximum temperature is reached later than on the surface. expansion anchor M16
temperature [°C]
900 800
100 mm
700
50 mm
600
0 mm
500 400
fixing element
300 200 100
tim e [h:m in]
Fig. 5: Temperature evolution
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1:00
0:55
0:50
0:45
0:40
0:35
0:30
0:25
0:20
0:15
0:10
0:05
0:00
0
In one of the slabs on the ceiling was measured the temperature in different depths inside the concrete. The results and a comparison with the temperature on the surface of the expansion anchor after 15 and 30 min is shown in fig. 6 and 7. It demonstrates very clearly the high temperature conductivity of the steel. Close to the surface the anchors are cooled down quickly. The difference between the various shapes of anchors is small. temperature after 15 min
600
tem perature [°C ]
temperature [°C]
concrete
500
expansion anchor M16 400 expansion anchor M12 300
temperature after 30 min
450
expansion anchor M8
200 100
400
concrete
350
expansion anchor M16
300
expansion anchor M12
250
expansion anchor M8
200 150 100 50
0
0
0
20
40
60
80
100
0
20
40
depth [mm]
60
80
100
depth [mm]
Fig. 6: Temperature distribution after 15 min
Fig. 7 Temperature distribution after 30 min
In fig. 8-11 are shown the average temperatures in different depths and after different times on the surface of the expansion anchors and of the bonded anchor M16 (without fixing element). On the fixing element the maximum temperature is reached between 10 and 15 minutes, in the concrete it is reached after 25 – 30 minutes. With increasing depth the maximum temperature is reached at later points of time. Under the protection of the fixing element the temperatures on the concrete surface are lower (fig. 9) than without fixing element ( fig. 8) for the same diameter of the anchor. bonded anchor M16
15 min 20 min
300
25 min
200
30 min
te m p e ra tu re [°C ]
te m p e ra tu re [°C ]
10 min
400
5 min
700
5 min
500
expansion anchor M16
800
600
100
10 min
600
15 min
500
20 min
400
25 min
300
30 min
200 100
0
0
0
60 depth [mm]
120
Fig. 8: Temperature distribution bonded anchor M16
-25
0
50 depth [mm]
Fig. 9: Temperature distribution expansion anchor M16
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100
expansion anchor M12
700
expansion anchor M8
600
5 min 5 min
600
500 te m p e ra tu re [°C ]
tem p eratu re [°C ]
10 min
500
15 min 20 min
400
25 min 30 min
300 200
10 min 15 min
400
20 min 25 min
300
30 min
200 100
100
0
0 -30
0
depth [mm]
40
Fig. 10: Temperature distribution expansion anchor M12
-30
80
0
depth [mm]
25
50
Fig. 11: Temperature distribution expansion anchor M8
3.2 Expansion anchor under axial loading in uncracked concrete After the fire test the residual load capacity was determined by a pullout test in uncracked concrete of the strength class C50/60. It is important to know this value for the assessment of the reliabilty of the system after a fire szenario and for future sanitation. The tests were performed displacement controlled with a servohydraulic testing machine at a speed of 0.08 mm/sec. For the present the comparison of the ultimate mean loads for the different shapes in the axial tension test in concrete with (Fu,m) and without (Fu,m,ref) fire exposure is shown in fig. 12. After the fire test the concrete surface was full of cracks mainly close to the anchors. The cracks propagated in radial direction and their width varied between 0.2 and 0.4 mm. This may be interpreted as a first indication of spalling. The expansion anchor exhibited mainly pull-throughfailure, in one case splitting failure. 50
Ultimate axial load expansion anchor
45 Fu,m/Fu,m,ref [%]
40 35 30 25 20 15 10 5 0 45
70 heff [mm]
85
Fig. 12: Relative ultimate axial load of expansion anchor in uncracked concrete
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3.3 Bonded anchor under axial loading in cracked concrete The displacement of the bonded anchor of the shape M12 during the axial loading and the corresponding temperatures in different depths are shown in fig. 13.
1
1000 temperature [°C]
1,2
800
0,8
600
0,6
400
0,4
200
0,2
80 mm 40 mm 0 mm fixing element anchor 1 anchor 2 anchor 3
1:20
1:10
1:00
0:50
0:40
0:30
0:20
0:10
0 0:00
0
Displacement [mm]
bonded anchor M12 axial
1200
time [h:min]
Fig. 13: Displacement and temperature during constant axial loading in cracked concrete Very interesting is the high temperature peak in the first 5 minutes even in 80 mm. It could be possible that there was some air included in the mortar which fovourished the heat transport at the beginning of the test and that a succeeding chemical reaction stopped the enormous heat transfer. To clear this phenomenon further investigations are necessary. The displacements after 90 min were 0.8 mm, 1.04 mm and 0.7 mm respectively. The creep of the chemical mortar is primarily a time dependent process. The first anchor displacement can be observed 10 minutes after the beginning of the fire test, whereas the maximum temperature in 40 mm depth is reached already in 15 minutes. The ultimate axial load in the pull-out test in cracked concrete after the fire is shown in fig. 14 in percent of the ultimate load in cracked concrete of the strength class C50/60 which has not been subjected to high temperatures. The crack width was the same as during the fire test (0.3 mm). The shapes M10 and M12 exhibited concrete cone breakout and the shape M16 pull-through failure. The spalling was more pronounced around the thread rods without fixing element (about 34 mm in fig. 15) than close to the anchors with fixing element. Hence the fixing element has a positiv influence by preventing concrete spalling close to the anchor.
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Ultimate axial load bonded anchor 100
F u,m /Fu ,m ,ref [% ]
90 80 70 60 50 40 30 20 10 0 60
80 heff [mm]
125
Fig. 14: Relative ultimate axial load of bonded anchor in cracked concrete
Fig. 15: Concrete spalling near a thread rod
An explanation for the relatively high ultimate load of the shape M12 (heff = 80 mm) may be the shielding effect of the mineral wool which was wrapped around the lever-arm in order to protect the steel from high temperatures.
4. Conclusions In a natural fire test the temperature distribution and evolution has been measured on the surface of expansion and bonded anchors. The displacement behaviour of axial loaded bonded anchors in cracks was investigated. After the fire test the residual ultimate axial load was determined and compared with the ultimate load in concrete which has not been subjected to high temperatures. The expansion anchors exhibit a larger decrease of the residual load capacity than the bonded anchors.
5. References 1.
Kordina, K., Meyer-Ottens, C., ’Beton Brandschutz Handbuch’ (1999)
2.
Wiesholzer, J., ’Berechnung der Temperaturverläufe von Befestigungsdetails infolge Brand mittels FEM-Programm’, Diplomarbeit, University of Innsbruck (1987)
3.
Nausse, P., ’Prüfung und Beurteilung des Brandverhaltens von Dübeln’, IBKBaufachtagung 153, Hannover (14./15.10.1992)
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DURABILITY OF GALVANIZED, POST-INSTALLED FASTENERS TO CONCRETE K. Menzel*, B. Hagmayer** * Otto Graf Institut, University of Stuttgart, Germany ** Schlaich, Bergemann u. Partner, Stuttgart, Germany
Abstract The paper discusses the mechanisms of zinc corrosion in contact with concrete with special emphasis on post-installed fasteners. Experimental results on the influence of cement type,carbonation, galvanic effects and results of exposure tests up to ten years are presented. Compared to corrosion of galvanized reinforcement embedded in concrete and galvanized metalwork exposed to the atmospere, differences in mechanism and type of corrosive attack are found. In case of weathered concrete, even hot dip galvanizing does not assure corrosion protection for more than ten years because of localized attack due to galvanic effects at the interface concrete/atmosphere.
1. Corrosion of zinc and galvanized steel Zinc is known as a cheap and reliable protective plating for wheathered steel components of any kind. With the exception of extreme industrial atmosphere (containing high amounts of sulfur dioxide) zinc suffers uniform corrosion at relatively low rates about one to seven micrometers/year (fig.1 [1-3]). Embedded in concrete, galvanized reinforcement resists chloride induced corrosion much better than bare steel [5]. In a first stage, up to one week,being exposed to a highly alcaline electrolyte, corrosion rates are high because hydrogen evolution is the dominating cathodic reaction. Passivation, followed by deposition of salt layers reduces the corrosion rate drastically later on (fig. 1 [4,5]). As to fasteners, installed in drilled holes after hardening of the concrete, not much information is available. The few sources on related subjects (e.g cavity wall ties [6] and facades [7](see fig.1) report corrosion rates in a range of 1 to 12 µm/year without further explication. It was the aim of the study presented here, to understand the specific of post installed, galvanized fasteners in concrete with regard to corrosion and life-time of the protective coating.
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Fig. 1: Corrosion rates of zinc
2. Experimental Samples were designed as close as possible to reality, using cylindrical concrete blocks of 100 mm diameter with drilled holes, where galvanized rods (∅ 12x100 mm) were introduced (fig.2). Two types of cement (portland and slag cement) were used. One set of samples was carbonated in an atmosphere of 1% CO2 after drilling the hole. The steel rods were either electroplated and chromated (zinc cover 3-4 µm) or hot dip galvanized (50-60µm zinc). As an additional parameter, some of the samples were sealed at the interface concrete/atmospere with natural rubber and a galvanized washer. To study galvanic effects, caused by the vicinity of carbonated and alcaline concrete, special samples with two rods were used (fig.3). Samples were exposed on a roof in Stuttgart for ten years. Corrosion potential was measured by means of a calomel electrode.More details on the experimental setup are given in [8].
330
Fig.2: samples with hot-dip galvanized steel rods (section, treated with phenolphtaleine to mark alcaline concrete ) after ten years of outdoor exposure
3. Results During the first stage of exposure, when the corrosion potential was regularily measured, potentials of –800 to –100 mV (SCE) were recorded. The potential drop in a range where hydrogen evolution is thermodynamically possible (as known from fresh concrete and galvanized reinforcement) was not observed (fig.4).In the course of exposure potentials tend to steadily increase, until „iron-like“ behavior is observed (fig.5). The increase is earlier for electroplated samples. It is interesting to note, that the differences regarding the parameters carbonated/not carbonated, sealed/open or type of cement are much smaller than expected. Evaluation after ten years of exposure gives the pictures presented in fig.6 to 8). In all cases, corrosion attack is pronounced about 1 to 2 cm from the outer end of the borehole. An experimental galvanic couple, consisting of identical samples in alcaline and carbonated boreholes subjected to wet/dry-cycles produces maximum current densities of 3,6 µA/cm² corresponding to about 50µm/year corrosion loss of zinc (fig.3). After 10 years of exposure, the percentage of still zinc covered surface is found to be in the range of 35 to 90 % for hot dip galvanized samples and of only 0 to 30 % for electroplated samples (fig.9). Electroplated samples in slag cement are heavily corroded (fig.8 below). About 30% of the samples of this type already caused spalling of the concrete cylinder whereas the outer (atmospheric) end is only slightly stained without significant loss of material.
331
Fig.3: Current density of a galvanic element (carbonated/alcaline) during wet-dry cycles
Fig.4: Corrosion potentials of galvanized steel
332
Fig.5: Corrosion potential of post-installed galvanized fasteners vs. Time
Fig. 6
333
Fig.7
334
Fig. 8
Fig.9: Percentage of still zinc covered area after ten years outdoor exposure
335
Fig. 10: Average corrosion loss after ten years exposure (calculated from total weight loss)
4. Discussion The mechanisms of corrosion of galvanized fasteners to concrete do not compare directly to corrosion in concrete and atmospheric corrosion. Specific effects have to be taken into account: • •
Contact to concrete of different pH (alcaline-carbonated) with the effect of additional corrosion loss due to galvanic elements Crevices within the borehole with high humidity and depletion of carbon dioxide (CO2 is consumed by the carbonation reaction) hindering the formation of protective carbonate layers as known from atmospheric corrosion.
These effects lead to local differences in corrosion rate, which will be highest at the outer end of the borehole. Zinc dissolution can be estimated to a rate of 2,5 µm/year (fig. 10) in the average and more than 50 µm/year locally. After consumption of the zinc layer cathodic protection of bare steel by surrounding zinc is given to a certain extent. Newertheless steel corrosion should not be neglected after a period of about ten years exposure for hot dip galvanized and one year for electroplated fasteners in wheathered concrete.
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5. References 1. Korrosionsverhalten von feuerverzinktem Stahl ; Beratung Feuerverzinken, Hagen (1983) 2. Nürnberger, U.: Korrosion und Korrosionsschutz im Bauwesen; Bauverlag Wiesbaden (1995) 3. Menzel, K.: Korrosionsschutz in der Befestigungstechnik; VDI Berichte 653 , Düsseldorf (1988) 4. Rauen, A.: Deutsche Verzinkertagung, München (1971) 5. Andrade, M.C., Macias, A.: Galvanized Reinforcements in Concrete; Surface Coatings-2 Elsevier Applied Science ISBN 1 85166 194 8 6. Moore, J.F.A.: Building Research Current Paper 3 (1981), U.K. 7. Hermann, P.: Korrosion (Dresden) 14, (1983) 1 8. Menzel, K.: Zur Korrosion von verzinktem Stahl in Kontakt mit Beton; Stuttgart,Institut für Werkstoffe im Bauwesen, (1992) 1
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DURABILITY OF STAINLESS STEEL CONNECTIONS WITH RESPECT TO CORROSION Ulf Nürnberger Otto-Graf-Institute, University of Stuttgart, Germany
Abstract In structural engineering connection elements for ventilated curtain walls and suspended ceilings are more and more made of stainless steel due to reasons of corrosion protection. A special approval process regulates the use of the steel grade in Germany. The permitted stainless steels for substructures, connectors, fastenings, hangers and anchorage devices are defined in dependence of environmental conditions and installation. Normally austenitic Cr-Ni-(Mo)-steels are applied. The use of hardened martensitic steels for self-drilling screws and concrete screws should be desirable but such fasteners are not sufficient sure. In strong acid and/or chloride containing environment (see-atmosphere, de-icing salt) connection elements might be endangered by pitting corrosion, crevice corrosion and stress corrosion cracking, if these products are made of unsuited alloys. In the contribution the corrosion situations are described in detail. Further typical corrosion damages are discussed if unsuited stainless steel products are applied.
1. Introduction During the last decades pollution has eminently increased in urban agglomerations, industrial areas and traffic structures. Because of this fact, the corrosion exposure of metallic structural elements with a security risk is growing in constructional engineering. Mechanical connection elements between steel and concrete, e. g. in claddings for external walls that are ventilated at the rear and comply with DIN 18516 [1], in suspended ceilings in special climates (humid premises, indoor swimming-pools) or in flat roofs, are also affected. Due to corrosion, connection elements can undergo an impairment of their functionality as well as a security risk for the whole construction. In the past, steel fastenings, that are galvanized and plastic coated, have been particularly affected in the exterior. Corrosion could especially be explained by high chloride pollution of the atmosphere and the building materials and/or contact with moist
338
building materials during failures [2-5]. At contact with moist, neutrally reacting building materials (e. g. heat insulation, wood), corrosion–protective films can not develop and corrosion–promoting aeration cells become effective [6]. Additional serious corrosion damages occurred in indoor swimming-pools in connection elements, that consisted of stainless steel [6,7]. The use of unsuitable steel grades in an aggressive atmosphere was responsible for these damages (v. paragraph 2). Because of the above–mentioned correlation, high-quality stainless steels have been subsequently tested in regard to an application in structurally critical climates [8-10] and have also been increasingly used for steel connections, fastenings, substructures, hangers and anchorage devices in structural elements outdoors [11]. The adequate steel grades are regulated in a special approval (paragraph 5) depending on corrosion exposure and installation conditions.
2. Corrosion problems pointed out exemplary in claddings for external walls that are ventilated at the rear Under critical exposure conditions various corrosion processes are possible in mechanical connection elements as well as adjacent metallic structural elements. This is illustrated in fig. 1 at the example of a ventilated curtain wall. Table 1 quotes the structural elements resp. the building materials of the cladding for external walls as well Table 1: Structural elements in an external ventilated curtain wall mark structural type of construction material element 1 cladding moulded metal sheet, ceramics, nature stone, fiber plate cement, high pressure laminated plate, aluminium alloy, copper, titan zinc, galvanized and/or coated steel, stainless steel 2 fastening screw, rivet, cramp, aluminium alloy, copper alloy, element hook stainless steel 3 connection screw, rivet element 4 substructure profile (load-bearing aluminium alloy, copper alloy, rail) galvanized and/or coated steel, stainless steel, wood 5 anchorage post-installed fastener, stainless steel, plastic sleeve plus device anchor rail, concrete galvanized screw screw 6 insulation mat mineral fiber, glass fiber, styrofoam
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Fig. 1: Situation of claddings for external walls that are ventilated at the rear as fastening elements, connection elements and anchorage devices, that have to be put in. With the help of constructive measures (construction of external walls) as well as the choice of suitable building materials, it has to be secured that damaging influences in case of an attack of water and especially aqueous, acidulous and/or chloride-enriched media do not lead to an impairing corrosion. On principal, stainless steel can be used for all metallic structural elements and it can also get into contact with different structural metals.
3. Exposure conditions for connection elements [6,12] Corrosion in the open atmosphere increases depending on rising humidity and temperature as well as concentration of gaseous and/or solid contamination in the air. Therefore, corrosion exposure of structural elements in the open air is distinguished by
340
• •
•
Climatic zones (dry, temperate, warm-humid climate). The type of atmosphere, that is characterised through local environmental conditions: inland atmosphere, as a rule, is not very aggressive, at all. Urban atmospheres and especially industrial atmospheres can, above all, be more or less bad polluted with dirt and sulphur-dioxide or whirled-up de-icing salt. Sea atmospheres are, depending on the distance to the shore, polluted with variable contents of chloride aerosols. Micro-climate at the interface between structural element and environment, which is of the greatest influence for the expected corrosion exposure. It is specified by the type of atmosphere, constructive influences (heat-leaks, crevices) and the position of the structural element in regard to its environment. Above all, a micro-climate is influenced by humidity, temperature, short-falls of the dew-point as well as duration of local moistening, even in combination with polluting agents and contamination as well as air flows.
Special applications, where the corrosion exposure and the above-mentioned classification differ, do exist: Interior work The external surfaces of structural elements and connectors inside buildings do not duly get in contact with aqueous corrosion media. A corrosive exposure only takes place, if water, moistness of structural elements or other polluting agents are affecting because of failures. Road tunnel In road tunnels, fastening elements of steel are exposed to an enhanced relative humidity, a high portion of dust, soot, abrasion of car tire and chloride salts out of deicing salts and acid gas such as SO2, HCl and NOx (as a consequence of diesel vehicles). Because of the lack of detergent rain, a concentration of polluting agents occurs. Since, in addition, the tunnel wall and the metallic components, that are fastened to it, usually have lower temperatures than the surrounding air, suitable conditions are given for the formation of water of condensation. Under the exposure of water of condensation a water film, that is acidulous and rich in chloride ions, exists on the metallic components and, because of dirt depositions, the basic requirements for crevice corrosion are given, too. In particularly adverse cases, the corrosion conditions are thus comparable to those in indoor swimming-pools. Indoor swimming-pools In the swimming-pool atmosphere very thin electrolyte films generate because of the content of water vapour in the indoor air and, depending on aeration and structural conditions, water of condensation develops after the short-fall of the dew-point. Further, salts and dusts, that, among others, have contents of MgCl2, CaCl2 and especially NaCl, settle down. Because of their hygroscopic character, these salts do already generate saturated salt-solutions in the typical relative atmospheric humidity of “dry“ interiors.
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A further characteristic of corrosivity of the atmosphere in indoor swimming-pools results from the disinfection treatment of the bath-water. The chlorinated gas process is applied to most times. Chlorine, that is in the hall’s air, can - in reaction with water build hydrochloric acid (HCl) and hypochloric acid (HOCl) in the films, that are rich in neutral salt, according to the reaction Cl2 + H2O → HCl + HOCl As a matter of fact, the latter one is the disinfectant, because of its strong oxidation effect. In water it disintegrates into hydrochloric acid and oxygen according to 2HOCl → 2HCl + O2 This way, an acidulous and saline electrolyte with a high concentration of chloride ions develops on the surface of the structural element. Polluting agents accumulate on surfaces of structural elements, that are not cleaned and washed around by water. Characteristics of connection elements Connection elements often are not accessible. They are, e. g. behind walls or at covered ceilings, not within reach for inspections and maintenance. In addition, connection elements can, at least, be partially in contact with mineral building materials, insulation or wood. Then, with regard to corrosion exposure, the before-mentioned conditions, especially the micro-climate, are of importance for those zones that come into contact with air. The corrosive exposure, that e. g. has to be expected in claddings for external walls that are ventilated at the rear according to DIN 18516, part 1 [1], results from atmospheric influences (relative atmospheric humidity, access of acidulous gases and chloride aerosols) in close connection with structural parameters of the wall construction and chemical influences from (moist) building materials. In walls and façades, that meet the technical standards concerning humidity (proof of protection against interior condensation and absence of dew-water in the area that is ventilated at the rear [13]) or comply with the standards mentioned in [1] (incurring moisture has to be eliminated because of ventilation at the rear), it can be assumed in case of flawless protection against outdoor weathering (joints have to be formed that way, that no rain can ooze in from outside) that in normal case the corrosion exposure is less than it is in outdoor weathering. Formation of condensate only occurs short-time, e. g. as a result of the heatleak effect of fastening components. Though, corroding polluting agents, especially chlorides (from some building materials or aerosols), can concentrate, because they can not be washed off by the rain. First of all, at connection elements that get into contact with building materials, it is of importance, whether they contain in their pores and (inner) cavities the free water that is necessary for corrosion [6,14]. Furthermore, in the case of stainless steels, conditions that inhibit or destroy passivity have to exist. In all cases of corrosion, there is a complicating effect, if water dissolves ingredients from the building material, that are aggressive against steel, or eases the transport of polluting agents from the environment to the building material.
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A corrosion influence of materials in connection with stainless steels can only be expected, if these materials contain a sufficient concentration of chloride ions and/or acids in addition to water. Chlorides can only get into normal concrete in high concentration, if there is a direct impact with sea-water or water containing de-icing salt [6]. Normally, a such exposure of connection elements and building material with chlorine water does not happen in practical operation. In moist wood, in contrast, acetic acid, which is able to attack stainless steels, too, can be released depending on the type of wood because of hydrolysis at increased temperatures [6]. In special cases chemicals for wood protection can also contain chlorides. Moist insulation is not only conducive to general corrosion. Because of their electrolytic conductivity, they can also promote the formation of elements between structural elements in the insulation (e. g. of galvanized or non-galvanized, unalloyed steel) and more precious components. So-called foreign cathodes are e. g. steel in concrete, copper materials and stainless steels, if they are conductively connected to the steel elements in the insulation, that are effective as anodes. In most cases, insulation is free of corrosionpromoting components, which could be dissolved due to an access of water. In moist and nearly neutral building materials with open pores, the corrosion exposure of structural metals is normally higher than e. g. in the atmosphere behind a wall, that is ventilated at the rear. The opposite reaction rather is the case, if there is a contact with alkaline mineral building materials.
4. Steel grades and types of corrosion [6] High alloyed steels, which in contrast to unalloyed steels do not show general corrosion and noticeable rust formation in normal environmental conditions (atmosphere, humidity) and in aqueous, nearly neutral to alkaline solutions, are called stainless steels. Basic requirement for the before-said reaction is a minimum concentration of that steel on particular alloying elements and the existence of an oxidising agent (e. g. oxygen) in the surrounding medium. This causes a passivation of the surface. "Passivity" describes a condition that produces a strong inhibition of the reaction of resolving iron after forming a passive layer on the surface. Chromium, in particular, is an element that tends to passivation. This property is transmitted on iron resp. steel through alloying: General corrosion decreases in corrosion-promoting media contrary to the content of chromium (fig. 2). The content of chromium that causes passivity when exceeded depends on the attacking agent. The content of chromium in water and in the atmosphere should at least be 12 M.-%. For particular types of corrosion, e. g. pitting corrosion and stress corrosion cracking, the existence of a passive layer is a necessary requirement. Because of that, passive steels are resistant against general corrosion, but are sensitive to local corrosion in presence of specific media (e. g. chloride ions) in case of an insufficient content of alloy. First of all,
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Fig. 2: Corrosion of chromium steel in industrial air (referring to Binder and Brown) the specific standards for stainless steels concerning alloy result from the particular corrosion exposures (e. g. attack of chloride ions or acids) and such resistivity as may be required against pitting corrosion, crevice corrosion and stress corrosion cracking. A special state of structure is generated through the selection of the alloying elements and their concentration. Therefore, stainless steels are classified according to their structure. For metallic connection elements and adjacent structural elements, ferritic, austenitic, ferritic-austenitic and martensitic steels can be used. However, ferritic and martensitic steels are only used for screws exceptionally. The use of austenites is predominant. They are used in different strength levels from a solution-annealed to a cold deformed state. In common conditions, that prevail in construction engineering (attack of light acid to alkaline aqueous media), ferritic steels with about 11 to 17 % of chromium have a sufficient resistivity against general corrosion. With an addition of a sufficient content of chromium and molybdenum up to about 2 %, resistivity against pitting corrosion can be achieved as well. Besides, ferrites have a high resistivity to stress corrosion cracking in an environment containing chlorides. Above all, if you assume comparable contents of chromium, the reaction of ferritic steels towards crevice corrosion is much more adverse than it is e. g. at austenitic steels. Austenitic steels have at least 17 to 18 M.-% of chromium and 10 to 12 M.-% of nickel. These steels are especially used because of their positive corrosion properties and their superior workability in comparison with other stainless steels. In case of a proper content of alloy, they have got a high resistivity to general corrosion, pitting corrosion and crevice corrosion, but are sensitive to stress corrosion cracking in their typical compound with about 10 M.-% of nickel. The resistance to pitting corrosion, crevice corrosion and
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stress corrosion cracking can be improved with an addition of molybdenum. Ferritic-austenitic steels have a binary structure of ferrite and austenite. The typical range of their chemical analysis is 22 to 28 M.-% of chromium, 4 to 8 M.-% of nickel. Molybdenum can be added in order to improve the corrosion resistivity. These steels combine good properties of ferritic steels (high yield strength) and austenitc steels (good ductility, improved corrosion properties). Martensitic steels with an analysis comparable to ferritic steels, but an enhanced content of carbon, are distinguished from all other stainless steels by a substantially higher hardness resp. strength. Because of that, especially the usual carbon martensites are very sensitive to hydrogen-assisted stress corrosion cracking [15]. However, through a limitation of the content of carbon to a max. of 0.05 M.-% and the addition of up to 5 % of nickel, the reaction towards stress corrosion cracking of these “soft martensites” can be improved very much. Assuming a comparable content of chromium and molybdenum and an equal surface quality, these materials can be classified similar to ferritic steels in regard of corrosion. The above-mentioned steel grades are basically chosen considering their resistivity in the attacking medium, but particular technological characteristics are aimed at with regard to processing and application, as well. For economic reasons, the concentration of alloy should not be incongruously high, but likewise not too low considering the intended application conditions, so as to achieve the necessary resistivity in the attacking medium. The reaction of stainless steels with respect to general corrosion, pitting corrosion and stress corrosion cracking has to be considered (fig. 3). They can only be attacked in acid through more or less regular general corrosion. The lower the pH-value and the higher the temperature, the more difficult it is to achieve a passivation here. Under such conditions the steels must have higher contents of particular alloying elements in order to reduce a corrosion wastage or to achieve passivity. It is important, that - at atmospheric corrosion - the corrosion rate in the active state decreases very much, if there is an increasing pH-value. Corrosion resistivity generally exists above pH 4. Therefore, in weakly acidulous media, thus as well in an usual atmosphere and more than ever in concrete, chromium steels with > 12 M.-% of chromium and all higher alloyed steels are passive (fig. 2). In case of pitting corrosion an interaction between chloride ions and the passive layer develops, in which the passive layer is locally interrupted and a pit expansion occurs after the depassivation. Crevice corrosion is an intensified pitting corrosion running down in crevices. Crevice corrosion occurs whenever structural elements are in more or less narrow contact with each other and crevices develop (fig. 1). On this occasion, it can come to a concentration of chloride ions below corrosion products in the crevice and to a decline of the pH-value as a result of a hydrolysis of the corrosion products. Because of that, corrosion in crevices already occurs at even lower corrosion exposure than pitting
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Fig. 3: Types of corrosion (schematically) corrosion occurs in areas, that are free of crevices. Corrosion endangering towards pitting corrosion and crevice corrosion decreases depending on declining content of chloride, declining temperature and rising pH-value. Acid chloride enriched media are therefore particularly critical. Because of that, stainless steels are basically more resistant in concrete construction with a pH-value of about 8 to 13 than e. g. in atmospheric weather conditions. As a result, the standards for reinforced steels and e. g. anchorage devices in matters of concrete are normally lower than for structural elements in the open atmosphere. Fig. 4 gives a general view of the corrosion behaviour of stainless steel reinforcement that are admitted in Germany at the moment [6,16]. This situation would be analogously transferable to post-installed fasteners and anchor rails. Corrosion resistivity in media that generate pitting corrosion further depends on the quality of the steel surfaces. Improvement ensues around the following order: scaled - raw grinded blasted - fine grinded - pickled - polished. Pitting corrosion and crevice corrosion is especially influenced in means of material by the alloying elements chromium, nickel, molybdenum and further nitrogen. Without influence of the steel grade, resistivity can be roughly estimated with the “pitting resistance equivalent number” W = 1 % Cr + 3,3 % Mo + 15 % N . Improvement of resistivity to chloride-assisted local corrosion depends on a rising “pitting resistance equivalent number”. Nickel improves the corrosion reaction under conditions of crevice corrosion, as it raises the resistivity to acid. Weld joints are, above all, more exposed to the danger of pitting corrosion than similar nonwelded steels, because oxide films (temper colours) or scale layers have developed in the weld joint area during the welding, because of incomplete or lacking gas metal arc. At an increasing thickness, these layers restrain passivation. steels are sufficiently secured against stress corrosion cracking all the time. Resistivity of stainless steels to chlorine-assisted stress corrosion cracking decreases in the following order: ferritic chromium steels, ferritic-austenitic steels, austenitic chromiumnickel(molybdenum) steels. Above all, this can be explained with the influence of the content of nickel on the sensitivity of steels, containing a high portion of chromium, to
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Fig. 4: Corrosion of stainless steel reinforcement (overview) [16] stress corrosion cracking. A minimum resistivity exists at about 10 M.-% of nickel. From this minimum on, resistivity decreases depending on rising or declining content of nickel. In martensitic stainless steels, the reaction towards hydrogen-assisted stress corrosion cracking is decisive (see above). Stainless steel can cause galvanic corrosion in another less precious metal (steel, aluminium, zinc). Basic requirements are: both metals are connected to be electrically conductive and are located in a well-conducting electrolyte. However, there are normally no electrolyte films in atmospheric corrosion conditions. Being so-called „pure“ water, rain or dew, in addition, have a very slight conductivity. Not until salts or gases, that develop acid, dissolve in the electrolyte and e. g. an aqueous solution remains at the contact area (e. g. in crevices) for a longer period, is a certain galvanic corrosion possible.
5. Definition of the grades of resistance according to the approval of the German building supervisory board Reduction of the cross section, pitting corrosion and stress corrosion cracking are of importance for the technical corrosion resistivity of connection elements. Table 2 gives a general view of the admitted steels as well as the classification according to the grades of resistance [17]. The quality of the steels increases depending on the rising grade of resistance.
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In normal case, connecting agents in structural elements in the outdoors should be classified in the third grade of resistance. In many cases, e. g. behind walls, connecting agents are not accessible to inspections and maintenance and a moderate exposure with chloride and sulphur-dioxide from industry, traffic and sea atmosphere is often inevitable. A concentration of polluting agents has to be excluded, otherwise the use of steels of the fourth grade of resistance is necessary. Because of damages, special regulations have been adopted for structural elements in indoor swimming-pool atmosphere. For fastening elements without regular cleaning (e. g. hangers for ceilings) and for anchorage devices the regulations mentioned in table 3 have been adopted with particularly high standards for the steels. Today, structural elements and connecting agents, e. g. in ventilated curtain walls, are mainly made of the materials 1.4301 (A2) and 1.4401 (A4) and therefore only comply with the second resp. third grade of resistance. Steels of higher valence (e. g. 1.4529) are merely already used for anchorage devices (post-installed fasteners), which even have to comply with much higher demands.
6. Review and preview The development of stainless steels for the field of construction as well as for mechanic connectors has been very much influenced by damages in indoor swimming-pools due to stress corrosion cracking over the last ten years. In 1985 the grave crash of a reinforced concrete roof, that was hung on hangers of stainless steel 1.4301 became public [6]. On the occasion of this accident, examinations of important construction elements have been conducted in many other indoor swimming-pools in Switzerland, Germany, England and the U.S. and additional examples for stress corrosion cracking were found [6,7,12]. The materials containing molybdenum (e. g. 1.4401) indeed proved to be more resistant, but stress corrosion cracking was detected there, as well. Analysis of the damages and results of the research [8-10] finally lead to the conclusion, that only those higher alloyed materials mentioned in table 3 are sufficiently secure under these critical environmental conditions. Present and future efforts are aimed at the creation of self drilling screws for steel substrates (e. g. for the connection of coverings and substructure) and concrete screws made of very high strength martensitic steels. Self drilling screws are screws that drill their pilot hole in the steel themselves during the mounting. Concrete screws are special screws made to be anchored in concrete. They are screwed into a prepared hole in the concrete. In both cases cold deformed austenitic steels are used at present, as well. Since they can not yet be screwed into hard substrates (steel, concrete) in the required way, e. g. a tip of screw of a hardenable unalloyed steel is butt welded. There are efforts to completely produce the above-mentioned fastenings resp. anchors of a martensitic steel of high hardness. However, the corrosion resistivity of such materials is limited.
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Martensitic steels proved to be susceptible to crevice corrosion and stress corrosion cracking, especially in case of an attack of chlorine electrolytes [15]. Table 2: Classification of the steel grades for structural elements and connection elements according to strength levels and grades of resistance against corrosion [17] material symbol strength level grade of corrosion exposure, resistance typical applications 1.4003 X2Cr 11 S235, S275 indoor exposure S460 I 1.4016 X6Cr 17 S235 1.4318
X2CrNiN 18-7
S355, S460 II
1.4567
X3CrNiCu 18-9
S235, S275, S355, S460
1.4301
X5CrNi 18-10
1.4541
X6CrNiTi 18-10
1.4401
X5CrNiMo 17-12-2
S235, S275, S355, S460 S235, S275, S355, S460 S235, S275, S355, S460
1.4404
X2CrNiMo 17-13-2
1.4571
X6CrNiMoTi 17-12-2
1.4439
X2CrNiMoN 17-13-5
S235, S275, S355, S460, S690 S235, S275, S355, S460, S690 S275
1.4462
X2CrNiMoN 22-5-3
S460,S690
III
IV 1.4539
X1NiCrMoCuN 25-20-5
S235, S275, S355
1.4529
X1NiCrMoCuN 25-20-7 X3CrNiMnMoNbN 23-17-5-3 X1CrNiMoCuN 20-18-7
S275, S355, S460, S690 S460
1.4565 1.4547
S275,S355
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accessible constructions without appreciable contents of chloride and sulphur-dioxide
non-accessible constructions with moderate chlorideand sulphur dioxide exposure
constructions with high corrosion exposure by chloride and sulphur dioxide (also in cases of concentration of polluting agents, e. g. elements in seawater and road tunnels)
Table 3: Structural elements in indoor swimming-pool atmosphere without regular cleaning domestic water chloride enriched water (e. g. saline water) (Cl¯ ≤ 250 mg/l) 1.4539 (X1NiCrMoCu 25-20-5) 1.4565 (X2CrNiMnMoNbN 23-17-5-3) 1.4529 (X1NiCrMoCuN 25-20-7) 1.4547 (X1CrNiMoCuN 20-18-7)
References 1. 2. 3. 4. 5. 6. 7. 8.
9.
10.
11. 12.
13.
DIN 18516, Teil 1, 'Außenwandbekleidungen, hinterlüftet; Anforderungen, Prüfgrundsätze' (1990) Rehm, G., Lehmann, R. and Nürnberger, U., 'Korrosion der Befestigungselemente bei vorgehängten Fassaden', (FMPA BW, Stuttgart, 1980) Menzel, K., 'Korrosion von Befestigungselementen hinter vorgehängten Fassaden.' VDI-Seminar 'Befestigungstechnik im Ingenieurbau' (Stuttgart, 1987) Wieland, H., 'Korrosion von Befestigern in nicht belüfteten Flachdächern' (SFS Stadler, Heerbrugg/Switzerland, 1992) Nürnberger, U., 'Korrosionsverhalten von Wellplattenbefestigern im Dachbereich.' Bericht 33-19947 (FMPA BW, Stuttgart, 1996) Nürnberger, U., 'Korrosion und Korrosionsschutz im Bauwesen' (Bauverlag, Wiesbaden, 1995) Nürnberger, U., 'Spannungsrißkorrosion an Bauteilen aus nichtrostendem Stahl in Schwimmbadhallen', Stahl und Eisen 110 (1990) 142-148 Haselmair, H. Übleis, H. and Böhni, H. 'Corrosion-resistant materials for fastenings in road tunnels - field test in the Mont Blanc Tunnels' Structural Engineering Internat. (1992) Arlt, N., Busch, H., Grimme, D., Hirschfeld, D., Michel, E., Beck, G. S. and Stellfeld, I., 'Stress corrosion cracking behaviour of stainless steels with respect to their use in architecture', Steel research 64 (1993), part 1: 'Corrosion in active state', 461-465, part 2: 'Corrosion in the passive state', 526-533 Arnold, N., Gümpel, P. and Heitz, T. W. 'Chloride induced corrosion on stainless steels at indoor swimming pools atmospheres. Part 3: Influence of a real indoor swimming pool atmosphere', Materials and Corrosion 50 (1999) 140-145 Informationsstelle Edelstahl Rostfrei, Dokumentation 843, 'Edelstahl Rostfrei in der Verbindungstechnik am Bau' (Düsseldorf, 1999) Mietz J., 'Problemlösungen für Bauteile und Verbindungselemente im Ingenieurbau' in: 'Nichtrostende Stähle in der Bautechnik Korrosionsbeständigkeit als Kriterium für innovative Anwendungen', GfKORRJahrestagung 2000, 69-89 Liersch, K., 'Belüftete Dach- und Wandkonstruktionen' (Bauverlag, Wiesbaden, 1981)
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14.
15.
16. 17.
Nürnberger, U., 'Korrosion der Baumetalle im Kontakt mit mineralischen Baustoffen' in: ibausil, Tagungsbericht - Band 1 (Bauhaus-Universität, Weimar, 2000) 1019-1027 Nürnberger, U. 'Hochfeste nichtrostende Stähle - Alternative für Zugglieder im Ingenieurbau und Blechschrauben für den Dach- und Wandbereich' in: 'Nichtrostende Stähle in der Bautechnik - Korrosionsbeständigkeit als Kriterium für innovative Anwendungen', GfKORR-Jahrestagung 2000, 91-118 Nürnberger, U., 'Stainless Steel in Concrete', EFC Publications, Number 18 (The Institute of Materials, London, 1996) Allgemeine bauaufsichtliche Zulassung Z-30.3-6 'Bauteile und Verbindungselemente aus nichtrostenden Stählen' (Berlin, 25.09.1998)
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FIRE RESISTANCE OF STEEL ANCHORS IN CONCRETE Michael Reick Institute of Construction Materials, University of Stuttgart, Germany
Abstract With the increasing use of fasteners in the field of civil-engineering the need to estimate the fire resistance of these connections is obvious. Different test procedures for fire tests and no commonly accepted rules to design fasteners for this use show the problems in present. Scientific work to estimate the different failure modes known from tests with ambient temperature has been missing so far. To investigate the fire resistance of fasteners several numerical simulations were performed. Programs have been developed to calculate temperature fields for fasteners in concrete and to calculate stress-strain relationships in concrete slabs in bending and under fire load. Qualified non-linear finite element programs have been extended to calculate concrete cone failure in case of fire. To check the numerical simulations several large scale fire tests with fasteners installed in loaded concrete slabs were done.
1. Introduction In fire tests from various manufactures for their specific products, mainly steel failure was observed. But the test methods used did not consider the worst circumstances for concrete cone failure and pullout. Therefore theses failure modes had to be examined in detail using scientific methods. Also the influence of the test setup on the steel temperature of the fastener had to be investigated to clear the comparability of the various test results and the obtained differences. The fire resistance of steel anchors in concrete under tensile loading has been an research project at the Institute of Construction Materials for the past 6 years. During this period, a lot of numerical calculations and large scale fire tests have been performed. This article gives a brief introduction in the basic results.
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The results are documented in detail in different working papers of the Institute of Construction Materials as well as in Reick (2001).
2. Calculation of temperature fields The temperature field of concrete structures under fire attack is known for special geometric shapes by measurements during fire tests and by numerical simulation. For fasteners under ISO fire load up to 90 minutes no published calculations are known so far. To obtain more than just a few calculations it seemed to be better to develop a special computer program (using the finite difference method) instead of working with a commonly available program. Besides the well known equations of thermodynamic, the special circumstances to obtain ISO fire loading had to be referred in the program code. Also the non-linear thermal properties of concrete had to be implemented. For the temperature field in a concrete body around a metallic fastener, axis symmetry can be used. In a parameter study up to 150 different shapes of fasteners have been calculated. The results showed that the geometry of the metallic parts has a very big influence on the temperature field in the steel and in the surrounding concrete. The steel temperature is of great interest to judge steel failure and the concrete temperature influences the concrete cone capacity. For the steel temperature a comparison for a bolt diameter of 4 mm and 20 mm shows the influence very clear. Using an embedment depth of 50 mm, a steel length subjected to fire of 30 mm and comparing in a distance of 21 mm from the concrete surface, the calculated temperatures after 30 (90) minutes are 4 mm diameter: 764 °C (981 °C) 20 mm diameter: 618 °C (923 °C). Figure 2.1 shows the decrease of steel temperature for the above mentioned conditions from 4 to 20 mm steel diameter. Comparing the reduced tensile strength of steel at these temperatures, remaining relative tensile capacity of the steel bars compared to ambient temperature are 4 mm diameter: 15 % (4,4 %) 20 mm diameter: 43 % (5,5 %)
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temperatur [°C] 1000 981 °C
fire duration
21 mm below concrete surface 923 °C
908 °C
90 min.
900 60 min. 824 °C 30 min.
800 763 °C
700
618 °C 600
diameter of fastener [mm]
500 0
4
8
12
16
20
24
Figure 2.1: Influence of diameter of fastener on steel temperature 21 mm below the concrete surface (most relevant location for steel failure)
These calculations show that the steel geometry has a dominant influence (especially for short duration of fire attack) on the remaining tensile capacity of the metallic fasteners.
3. Calculation of concrete cone failure under fire load Having calculated the temperature field around a fastener, the concrete cone capacity of the heated concrete body was calculated using the nonlinear finite element program MASA (Ozbolt 1998 and 1999). To simulate the fire load it was necessary to extend the program with several subroutines. First it was necessary to calculate the concrete temperature. This must be a function of (a) distance form the heated surface, (b) distance from the fasteners symmetry axis and (c) embedment depth of the fastener. With this subroutine the results form chapter 2 are considered. Second some subroutines were programmed to calculate the concrete properties as a function of temperature. Figure 3.1 shows the calculated relative concrete cone capacities as a function of the embedment depth. The results of a calculation from the author in 1995 using a former version of the program MASA are shown as well.
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relative concrete cone capacity [%]
70 60 50 40 30
Microplane (1995)
20
MASA (1999)
10 0 0
50
100
150
200
embedment depth [mm]
Figure 3.1: Calculated relative concrete cone capacity as a function of embedment depth (after 90 min. ISO fire)
4. Stress and Strain in a concrete slab in fire During a fire the temperature in a concrete slab increases non linear. The concrete fibres next to the heated surface try to expand according to the free thermal strain and develop compressive stress on the heated side of the slab. Figure 4.1 shows in a qualitative manner the strain and stress distribution over the height of a loaded concrete slab in fire. Using the equations and material properties from EC 2 part 1-2 (DIN V ENV 1992-1-2) a program was developed to calculate the stress and strain distribution for numerous cases. The results of a parameter study are illustrated in Reick 2001. A variation of the height and the steel ratio in the cross section of the concrete slab has been calculated. This showed that at 90 % of the design bending moment according to EC 2 for a slab height of 20 cm and a steel ration of 15 cm2/m a tensile strain of 10 O/OO at a distance of 55 mm from the heated surface must be expected.
355
pos. strain
neg. strain
compression tensile stress stress
Figure 4.1: Strain and stress distribution in a loaded concrete slab with a fire loading from the lower side
This result is rather serious because internal cracks in the embedment zone of fasteners can have severe influence on the pullout capacity of anchors.
5. Fire tests In the research project an overall of 11 large scale fire tests with concrete slabs loaded with 70 to 90 % of the design bending moment according to Eurocode 2 were done. In these tests 56 fasteners have been tested in fire and additional 24 fasteners have been installed to measure steel temperatures. The test results are presented in detail in Reick 2001. In these large scale fire tests it has been shown, that concrete cone and pullout failure can be achieved under special circumstances. These failure modes should be considered for the development of an overall testing procedure for fire resistance of fasteners. Pullout failure was observed when the deflection of the concrete slab was increasing faster shortly before failure of the concrete slab. Fasteners with less capacity to react to opening cracks show pullout up to 10 mm for embedment depths of 50 mm. This is an important result also for fastening groups. The concrete cone failure loads at 90 minutes fire for an embedment depth of 40 mm showed relative values of more than 40 % compared to ambient temperature. This is better than the calculated results according to chapter 3. Only a fastener group using four anchors (embedment depth of 50 mm) showed less than 30 % relative capacity at only 75 minutes in fire.
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The temperature measurements have been made to check the calculations according to chapter 2. These measurements demonstrated how much the steel parts used for loading the fasteners influence the temperature in the anchor. This seems very reasonable and corresponds to the knowledge about the profile factor in steel construction for fire resistance. In some cases a big influence of water from the concrete appearing at cracks in the concrete slab could be observed.
6. Summary In this short article only some important results from a 6 years research program are presented. The main conclusions for the different failure modes can be summarised as follow: Steel failure: It is the most important failure mode and the test results from companies can be used to estimate steel failure loads for new fasteners only very conservative. According to numerous calculations about temperature fields and measurements of temperatures during fire tests the geometry of fastener and anchor plate as well as the test setup have a major influence on the steel temperature. Concrete cone failure: Test results and finite element calculations are achieved showing that this failure mode can be important for anchors with a small embedment depth and for anchor groups. Regarding these theoretical and experimental results rules to design and test anchors for fire resistance are presented in Reick 2001.
7. Acknowledgements This work was supported by the following companies: Fischerwerke, Hilti and Würth. The support is very much appreciated.
8. References 1. 2. 3. 4.
Reick, Michael (2001): Brandverhalten von Befestigungen in Beton bei zentrischer Zugebeanspruchung, Dissertation in Vorbereitung, 2001. Ozbolt, Josko (1998): MASA – Macroscopic Space Analysis. Institut für Werkstoffe im Bauwesen, Stuttgart, 1998. Ozbolt, Josko (1999): Nonlocal fracture analysis – stress relaxation method. Institut für Werkstoffe im Bauwesen, Stuttgart, 1999. DIN V ENV 1992-1-2: Eurocode 2 Planung von Stahlbeton- und Spannbetontragwerken, Teil 1-2 Allgemeine Regeln – Tragwerksbemessung für den Brandfall, Vornorm, 1997.
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ANCHORING WITH BONDED FASTENERS Ronald A. Cook and Robert C. Konz Department of Civil Engineering, University of Florida, USA
Abstract Bonded fasteners have been used extensively during the past twenty years. In most cases, the estimated strength of these anchors has been determined from information provided in manufacturers literature and has not been based on rational design models. During the past several years, research in the US, Europe, and Japan has led to a better understanding of the behavior of bonded fasteners. The results of this research has led to the development of rational design models for determining strength and to proposed product approval test procedures that can be used to ensure that bonded anchor products will perform as intended by the designer. This paper presents an overview of the stateof-the-art in bonded fasteners. Basic bonded fastener behavior, design models, and factors influencing bond strength are discussed.
1. Introduction Bonded fasteners can be divided into two distinct areas: adhesive bonded fasteners and grouted fasteners. An adhesive fastener is a reinforcing bar or threaded rod inserted into a drilled hole in hardened concrete with a structural adhesive acting as a bonding agent between the concrete and the steel. Typically, the hole diameter is only about 10 to 25% larger than the diameter of the reinforcing bar or threaded rod. Structural adhesives for this type of anchor are available prepackaged in glass capsules or foil packets, in dualcartridge injection systems, or as two-component systems requiring user proportioning. A grouted fastener may be a headed bolt, threaded rod with or without a nut at the embedded end, or deformed reinforcing bar with or without end anchorage installed in a pre-formed or drilled hole with a cementitious or filled polymer based grout. Grouted fasteners are typically installed in holes at least one and one-half times the diameter of the fastener. Figure 1 shows typical adhesive and grouted fasteners.
361
hef
Un-headed Grouted
Adhesive
Headed Grouted
Figure 1. Schematic diagram of adhesive and grouted fasteners
2. Bonded Fastener Systems Figure 2 shows the general types of bonded fastener systems available. Adhesive and grouted fastener systems are typically composed of organic polymers or inorganic cementitious materials. In some cases, hybrid systems utilizing both organic and inorganic materials are available. The primary difference between the adhesive and grouted systems is the introduction of a filler material (e.g., fine sand) into the bond mixture. Bonded Fasteners
Adhesive Fasteners
Injection Type
Capsule & Foil Type
Organic Compounds
Grouted Fasteners
Organic Compounds
Epoxy
Epoxy
Polyester
Polyester
Vinylester
Vinylester
Manually Mixed
Inorganic Compounds
Cementitious others
Organic Compounds
Epoxy Polyester others
Figure 2. Types of bonded fastener systems
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Inorganic Compounds
Cementitious others
3. Behavior of Bonded Fasteners Tests of adhesive fasteners have shown failure modes as indicated in Figure 3. For shallow embedments, the failure mode appears to be the same as that of headed cast-inplace and mechanical fasteners. For deeper installations (the type typically used in practice), embedment failure results in a shallow concrete cone with a bond failure below the shallow cone. Given the thin bond line between the fastener and the concrete, it is very difficult to determine which of the three center failure modes shown in Figure 3 actually occurred. For very deep embedments, steel failure will occur as shown on the far right of Figure 3.
concrete cone
adh./conc. interface
steel/adh. interface
adh./conc. and steel/adh. interface
steel
Figure 3. Failure modes of adhesive bonded fasteners Un-headed grouted fasteners typically fail at the grout/steel interface. The left diagram in Figure 4 shows the typical failure mode of un-headed grouted fasteners (i.e., a shallow cone with a bond failure at the grout/steel interface). Headed grouted fasteners eliminate the possibility of bond failure at the grout/steel interface due to the anchor head and force the bond failure to the grout/concrete bond line (with a shallow cone) for low bond strength grouts or result in a full concrete cone failure for high bond strength grouts (as shown in the right diagram of Figure 4. Test reports on the behavior of adhesive fasteners have been collected in Europe, in the USA and in Japan. From 38 reports, a database containing the results of 2929 tests has been established. The database contains tensile and shear load testing in uncracked and cracked concrete with single fasteners, groups of two fasteners and groups of four fasteners. The database contains tests carried out with threaded rods, insert sleeves and rebars. Finally, the database contains tests with epoxies, vinyl esters, unsaturated polyesters, hybrid adhesives and inorganic adhesives. A database for grouted fasteners is also being developed. Currently there are over 400 single grouted fasteners tests available using both polymer and cementitious grouts. Both the adhesive anchor
363
database and grouted fastener database are being maintained for ACI 355 by Ronald A. Cook, Department of Civil Engineering, University of Florida, Gainesville, Florida 32611.
Un-headed Bond Failure
Headed Bond Failure
Headed Cone Failure
Figure 4. Failure modes of unheaded and headed grouted fasteners (excluding steel failure)
4. Design of Bonded Fasteners Several design models have been presented for adhesive fasteners over the last several years These are summarized in Cook et al (1998)1 and Kunz et al (1998)2. A wide variation of possible models for single fastener strength were evaluated in Cook et al (1998)1. These models included: • • • • •
Concrete cone models Bond models Bond models neglecting the shallow concrete cone Combined concrete cone models and bond models Bond models considering bond failure at two interfaces
The results of the Cook et al (1998)1 paper indicate that a simple model based on a uniform bond stress fits the test data from the international database best. The expression for determining the mean strength of single fasteners in tension is given by Eqn. 1. N bond = τ π d he
(1)
Terms in Eqn. 1 and other equations are given in the “Notation” section at the end of the paper.
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Although each individual product has a unique mean bond stress (τ), it is possible to normalize all products to a unique bond stress value. Figure 5 shows a comparison of Eqn. 1 with 888 single anchor tests of products in the international data base normalized to 10 MPa. Figure 5 also shows a comparison of a nominal strength of 0.67 of the mean strength compared to the test data. Note that the final design strength will also include an appropriate capacity reduction factor, φ.
700
600
500
Load (kN)
Uniform Bond Model (mean) 400
300
200 5% fractile, V=0.20 (0.67 mean) 100
0 0
10000
20000
30000
40000
50000
60000
70000
2
Bond Area (mm )
Figure 5. Comparison of measured loads with the uniform bond model As an additional verification of the uniform bond stress model, non-linear computer analyses were performed (McVay, et al 1996)3. A typical result is shown in Figure 6. As shown by Figure 6, as the load increases (curves moving from left to right) the bond stress distribution changes from what might be expected in elastic analysis to a nearly uniform bond distribution at failure. Both the database and the non-linear finite element analysis indicate that a uniform bond stress model is appropriate for adhesive fasteners.
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0 -0.2 -0.4 -0.6 -0.8 -1 0
4
8
12
16
20
Bond Stress (MPa)
Figure 6. Bond stress distribution versus normalized depth with increasing load The strength of grouted fasteners depends on whether or not the fastener is headed. Detailed test results and design recommendations for grouted fasteners are presented in another paper in these symposium proceedings. The information provided here is only intended to provide a brief summary of the results presented in that paper. For unheaded fasteners, bond failure typically occurs at the grout/steel interface and Eqn. 1 provides the basis for determining the mean strength of the fastening. For headed grouted fasteners, two failure modes are possible. For low bond strength grouts, bond failure at the grout/concrete interface may occur. Tests have shown that this failure mode can best be represented by a uniform bond stress model calculated using the grout/concrete bond strength of the product (τ0) applied to the bonded area at the grout/concrete interface. This is given by Eqn. 2: N bond ,d 0 = τ 0 π d 0 he
(2)
For higher bond strength grouts, a full concrete breakout failure occurs and the mean concrete breakout strength developed by Fuchs et al (1995)4 is appropriate. This is given by Eqn. 3: N cone = 16.7
f c he1.5
(3)
The predicted mean strength of a headed bonded fastener is determined by the lower value of Eqn. 2 and Eqn. 3. Although grout/concrete bond failure is typically not observed in tests of unheaded fasteners using engineered grouts, it may be prudent to base the strength of these
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fasteners on the smaller of the bond strength determined at the grout/steel interface (Eqn. 1) and the bond strength determined at the grout/concrete interface (Eqn. 2). Eqns 1-3 provide predictions for the mean strength of bonded fasteners. For design purposes, these strengths must be reduced. For Load and Resistance Factor Design, the determination of design strength from behavioral models which represent mean strengths is typically based on establishing a nominal strength (some lower bound fractile of the mean strength) and then applying a capacity reduction factor (φ) to limit the probability of failure. In current US and European design standards, the nominal strength is commonly taken as the lower 5% fractile of the test data. The 5% fractile represents the value where it would be expected that 95% of the tests performed would exceed the specified nominal strength. The determination of the 5% fractile depends on the number of tests available and the scatter of the test results. The scatter of the test results is typically expressed as the coefficient of variation (V) which is defined as the standard deviation of the test results divided by the mean. This leads to the following for nominal bond strengths:
τ ' = τ (1 - α V)
(4)
τ 0' = τ 0 (1 - α V)
(5)
The selection of the α factor depends on the number of tests available. The selection of an appropriate capacity reduction factor (φ) for bond can be based on detailed studies of probability of failure and/or on what φ factors are used for similar failure modes in existing building codes. Bond failure can be compared to shear-friction since it involves slip along an interface. In ACI 318, the φ factor for shear-friction and shear is 0.85. A capacity reduction factor (φ) for bond of 0.85 is recommended for designs controlled by bond failure. Various behavioral models for both edge effects and group effects for bonded fasteners are being studied in both the US and Europe. Proposals for modification factors for edge effects and group effects for bonded fasteners are presented in other papers in these symposium proceedings.
5. Factors Influencing the Strength of Bonded Fasteners The evaluation of both the mean bond stress (τ and τ0 ) and design bond stress (τ’ and τ’0) must be based on product approval tests that include the effects of installation and in-service conditions. As noted in Cook et al (2001)5, there are significant differences
367
15.9
14.5 11.4
19.8
5
17.8
4
17.8
21.0
2
20.9
20.3
1
17.7
20.0 5.5
7.3
10
17.1 13.9
10.0
11.2
12.3
15.3
15.9
19.6
18.2
15.6
16.1 11.4
15
Grouted τ mean = 17.9 MPa
Adhesive τ mean = 12.7 MPa
11.2
25
12.4
5
2.3
3.1
Average Uniform Bond Stress, [MPa]
between adhesive products. Basic tests for mean bond stress in clean, dry holes at room temperature indicate that the mean bond stress can range from 2 MPa to 20 MPa for adhesives and 7 MPa to 21 MPa for grouts as shown for 20 adhesives and 9 grouts in Figure 7. The coefficient of variation for these tests can vary between 0.05 and 0.25. In many cases, products that exhibit high bond stress in clean, dry holes at room temperature are inadequate under typical installation and in-service conditions such as damp holes and elevated temperatures. It is mandatory that designers require product testing for expected in-service and installation conditions prior to the final design.
0 A B C
D
E
F
G
H
I
J
K
L M
N O P
Q
R S
T
3
6
7
8
9
Product
Figure 7. Bond stress variation for adhesive and grout products The following provides examples of the factors influencing bond strength that need to be considered for product approval tests of bonded fastener products: • • • • • • • • • • • • •
Concrete mix (equal concrete strength does not ensure equal results) Temperature effects Damp hole Improperly cleaned hole Curing time Freeze-thaw effects Installation direction (vertical down, horizontal, overhead) Creep (normal and elevated temperatures) Mix proportioning (primarily manually-mixed products) Fire resistance Wet (submerged) hole Maximum torque Repeated load
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• • • •
Seismic load Environmental effects (chemicals) Cracked concrete (static cracks and moving cracks) Other possible tests: • Age of concrete • Oil presence (compressed air cleanout of holes) • Capsules driven rather than drilled • Hammer installed capsules installed upside-down • Hole size • Hole drilling • Radiation
As can be observed from the above list, a product approval standard for bonded fasteners must be quite comprehensive to ensure reliable performance of products.
6. Status of Design and Product Approval Standards Design models for bonded fasteners are currently being finalized in the United States and Europe. Many of these design recommendations are presented in the symposium proceedings. Product approval standards are also underway with the European Organization for Technical Approvals leading the way with Part Five of the ETAG No 001 standard. In the United States, the American Society for Testing and Materials Committee E06.13 is currently developing draft product approval standards.
Notation: d d0 fc he Nbond Nbond,d0 V α
= = = = = = = =
φ τ τ0 τ‘ τ 0‘
= = = = =
outside diameter of fastener [mm] drilled hole diameter of fastener [mm] concrete strength, measured on 150 by 300 mm cylinders [MPa] embedment depth [mm] mean strength of the fastener as controlled by bond strength mean strength of the fastener as controlled by grout/concrete bond strength coefficient of variation (standard deviation divided by the mean) a statistically determined coefficient based on the tolerance limit and confidence to be used for design capacity reduction factor (0.85 is recommended for bond failure) mean uniform bond stress for adhesive fasteners (MPa) mean uniform bond stress for headed bonded fasteners (MPa) nominal uniform bond stress (MPa) at the fastener/adhesive interface nominal uniform bond stress (MPa) at the grout/concrete interface
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References: 1.
Cook, R. A., Kunz, J., Fuchs, W., and Konz, R., “Behavior and Design of Single Adhesive Anchors Under Tensile Load in Uncracked Concrete,” ACI Structural Journal, ACI, V. 95, No. 1, January-February 1998, pp. 9-26.
2.
Kunz, J., Cook, R. A., Fuchs, W. and Spieth, H, “Tragverhalten und Bemessung von chemischen Befestigungen (Load Bearing Behavior and Design of Adhesive Anchors),” Beton- und Stahlbetonbau 93 (1998), H.1, S. 15-19, H. 2, S. 44-49.
3.
McVay, M., Cook, R. A., and Krishnamurthy, K., "Behavior of Chemically Bonded Anchors," Journal of Structural Engineering, American Society of Civil Engineers, V. 119, No. 9, September, 1993, pp. 2744-2762.
4.
Fuchs, W., Eligehausen, R., Breen, J. E., "Concrete Capacity Design (CCD) Approach for Fastening to Concrete," ACI Structural Journal, American Concrete Institute, V. 92, No. 1, January-February 1995, pp. 73-94.
5.
Cook, R. A., and Konz, R., “Factors Influencing the Bond Strength of Adhesive Anchors,” ACI Structural Journal, American Concrete Institute, V. 98, No. 1, January-February 2001, pp. 76-86.
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EXPERIMENTAL STUDY ON PERFORMANCE OF BONDED ANCHORS IN THE LOW STRENGTH REINFORCED CONCRETE Tomoaki Akiyama*, Yasutoshi Yamamoto**, Shigekatsu Ichihashi*** and Taichi Katagiri**** *Building Research & Engineering Department, Tokyo Soil Research. Co., Ltd., Japan **Dept. of Architecture, Shibaura Institute of Technology, Japan ***Dept. of Architecture Nippon Institute of Technology, Japan ****Zen Design Office, Japan
Abstract With existing RC buildings, in extreme cases, compressive strength is even less than 1/3 of design characteristic. No useful documents showing range of shear/pull-out loads for post-install anchors are available when anchoring at connections between new and existing concrete to retrofit such the buildings. From this background, planned research about anchoring with the object of seismic retrofit for low strength concrete buildings. Defined, as low strength concrete is one whose compressive strength is 13.5MPa or less as per seismic diagnosis guideline. Used, as test parameters are compressive strength, anchor rod diameter/embedment, and edge distance. Tested group shear and single shear/pull-out. Also, from tests this time, shear and pull-out strength equations of post-install bonded anchors used for low strength concrete were proposed. These equations, on seismic reinforcement of low strength concrete buildings, concerning design of post-install bonded anchors, useful equations were proposed.
1. Introduction With existing RC buildings, compressive strength is even less than 1/3 of standards one. No useful documents for behaviors in concrete blocks and post-install anchors on shear/pull-out force have been available when anchoring at connections between new and existing concrete to retrofit such the buildings. From this background, planned research about anchoring with the object of seismic retrofit for low strength concrete buildings. Defined, as low strength concrete is one whose compressive strength is 13.5MPa or less as per seismic diagnosis guideline. Used as test parameters are compressive strength, anchor rod diameter/embedment, and edge distance. There were tests for group shear and single shear/pull-out. Also, from tests, at this time, shear and pull-out strength formulas of post-install bonded anchors used for low strength concrete were proposed. These formulas, on seismic reinforcement of low strength concrete buildings, concerning design of post-install bonded anchors, useful formulas were
371
proposed and retrofit design guideline’s formulas and test values were compared. 2. Outline of the tests (1) Concept for tests The testing plans were made to reflect the results from tests into the actual design as soon as possible with considering the present situation that the quick working for the reinforcement on buildings to resist against earthquakes would be needed. Especially, bonded post-install anchors were taken into consideration as the method of construction to resist against earthquakes with the steel frames and many embedded anchors. (2) Kinds of tests and summary for tests (a) Shear tests on the group anchor The part of connections between new and existing concrete to retrofit was made to tests relationship with strength and displacement and investigate the behaviors at cracks in the brace with steel frames. (b) Shear/pull-out tests on the single anchor Single anchor shear/pull-out tests were performed to investigate basic behaviors between strength and displacement and crack ones. The number of concrete blocks on which the anchor was embedded, were saved with tests at both sides. (3) Parameters were decided as followings. (a) Compressive strength in the concrete blocks: Ordinary concrete, 5.0MPa, 10.0MPa and 15.0MPa. (b) Post-install anchors: D16, D19 and D22. (D means “deformed rods”) (c) Edge distances: Distance(c) is equal to 200mm in shear force tests, and 300mm in pull-out tests. It was the standard types and distance(c) is equal to 100mm in all eccentric types. Two types for effective embedded length of anchors: 7da and 10da (da; anchor diameter). However, there was one kind of 7da for group shear test. (4) Configurations of specimens (a) Shear test with group anchors The standard specimen with edge distance as 200mm, and the eccentric specimen with edge distance as 100mm are showed in Fig. 1. There were 15 specimens as all cases in Table 1. There was one additional specimen for each concrete strength that had strain gauges to investigate behaviors in the anchor at the center of the concrete blocks and in the concrete around this anchor. (b) Shear test with a single anchor The detail bar arrangement is showed in Fig.2. There were 108 specimens for all in Table 2. (c) Pull-out test with a single anchor The bar arrangement is the same for the case of shear test.
372
Steal Flame
Table1 All case of Group Anchors Specimens
Mortar
C o n crete
A n ch o r
Q u a liti e s
D i a m e te r
(M
a)
Fc
Skeleton Concrete
(m m )
E d g e D is ta n c e T o ta l S ta n d a r d
E c c e n tric
D19
2
1
3
D22
1
1
2
5 D19
2
1
3
D22
1
1
2
Fc 10 D19
2
1
3
D22
1
1
2
Fc 15
a)Side Section
b)Standard
c) Eccentric
Fig.1 Group Shear Test Specimens
Table2 All case of Single Anchor Specimens Concrete Anchor Effective Edge Distance Qualities Diameter Embeded Standard Eccentric
S hear S urface
a) Floor Plan
Pull-out Surface
b) Side elevation
c) Section
Fig.2 Single Shear&Pull-out Test Specimens
However, difference between shear tests is the embedded positions. The number of specimens is 108 same as shear test cases in Table 2.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
3. Equipment for loading and method of measurement 3.1 The case for test on group anchors with shear force The equipment for loading is showed in Fig.3. It was the real object to apply the horizontal force only along the surface between the concrete block and the filler mortar with a steel member. However, self-loading from equipments about 0.1MPa was also applied as lateral force. Without this influence, shear force (Q) and displacement ( ) in the horizontal direction were measured. Displacement ( ) would be measured able to separate into the slip displacement ( SM) at the boundary part on the steel member and the filler mortar, and the slip one( MC) among the filler mortar and the concrete block. The five cyclic loadings were basically applied.
3.2 Test on the single anchor with shear force We developed the special equipment with an oil jack showed in Fig.4 to apply the shear
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force in the exact direction coincided with the edge line of the concrete block. The value of loading was measured with the load cell. The relative horizontal displacement between concrete block and an anchor was measured at each loading steps. The loading was performed as monotonic load in each step.
'
'
( &
)
!
" # $ %
Specimen
Fig.3 Apparatus for Group Shear Test
Tension Rod
Hydraulic Jack
Test Anchor
Load Cell
Skeleton Concrete
Shear Block Test Anchor Support
Teflon
Displacement Meter
Fig.4 Apparatus for Single Shear Test
Skeleton Concrete
Fig.5 Apparatus for Single Pull-out Test
3.3 Test on single anchor with pull-out force The loading equipment showed in Fig.5 was used in this test. The monotonic pull-out loading was applied for an anchor. It would be possible to give influence for the measured strength in the case of the corn type failure with interference between the each failure, as anchors put in nearly every 300mm. By this reason, tests were performed at first time for the left anchor, and next for the right anchor. Lastly, the center anchor was applied with pull-out force. Please reference the diagram in Fig.8. The quantity of the relative displacement ( ) by pull-out force between the concrete block and the anchor was measured.
4. Materials 4.1 Concrete (1) Mixing plan for the low strength concrete Three types of specimens were made as 5MPa, 10MPa, and 15MPa for the compressive strength after 4 weeks from making them such as standard curing. Specimens with lower strength were made by reduction of quantity of cement with keeping the same quantity of water. As water-cement ratio for the lower strength concrete are larger, rock
374
powder was installed instead of cement. Ratio of water/(cement + rock powder) was keeping as the same value (=0.66). As the results, slump values were almost same such as about 18cm for every strength concrete. Specimens were made of ready mixed concrete. (2) Test results Compressive strength on the three types of concrete were curing standard and sealed. Test results are showed in Table 3. Compressive strengths of concrete in sealed curing were used in the analysis for shear test and pull-out test. Table3 Test Results of Concrete with Age
# " !
"
#
’
Table4 Test Results of Rebars
#
4.2 Filling mortar without contraction Pre-Mix type mortar without contraction was used to fill another parts of specimens. Compressive strength from test results are showed in Table 3. 4.3 Steel bars and anchors Material characteristics for the steel bars and anchors are showed in Table 4. All steel bars were standardized steel at the Japanese Industrial Standard G 3112 and SD345, without steel bars for the wire net (D6). 5. Results from test 5.1 Shear test on the group of anchors Relation between shear force (Q) and displacement ( ), and crack diagram in the concrete block on two standard specimens, QG-C05-19S and QG-C15-19S are showed in Fig.6. There is not much difference in two specimens, though maximum strength (Qmax) is larger with the compressive strength. The number of cracks at the concrete blocks decreased in the concrete block with stronger compressive strength. However, the number of crack at filler mortar increased in the model of the concrete block with the stronger compressive strength. With comparing two specimens by putting anchors in the eccentric lines, QG-C05-19E and QG-C15-19E, loading values increased on according to the larger displacements. The number of cracks in the concrete blocks increased in the eccentric models. There were many cracks on the surface of the
375
concrete block in C05 model with lower concrete strength, as many cracks on the filler mortar in the C15 model were able to see, by the reason that loading values were larger than C05 model.
5.2 Shear test on a single anchor Relation between shear force (Q) and displacement ( ), and crack diagram in the concrete block on two standard a) QG7-C5-19E b) QG7-C15-19E specimens, Q7-C05-19S and Fig.6 Q-Curve & Clacks of Group Shear Test QG-C15-19S are showed in Fig.7. Initial stiffness for both specimens with different compressive strength were almost same in the Qcurve, as there was the polyethylene sheet under the block for working shear force. Loading values were increased with accord to increase on the displacement. The maximum shear strength (Qmax) in the C15 model was about twice as much as the value in C05. The number of crack decreased in accordance with higher compressive strength in the concrete block. However, the zone with the compression failure in the concrete block was enlarged with the higher compressive strength. The maximum shear strength (Qmax) was larger in the concrete block with the higher compressive strength from the results in the cases of eccentric anchors. There were not influences with the difference between initial stiffness. The slip displacement in the case of eccentric model was small with compare to the case of central
anchor model and, also there were not toughness in the lower concrete and the maximum shear strength (Qmax) was also small. There was a a) Q7-C05-19E
tendency that failure in the edge
distance was severe on the concrete blocks with low compressive strength.
b) Q7-C15-19E
Curve & Clacks of Single Shear Test
Fig.7 Q-
5.3 Pull-out test with a single anchor Relation between pull-out forces (T) and displacements ( ) with those force and the diagrams for cracks are showed at the cases of T7-C05-19S and T7-C15-19S that had the distances from edges to the center of anchors as 300mm in Fig.8. There was not much difference at the initial stiffness for the compressive strength. However, the maximum pulled-out force in the concrete block with the larger compressive strength was about twice as high as the other pulled-out force. There is better capacity to correspondence to large displacement for concrete blocks with the higher compressive strength than the lower one; there is much difference for the ability to absorb the total
376
energy between them. The cracks are spread out in the entire concrete block with the lower compressive strength. It is clear that there are much influences with the compressive strength. There were same behaviors in the case of eccentric models with embedded anchors a part from the edge of concrete block as 100mm (C).
a) T7-C5-19E
However, there was much influence with edge distance even in the larger Fig.8 P-Curve & Clacks of Single Pull-out Test compressive strength model. Cracks concentrated on the surface of the concrete block in spite of the compressive strength.
b) T7-C15-19E
6. Investigation for experimental results
With the results from serial of tests, we propose the formulas for shear strength and also pull-out strength on the post-install bonded anchors in the concrete block with low compressive strength. In this paper, our proposed formulas were induced by using the values in the case of only one kind failure mode that means the mode with failure of concrete, as the compressive strength of concrete ( B) would be smaller than equal to 15MPa. There were the cases that the anchors had been yielded before concrete blocks had been crashed in cases of D16 or D19 were used. In these formulas, there were not considerations about those, as those problems would be exceptions. This is the difference between the old and new formulas.
6.1 Induction of the formula for shear strength The relations between the compressive strength of the concrete ( B) and the unit shear strength of the group anchor testing ( mg) and a single anchor testing ( ms) from the testing results are showed in Fig.9.a. mg > ms are understood if the same B was used in the concrete block. The difference in the results between the group anchor testing and a single anchor testing would be hypothesized by the fact that though there are large resistance on the boundary among the concrete block and filler mortars, there are not resistance between the equipment to perform the shear force and the concrete block with the polyethylene. With considering the tensile yielding strength y of SD345 used as anchors, formulas for group anchor testing and a single anchor testing were induced without falling down the experimental data by the bearing strength line paralleled to two regression lines as showed in Fig.9a. Group anchor testing : mg = {0.602 + 0.019 B} y ------(1) Single anchor testing : ms = {0.205 + 0.036 B} y ------(2)
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It is remarks : mg, ms y y : tensile yielding strength Factors ( 1) was evaluated by using the results in Fig.9 b and by the hypothesis that the bearing shear strength was fallen down like a line with thickening the diameter of anchors as followings. 1 = 0.84 – 0.05(da-22) ------(3) It is the fact that the bearing shear strength would be generally larger with big edge distance. However, influence with edge distance (C) would be smaller with needing 100mm at edge distance (C) in Fig.9c. By these reasons, Factors ( 2) was decided as followings. 0.15 ------(4) 2 = 0.85(C/100) 2 is smaller However, than equal to 1.0. Unit of C is “mm”. 3 is evaluated as standard value “1.0” at 7da as putting
length (le), and “1.15” at a) B-mg & ms Relationship b) -mg & ms Relationship 10da by inspecting the diagram in Fig.9d. By considering these
parameters, shear strength
(QA) is evaluated as followings.
c) C-
mg & ms
Relationship
mg & ms
Relationship
b) le-
Fig.9 Influence of Parameter
A ------(5) A ------(6)
For the group anchors : QA = For a single anchor : QA =
1
2
3
mg
a
1
2
3
ms
a
Aa: Section area for anchors Those formulas were evaluated by only using maximum bearing shear strength without considering the displacements. It is necessary to take the caution that the result (QA) would be dangerous side, when D22 and compressive strength ( B) in the concrete block is smaller than and equal to 10MPa.
6.2 Strength for pull-out force on a single anchor Similarly, some formulas were evaluated with results by pull-out test for a single anchor .The basic raw formula was evaluated with the low limit from a regression line in Fig.10a by the results for the standard specimens as followings. t =10.0 B+63.7-------(7) Factors ( 1) was evaluated by the regression lines in Fig.10b. Factors ( 1) are 1.16 for D16, 1.00 for D19, and 0.94 for D22. Factors ( 2) was decided with the result in Fig.11a as followings.
378
B
ხ
Relationship
a) C-
3
value “1.0” at 7da as embedded length (le), and “1.15” at 10da by inspecting the diagram in Fig.11b. Lastly, the maximum bearing pulling-out strength
t
(TA) is expressed as followings. TA= 1 2 3 t Aa-(9) t : Tensile yielding stress for anchors Aa: Section area for anchors
ხ
Relationship
b) le-
t
0.15
2
b) t &
= 0.85(C/100) -----(8) is evaluated as standard
ხ
- Relationship Fig.10 Influence of
t
- Relationship (All Specimens)
a)
t
Fig.11 Influence of C & le
7. Comparison every bearing strength with the testing results 7.1 Relation between the proposed formulas and the test results The basic formulas for shear strength, and for pull-out strength, formulas for them with amendment by the influence factors, and the results from the test are showed together from Fig.12a to Fig.12c. The tensile yielded strength for anchors were hypothesized as 350MPa (correspond to SD345) to evaluate the bearing strength for the shear and pull-out strength. And also, the standard strength for design of concrete was used as B, and Young’s Modulus for concrete was showed as followings. : Weight of concrete per unit value Ec = 2.1 104 ( /2.3)1.5 ( B/20)
ყფ
ხ
a) Shearing stress of Group Shear Test
b) Shearing stress of Single Shear Test
c) Pulling-out stress of Group Shear Test
Fig.12 Comparison of Design - Results
7.2 Investigation for calculated data and test results All test results are larger than calculated results in Fig.12a. It would be reason that large strengths on the tests were influenced with the values of y on anchors. These values were from 375 377 MPa. The test strengths were bigger than calculated data by about 1.07(375/350). However, as mg that concrete strengths were smaller, reserved power was small. It will be necessary to check it carefully. ms , that means shear stress for a
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single anchor, is coincided the test results almost in Fig 12b. It is clear there are no reserved power scarcely among calculated data and test results. In checking data in Fig.12c, pull-out strength with calculation is almost proportional to the testing results. There are some lower calculated values than the testing results. It is the case the lower compressive strength of concrete (5MPa) was used by anchors with D22. It is necessary to take care for using calculated values. 7.3 Treatment for safety faction It is important to evaluate the safety factor for the proposal formulas in order to work effectively for the actual design. It would be real to decrease the proposed formulas with taking about 1.33 for safety factor, though calculated formulas would be safer than testing values. There is basically reserved strength at the yielding stress in anchor with comparing to design values for this reason. It would be a idea to multiply bearing shear strength mg by 0.8 still more in the case that slope by relative member displacement would be limited as 1/250.
8. Conclusion There was sufficient bearing strength for the cases of the putting anchors in the low strength concrete block, when the results from testing were corresponding with the design formulas in the guideline recommended by the agency. However, proposed formulas were issued with considering many parameters in the concrete blocks that anchors were put in, by referencing to the ACI318. There were narrow variations in the formulas for strength with considering diameter of anchors, embedded length, and the edge distance. In the case of the lower concrete strength, B 15MPa, applicability on the proposed formulas is better than the formulas used to now. The better results were gotten. It is urgent to reinforce the concrete building with low strength. There would be many cases that bonded post-install anchors would be used to reinforce these buildings. It is one main object to investigate definitely the efficient values to design. From now, still the meaningful study must be performed with the simulation by using Finite Element Method.
9. Reference 1. 2. 3. 4.
JBDPA / Japan Building Disaster Prevention Association, ‘Guideline for Seismic Evaluation of Existing Reinforced Concrete Buildings’, 1990, 62 JBDPA / Japan Building Disaster Prevention Association, ‘Guideline for Seismic Retrofitting Design of Existing Reinforced Concrete Buildings’, 1990, 198 Ronald. A. Cook, Bonded Anchors in the US, ‘Testing of Bonded Anchors’, SCFT Workshop, Shaan, Principality of Liechtenstein, 1999 YAMAMOTO.Y. et al, ‘Load Carrying Capacity of Bonded Anchor at Low Strength Concrete Members’, Proceedings of Japan Concrete Institute vol.22, No.1, 2000, 553-558
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BEHAVIOR OF GROUTED ANCHORS Ronald A. Cook, Noel A. Zamora, and Robert C. Konz Department of Civil Engineering, University of Florida, USA
Abstract An experimental research program was undertaken at the University of Florida with funding from the Concrete Research Council and various grout manufacturers to determine the behavior of grouted anchors and to develop rational design procedures for grouted anchor installations. For purposes of this research, a grouted anchor was defined as an anchor (headed or un-headed) installed into a hole in hardened concrete with a structural grout (cementitious or polymer). Grouted anchors typically have hole diameters that range from 150-300% larger than the anchor diameter. This is different from adhesive anchors, which typically use a polymer material with an unheaded anchor installed in a hole diameter only 10-25% larger than the anchor diameter. This paper presents the results of this research, including 229 tests of both headed and un-headed anchors installed using six cementitious and three polymer grouts. The results indicate that the behavior of unheaded grouted anchors is similar to that of adhesive anchors while the behavior of headed grouted anchors is similar to that of castin-place headed anchors. For some grout products, a bond failure at the grout/concrete interface is possible and needs to be considered.
1. Introduction Post-installed bonded anchors can be classified as adhesive or grouted depending on the bonding agent, anchor type, and hole dimensions. These types of anchors can be installed with or without a head at the embedded end (Fig. 1). Adhesive anchors are installed using an unheaded threaded rod or a reinforcing bar inserted in a predrilled hole that is 10-25% larger than the anchor diameter using a polymer-based bonding agent including epoxies, polyesters, vinylesters, and hybrid systems. A grouted anchor is a threaded rod, stud, or reinforcing bar installed using structural grout as the bonding
381
agent. Grouted anchors are typically installed with a cementitious or polymer grout in a predrilled hole having a diameter range of 150-300% larger than the diameter of the fastener. Cementitious grouts are primarily composed of fine aggregates and portland cement. Polymer grouts are similar to adhesive anchors but with a fine aggregate component.
d
d
hef
Grout
Grout
d0
hef
d0
Unheaded Anchor
Headed Anchor
Fig. 1-Headed and unheaded grouted anchors
2. Grouted Anchors Grouted anchors can be distinguished from adhesive anchors by a larger hole-to-anchor diameter ratio that can accommodate a headed anchor, which ultimately affects the load transfer mechanism. Headed anchors transfer the load to the grout primarily by bearing on the anchor head. Unheaded anchors installed with threaded rod take advantage of mechanical interlock between the threads and the grout. In both cases, the load is transferred from the anchor to the grout and the grout then transfers the load to the concrete resulting in one of three potential failure modes (Fig. 2). Unheaded grouted anchors were expected to exhibit a failure mode similar to adhesive anchors; bond failure at the steel/grout interface with a secondary, shallow concrete cone. Headed anchors were expected to exhibit either bond or cone failure modes depending on the concrete strength, embedment depth, and grout/concrete bond strength. An obvious fourth failure mode, yielding and fracture of the steel anchor rod, is excluded from this discussion.
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Unheaded Bond Failure
Headed Bond Failure
Headed Cone Failure
Fig. 2-Potential failure modes for grouted anchors
3. Behavioral Models The behavior of grouted anchors was expected to be similar to either cast-in-place headed anchors or post-installed adhesive anchors depending on the anchor configuration (headed or unheaded) and material properties. The following presents a general discussion of appropriate behavioral models. 3.1. Concrete Capacity Design Method (CCD) The CCD model evolved from a series of concrete cone models that were developed for fasteners that were observed to have full concrete cones at failure. These behavioral models assumed that the concrete failed in tension and that a full concrete cone formed from the embedded end of the anchor to the top of the concrete. There are several versions of the concrete cone model, but the CCD method is widely accepted. The CCD method evolved from the Kappa-method and predicts the ultimate load of an anchor loaded in tension or in shear1. This method was developed for cast-in-place headed anchors and post-installed mechanical anchors installed in uncracked concrete that developed a full concrete cone at failure. The CCD equation used to predict the tensile capacity of a single anchor installed in uncracked concrete is as follows: N cone = k f c′ h1.5 ef
Where: Ncone f ’c hef k
= = = =
(1)
mean tensile strength of concrete cone, N. concrete compressive strength (150mm x 300mm cylinders), N/mm2. effective embedment length, mm. 16.7, for cast-in-situ headed studs and headed anchors.
3.2. Uniform Bond Stress Model The uniform bond stress model was developed to predict the failure loads of adhesive anchors in uncracked concrete by assuming a uniform bond stress throughout the
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embedment length of the anchor system2,3. This model assumes that the failure surface could occur either at the steel/adhesive or adhesive/concrete interface. Because the holeto-anchor diameter ratio for adhesive anchors is close to unity, however, the nominal anchor diameter can be used. Cook, et al.2,3 showed that for adhesive anchors the uniform bond stress is product dependent and its value, τ, must be determined experimentally. Grouted anchors can also develop failure surfaces at the steel/grout or grout/concrete interface but the hole-to-anchor diameter ratio is generally larger than 1.5. Therefore, the bond strength of each product should be evaluated at both potential failure surfaces. The uniform bond stress model equation is as follows:
Where: Nbond Nbond,do τ τ0 d d0 hef
= = = = = = =
N bond = τ π d h ef
(2)
N bond,do = τ o π d o h ef
(3)
mean tensile strength for a steel/grout failure, N. mean tensile strength for a grout/concrete failure, N. uniform bond stress at the steel/grout interface, MPa. uniform bond stress at the grout/concrete interface, MPa. diameter of the anchor, mm. diameter of the hole, mm. effective embedment length, mm.
4. Experimental Program The objective of this test program was to determine the strength and behavior of grouted anchors. The investigation included parameters typically encountered during design and installation including binding agent (cementitious or polymer), anchor configuration (headed or unheaded), anchor and hole diameters, embedment depth, and concrete strength. Testing was performed in general accordance with ASTM E 488 with test matrices shown in Tables 1 and 2.
5. Test Results for Unheaded Anchors 5.1. General Behavior As hypothesized, the observed failure mode for unheaded anchors was a bond failure located at the steel/grout interface with a secondary shallow cone. From all the test series evaluated in this test program, only one test series (four anchors) exhibited a failure mode at a location other than at the steel/grout interface. This series was installed with product CE and produced a failure mode at the grout/concrete interface. Two other test series were performed using the same product, but they developed a steel/grout failure mode. The only difference between these tests series was the dimensions of the anchor system. Therefore, transition from one failure mode to another can be explained
384
by observing that the anchors in the test series exhibiting bond failure at the grout/concrete interface were installed using large diameter anchors. This allowed the anchor system to develop the ultimate bond strength of the grout/concrete interface before it could develop a steel/grout failure mode. Table 1: Test matrix for unheaded anchors. d (mm)
hef (mm)
f 'c at test (MPa)
d0 (mm)
Product
n
Series 2
Series 3
Series 1
Series 2
Series 3
CA
25
15.9
19.1
25.4
102
127
172
50.8
50.8
50.8
35.6
35.6
50.8
CB
12
15.9
19.1
25.4
102
127
178
50.8
50.8
50.8
35.6
33.4
31.0
CC
15
19.1
25.4
12.7
127
178
76
50.8
50.8
50.8
34.1
34.1
33.4 35.8
Series 1 Series 2 Series 3 Series 1 Series 2 Series 3 Series 1
CD
15
15.9
19.1
25.4
102
127
178
50.8
50.8
50.8
39.9
39.9 35.8
CE
14
15.9
19.1
25.4
102
127
178
50.8
50.8
50.8
34.4
34.4
33.6
CF
5
19.1
-
-
127
-
-
50.8
-
-
38.0
-
-
34.5
34.5
33.9
34.4
37.8
-
PA
15
15.9
19.1
25.4
102
152
178
50.8
50.8
50.8
PB
15
15.9
19.1
25.4
102
152
178
50.8
50.8
50.8
PC
5
19.1
19.1
-
127
127
-
50.8
50.8
-
Note:
33.9 35.6 33.9 35.9 37.8
Products starting with the letter “C” are cementitious grouts Products starting with the letter “P” are polymer grouts
Table 2: Test matrix for headed anchors. Product
d (mm)
n Series 1
CA
25
19.1
hef (mm)
f 'c at test (MPa)
d0 (mm)
Series 2 Series 3 Series 1 Series 2 Series 3 Series 1 Series 2 Series 3 Series 1 Series 2 Series 3
19.1
25.4
127
127 152
178
50.8
38.1
50.8
CB
15
19.1
19.1
25.4
127
127
178
50.8
50.8
50.8
CC
15
19.1
19.1
25.4
127
127
178
50.8
50.8
50.8
CD
15
19.1
19.1
19.1
114
127
127
38.1
38.1
38.1
CF
13
15.9
19.1
19.1
102
114
127
50.8
38.1
50.8
PA
10
19.1
19.1
-
127
127
-
50.8
50.8
-
PB
5
19.1
-
-
127
-
-
50.8
-
-
PC
10
19.1
19.1
-
127
127
-
38.1
38.1
-
Note:
35.7 32.7 35.7 33.4 31.0 31.2
50.1 49.8 32.3 32.1
32.3 32.1
31.0
31.0
59.2
35.8
35.8
32.6
30.9
59.2
35.8
27.8 27.4 27.8 27.4
27.8 27.4
-
-
-
63.7
36.9
-
Products starting with the letter “C” are cementitious grouts Products starting with the letter “P” are polymer grouts
5.2. Product Variability and Anchor Strength Table 3 provides a summary of the steel/grout bond stress (τ) and coefficient of variation for the products tested with unheaded anchors. For the entire unheaded data set, the
385
mean bond stress was 18.4 MPa with a coefficient of variation of 0.27. As shown in Table 3, the variation between all products is greater than that within any individual product. This indicates that the unheaded bond strength is product dependent. Table 3- Steel/Grout Bond Stress and Coefficient of Variation for Unheaded Anchors Product Avg. Bond Stress (MPa) Coefficient of Variation
CA 20.5 0.11
CB 21.8 0.18
CC 7.3 0.22
CD 21.1 0.08
CE 21.6 0.09
CF 15.9 0.20
PA 17.8 0.06
PB 19.4 0.09
PC 17.8 0.13
5.3. Behavioral Model Comparison Figure 3 illustrates the observed failure loads for all data sets as a function of bonded area. Failure loads shown in Fig. 3 were normalized to the mean steel/concrete bond stress (τ) of 18.4 MPa by multiplying actual failure loads by the factor 18.4/τproduct. The solid line shown in this figure represents the mean value for the uniform bond stress model based on the bonded area and τ = 18.4 MPa. Figure 3 shows a linear relationship, indicating that the uniform bond stress model is appropriate for unheaded grouted anchors. Also shown in Figure 3 is a 5% fractile boundary based on a coefficient of variation of 0.20 and a large database. Figure 3 indicates that out of the 121 anchors tested, only 2 anchors (1.6%) fall below this 5% fractile boundary line. 350
N = τ π d h ef
300
Uniform Bond Stress Model τ = 18.4 MPa (mean)
Load (KN)
250
200
150
100 Uniform Bond Stress Model 5% fractile, 90% confidence, COV = 0.20, Value = 0.67 mean
50
0 0
2000
4000
6000
8000
10000
12000
14000
16000
2
Bond Area (mm )
Fig. 3- Unheaded grouted anchor test results compared to the uniform bond stress model for adhesive anchors
386
6.
Test Results for Headed Anchors
6.1. General Behavior Headed grouted anchors were expected to develop either a bond failure at the grout/concrete interface or tensile failure leading to the development of a full concrete cone. A total of nine different products were tested and included six cementitious grouts and three polymer grouts. Test results showed that out of the 108 tests included in the headed grouted anchor test program, 61 (56 %) anchors developed a bond failure at the grout/concrete interface and 47 (44 %) anchors developed a concrete tensile failure that resulted in a full concrete cone. This confirms the assumption that headed grouted anchors can develop either a concrete cone failure mode or a bond failure at the grout/concrete interface depending on the properties of the grout and the dimensions of the anchor system. 6.2. Product Variability and Anchor Strength The strength of a headed grouted anchor system is dependent on the grout/concrete bond strength and the concrete cone breakout capacity of the concrete. Therefore, headed anchors that produced a bond failure were analyzed separately from those that developed a concrete cone. Table 4 illustrates the average bond strength and corresponding coefficient of variation calculated for the different products that exhibited bond failure at the grout/concrete interface. For all eight products tested with headed anchors and exhibiting grout/concrete bond failure, the mean grout/concrete bond stress was 8.1 MPa with a coefficient of variation of 0.30. This indicates that the variation between all products is greater than that within any individual product. Therefore, there is enough evidence to indicate that the unheaded bond strength is product dependent. Table 4- Grout/Concrete Bond Stress and Coefficient of Variation for Headed Anchors Product Avg. Bond Stress (MPa) Coefficient of Variation
CA 10.2 0.12
CB 7.8 0.15
CC 4.8 0.12
CD 9.1 0.21
CF 8.4 0.24
PA 7.9 0.10
PB 7.7 0.06
PC 11.1 0.07
The other failure mode observed in headed grouted anchors was a full concrete cone failure. As indicated by Eqn. 1, the capacity of this failure mechanism depends on the strength of the concrete and embedment length of the anchor. As shown in Table 2, the compressive strength of the concrete for the headed anchor tests ranged from 27.4 MPa to 63.7 MPa and the embedment length ranged from 102 mm to 178 mm. 6.3. Behavioral Models Comparison The presence of two failure mechanisms in headed grouted anchor systems requires the use of two different behavioral models to predict behavior. For grouted anchors that exhibited a concrete cone breakout, the failure loads were compared to the CCD method (Eqn. 1). Anchors that exhibited a grout/concrete bond failure were compared to the uniform bond stress model for failure at the grout/concrete interface (Eqn. 3). The results of these comparisons are presented in Figures 4 and 5.
387
Figure 4 shows a graph of the tensile failure load versus bonded area for all headed anchors that developed a bond failure at the grout/concrete interface. In Figure 4, actual failure loads were normalized to τ0 = 8.3 MPa, which is the mean value for τ0 for all tests that exhibited grout/concrete bond failure. Figure 4 shows a linear relationship, indicating that the uniform bond stress model for failure at the grout/concrete interface (Eqn. 3) is appropriate for headed grouted anchors that exhibit grout/concrete bond failure. Also shown in Figure 4 is a 5% fractile boundary based on a coefficient of variation of 0.20 and a large database. Figure 4 shows that out of the 59 anchors that exhibited the grout/concrete failure mode, only 2 anchors (3.3%) fall below this 5% fractile boundary. Figure 5 shows a comparison of the headed grouted anchor tests that were observed to develop a full concrete cone breakout failure to the CCD method (Eqn. 1 as represented by the solid line in Figure 5). As shown by Figure 5, the test data typically fall above the solid line indicating a conservative model. It is believed that the conservative results indicate that the threaded rod used in the majority of the headed anchor tests may have contributed to the increased capacity due to a combination of thread/grout interlock and bearing at the head of the anchor. A dashed line representing the 5% fractile associated with the CCD method is also shown in Figure 5. 350 Uniform Bond Stress Model τ0 = 8.3 MPa (mean)
N pred. = τ π d h ef 0 0
300
Load (KN)
250
200
150
100 Uniform Bond Stress Model 5% fractile, 90% confidence, COV = 0.20, Value = 0.67 mean
50
0 0
200
400
600
800
1000
1200
1400
2
Bond Area (mm )
Fig. 4- Headed grouted anchor tests exhibiting grout/concrete bond failure compared to the uniform bond stress model for grout/concrete bond failure
388
300
Concrete Capacity Design Model
N no
250
= 16.7 f c′ h 1.5 ef
Ntest (KN)
200
150
100
Concrete Capacity Design Method 5% fractile, 90% confidence, COV = 0.20, Value = 0.67 Mean
50
0 0
50
100
150
200
250
300
Npred. (KN)
Fig. 5- Headed grouted anchor tests exhibiting concrete cone failure compared to the CCD method
7. Conclusions The behavior of grouted anchors is dependent on the product and whether or not the anchor is unheaded or headed. For most engineered grout products, the behavior of unheaded grouted anchors can be predicted by the uniform bond stress model recommended for adhesive anchors (Eqn 2). This model is based on a product’s bond strength (τ) at the steel/concrete interface. For products with a low grout/concrete bond stress (τ0), bond failure may occur at the grout/concrete interface (Eqn. 3). In general, product approval tests need to be developed to establish both the grout product’s steel/grout bond strength (τ) and grout/concrete bond strength (τ0). The controlling embedment strength can then be determined as the smaller of the strength controlled by steel/grout bond failure (Eqn. 2) and grout/concrete bond failure (Eqn. 3). For headed grouted anchors, bond failure at the steel/grout interface is precluded by the presence of the anchor head. For headed grouted anchors, embedment failure can occur by bond failure at the grout/concrete interface (Eqn. 3) or more likely by a full concrete cone breakout failure as occurs with cast-in-place headed anchors (Eqn. 1). For headed grouted anchors, the controlling embedment strength should be determined as the smaller of that determined by grout/concrete bond strength (Eqn. 3) or concrete cone breakout strength (Eqn. 1).
389
References: 1.
2.
3.
Fuchs, W.; Eligehausen; R.; and Breen, J. E., “Concrete Capacity Design (CCD) Approach for Fastening to Concrete,” ACI Structural Journal, V. 92, No. 1, January-February 1995, pp. 73-94. Cook, R. A.; Kunz, J.; Fuchs, W.; and Konz, R. C., “Behavior and Design of Single Adhesive Anchors under Tensile Load in Uncracked Concrete,” ACI Structural Journal, V. 95, No. 1, January-February 1998. Kunz, J., Cook, R. A., Fuchs, W. and Spieth, H, “Tragverhalten und Bemessung von chemischen Befestigungen (Load Bearing Behavior and Design of Adhesive Anchors),” Beton- und Stahlbetonbau 93 (1998), H.1, S. 15-19, H. 2, S. 44-49.
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LONG TIME LOAD-CARRYING CAPACITY OF BONDED ANCHORS Lennart Elfgren*, Georg Danielsson**, Ingvar Holm**, and Gunnar Söderlind*** *Division of Structural Engineering, Luleå University of Technology, Luleå, Sweden **Testlab, Luleå University of Technology, Luleå, Sweden ***Swedish National Testing and Research Institute, Borås, Sweden
Abstract Bonded anchor bolts with diameters of 16 and 20 mm have been tested with constant static loads for up to 15 years indoors and outdoors. Creep deformations were measured for different load levels. Some of the remaining bolts have been tested to failure and the load carrying capacities were compared to design recommendations. For indoor conditions the design recommendations were quite satisfactory. For outdoor conditions the concrete quality is of importance and the remaining capacity of vital anchors ought to be checked regularly.
1. Background Bonded or adhesive anchors with polymeric resins were developed for rock strengthening in Germany around 1955 and were further developed for use in concrete structures during the sixties, Klöker (1984), Schuerman et al (1970). In this paper results are given from a long time test series that were started in 1984. The first results from the tests have earlier been presented by Elfgren et al (1988, 1993).
2. Adhesives The resin used in the tests is an unsaturated polyester with the name of Leguval K27, Bayer (1981). It is made of diols and dicarbolic acids. The acids are unsaturated, that is they have double bonds between some of their coal atoms which make them very reactive. This is a prerequisite for the curing (cross-linking) later in the process. The reaction between the diols and the dicarboxylic acids is a polycondensation in which a polyester and water is formed. The polyester contains long chains of molecules and it is initially very viscous, that is it can be hard and brittle.
391
In order to adopt the polyester to further processing, it is dissolved in a liquid as monomeric styrene, which is also unsaturated and has reactive cross-linking agents. During curing, the unsaturated, reactive groups of the cross-linking agent (the styrene) react with those of the polyester. In this reaction the molecules of the cross-linking agents are incorporated as connecting links between the polyester chains resulting in steric cross-linking. To start the curing process the formation of radicals is necessary. Radicals are highly reactive molecule fragments which stimulate the cross-linking. Organic peroxides are used as donors and their mode of action is set off by adding an accelerator (initiator). Tertiary amines are particularly effective as accelerators with benzoyl peroxide. During curing the unsaturated polyester resin shrinks 6-8 % by volume (chemical shrinkage). It is brought about by the chemical linkage which takes place between the individual molecules during curing. The linkage process causes the chains to draw closer together. By adding a filler of ballast, the shrinkage can be greatly reduced as in the case with adhesive resins where quartz fragments and glass are added. The proportion of resin to quartz may usually vary from 1:1.5 to 1:4. The cured Leguval K27 resin without filler or ballast has the following mechanical properties according to the producer: Tensile strength Elongation at rupture Compression yield strength Modulus of elasticity Shear modulus Poissons ratio Thermal expansion
frt εru frc Er G νr α
50 Mpa 2% 160 Mpa 4 Gpa 1.5 Gpa 0.33 1.5 10-4
For most bonded anchors the resin is delivered in glass cartridges (glass phials). There are two systems. In one system the radical donor (benzoyl peroxide) is stored as a powder in an inner glass phial. The phial is placed in an outer phial together with the resin, quartz sand and an initiator (tertiary amines). We have tested two products with this system (Anchors of type B and E). In the other system the quartz sand and the radical donor are stored in the inner glass phial whereas the resin and the initiator are stored in the outer phial. We have tested one product with this system (Anchor type A). To start the curing, the glass cartridge is placed in a hole drilled into the concrete, see Figure 1. An anchor rod is then mounted to a rotary drill hammer. The rod is driven into the hole. The cartridge is then crushed, the components of the resin are mixed with each other by the rotating rod and the curing starts. Curing time varies from 10 to 20 minutes at room temperature and up to several hours at –5oC.
392
Figure 1. Bonded anchor of capsule-type, Eligehausen (1994) Resins with improved properties have been developed successively, e.g. epoxy acrylats and vinyl esters, Ammann (1991), Eligehausen (1994), Zavliaris & Speare (1992).
3. Materials The concrete used in the tests had mix and strength properties according to Table 1. The compression strength was determined on 150 mm cubes. The tensile strength was determined by splitting tests on the same size of cubes according to Swedish Concrete Standard (1978). The steel in the bolts had a yield stress of 240 or 400 MPa.
4. Long time tests The concrete was cast in foundations of the dimensions 0.40 x 0.75 x 0.75 m provided with transport reinforcement of 12 mm Ks 400 (fyk ≥ 400 Mpa). The top 200 mm of the foundations were reinforced only along the edges. Bonded anchors of dimension 16 and 20 mm were used of Type A, B and E. The anchors were tested under the following environmental conditions:
393
Table 1. Concrete mix and properties
Cement, kg Gravel 0-8 mm, kg Stone 8-16 mm, kg Silica, kg Water reducer, kg Water-cement ratio Compression/tensile strength fcc/fct, Mpa/Mpa 100 days 150 days 269 days
Long time tests Luleå 210 1050 950 10 0.8 0.81
Borås 255 1245 620 0.82
37/3.0 40/3.5 32/2.9
Figure 2. Test arrangement for long time outdoor tests in Luleå. The loads are applied by means of lever arms (approximately 1 to 10) loaded by concrete blocks.
394
I O S W
12 anchors were placed indoors with approximately constant temperature and humidity (20oC, RH 30-40 %). 4 anchors were placed outdoors in Luleå in order to check the influence of varying temperatures and humidities. 6 anchors were placed indoors but had an additive (salt) of 2 % Pozzolith 122 He to the cement in the foundation blocks. 2 indoor anchors had a 10 mm layer of water on the top of the foundation around the anchor.
The resin had an age of 24 hours or more when tests were started.
Figure 3. Creep tests with M16 anchors of types A and B loaded with 15 kN under different environmental conditions.
395
Figure 4. Creep tests with M16 anchors of types A, B and H loaded with 45 kN. Results for anchors of type H are quoted from Rankweil (1980).
5. Test results Some of the test results are summarized in Table 3 and in Figures 3-5. In Figure 5, photos of six indoor anchors are showed loaded to failure due to storage shortage after 13.5 years. They all had Fult >70 kN. The numbers in the photos refer to the following anchors No 1 = I 15 A1, No 2 = I 15 A2, No 3 = I 45 A1, No 4 = I 45 A2, No 5 = W 45 A, and No 6 = W 15 A. Out of the original program of 26 anchors 12 anchors are still loaded after 15 years (5 with 15 kN, whereof one outdoors; 3 with 30 kN; and 4 with 45 kN).
396
6. Analysis and conclusions Design methods for bonded anchors are given in Eligehausen (1994). Fracture mechanics methods are discussed in Elfgren et al (1989, 1991). A general state of the art of bond of reinforcement in concrete is given in Tepfers (2000). Table 3. Summary of test results for long time loading Test No
Load F (kN)
I 15 A1 I 15 A2 I 15 B1 I 15 B2 O 15 A1 O 15 A2 W 15 A S 15 B1 S 15 B2
15.9 M16 15.6 M16 15.0 M16 15.0 M16 16.6 M16 17.5 M16 15.5 M16 15.0 M16 15.0 M16
Mean stress τ (MPa) 2.25 2.21 2.12 2.12 2.35 2.48 2.19 2.12 2.12
I 30 B1 I 30 B2 I 30 B3
30.0 M16 30.0 M16 30.0 M16
4.24 4.24 4.24
1.71 0.52 0.83
2.10 0.54 0.96
2.15 0.54 1.02
-
-
I 45 E1 45.0 M20 I 45 E2 45.0 M20 S 45 E1 45.0 M20 S 45 E2 45.0 M20 I 45 A1 43.7 M16 I 45 A2 41.4 M16 I 45 B1 45.0 M16 I 45 B2 45.0 M16 I 45 B3 45.0 M16 S 45 B1 45.0 M16 S 45 B2 45.0 M16 O 45 A1 46.8 M16 O 45 A2 43.4 M16 W 45 A 39.9 M16 (a) After 5.75 years
3.37 3.37 3.37 3.37 6.18 5.86 6.37 6.37 6.37 6.37 6.37 6.62 6.14 5.64
0.99 0.58 0.43 0.47 0.62 0.79 0.80
0.70 0.95 1.00
1.06 (a) 0.62 (a) 0.47 (a) 0.54 (a) 0.75 1.04 1.02
0.72 1.06 1.00
72 / 4690 (b) 77 / 4690 (c) 45 / 42 (c) 45 / 96 (c) 45 / 35 (c) 45 / 79 (c) 45 / 2 (c) 45 / 235 (c) 45 / 284 (c) 114 / 4690 (c)
1 year def. (mm)
3 years def. (mm)
7 years def. (mm)
14 yrs. def. (mm)
Load / Age at failure (kN / days)
0.14 0.33 0.22 0.35 0.24 0.72 0.25 -
0.15 0.35 0.26 0.37 0.32 0.80 0.30 0.10 0.12
0.13 0.34 0.26 0.38 0.46 1.00 0.33 0.10 0.15
0.13 0.33 0.55 1.10 0.33 -
79 / 4960 (b) 72 / 4960 (c) 15? / 5700 (d) 60 / 4960 (e) -
(b) Bolt failure in steel thread above concrete surface (c) Bolt drawn out of hole (d) Bolt drawn out of hole. It may have been caused by an accidental overload (e) Bolt failed by corrosion at the concrete surface
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Figure 5. Test of remaining load-carrying capacity of bolts after 13.5 years with constant load (Fult =79, 72, 72, 77, 114, and 60 kN respectively for Nos 1 to 6).
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Normal design loads for static conditions (15 kN for M16 anchors) and indoor storage have not shown any deformation increase during the last eleven years. The two anchors that were stored outdoors show on the other hand a continuous increase in deformation (about 0.05 mm/year during the first years and then gradually slowing down to 0.01 0.02 mm/year). One bolt stored outdoors (O15A1), failed after 15 years. Unfortunately it is not clear if the bolt failed through an accidental overload or if it was only the long time and the climate that caused the failure. The companion bolt (O15A2) is still going strong after 16 years. It should be born in mind that the concrete that the anchors are installed in is not freeze-thaw resistant as it has a high water-cement ratio and contains no air-treatment. The daily and annual temperature changes with freeze-thaw cycles can here lead to a gradual break down of the concrete and a slow pull-out of the anchor. The load level is about one fourth of the bearing capacity in short time loading and the friction can alone, under favorable conditions, stand up to this load, even if the adhesion has completely broken down. Higher load levels (30 kN for M16 anchors) and indoor storage have caused considerable deformations but no failures. Still higher load levels, equal to three times the normal static design load (45 kN for M16 anchors), caused failure in seven out of 14 anchors after 2-284 days. Three of the remaining seven anchors were tested to failure after 13.5 years and had then loadcarrying capacities of 72, 77 and 114 kN respectively. Tests reported by Ammann (1991) and Eligehausen (1994) indicate that newly developed epoxy accrylate resins have better resistance to water saturation and freezethaw cycles than the unsaturated polyesters discussed here. Tests reported by Håkansson et al (1981) indicate that so called non-shrinkage grouts, used for anchors grouted in holes and recesses, usually have higher shrinkage and creep than ordinary concrete made of portland cement. To sum up, it can be said that the bonded anchors tested here have shown good long time properties. However, it must be emphasized that the concrete properties and the environmental conditions are of vital importance. Exposure of bonded anchors to water and to outdoor temperature variations and freeze-thaw cycles may increase deformations considerably. For that reason caution should be exercised in the design of anchors and high quality freeze-thaw resistant concrete and a regular (e g at five years intervals) checking of the remaining load-carrying capacity might be prescribed for vital anchors subjected to outdoor climate.
399
7. Acknowledgements The research program has been sponsored by the Swedish Council for Building Research; Luleå University of Technology; SP, the Swedish National Testing and Research Institute in Borås; and by producers of bonded anchors. In the preparation of the program guidance has been given by Krister Cederwall, Kent Gylltoft and Lennart Ågårdh. The program was planned and directed by Lennart Elfgren and Anders Eriksson. The following persons have made substantial contributions to various phases of the program during the 10 years it has been running: Roger Anneling, Stig-Ola Granlund, Ingvar Holm and Gunnar Söderlind. The tests of the remaining load-carrying capacity of the bolts in Luleå were carried out by Georg Danielsson.
8. References Ammann, Walter J (1991) Static and dynamic long-term behavior of anchors. Paper SP 130-8 in “Anchors in Concrete – Design and Behavior” (Edited by George A Senkiw and Harry B Lancelot III), Special Publication SP-130, American Concrete Institute, Detroit 1991, pp 205-220. Bayer (1981) Leguval – Unsaturated polyester resins. Bayer AG, KL Division, D5090 Leverkusen. Order No KL 43016e, Edition 6.81, 40 pp and Leguval K27. Unsaturated polyester resin (UP Resin), Order No KL 43123e, Ed 1.12.1975, 10 pp. Elfgren, Lennart; Anneling, Roger; Eriksson, Anders and Granlund, Stig-Ola (1988) Adhesive anchors. Tests with cyclic and long-time loads. Swedish National Testing Institute, Technical Report SP-RAPP 1987:39, Borås 1988, 87+25 pp (ISBN 91-7848080-9). Elfgren, Lennart, Editor (1989) Fracture Mechanics of Concrete Structures. From theory to applications. A RILEM Report. Chapman and Hall, London 1989, 407 pp (ISBN 0 412-30680-8). Elfgren, Lennart and Shah, Surendra P, Editors (1991) Analysis of Concrete Structures by Fracture Mechanics. Proceedings of the International RILEM Workshop dedicated to Professor Arne Hillerborg. Chapman and Hall, London 1991, 305 pp (ISBN 0-412369870-x). Elfgren, Lennart and Söderlind, Gunnar (1993) Bonded anchors subjected to long time and cyclic loads. Fracture and Damage of Concrete and Rock – FDCR-2. Edited by H. R. Rossmanith, E&FN Spon, London 1993, ISBN 0 419 18470 8, pp 513-526.
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Eligehausen, Rolf, Editor (1994): Fastenings to concrete and masonry structures. State of the art report. Comité Euro-International du Béton, CEB Bulletin 216. Thomas Telford, London 1994, 249 pp. ISBN 0 7277 1937 8. Håkanson, Mats; Johansson, Håkan E; Broms, Carl Erik and Elfgren, Lennart (1981) Ingjutningsbruk. Tidsberoende egenskaper (Time dependent properties of grouts for anchor bolts. In Swedish. Summary in English). Division of Structural Engineering, Luleå University of Technology, Technical Report 1981:47T, Luleå 1981, 41 pp. Klöker, Werner (1984) 30 Jahre Reaktionsharzmörtel, -beton und –kunststein auf Basis ungestättiger Polyesterharze (Reaction resin mortar, reaction resin concrete and artificial stone based on unsaturated polyester resins – 30 years experience. In German). Fourth International Congress on Polymers in Concrete, 19-21 September 1984, Proceedings ICPIC ’84 (Edited by Herbert Schultz), Technische Hochschule Darmstadt 1984, pp 1119. Rankweil (1980) Long-time performance of HILTI HVA adhesive anchors. Test reports issued by Höhere Technische Bundes-, Lehr- und Versuchsanstalt, Rankweil, Austria. Size M12 No 186/78, Nov 1978, 15+15 pp; Size M20, No 170/79, July 1979, 16+24 pp; Size M16, No 52/80, April 1980, 5+26 pp (In German); Size M8, No 143/80, June 1980, 15+20 pp (In German). Schuerman, Fritz; Jankowski, Alfons and Novotny, Rudolf (1979) Die Weiterentwicklung des Klebeankers (Further development of adhesive anchors. In German). Glückauf (Essen), 26 Nov 1970, pp1145-1151. Swedish Concrete Standard (1978) Concrete testing – Hardened concrete – Cube strength. SS 13 72 10, 3 pp and SS 13 72 13, 3 pp. Swedish Steel Standard (1976) Skruvförbandsnorm St BK-N3 (Code for bolted connections. In Swedish). Statens Stålbyggnadskommitté, Svensk Byggtjänst, Stockholm 1976, 80 pp. Tepfers, Ralejs, Editor (2000): Bond of reinforcement in concrete. State-of-art report prepared by Task Group Bond Models. Féderation internationale du béton, fib, Bulletin No 10, Lusanne 2000, 427 pp. ISBN 2-88394-050-9. Zavliaris, K D and Speare, P R S (1992) The behaviour of adhesive anchorages installed in concrete. In “Proceedings from the International Conference Bond in Concrete – From research to practise”, Riga, Latvia, October 15-17, 1992 (Edited by A Skudra and R Tepfers), Technical University, Riga LV-1658, Latvia 1992, pp 11-1 to 10.
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TRANSMISSION OF SHEAR LOADS WITH POST-INSTALLED REBARS Kunz Jakob Hilti AG, Corporate Research, Liechtenstein
Abstract Often concrete ceilings are cast against roughened walls. Design methods and specifications for anchorage and splice lengths from literature and different construction standards have been compared. The examples of the connection with post-installed reinforcement of a bending slab to a wall and a short slab to a wall (here shear is outweighing) have been designed according to the standards requiring the minimum anchorage and splice lengths and tests have been performed. These investigations show that shear connections with post-installed reinforcement bars can be designed as connections with cast-in bars and that it is important to specify sufficient constructive reinforcement to limit the opening of cracks in the joints.
1. Introduction Concrete structures which consist of two or more parts cast at different moments can be designed as monolithic bodies if the internal tensile, compressive and especially shear forces can be transmitted across the joints. One possible way to ensure the force transfer is to install reinforcement bars into drilled holes by means of a bonding agent. In this case it is important that the connecting reinforcement is either fully anchored in both concrete parts or connected to the cast-in reinforcement by lap splices respectively. This paper deals with the transmission of shear forces across the joints. Structural design codes treat this problem with different methods, for example the shear friction model, the anchor model or the truss model normally used for monolithic concrete. The anchorage and splice lengths also differ from one code to another, which has a strong influence on the required drilling depth for the post-installed connecting reinforcement.
402
After a brief review of the design models used by different codes, two slabs with anchorage at the support and splices in the third points have been designed according to the codes, which required minimum anchorage and splice lengths for each case. Full scale test specimens were cast according to the design and tested at the designed working load as well as up to failure. The goal was to compare design and reality for the case of minimum joint reinforcement. Crack development and ultimate loads were observed.
2. Design Models A clear design basis is the truss model based on the classic truss analogy of Mörsch. There the flow of forces within a reinforced concrete part is approximated by a truss, where the compression beam and the inclined compression struts are allocated to the concrete, while the tensile strut and tensile tape are built by the reinforcement bars and the stirrups (figure 1a). At casting in parts a rough joint is required, which makes possible the forming of an inclined compression strut over the joint. The stress field model is a refinement of the truss model. It models the expected cracks and stress distribution within reinforced concrete more accurately (figure 1b). Also here a rough joint is presupposed. Strut and tie models and stress field analysis are generally used in european standards. tensile strut
rough joint
compression beam
inclined compression strut
figure 1a) truss model
tension chord
rough joint
b) stress field model
In countries more influenced by American standards, the transmission of shear loads at joints is represented by the shear-friction model. The transmission of shear loads is achieved by roughening (working like a keying) and the dowel action of the reinforcement bars. There the displacement in the rough joint causes an opening (figure 2a). The shear friction reinforcement works against this opening of the crack and increases the friction through that. The formula shows the design of the needed reinforcement area. Shear friction models can be applied to different surface types. At smooth or insufficiently roughened concrete joint only the dowel action of the reinforcement bars penetrating the joint can be used for design; they can be considered as shear studs and work by bending, shearing and buckling of the bars (figure 2b).
403
shear / friction reinforcement A vf works against opening of the crack and increases the friction through that A vf = (V d / (0.75 µf) - N d) / f y
bending
shearing
2• M 4• db • As • f y Vd = = l 3•π •l
figure 2a) shear-friction model
Vd =
As • f y 3
buckling
Vd = As • f y • cos α
b) working principles of shear studs
The application area of the design models can be classified in dependence from the surface of joint: from rough joints with roughness greater or equal 5mm from top to bottom of roughness (amplitude) to smooth joint with roughness smaller than 2mm. The truss model and the stress field model is used at rough joint, the model referring to the dowel action at smooth joint. Only the shear-friction model covers the entire range. Recently, a model taking into account bending, shearing and buckling of the anchor as well as shear-friction has been developed by Randl [1] (figure 2b) and is now implemented in engineering design guidelines [2]. Since this paper compares the approaches of different concrete structural design codes, the mentioned concept is not considered further here.
3. Bending Slab The first example considered was a bending slab with a length of 5m and a thickness of 20cm (figure 3). The supports and the middle part were prefabricated elements. The parts adjacent to the supports were cast in place and the connections to the support or to the middle part respectively were carried out with post-installed reinforcement. 500 150
175
F smooth joint upper reinforcement
cast in place
175
F
prefabricated
cast in place
20
100
rough joint
rough joint no upper reinforcement
rough joint
50 100 support
50 150
200
150
figure 3: geometry of the bending slab
404
support
The left support had a smooth joint and an upper and lower reinforcement, the right support has a rough joint and only a lower reinforcement. The joints between the prefabricated part and the cast-in parts is roughened and has a lower reinforcement. a) Design The slab was designed for a working load of F=2x10kN (cf. figure 3) according to DIN 1045. The concrete quality was C20/25. The connecting reinforcement to the supports and the splices to the middle part were designed according to the following 8 standards, which use different design models: German Code DIN 1045, Austrian Code ÖNORM B 4200, Swiss Code SIA 162, British Standard BS 8110, Norwegian Standard NS 3473 E, Eurocode 2 with design according to truss models and American Standard ACI 318-89 and New Zealand Standard NZS 3101 with design according to shear-friction models. Figure 4 shows the anchorage and splice lengths for bars 6 to 16mm nominal diameter according to the mentioned codes. It should be mentioned that the Austrian code ÖNORM B4200 has been replaced in the meantime by prescriptions similar to Eurocode 2 (ÖNORM B4700). Nevertheless, figure 4 shows that there is a large discrepancy between the different code prescriptions. slab of C20/25, spacing of rebars 10-times rebar diameter DIN 1045
EC2
ÖN-B4200
ACI 318
SIA 162
120
NZS 3101
BS 8110
NS 3473 E
100
splice length [cm]
anchoring length [cm]
90 100 80 60 40
80 70 60 50 40 30 20
20 0 6 mm
10
8 mm
10 mm
12 mm
14 mm
16 mm
rebar diameter
figure 4a) anchorage lengths
0 6 mm
8 mm
10 mm 12 mm rebar diameter
14 mm
4b) splice lengths
Since NZS 3101 generally yields the smallest values (figure 4), the anchorages and splices have been designed according to this code. The bottom reinforcement was carried out with reinforcement bars diameter 10mm with a spacing of 10mm. Only 40% of the bars were anchored to the supports and the anchorage length was 12cm for the smooth joint and 8cm for the rough joint. All bars were spliced to the middle prefabricated slab, and the splice length was 36cm. The differences in the standards are mainly caused by more or less rough simplifications of the formulae.
405
b) Test The load on the slab was introduced by a hydraulic cylinder and distributed to the two introduction points by a system of steel beams weighing 4kN in total. Therefore, the load acting on the slab is always the load displayed in figure 5 plus 4kN for the load distribution system. First, both forces were increased 5-times from F = 2x2 kN to service load F = 2x10 kN, held and decreased to 2x2kN again. The cracks appearing at service load were measured and recorded. Then the load was increased and stopped every 10kN in order to observe the appearing cracks. This procedure was continued until failure was reached.
piston force [kN]
The maximum load of 92kN (88kN piston force plus 4kN dead load of the load introduction parts) reached in the test corresponds to 4,6-times the calculated service load of 2-times 10kN. 90 80 70 60 50 40 30 20 10 0 0
10
20
30
40
50
60
displacement [mm]
figure 5: load-displacement curve of bending slab Figure 5 shows that the load displacement behavior between no load and the service load is stiff and that a softening occurs with loads higher than about 1.5 times service load. In figure 6a the results of the crack measurements after the fifth loading to service load of 2 F = 20kN are shown. A means the front side, B the back side of the slab. At service load only cracks in the area of the 4 joints were obeyed. In the smooth joint with upper reinforcement the cracks were in the range of the expected 0.3mm which are usually allowed by the codes for structures not exposed to rain. However, in the rough joint, without upper reinforcement, the cracks of 0.5mm are too wide. This underlines the importance of a constructive upper reinforcement for the limitation and distribution of cracks.
406
Figure 6b shows the cracks at 4,3-times service load, that is 86kN, that is shortly before failure. At the slab joints the crack widths remain small, at the support joints they become large. In spite of the large cracks at the supports, the slab still behaved as a bending slab and finally failed by yielding of the lower (bending) reinforcement (figure 7). A: crack, width = 0.30mm / length = 160mm A: crack 0.5mm / 170mm B: crack, width = 0.35mm / length = 150mm B: crack 0.55mm / 180mm smooth joint upper reinforcement
A: crack, width = 6mm / length = 180mm B: crack, width = 6mm / length = 180mm smooth joint upper reinforcement
rough joint no upper reinforcement
front side A: crack 0.1mm / 100mm back side B: crack 0.1mm / 100mm
A: crack 0.15mm / 130mm B: crack 0.15mm / 130mm
figure 6a) cracks at service load
A: crack 8mm / 190mm B: crack 8mm / 190mm
rough joint no upper reinforcement
front side A: crack 0.40mm / 140mm back side B: crack 0.35mm / 120mm
A: crack 0.50mm / 150mm B: crack 0.45mm / 140mm
b) cracks before failure
figure 7: shear slab after failure
4. Shear Slab For a short where the load is predominately shear slab on both sides anchored at the support, the design according to the 8 above mentioned standards was also performed. Between two stiff, prefabricated supports a one-span slab of 2m length and 1m breadth was cast. The lower reinforcement is spliced at the supports, the splice reinforcement bars are anchored into the supports by adhesive bond (figure 8). 200 25
F
F cast in place
smooth joint upper reinforcement
25
150
rough joint upper reinforcement
20 100 50 100 support
50 support
figure 8: geometry of shear slab
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The slab itself was designed according to DIN1045 for a service load of 2x30kN. The lower slab reinforcement consisted of bars of a diameter of 6mm with a spacing of 15cm. The connecting reinforcement at the supports was designed according to the shear / friction model of ACI 318-89 respectively NZS 3101. 6 bars with diameter 6mm were also used on each side. The anchorage length was 14cm for the smooth joint and 11cm for the rough joint. The splice length in the slab was 22cm.
piston force [KN]
During the test the forces were increased 5-times from 2x2kN to the calculated service load of 2x30kN, held for 10 minutes and again decreased. The reached maximum load of 351.7kN (338kN piston force plus 13.7kN dead load of the load introduction parts) is 5.9-times the service load of 2x30kN. At maximum load a crack appeared in 40cm distance from the left support and the force decreased to 210kN. Short time after that the slab sheared down at the smooth support on the left side. The load-displacement curve (figure 9) clearly shows the brittle shear failure. Therefore it seems logical that the reached safety factor of 5.9 is higher than that reached with the bending slab. 320
entire force 2 F = piston force + 13.7 kN dead load of load introduction parts
280 240 200 160 120
service load
80 40 0 0
2
4
6
8
10
12
14
16
18
20
displacement [mm]
figure 9: load-displacement curve of shear slab Figure 10 shows the results of the crack measurements after 5-times loading to the service load of 60kN. A means the front side, B is the back side of the slab. With maximum 0,05mm the cracks are much smaller than the allowed value of 0,3mm in this case. front side A: crack, width = 0.03mm / length = 130mm back side B: crack, width = 0.05mm / length = 50mm smooth joint
rough joint
A: crack 0.05mm / 90mm B: crack 0.03mm / 30mm
figure 10: cracks in shear slab at service load
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Figure 11 shows the specimen after shear failure of the reinforcement at the left side support. Even just before failure, at a total load of 340kN, only very little cracking could be observed. The crack openings were 0.6mm at the smooth joint (left side, where failure occurred) and 0.1mm at the rough joint. Only one additional crack appeared 30cm from the left side support shortly before failure. Its opening was 0.5mm. As seen in the loaddisplacement diagram (figure 9), the failure was brittle without any prior announcement by excessive deformations.
figure 11: shear slab after failure
5. Conclusions In many applications the use of post-installed reinforcement can substantially simplify the construction of shear connections between concrete elements. The reasons may for example be that the connecting reinforcement can be placed exactly where it is required, that installation in the part which is first cast was forgotten, that reinforcement bars sticking out of a wall or slab are not desired or that the connection has to be made in a renovation of the structure, i.e. that it was not planned from the beginning. Two possible applications are shown in figure 12.
figure 12a: connection to diaphragm wall
b: widening of a bridge slab
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The investigations presented here lead to the conclusion, that for simplifying the work on construction site the transmission of shear loads can be done with post-installed reinforcement bars bonded in with a suitable mortar. The common design rules from the applicable codes can be used, because the post-installed bars work like cast-in. In order to avoid excessive cracks in the joints, sufficient constructive reinforcement bars limiting and distributing the cracks should be installed.
References 1. 2.
Randl, N.: Untersuchungen zur Kraftübertragung zwischen Neu- und Altbeton bei unterschiedlichen Fugenrauhigkeiten. Dissertation. Univeristät Innsbruck, 1997. Connections for Concrete Overlays. Hilti Fastening Technology Manual B2.3. issue 7/97.
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DESIGN OF ANCHORAGES WITH BONDED ANCHORS UNDER TENSION LOAD Bernhard Lehr, Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract Bonded anchor systems (anchors bonded into concrete with the aid of chemical and nonchemical components) have been used for about thirty years. Their load bearing behavior and design have been intensively studied during the past years. To investigate the behavior of bonded anchors about 1200 tension tests with single anchors and about 350 tests with anchor groups have been performed at the Universtiy of Stuttgart to check the influence of main parameters on the failure load. Finite elemente analysis were caried out to study the load behavior of anchor groups. In this article the finite elemente simulations on anchor groups are presented. Furthermore the results of group tests and tests near the edge are shown and compaired with the finete elemente simulations. Based on the numerical and experimental results a design model for anchor groups and anchors near the edge is proposed.
1. Introduction Modern fastening technique is increadingly employed for the transfer of concentrated loads into concrete structures. Cast-in-place-systems (which are placed in the formwork before casting the concrete) and post-installed-systems (which are installed in hardened concrete) are common. Recently bonded anchors are often employed. The load diplacement behavior of single anchors were investigated by Meszaros [1]. Several influences on the load capacity of chemical anchors (drill-hole-cleaning, wet concrete, product, concrete compression strength, cracked concrete) were tested.
411
In order to understand the group effect of quadruple fastenings with bonded anchors an extensive numerical investigation and a series of experiments were performed. The studied specimens were adhesive anchors of the injection type based on resin mortar anchored in a concrete block and subjected to tensile loading. Quadruple anchor groups were considered. The geometry of these anchor groups is given in Fig. 1. Furthermore numerous tests with anchor groups with bonded anchors and bonded anchors at the edge were performed.
Figure 1 - Geometry of quadruple group anchors
2. Numerical simulation of quadruple anchor groups Totally 32 cases were calculated. The anchors diameters were 8mm, 12 mm and 20 mm. The analyzed cases are listed in Table 1 in which the calculated failure loads and failure modes are given. The embedment depth was variant from 48 to 240 mm (from 4d to 20d) and the spacing between anchors from 48 to 240 mm (from 0,2 hef to 2,5 hef). In addition calculations of single anchors were performed. The total depth of the specimen was hef + 188 mm, which corresponds to the value used in the experiments. The three dimensional numerical analysis were performed with the program MASA [2] [3]. Due to symmetry, only a quarter of the specimen is simulated. The simulated system includes the steel anchors, the adhesive mortar and the concrete block. The steel anchor
412
is assumed as a linear elastic material with Young´s modulus E = 210000 N/mm2 and Poisson´s ration v = 0.3. The adhesive mortar is simulated by a special interface model with shear strength of 16 N/mm2, Young´s modulus E = 2000 N/mm2 and Poisson´s ration v = 0. Table 1 - Numerical studies and failure of quadruple anchor groups Anchor diameter d [mm] 8
12
20
Embedment depth hef [mm] 96 144
hef / d [ -- ]
Spacing s [mm]
s / hef [ -- ]
Failure
12 18
160 48
20 4
96
8
144
12
192
16
240
20
144
7,2
96 48 96 144 216 160 48 96 144 192 48 96 144 192 240 48 96 144 216 48 96 144 192 48 96 144 240 96 144 180 216 240
1,0 0,33 0,67 1,0 1,5 1,0 1,0 2,0 1,5 2,0 0,5 1,0 1,5 2,0 2,5 0,33 0,66 1,0 1,5 0,25 0,5 0,75 1,0 0,2 0,4 0,6 1,0 0,67 1,0 1,33 1,50 1,67
CCB CC FPO B B B CC CC CC CCB CC CCB CCB B B CC CCB FPO B CCB FPO FPO B CCB FPO B B CC FPO B B B
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The concrete is modeled by the microplane model and the material parameters are taken from the average data of the experiments [2] with Young´s modulus E = 30000 N/mm2, Poisson´s ration v = 0.2, tension strength ft = 2.4N/mm2, compression strength fc = 23 N/mm2 and fracture energy Gf = 0.1 N/mm2. The load was applied at the top end of the steel anchor. Displacement control was used in order to get the post peak loaddisplacement curve. A fixed boundary condition, corresponding to support lines in experiments, is applied on the no-symmetry edges at the loaded side of the specimen (see Fig. 2).
Figure 2 - Finite element mesh with boundary conditions Concrete cone failure ( CC)
Pullout failure ( PO)
Concrete cone and bond failure ( CCB)
False pullout failure ( FPO)
Figure 3 - Failure modes observed in the numerical analysis In the calculations four types of failure modes were obtained which are shown in Figure 3 and listed in Table 1 as concrete cone failure (CC), bond failure (B), combined concrete cone and bond failure (CCB) and false pullout failure (FPO). The false pullout
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failure is characterized by cracks which initiated at the end of the anchors, propagated towards each other and connected at peak load. Because the concrete around the outside of the anchors is strong enough to carry the applied load the final failure mode is a bond failure, which looks like a pullout failure but the loading capacity is much smaller than with a real pullout failure. Therefore this type of failure is called “false pullout failure”. A stress analysis at the interface between mortar and concrete around the anchor perimeters revealed that the shear stresses at the part of the perimeter towards the neighboring anchors are much smaller than the shear stresses at the opposite side of the anchor. This can be explained by the crack between the anchors which does not allow to transfer tensile force into the bottom part of the specimen. Another reason for the lower shear stresses at the perimeter between anchors is tensile stresses occurring in the concrete between anchors which reduce the shear strength. These smaller shear stresses at peak load at the perimeter towards neighboring anchors explain the reduced failure load in case of pullout failure, which was observed in many experiments [2]. In order to study the group effect the calculated results are presented in Fig. 4. Plotted is the ration between calculated failure loads of groups and 4 times the calculated failure loads of single anchor with the same embedment depth as a function of the spacing. The group effect can be clearly observed. In the case of spacing s = 0 the failure load of the group should be the failure load of a single anchor. When the spacing is s = 4 d, the failure load of the group is 2.5 times the failure load of the single anchor. With s = 16 d the load capacity of four single anchors is available. With the critical spacings scr1 and scr2 like shown in Fig. 5 a model from FE-calculation is found. Nu,group / N u,single [ -- ]
Nu,group / N u,single [ -- ]
4,0
4,0
3,0
3,0 M12-hef = 240mm M12-hef = 192mm M12-hef = 144mm M12-hef = 96mm M12-hef = 48mm
2,0 1,0
2,0 M20 M12 M8
1,0
0,0
0,0 0
4
8
12
16
20 24 s/d [ -- ]
0
4
8
12
16
20
24 28 s/d [ -- ]
Figure 4 - Ratio between the failure load of an anchor group and a single anchor about the ration spacing to diameter from FE analysis
415
Nu,group / Nu,single [ -- ]
s cr2
s cr1
4,0 4•N
3,0
u,single
2,0 1,0 0,0 0
4
8
12
16
20
24 s /d [ -- ]
Figure 5 - Model for the influence of spacing of quadruple fastenings with bonded anchors according to results of FE calculations
3. Experimental studies To control the FE analysis a lot of experiments with quadruple fastenings were performed. Varied was the anchor diameter (d = 8 / 12 / 16 / 24 mm), the embedment depth (hef from 4 d to 16 d) and the spacing (s from 0.33 to 4 d). Tests were carried out in concrete with compression strength fcc ~ 25 N/mm2 and fcc ~ 55 N/mm2. Two injection mortars were used. Single anchors with the same embedment depth like the quadruple fastenings were tested too normally in the same slabs. In Fig. 6 the relation between the failure load for the quadruple fastenings and the single anchors (meanvalues) is plotted about the relation between the spacing and the embedment depth s / hef and about the relation between the spacing and the diameter d / hef. In Fig. 6 is to recognize, that with s = 16 d the critical spacing is found. At this spacing the failure loads of quadruple fastening are equal to four times the failure load of single anchors. Nu4 / 4 • N uE [ -- ]
Nu4 / 4 • N uE [ -- ]
4,0
4,0
mortar HH
3,0
mortar SP
3,0
2,0
2,0 hef = 192mm hef = 144mm hef = 96mm hef = 48mm
1,0
hef = 144mm hef = 120mm hef = 96mm hef = 48mm
1,0
0,0
0,0 0
4
8
12
16
20
24
0
s / d [ -- ]
4
8
12
16
20
24
s / d [ -- ]
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Figure 6 - Ratio between the failure load of an anchor group and a single anchor about the ration spacing to diameter from experiments
4. Model for the design of bonded anchors in non-cracked concrete Design models are given by Eligehausen, Mallée, Rehm [3], Cook [4] and others. At the University of Stuttgart the following design model has been developed to calculate the failure loads of fastenings with bonded anchors under centric tension loads. The model is valid for fastenings with single anchors and anchor groups far away from edges, at the edge and in a corner. The member thickness must be h ≥ 2hef to prevent splitting failure. A N u = ψ s, N • c0,N • N u0 (1) Ac ,N
N u,0 m = τ u,m • π • d • hef with
τu,m d hef Ac,N
= = = =
Ac0,N
=
ψ s,N c cr,N
= = = =
scr, N
(2)
mean value of bond strength from tests anchor diameter embedment depth actual projected area at the concrete surface assuming the fracture surface of the individual anchors (examples see Fig. 8) projected area of one anchor not affected by edges or overlapping stress cones at the concrete surface 2 2 scr, N = (16d) 0, 7 + 0,3 (c / c cr, N ) < 1,0 8d 16d
This design model produces a good agreement of calculated failure loads with results of tests. In Fig. 6 the measured failure loads of quadruple fastenings with bonded anchors are plotted as a function of the calculated failure loads. A similar level of agreement between test and calculation has been found in other cases (double fastenings, fastenings at the edge).
417
Nu,test [kN] 350 300
scr,N = 16d
250 200 150 100
X = 10,2 V = 23,6% n = 271
50 0 0
50 100 150 200 250 300 350 Nu,calc [kN]
Figure 7 - Comparison of test results with predicted capacities for four-anchor-groups If the diameter of the anchors is large and the bond strength of the mortar is high, the failure loads predicted according Eq. (1) will be higher than predicted according to the CC-method [6] (see Fig. 7). Quadruple tests with bonded anchors with diameter d = 24 mm are carried out. The bond strength was 12 N/mm2 (mortar HH) and 20 N/mm2 (mortar ED).
418
16d
single anchor: 16d
o Ac,N = (16d)2
single anchor at the edge :
8d
Ac,N = (c+8d) •16d 8d
c
c Š 8d
8d
8d 8d
c
s1
s Š 16d c Š 8d
s2 8d
s1
Ac,N = (c+s1 +8d) • 16d
8d
8d
c
double fastening at the edge :
quadruple fastening at the edge : Ac,N = (c+s1 +8d) • (16d +s2) s Š 16d c Š 8d
8d
Figure 8 - Design model for bonded anchors
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Nu [kN] 1600 headed anchor bonded anchor
1200
800 d = 20 mm
τ u = 16 N/mm2
400
hef = 240 mm 0 0
200
400
600
800 s [mm]
Figure 9 - Comparison of predicted capacities for anchor-group with for anchors In Fig. 10 the failure loads of the tests with anchors M24 are plotted. It can be recognized, that the failure loads of these tests are lower than the failure loads according Eq. (1). Therefore concrete cone failure must be checked. If the concrete cone failure load predicted by the CC-method is lower than the calculated value according Eq. (1) and (2), this load will be correct.
Nu [kN] 2000
8d = 192
3hef = 864
16d = 384 τu = 20 N/mm2
1600
headed anchors
1200
bondedanchors τu = 12 N/mm2
800
d = 24 mm hef = 288 mm = 12d f CC = 30 N/mm2
mortar ED mortar HH
400 0 0
250
500
750
1000 s [mm]
420
Figure 10 - Failure loads of quadruple fastenings with bonded anchors, d = 24 mm, hef = 12d = 288 mm The failure load with fastenings of bonded anchors must be limited by the concrete cone failure load of headed anchors calculated according to the CC-method (Eq. (3)). N u, m
= min (Nu,bond ; N u, conc )
N u,conc
= N u,conc according to CC − methode for headed anchors
(3)
5. Acknowledgement The primary funding for this research was provided by fischerwerke, Upat and Hilti. The support of these manufactures is very appreciated. Special thanks are also according to Yijun Li who spent many hours in preparing the FE calculations.
6. Conclusions In order to find a model for calculating the average failure loads of fastenings with bonded anchors FE-analysis and tests were done. Using the uniformed bond model to calculate the failure load of single anchors and the critical spacing scr = 16d a good agreement between tests and calculations could found. However, the failure load of fastenings with bonded anchors must be limited by the concrete failure load calculated according CC-method for headed anchors.
7. References [1] [2]
[3] [4] [5] [6]
[7]
MESZAROS, J., Tragverhalten von Verbunddübeln im ungerissenen und gerissenen Beton, Dissertation, Universität Stuttgart, Germany, 2001 OZBOLT, J., LI, Y.-J., KOZAR, I., Microplane model for concrete with relaxed kinematic constraint, International Journal of Solids and Structures, 38, 2683-2711, (2001) OZBOLT, J., and BAZANT, Z.P., “Numerical Smeared Fracture Analysis: Nonlocal Microcrack Interaction Approach”, IJNME, 39(4), p. 635-661, 1996. ELIGEHAUSEN, R., MALLEE, R., Befestigungstechnik im Beton- und Mauerwerksbau , Ernst & Sohn, Berlin, Germany, 1997. COOK, R., Behavior of Chemical Bonded Anchors, Journal of Structural Engineering, Vol. 119, No. 9, September 1993 FUCHS, W. ELIGEHAUSEN, R., Das CC-Verfahren für die Berechnung der Betonausbruchlast von Verankerungen, Beton- und Stahlbetonbau 90 (1995), H. 1, S. 6 - 9; H.2, S. 38 - 44; H.3, S. 73 - 76. LEHR, B., Tragverhalten von Gruppenbefestigungen und Befestigungen am Bauteilrand mit Verbunddübeln unter zentrischer Belastung, Dissertation, Universität Stuttgart, Germany, 2001
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LOAD BEARING BEHAVIOR AND DESIGN OF SINGLE ADHESIVE ANCHORS Juraj Meszaros, Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract In the present paper the results of tests investigating the load bearing behavior of chemical anchors used for fastenings to concrete are presented and discussed. The loaddisplacement behavior of this class of anchors depends on the properties of the base material, as well as on the installation procedures. To study the influence of the installation procedures and the material parameters on load-displacement behavior, nearly 2000 tests with single fastenings were performed at the University of Stuttgart. Stress distribution along the anchor rod was determined by experimental tests, as well as by FE analysis. To investigate the failure mechanism of bonded anchors, axisymmetric FE models were developed. Numerical analysis was carried out using a nonlocal mixed formulation of the microplane model for concrete.
1.
Introduction
Adhesive anchor systems composed of chemical and non-chemical components are increasingly employed as fastenings to concrete. The bond behavior is sensitive to a number of factors including the chemical components in the adhesive mortar and the different boundary conditions created by the installation procedures. To investigate the behavior of bonded anchors, about 2000 tension tests with single anchors were performed at the University of Stuttgart. The sensitivity of the anchor behavior to the concrete strength, the cleaning of the drill hole and the humidity of the concrete has been studied. Furthermore, the geometric parameters of anchors and the influence of concrete cracking on the load-displacement behavior have been investigated. To better understand the failure mechanism of bonded anchors, Finite Element (FE) analysis with varied anchor geometry (embedment depth, anchor diameter), concrete
422
confinement (confined and unconfined) and concrete strength (low and high) has been performed. The bond stress along the anchor length was determined from the difference of the axial loads. In a 2D-analysis a nonlocal microplane model was used. The top of the anchor was loaded by described displacements. The applied microplane material model [2] is a general macroscopical material model for friction-cohesive, quasi-brittle materials. The model is macroscopical, i.e. it does not model the material on the microstructural level. To prevent a localization of damage thus creating a zero volume element, the model was coupled with a so called localization limiting procedure (nonlocal concept). In the present paper a small part of the numerical and experimental results for a single adhesive fastener are presented and discussed.
2.
Numerical analysis
2.1 Investigated parameters and material properties The aim of the FE analysis was to study the failure mechanism of bonded anchors. Furthermore, the influence of the geometric characteristics of the anchors, as well as the influence of the concrete strength on the ultimate load, was investigate. The investigated parameters were as follows: Load-bearing behavior •
failure mechanism
•
bond stress anchor rod
•
along
load-displacement behavior
the
Influence factors •
embedment depth hef
•
anchor diameter da
•
confining of the tension loads
•
concrete strength
The study was carried out for an axisymmetric concrete element. The specimen was loaded by controlling the axial displacement on the small load transfer zone on the top of the anchor rod. The analysis was performed using four node quadralateral elements with four integration points. The region close to the bond zone where load transfer occured was modeled with a finer mesh with. The size of the elements increased moving away from the load transfer zone. In addition to the concrete constitutive law, a governing parameter in the nonlocal analysis is the so-called characteristic length [3]. In
423
the present study the characteristic length was set to lch = 5 mm. For the C20/25 and C45/55 concrete member the following material properties were used:
Material properties Uniaxial tensile strength Uniaxial compressive strength Fracture energy Modulus of elasticity Poisson’s ratio
ft fc GF E ν
MPa MPa N/mm MPa -
Concrete C20/25 2.4 23.0 0.15 30000 0.15
Concrete C45/55 3.8 45.1 0.12 36000 0.20
Table 1: Material properties of concrete members
2.2 Numerical results For the bonded fastenings in unconfined concrete, two different failure modes were obtained. Failure of bonded anchors with embedment depth hef/d= 4 occured by a concrete cone failure (Fig. 1). Bonded anchors with embedment depth hef/d≥ 8 failed by a combination of concrete cone failure and anchor pull-out (Fig. 2). In calculations with confined concrete, share failure in the bond layer and in the first concrete element layer was observed [4]. In the middle of the anchor embedment depth, nearly constant bond stress for the confined anchors was obtained (Fig. 3). For the anchors in unconfined concrete a slight increase in the bond stress along the anchor length occured. The calculated loaddisplacement curves show nearly the same behavior as the experimental results (Fig. 4).
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Output Set: masa2 v48w070 Contour: Avrg.E11 stra.
0.15 0.125 0.1 0.075 0.05 0.025 0. Y Z
X
Figure 1- Failure of M12 bonded anchors hef / d= 4
OutputSet:masa2v144w060 Contour:Avrg.E11stra.
0.15 0.125 0.1 0.075 0.05 0.025 0. Y Z
X
Figure 2- Failure of M12 bonded anchors hef / d= 12
425
30 M12 /144-B25-confined
(Concrete Element: h= 400 mm, b= 600 mm)
[N/mm²]
25 hef= 144 [mm] 0.40Fu
20
0.812Fu 1.0Fu
Bond Stress
15
0.89Fu (post-peak)
10 5 0 0.0
0.2
0.4
0.6
0.8
1.0
Normalized depth hef /d [-]
Figure 3- Stress distribution along the normalized depth
280 hef/d= 32
Load F [kN]
240
hef/d= 24 hef/d= 16
200
hef/d= 12
160
hef/d= 8 hef/d= 4
120
B25 M12 confined
80 40 0 0
2
4
6
8
Displacement s [mm]
Figure 4- Load-Displacement curves
426
10
To determine the influence of confined and unconfined concrete on the failure load, calculations with anchors of different embedment depths were carried out. The anchor diameter and the concrete strength, as well as the member geometry, were kept constant. In Figure 5 the relationships between the ultimate bond strength (τ= Nu / π·d·hef) for confined and unconfined calculations is plotted as a function of the relative embedment depth. As expected, when the normalized embedment depth increases, the relative bond strength between confined and unconfined anchors approach 0.90 to 0.95. The results of FE analyse shows practically no Influence of the anchor length on the ultimate bond strength. In contrast to this increasing anchor diameter leads to the decrease of the ultimate bond strength (Fig. 6). In the Figure 7 the influence of the concrete strength on the ultimate bond strength is plotted. Concrete with uniaxial compressive strengths fc = 23 MPa and fc = 45.1 MPa, were used. Influence of the concrete strength on the ultimate load of bonded anchors is low.
τu,unconfined / τu,confined [-]
1,5
1,0 y = 0,7962x0,0493 y = 0,7683x0,0578
0,5 M12, B25 M12, B55
0,0 0
4
8
12
16
20
24
28
32
36
hef / d [-]
Figure 5- Relationship between confined and unconfined bearing of the tension loads for M12 bonded anchors as a function of relative embedment depth.
427
24 hef/d=4 hef/d=8
τu [N/mm 2]
20
hef/d=12 y = 31,423x-0,3167
16 12 B25 unconfined
8 4
8
12
16
20
Anchor diameter [mm]
Figure 6- Influence of the anchor diameter on the ultimate bond strength
1,4
τu / τu (fc=23 N/mm2) [-]
y = 0,3706x0,3166
1,2
y = 0,5849x0,1711 y = 0,8188x0,0637
...für hef/d=4 ...für hef/d=8 ...für hef/d=24
1,0 M12, hef=48 mm M12, hef=96 mm M12, hef=144 mm M12, hef=192 mm M12, hef=288 mm M12, hef=384 mm
0,8 unconfined
0,6 23
45 fc
2
[N/mm ]
Figure 7- Influence of the concrete strength on the ultimate bond strength
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3.
Influence of installation procedure
3.1 Influence of drill-hole cleaning Adhesive anchors transfer load from a steel rod through an adhesive layer, into the concrete along the bonded surface. The bond strength between the adhesive and concrete surface can be adversely influenced by a number of factors. In particular the drill hole cleaning or a wet drill-hole surface can influence the bond capacity of chemical anchors. To study the influence of installation related factors, approximately 400 tests with single anchors in uncracked concrete were performed. Figure 8 shows the ratios of the bond strength in an uncleaned hole to the average values for well-cleaned holes for various adhesive products [4]. Capsule-type bonded anchors (product 1) and injection-type bonded anchors (product 2, 3 and 4) were used. The figure shows that capsule-type bonded anchors installed by hammering and rotation are less sensitive to drill hole cleaning than injection type bonded anchors. The bond strength variation can be explained by the following observation. During the installation of capsule-type bonded anchors, the drill dust along the wall of uncleaned drill hole is mixed into the mortar. During the installation of injection-type bonded anchors, however, the loose concrete particles along the surface of the drill hole can build a boundary with decreased bond strength. A load reduction of about 20% to 60% compare to the well-cleaned holes was observed for injection-type anchors. In the experimental investigations of Cook and Konz [5] for 20 different adhesive products applied to an uncleaned holes, the average relative bond strength were about 71% of their respective baselines. The average coefficient of variation of was about 20 %. 3.2 Influence of wet concrete Anchors installed in “wet concrete” (i.e. concrete saturated with water prior to hole boring) or installed in “damp holes” (i.e. holes bored prior to concrete wetting) show for most products a significant decrease in capacity compared to installation in dry concrete. For anchors installed in “completely submarged conditions” (i.e. under water installation) a larger reduction of the capacity was observed. The influence of wet concrete on the bond strength, however, is product dependent. After investigations by Cook and Konz [5] for twenty different products installed in damp holes, the average relative bond strengths were 77% of their respective baselines, with an average coefficient of variation of 23%. Figure 9 shows the bond strength of bonded anchors installed a the concrete that was stored for 7 days under water compared to the capacity measured in dry concrete [4]. In the tests, capsule-type bonded anchors with vinylester based mortar (product 1) and injection-type anchors (product 2 to 5) were used. The bond strength in wet concrete was reduced by as much as 60% compared to the dry hole strength. In improperly cleaned, wet drill holes, a further reduction of the bond strength must be expected.
429
[-]
1,0
τu,uncleaned / τu,cleaned
1,2
0,8 0,6 0,4 0,2 0,0 1
2
3
4
Product
Figure 8- Relation between bond strength of bonded anchors installed in cleaned and uncleaned drill holes, after [4]
1,2
τu,wet / τu,dry [-]
1,0 0,8 0,6 0,4 0,2 0,0 1
2
3
4
5
Product
Figure 9- Relation between bond strength of bonded anchors installed in wet and dry concrete, after [4]
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4.
Design of single bonded anchors
Present design models for bonded anchors are given by Eligehausen, Malée, Rehm [1], Cook et al. [6] and others. Based on the results of theoretical and experimental investigations, a design model with a constant distribution of bond stress along the embedment depth (uniform bond model) to calculate failure loads of fastenings with bonded anchors under centric loads has been developed. Mean values of bond strength τu take the characteristic mortar behavior into consideration. A design model for fastenings with anchor groups far away from edges, at an edge and in a corner is given in [7]. This design model is valid for embedment depths from 8d ≤ hef ≤ 12d. To prevent splitting failure, the member thickness must be h ≥ 2hef. The failure load of single bonded anchors far away from edges can be calculated by the Eq. (1).
N u0 = τ u ⋅ π ⋅ d ⋅ hef where
τ u= d= hef=
(1)
mean value of bonded strength anchor diameter embedment depth
This design model for single bonded anchors shows a good agreement of calculated failure loads with experimental results (Fig. 10). 140 M8, M12, M16 hef/d= 4 to 12 unconfined
120 Nu,test [kN]
100
HH,SP,UU,WW
80
n= 345 x= 0,98 V= 16,4 %
60 40
Nu,calc= τu*π*d*hef τu= f(d, fcc ,System)
20 0 0
20
40
60
80
100
120
140
Nu,calc [kN]
Figure 10- Failure loads of tests with single bonded anchors versus calculated failure loads according to Eq.(1), after [4].
431
5.
Conclusions
The present paper deals with the behavior of single bonded anchors. Results from numerical analyses are presented to help illustrate the failure mechanism of bonded anchors. In the numerical analyses, the influence of different anchor geometries and concrete strengths on the failure load has been investigated. The results shows practically no influence of the anchor length on the ultimate bond strength. With increasing anchor diameter, a decrease of the ultimate bond strength was observed. Additionally the influence of the concrete strength on the ultimate load is small. This has also been show by experimental tests. The influence of external factors, such as drill-hole cleaning and wet concrete, on the load-bearing behavior, is discussed. These influences shown to be product dependent. In a particular for injection-type bonded anchors, a significant reduction of the bond strength can be expected. Based on the results of theoretical and experimental investigations, a design model with constant distribution of bond stress along the embedment depth is presented. The calculated failure loads for single bonded anchors according to the presented design model are shown to be in good agreement with experimental studies.
6.
Acknowledgement
The primary funding for this research was provided by the fischerwerke, Hilti, Upat. The support of these manufacturers is very much appreciated. Special thanks are also accorded to Matthew Hoehler who reviewed the paper.
7.
References
1.
Eligehausen, R., MaléeE, R., Rehm, G., “Befestigungstechnik, Betonkalender 1997 ”, Ernst & Sohn, Berlin, Germany, 1997. Bazant; Z.P., “Size Effect in Blunt Fracture: Concrete, Rock and Metal”, JEM, ASCE, 110(4), p. 518-535, 1984. Ozbolt, J., and Bazant, Z.P., “Numerical Smeared Fracture Analysis: Nonlocal Microcrack Interaction Approach”, IJNME, 39(4), p. 635-661, 1996. Meszaros, J., “Tragverhalten von Einzelverbunddübeln unter zentrischer Kurzzeitbelastung”, Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 2001. Cook, R.A. and Konz, R.C., “Factors Influencing Bond Strength of Adhesive Anchors”, ACI Structural Journal, Jan.-Feb. 2001, p. 76-86, 2001. Cook, R.A., Kunz, J., Fuchs, W. and Konz, R.C., “Behavior and Design of Single Adhesive Anchors under Tensile Load in Uncracked Concrete”, ACI Structural Journal, Jan.-Feb. 1998, p. 5-26, 1998. Lehr, B., “Tragverhalten von Gruppenbefestigungen und Befestigungen am Bauteilrand mit Verbundankern unter zentrischer Belastung”, Dissertation, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, 2001.
2. 3. 4.
5. 6.
7.
432
REBAR ANCHORAGE IN CONCRETE WITH INJECTIONS ADHESIVE Martin Reuter*, Thomas Greppmeir*, Fritz Münger** *Hilti Deutschland GmbH, Germany **Hilti Corporation, Liechtenstein
Abstract Subsequently installed reinforcement bar connections with injection adhesive have at all times been applied, although design rules and installation have not been clearly regulated in any way until recently. This status basically changed through the issue of the first general construction supervisory authority approval No. Z-21.8-1648 on 7th February 2000, for subsequently installed reinforcement bar connections with an injection adhesive [1]. This paper describes the regulations of the first approval by the Deutsches Institut für Bautechnik, Berlin, for the subsequently installed reinforcement bar connections with injection adhesive and demonstrates the requirements of the planning civil engineer, the jobsite personnel and the companies in theory and practice.
1. Introduction For many years, i.e. post-installed rebar connections have been made to in-place concrete components for restoration and renovation work, extensions to existing buildings and to strengthen reinforced-concrete structures. Parts cast in when concreting (inserts) call for careful prior planning before the concrete is poured, i.e. socket joints, rebar screw connections [3, 4, 5 and 6]. To date, the design of rebar connections post installed with construction adhesive, including their spacing, edge distance and installation (hole cleaning and filling), has been specified solely in manufacturers‘ instructions and with different quality levels, even though such connections are subject to construction authority supervision in many cases. This situation changed fundamentally when the first general construction supervisory authority approvals were granted for rebar connections post installed with injection adhesive [1, 7]. These approvals define examples of applications in reinforced concrete construction. In addition, anchoring close to component edges is possible using sleeve /
433
socket joints or rebar screw connections. In this case, the tensile loads are transferred to the existing reinforcement (overlap joint) or the base material (anchorage) via the bond. In the first case, even heavy steel structures can be joined to concrete base material close to the edge.
2. First general construction supervisory authority approval Z-21.8-1648 This approval [1] was granted in February 2000 and was granted new in November 2000 due to the extension of the rebar diameters 20 and 25 mm [2]. It provides the first rulings on how to design rebar connections post installed with construction adhesive in Germany. The rulings given in reinforced-concrete standards apply, i.e. those in DIN 1045 [8] and EC 2 [9]. Further details about the loadbearing behaviour of rebars post installed with adhesive were published in [10] and [11]. Reinforcing steel of the BSt 500S grade, as per DIN 488-1:1984-09 [12], may be used as well as steel with a general construction supervisory authority approval, for example stainless-steel rebars [13 and 14] or rebars with a subsequently cut thread [3, 4], with rolled thread [5] or with internal thread connections [6]. Furthermore, the approval particularly stipulates the min. concrete coverage, the min. rebar spacing, the min. and max. anchorage depths and the passive fire prevention measures to be observed. tensile load [kN] lv = 30ds = 600 mm
200
160
lv = 15ds = 300 mm
120 lv = 10ds = 200 mm 80 diameter ds = 20 mm concrete C20/25 BSt 500S, fyk,nom = 500 N/mm2 ⇒ lb = 95 cm
40
0
5
10
15
20 Displacement [mm]
Fig.1: Load-displacement-diagram of rebars ds = 20mm installed with HIT-HY 150 The connections must be designed by an experienced structural designer who must produce verifiable calculations and work execution drawings / plans for the construction site. The approval stipulates that certified companies must post install the rebars with adhesive. These companies must have trained, skilled construction site personnel and the
434
equipment necessary for post installing rebars with adhesive. This paper explains the rulings in the approval [1, 2] on making a post-installed rebar connection with injection adhesive and provides information about the requirements to be met by the designers, skilled construction site personnel and work execution companies. 2.1 Minimum concrete coverage and drilling the rebar hole The engineer responsible must design rebar connections post-installed with adhesive like cast-in rebars according to valid reinforced-concrete standards. In addition, the approval specifies the min. concrete coverage. The concrete coverage is necessary to ensure that there is sufficient concrete around the rebar to take up bond stresses resulting from the interplay of forces at the rebar ribs, and also to protect the rebar from corrosion and heat in the event of a fire. Also, the min. concrete coverage specified in this approval ensures that no concrete spalling takes place due to impacts, shockwaves, etc. set up when producing the rebar holes. Basically, the approval covers the hammer drilling and pneumatic drilling methods of producing rebar holes. Impacts, shockwaves, etc. of various strengths are caused by the different drilling methods by their very definition. This leads to the basic figure of 30 mm as the min. concrete coverage for hammer drilling and 50 mm for pneumatic drilling. In order to observe the specified concrete coverage at the end of the hole too, the predetermined dimension amounts to 6% or 8% of the depth drilled, depending on the drilling method. If a drilling aid is used, the dimension predetermined for both drilling methods may be reduced to 2% of the hole depth. The drilling aid is a device intended to ensure that the hole is drilled parallel to the building component surface or edge.
Fig. 2: Using of the drilling aid for holes near to the concrete edge
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This means that the min. concrete coverage must be 9 cm at the entrance of a hole one metre deep produced by hammer drilling. This figure reduces to 5 cm if a drilling aid is used. without drilling aid cmin = 3 cm + 0,06 ⋅ lv cmin = 3 cm + 0,06 ⋅ 100cm cmin = 9 cm
with drilling aid cmin = 3 cm + 0,02 ⋅ lv cmin = 3 cm + 0,02 ⋅ 100cm cmin = 5 cm
100cm
100cm
5 cm 3 cm
3 cm
9 cm
Fig.3: Edge distance of rebar to be bonded in, ds = 20mm, rotary hammer drilling 2.2 Minimum rebar spacing and anchorage depths The distance between rebars post installed with adhesive must be greater than 5 ds and at least 50 mm according to [1, 2]. If not, there will be a risk of the holes overlapping and of the adhesive seeping away into an other hole when it is injected. The min. anchorage depths are given on principle in applicable reinforced-concrete standards. Furthermore, the diameter-related min. values in these standards are multiplied by a factor of 1.5, as given in [1, 2]. Taking into account the stipulations in DIN 1045 [8] and in EC 2 [9], results in the actually required anchorage depths, which are, in fact, far greater than the anchorage depths of metal anchors.
Fig. 4: Differences between anchor theority and reinforced concrete theority
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2.3 Maximum anchorage depths The max. anchorage depths are limited by the adhesive dispensers. According to [1, 2], different dispensers are available for injecting HIT-HY 150 adhesive, i.e. a manual MD2000 dispenser, a battery-powered BD2000 dispenser and a pneumatic P5000HY dispenser. The max. anchorage depths given in [1, 2] are shown in fig. 5 according to their dispensing capacities. During actual use, it soon becomes clear that users very quickly comes up against limits when using the MD2000 manual dispenser. The dispenser powered by a 9.6-volt battery is much more suitable here because it enables effortless, speedy injection of the adhesive, independent of compressed air or power lines, while ensuring a constant quality of the adhesive, even after work breaks. The 330-ml foil cartridge used has the advantage of leaving a far smaller amount of waste after dispensing the adhesive compared to hard cartridges. Use of the pneumatic P5000HY dispenser and 1100-ml jumbo cartridge becomes meaningful when anchorage depths are very large and many fastenings have to be made. slapdiameter ds
drilling diameter
Maximum anchorage depth lv
d0
dispensers
hammer drilling
pneumatic drilling
MD 2000 P3000HY
BD 2000
P5000HY
8 mm
12 mm
10 mm
14 mm
12 mm
16 mm
14 mm
18 mm
130 cm
16 mm
20 mm
150 cm
20 mm 25 mm
25 mm
26 mm
32 mm
100 cm 100 cm 70 cm
115 cm
50 cm
50 cm
200 cm
50 cm
50 cm
200 cm
Fig. 5: Maximum anchorage depths limited by dispensers 2.4 Passive fire prevention If passive fire prevention requirements have to be met, the approval covers two cases, namely rebar connections at right angles to the surface exposed to fire and those parallel to it.
3. Design of rebar connections with a computer program In the course of planning rebar connections, the structural engineers responsible produce verifiable designs and drawings for the construction site (forming and rebar layout drawings). Suitable software supports this design work in accordance with [1, 2]. It implements the rules and regulations of reinforced-concrete standards and the approval [1, 2] in practical reinforced-concrete construction for rebar anchoring and rebar overlap joints.
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4. Notes on installing rebars with adhesive A key prerequisite for proper functioning of an injection adhesive is the micro-keying action between hole wall and injection adhesive. Consequently, cleaning the entire drilled hole and injecting the adhesive without bubbles are of major importance. Fig. 6 shows the exact cleaning process in accordance with [1, 2]. How to clean the rebar hole is dealt with in depth when training jobsite personnel. If the cleaning process is “forgotten“ - which must be regarded as pure negligence - the same effect takes place after injection and curing of the adhesive in the hole as when intentionally spreading flour on a baking tray - no bond results. Fig. 7 shows a hole being cleaned with a compressed-air lance on a construction site at Mannheim, Germany. The very considerable amount of drilling dust removed can be clearly seen. Blow out hole 3 times using compressed-air lance from bottom of hole. Use oil-free compressed-air ≥ 6 bar
Brush out hole 3 times using round brush with spindels
Blow out 3 times as a check using compressed-air lance from bottom of hole. Use oil-free comoressed-air ≥ 6 bar
Fig. 6: Cleaning of the drilled hole
Fig.7: Hole cleaning on a jobsite using a compressed-air-lance
During a subsequent operation, HIT-HY 150 adhesive is injected, without air inclusions, into the cleaned hole from the bottom upwards using a pressure build-up plug specially developed for this purpose (fig. 8). Owing to the back pressure set up at the plug endface during injection, the mixer extension is gently but noticeably pushed out of the hole. Prior to injection, a mark on the mixer extension is made to ensure that sufficient adhesive is injected into the hole. Immediately after sufficient adhesive has been injected, the rebar is pushed into its hole. When the time for use / pot life, which is defined in [1, 2], has expired, the injection adhesive begins to cure from the bottom of the hole upwards. It is impossible to push the rebar into partially cured adhesive. In view of this, it is recommended that two people inject the adhesive, especially when temperatures are high, to ensure that the work progresses quickly and smoothly. During the mentioned installer training, a time limit is set for injecting the adhesive and a cartridge is also changed during this injection work. Criteria for correct rebar installation are that the anchorage depth mark previously applied to the rebar aligns with the hole entrance and that some adhesive emerges from the hole entrance after rebar insertion.
438
Fig. 8: Injection from the bottom of the cleaned hole without air inclusions The individual parts, including drilling aid, required for rebar installation are contained in a clearly set out, so-called rebar box . The installation steps are recorded in an installation report . As a result, jobsite personnel carrying out the work can describe and record the execution of the rebar connections, and have this signed by the site manager. If the installation report is archived in construction files, everyone responsible has proof at hand that the rebars were post installed with adhesive in compliance with the approval.
5. Certified companies Companies entrusted with this work according to [1, 2] require verification of their suitability for making rebar connections post installed with adhesive from an independent testing / inspection authority. Trained, skilled construction site personnel are required for this purpose. Suitable training courses have been carried out throughout the country since March 2000.
Fig.9: Rebar installer training: injection into plexiglas tube
Fig. 10: Certification for installer and company
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Hilti engineers responsible for the training, to quote, are “Extremely competent and can communicate the subject matter very well” [15]. After successfully completing this oneday training course, participant receives a certificate with an unrestricted duration of validity from an independent testing authority, for example the Universities of Stuttgart and Dortmund and the Darmstadt Technical University. The company concerned must prove they have the tools required for rebar installation and define a qualified manager as well as a site manager. If these prerequisites can be fulfilled, the company fills out an application form. The independent testing authority, which also certified the company‘s installers, provides formal recognition. Since the approvals [1, 2 and 7] were granted, as a result, only certified companies with trained personnel have been the contacts where rebar connections post installed with adhesive subject to construction authority supervision are concerned.
6. Typical application example An example of implementing this pioneering achievement in reinforced-concrete construction is the new construction of a diaphragm roof covering for the ice rink of the Bundesleistungszentrum at Grefrath near Düsseldorf, Germany (fig. 11). Here, the inserts responsible for taking up, i.e. anchoring, bending moments acting on the column bases were wrongly installed. This would have resulted in the bases not being able to take up the imposed bending moments to a sufficient degree. To solve this problem, rebars of BSt 500S, ds = 25 mm, with an anchorage depth lv = 1.0 m were anchored in the existing foundation and the steel columns fastened via a turned-on thread.
Fig. 11: Diaphragm roof covering on bending-resistant round steel columns
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Apart of that the rebar anchorage with injection adhesive was extensively used on the new Düsseldorf airport jobsite (airport 2000 plus).
7. Summary The present method of post installing rebar connections was developed primarily to join concrete building components. The basic idea is to smoothly tie up various well considered steps in planning and work execution. After due engineering consideration, this method can also be applied to the connection of steel structures with concrete components. In this case though, attention must be paid to the peculiarities of shear force transfer and the transfer of tensile forces to the concrete. Bearing in mind the ever increasing attention that is being paid to renovating and repairing existing buildings, the approvals [1, 2 and 7] provide consulting engineers and the construction industry generally with an aid that permits rebars to be anchored reliably and in compliance with construction supervision.
Reference literature [1] DIBt approval Z-21.8-1648, issued 07.02.2000, valid until 28.02.2005: Reinforcement connection with HIT-HY 150 Hilti injection adhesive [2] DIBt approval Z-21.8-1648, issued 22.11.2000, valid until 28.02.2005: Reinforcement connection with HIT-HY 150 Hilti injection adhesive [3] DIBt approval Z-1.5-81, issued 25.03.1997, valid until 30.04.2002: Coupling connection of reinforcing steel BSt 500S, nominal diameter: 12.0 to 28.0 mm “Reinforcement connection PH“ [4] DIBt approval Z-1.5-103, issued 01.08.1997, valid until 31.07.2002: Mechanical connection of reinforcing steel BSt 500S, nominal diameter: 12 to 28 mm, by means of threaded coupling “Reinforcement screw connection HBS“ [5] DIBt approval Z-1.5-76, issued 24.04.1997, valid until 30.04.2002: Threaded coupling connections and anchorage of reinforcing steel with threadlike ribs BSt 500S-GEWI diameter: 12.0 to 32.0 mm [6] DIBt approval Z-1.5-96, issued 26.01.1998, valid until 31.01.2003: Mechanical connection of reinforcing steel BSt 500S by means of threaded sleeves and coupling bolts, diameter: 8 to 32 mm „PFEIFER reinforcement screw connections PH“ [7] DIBt approval Z-16.8-1647, issued 17.08.2000, valid until 31.08.2005: Reinforcement connection with UPAT UPM 44 adhesive [8] DIN 1045:1988-07, Concrete and reinforced-concrete; design and execution [9] DIN V ENV 1992-1-1:1992-06 (EC 2), Planning of reinforced-concrete and prestressed-concrete structures [10] Eligehausen, R.; Spieth, H.; Sippel,T.: Reinforcing bars secured with adhesive, loadbearing behaviour and design. Beton- und Stahlbetonbau 94 (1999), Heft 12, page 512 - 523, Ernst & Sohn Verlag
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[11] Eligehausen, R.; Spieth, H.: Reinforcing bars secured with adhesive, loadbearing behaviour and design. Der Prüfingenieur 04/2000, page 14 - 28, Bundesvereinigung der Prüfingenieure für Bautechnik e.V., 20095 Hamburg [12] DIN 488-1:1984-09, Reinforcing steel - grades, properties, characteristics [13] DIBt approval Z-1.6-IV NR1: Stainless, cold-formed, ribbed reinforcing steel in coils BSt 500 NR (IV NR), nominal diameter: 6.0-8.0-10.0-12.0-14.0 mm [14] DIBt approval Z-1.4-80, issued 05.06.1997, valid until 30.06.2002: Stainless, cold-formed, ribbed reinforcing steel BSt 500 NR, nominal diameter: 6, 8, 10, 12, and 14 mm [15] Lieberum, K.H.; Trägler, K.-D.: Evaluation report no. 127.3.00 dated 20.04.2000 about the rebar installer training course held on 18.04.2000 at Munich (not published)
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INVESTIGATIONS ON BONDING BEHAVIOUR OF TIE REINFORCEMENTS IN HISTORIC MASONRY Michael Raupach, Jeanette Brockmann, Axel Dominik, Michael Schürholz Institut für Bauforschung Aachen, RWTH Aachen, Germany
Abstract The masonry of historic buildings usually has been built in several layers. Damage often results from the fact that the masonry structure is no longer able to absorb the shear stress and transverse tensile stress which occurs in the masonry. In such cases, tie reinforcement can be installed as a repair measure in conjunction with mortar injection. As tie reinforcement involves interfering with the historic structure in an irreversible manner, bond testing has been carried out by means of pull-out tests on two types of bond specimens (tie anchor/injection material and tie anchor/injection material/natural stone), with the aim of minimising interference with the historic structure by selecting the smallest possible drill hole diameter. A mortar which is compatible with the surrounding material in many historic buildings was used for the experiments. The tie anchors took the form of threaded rods with and without screwed-on nuts and ribbed steel reinforcing rods (in each case in stainless steel). Greywacke, Obernkirchen sandstone and Weibern tuff were employed for the pull-out tests with natural stone specimens. The test results show that the type of stone can have a substantial influence on the properties of the injection mortar and thus on the quality of the bond between the tie anchor and the mortar. It is also evident that a reduction in the customary drill hole diameter and subsequent reduced interference with the existing building structure is possible under certain conditions.
443
1. Introduction The exterior masonry of historic buildings usually consists of several layers. It often comprises an ashlar facade layer, an interior layer and a filling between these two layers, consisting of rubble and mortar, for example. The interior layer in conjunction with the filling is frequently referred to as the "back-up masonry". The internal filling of such masonry may incorporate large cavities as a result of poor workmanship and/or leaching out of the mortar. The bond between the facade masonry and the "back-up masonry" and the bond within the "back-up masonry" itself is often no longer adequate and may compromise the stability of the facade and of the entire masonry. The inadequate bond in the "back-up masonry" itself can lead to "sagging" of the masonry and ultimately to its collapse. The example in Figure 1 shows the structure of typical historic multi-layer masonry. In order to anchor facade masonry ("facing shell") to the "back-up masonry" or to absorb the tensile stress which is present in the masonry and to restore the bond, repair work is generally carried out by means of tie reinforcement of the masonry in conjunction with mortar injection. Filling
Outer shell
Inner shell
Natural stone plug
Injection mortar
Figure 1: Cross-section through multi-layer historic masonry after repair by means of tie reinforcement Tie reinforcement in conjunction with mortar injection constitutes a consolidation measure which, when carried out correctly, is able to prevent or markedly reduce progressive damage to historic masonry as a result of stress and structural deficiencies. Due consideration must also be accorded to the fact that tie reinforcement involves the introduction of substantial quantities of foreign materials such as steel and injected mortar into the historic structure, however, whereby these materials must be compatible with the existing structure. Drilling of
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the holes which are required for tie reinforcement also always entails a significant loss of historic material. Such attendant damage is irreversible. To date, it has often been customary to use steel reinforcing rods as tie anchors. For reasons of corrosion protection, this has necessitated all-round encasement in a 20 mm coating of cement paste, which in turn has led to drilled holes with a diameter of 50 mm and more. Follow-up examinations /incl. 1/ have shown that the injection often failed to guarantee adequate corrosion protection. Today, it is thus recommendable to use tie anchors made of stainless steel. A comprehensive study of relevant literature has revealed a lack of research into tie reinforcement, in addition to which neither standards nor guidelines exist.
2. Objective The aim of the investigations was to expand the current extent of knowledge with regard to tie reinforcement measures. Information is to be obtained on the suitability for tie reinforcement applications of materials whose compatibility with historic structures has already been verified on various buildings. The conducted investigations serve to establish ways of reducing the extent to which historic structures are interfered with as a result of tie reinforcement. In this context, it is to be ascertained whether it is possible to reduce the drill hole diameters which are customary to date while at the same time maintaining a sufficiently strong bond between the tie anchor and the surrounding material. In practice, the use of tie anchors made of reinforcing steel has been predominant to date, with cement suspensions serving as the injection material. Anchoring elements made of stainless steel and screwed-on nuts were to be examined to ascertain their suitability in combination with a given injection mortar. The effects of different types of natural stone on the properties of the injection mortar and thus on the quality of bond also received due consideration.
3. Investigation programme 3.1 General In order to obtain information on the bonding behaviour between the tie anchor and the surrounding material, pull-out tests were carried out. These represent an empirical method which is also applied in reinforced concrete and reinforced masonry. The bond between various types of tie anchors and the injection mortar, which was not bonded with the surrounding material and thus was not subject to any changes in its properties as a result of the surrounding material, was to be investigated on the bond specimen consisting of the tie and injection material.
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The above-stated bond specimens consisting of stainless steel reinforcing rods and threaded stainless steel rods were employed as anchor variants. It was to be examined whether an improvement in bond quality is possible by varying the number of nuts and the spacing between the nuts. The influence of the rod diameter was to be determined by means of pullout tests with stainless steel reinforcing rods of 6 mm and 12 mm in diameter. Pull-out tests were carried out on the bond specimen consisting of tie/injection material/natural stone in order to assess the anchorage of the tie anchors in the ashlar shell of a historic masonry structure. As the stone properties can have a substantial influence on the mortar properties and thus on the bond quality (see e.g. /2/), the tests were performed with three different types of natural stone. The key stone properties affecting the mortar properties, such as capillary water absorption and pore radius distribution, were determined for each type of stone. As the manner in which the diameter of the drilled hole affects the supporting effect of tie anchors is of interest, holes of three different diameters (25, 41 and 51 mm) were drilled in the natural stone specimens. The suitability of various types of anchor for use as anchoring elements in the area of ashlar facing was investigated with the aid of bond specimens consisting of tie anchor/injection material/natural stone. As in the experiments on the tie/injection material bond specimens, stainless ripped steels and threaded stainless steel rods were employed. In order to determine the possible influence of nuts screwed onto the threaded rods, threaded rods were used without nuts, with one nut and with two nuts. As the mortar properties can have a substantial influence on the quality of the bond between the tie anchor and the injection mortar and on the properties of the mortar in conjunction with natural stone, they were also determined both for mortar bonded and non bonded with the respective natural stones.
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Pull-out tests
on composite specimen tie/ injection material/natural stone Greywacke Obernkirchen sandstone
on composite specimen tie/injection material
Weibern tuff
Key stone properties
Drilled hole diameter, dB dB = 25 mm dB = 41 mm dB = 51 mm
Reinforcing elements ripped rod dS = 6 mm
threaded rod dS = 6 mm without nuts
with
nuts
Threaded rod dS = 6 mm Different nut spacing
ripped rod
d S = 6 mm d S = 12 mm
Variation in no. of nuts
Figure 2: Test plan for the investigations 3.2 Materials 3.2.1 Tie anchors Steel rods ribbed of stainless steel (material reference number 1.4571 with an modulus of elasticity of about 166 MN/m²) were used exclusively as tie anchors for the experiments described below, in the form of stainless steel reinforcing rods and threaded rods with and without screwed-on nuts.
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3.2.2 Natural stones For each of the examined natural stones the capillary water absorption and pore radius distribution were determined. The pore radius distribution was determined by means of highpressure mercury porosimetry. The capillary water absorption of the natural stones was determined on the basis of DIN 52617, 05.81. Following determination of the capillary water absorption, the specimens were stored fully submerged in water, so as to determine the water absorption under atmospheric pressure in accordance with DIN 52103, 10.88. The properties of the three natural stones differ substantially in some instances. The greywacke stone possesses only very minimal capillary-active pore content, resulting in a correspondingly low level of capillary water absorption. The Oberkirchen sandstone possesses a markedly higher level of capillary-active pore content, resulting in a water absorption level four times higher than that of the greywacke. The Weibern tuff possesses by far the largest capillary-active pore content. The capillary water absorption level here is around 20 times higher than that of the greywacke stone. In comparison to the Obernkirchen sandstone, the tuff stone possesses a substantially higher proportion of capillary-active pores of small diameter, resulting in a markedly higher suction capacity for the tuff stone. Table 1 shows a summary of the investigated properties of the three natural stone types. Table 1: Properties of the different natural stones (mean values), natural stone type, apparent density (air dry), ρl, water absorption under atmospheric pressure, Wm,a, coefficient of capillary water absorption, ω, and total porosity, P Natural stone type 1 Greywacke Obernkirchen sandstone Weibern tuff
ρl kg/dm³ 2 2.56 2.15 1.25
Wm,a M.-% 3 1.47 5.46 28.43
ω kg/m²h0,5 4 0.28 2.59 19.74
P Vol.-% 5 2.0 15.8 40.3
On the basis of the classification of capillary water absorption according to Klopfer /3/, at ω=0.28 kg/m²h0,5 the greywacke may be regarded as a water-repellent building material, while the Oberkirchen sandstone and the Weibern tuff are to be regarded as highly absorbent building materials. 3.2.3 Injection mortar An injection mortar should be used whose compression strength and modulus of elasticity are adapted to the properties of the surrounding material, e.g. the existing mortar /4/. Higher compression strength is required when using the injection mortar to produce the bond
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between tie anchor and surrounding masonry in tie reinforcing operations, however, because the absorbable bond stress increases as the compression strength of the mortar rises. A modification of a commercially available mortar was employed in the planned tests. The following characteristics were determined on the mortar: -
Tensile bending strength after 28 d: Compression strength after 28 d: Shrinkage rate after 28 d: Water absorption:
1 N/mm² 3.5 N/mm² -2.4 mm/m 39.8 % by mass
The compression strength of the mortar as tested on a two-stone bond specimen, was as follows: -
Greywacke: Obernkirchen sandstone Weibern tuff
5.4 N/mm² 5.1 N/mm² 8.6 N/mm²
The investigations on the injection mortar are described in detail in /5/. A comparison of the compression strength values obtained here with those determined on the standard prisms (ßD,N=3.5 N/mm²) shows that the compression strength of the mortar attains greater values in conjunction with all three stone types. A value corresponding to approx. 1.5 times the standard value is attained for mortar bonded with greywacke and Obernkirchen sandstone, rising to almost 2.5 times with the Weibern tuff. In due consideration of the results of pull-out tests on reinforced masonry and reinforced concrete such as those conducted by Barlet /6/, Schießl/ Schwarzkopf /7/ and Rehm /8/, which reveal rising compression strength on the part of the mortar to be accompanied by an increase in the absorbable bond stress, the substantially greater joint compression strength of the drill hole suspension when bonded with the Weibern tuff would be expected to result in greater bond stress in the pull-out tests than applies with the other stone types.
4. Pull-out tests for tie/injection material The bonding behaviour between tie anchors and injection mortar was to be investigated by means of pull-out tests on anchors from mortar cubes, on the basis of the RILEM/CEB/FIP recommendations. The following changes were carried out with regard to the recommendations: -
The edge length of all mortar cubes was 200 mm, irrespective of the diameter of the anchor elements. The bond length was set at lv=200 mm.
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The anchor rods were secured in horizontal position in the centre of the formwork such that they protruded out of the concrete cube by approximately 15 mm on either side. The formwork was filled with the injection mortar according to standard practice by carefully pouring from above at right-angles to the reinforcing element. Figure 3 shows an overview of the produced test specimens. Filling direction
F
6
F
50 mm 4 25 4 25 4 25 4 25 4 30
F
50 mm 4
6
50 mm 4
75
4
4
50
4 38
6
50 mm 4
6
50
F
67
F
6
100
F
4 42
6
Ripped rods ∅ 6mm und 12 mm
Threaded rods ∅ 6mm
200 mm
200 mm
Figure 3: Overview of produced test specimens The pull-out tests to retrieve the anchor rods from the injection mortar produced the following results:
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-
The maximum pull-out forces stood at approx. 5-6 kN for the threaded rods with and without nuts, while for the ripped rod they were below 4 kN.
-
A doubling of the rod diameter from 6 to 12 mm resulted approximately in a two-fold increase in the maximum absorbable pull-out force.
The threaded rods with screwed-on nuts provide the highest pull-out forces, irrespective of the number of nuts. Although the threaded rods without nuts attain a comparable maximum pull-out resistance, at a very low level of attendant slippage failure of these rods abruptly ensues after reaching this maximum. By screwing on nuts, failure of the rods is heralded by increasing slippage, while a high load level is maintained (see fig. 4). The ripped rods sustain substantial forces under the given conditions only after a certain degree of slippage (approx. 0.5 mm). This means that such rods can be deployed where such measured deformations are not of vital importance to the load-bearing behaviour of a building. Although the rod does not fail abruptly when bonded with the mortar, as is the case with threaded rods without nuts, a rapid decrease in strength is nevertheless observable, in combination with increasing slippage.
Figure 4: Bond failure in test specimens with threaded rods and screwed-on nuts
5. Pull-out tests for tie/injection material/stone After production, the test specimens were covered with a moist jute tarpaulin and a layer of PE foil for 7 days. The test specimens were subsequently stored in a room climate of 20°C/65% rel. humidity for a further 21 days. The pull-out tests were conducted 28 days after production of the test specimens. The loading rate was selected to be 50 N/sec. As in the pull-out tests on the tie anchor/injection mortar test
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specimen, the deformations of the tie anchor were measured both on the load side and on the side facing away from the load, by means of inductive displacement sensors.
Figure 5: Test device for pull-out tests A load-distributing metal plate was placed on the test specimen, in order to eliminate additional deformation components, such as might occur as a result of compressive strain on the natural stone under the legs of the test device. The standard bond stress, τm, is determined at a slippage, x2, of 0.1 mm, in accordance with /9/. For comparative purposes, the mean bond stress levels at x2=0.5 mm and at x2=1.0 mm are also specified. Three different failure modes were determined in the course of the pull-out tests. 1 Failure mode I:
Failure in the injection mortar/natural stone bond zone (only occurred at Weibern tuff with drill hole ∅ 25 mm)
2 Failure mode II:
Failure in the tie anchor/injection mortar bond zone (occurred at nearly all specimens with Oberkirchen Sandstone and some with Greywacke)
3 Failure mode III:
Combined failure mode consisting of failure modes I and II (occurred at nearly all specimens with Weibern tuff and Greywacke)
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Ancher Slippage
no nut 0,1
0,5
1 nut 1
0,1
0,5
mm
2 nuts 1
0,1
ripped
0,5
1
0,1
0,5
1
N/mm² Greywacke
∅ 25
0,21
0,32
0,22
0,48
0,51
0,45
0,21
0,40
0,44
1,38
1,74
1,67
∅ 41
0,51
0,48
0,42
0,53
0,61
0,61
0,78
0,71
0,63
1,37
1,62
1,59
∅ 51
0,90
0,74
0,58
1,19
1,16
0,75
0,88
0,92
0,88
1,38
1,63
1,57
∅ 25
0,00
0,00
0,00
0,02
0,03
0,11
0,21
0,18
0,33
0,18
0,27
0,45
∅ 41
0,19
0,20
0,22
0,32
0,37
0,51
0,18
0,18
0,41
0,45
0,51
0,73
∅ 51
0,34
0,33
0,41
0,16
0,15
0,15
0,31
0,35
0,55
0,42
0,33
0,35
∅ 25
0,03
0,06
0,10
0,12
0,23
0,27
0,12
0,14
0,20
0,20
0,33
0,49
∅ 41
0,27
0,11
0,10
0,05
0,16
0,28
0,17
0,29
0,34
0,11
0,21
0,30
∅ 51
0,30
0,26
0,23
0,28
0,25
0,21
0,33
0,24
0,22
0,04
0,16
0,24
Oberkirchen Sandstone
Weibern tuff
Table 2: Bond stress measured at the specimens tie/injection material/stone
6. Discussion of the results It is evident that the surrounding material in contact with the mortar can have a substantial influence on the quality of the bond between tie anchor and mortar and between mortar and stone. The correlation between an increase in the compression strength of concrete or mortar and an attendant rise in absorbable bond stress which has been established in tests in the fields of reinforced concrete and reinforced masonry does not apply to the tests conducted here. Although the lowest joint compression strength was determined in the test specimens made of greywacke, the attained bond stress levels are substantially higher than those for the test specimens consisting of Obernkirchen sandstone and Weibern tuff. Despite the fact that the joint compression strength is markedly higher in some instances, no absorbable pull-out forces or bond stress levels which would be adequate in practice are attainable with the Oberkirchen sandstone or the Weibern tuff, irrespective of the drill hole diameter and the type of tie anchor. A reduction in the drill hole diameter which is predominantly used in practice at present and an attendant reduction in the scope of interference with the historic structure while maintaining sufficiently large pull-out resistance appears to be possible for greywacke only, using ripped rods. When using threaded rods with screwed-on nuts it must be considered in each individual case whether the drill hole diameter can be reduced at the expense of reduced load-bearing capacity.
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When threaded rods are to be employed in practice, with regard to the load-deformation behaviour it appears expedient to screw on nuts, as deformation-induced failure will then be indicated beforehand, whereas threaded rods without nuts fail abruptly, without prior warning. As the tests did not reveal the number of nuts to have any influence, it is recommended to screw on one nut in the area of end anchorages and 4 nuts per metre of length over the entire length of the tie anchor. No optimum spacing between the nuts was ascertainable. The theoretically most favourable nut spacing would appear to be smaller than the smallest spacing selected in the tests. Investigations into a further reduction of the nut spacing will not be expedient until the factory production of such rods is in prospect, as screwing on nuts at such a minimal spacing is very work-intensive. It would appear expedient to develop a tie anchor with idealised rib spacing, which could be used in conjunction with a "low-strength" bonding mortar for tie reinforcement applications. In the tests in which bond stress levels which permit practical application were attained, the ripped rods proved the most effective type of tie anchor, on account of their favourable surface structure and the attendant superior load transfer between tie anchor and injection mortar.
7. Outlook As the failure of the bond between mortar and stone prevented the absorption of large pullout forces in a large proportion of the tests, particularly with regard to the test specimens consisting of greywacke, it should be investigated whether the bond between stone and mortar can be improved by roughening the walls of the drill hole. The investigations with the given materials in conjunction with the study of the relevant literature underline the fact that no sound findings which would enable generally valid conclusions are available on the load-bearing behaviour of tie anchors in masonry. It is thus imperative to carry out preliminary tests on the building concerned in each individual case. The mortar property should be adapted to the specific applications concerned, particularly as tests on injection mortars which are commonly used in practice have shown that there is no such thing as a "shrinkage-free" mortar. The ideal mortar should be capable of sustaining deformations, guaranteeing an adequate bond between the mortar and the surrounding material and, where applicable, between tie anchor and mortar, while maintaining compatibility with the existing building structure. Investigations aimed at researching the bonding behaviour of reinforcing elements with various modules of elasticity adapted to historic building structures would be expedient.
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8. References 1.
Maus, H.: Injiziertes und bewehrtes altes Mauerwerk: Untersuchungen zur Wirksamkeit und Dauerhaftigkeit der Instandsetzungsmaßnahmen. In: Arbeitshefte des Sonderforschungsbereiches 315 “Erhalten historisch bedeutsamer Bauwerke“, Heft 32, Karlsruhe, Technische Hochschule, Diss., 1995
2.
Stein, Chr.: Verfugmörtelentwicklung für drei Natursteinarten (Postaer und Cottaer Sandstein sowie Zwickauer Kohle-Sandstein). Aachen, Technische Hochschule, Fachbereich 3, Diplomarbeit, 1993
3.
Klopfer, H.: Feuchte. – In: Lehrbuch der Bauphysik; Schall, Wärme, Feuchte, Licht, Brand, Klima. Stuttgart, Teubner-Verlag, 3. neubearbeitete und erweiterte Auflage, 1994
4.
Haberland, D.; Debilius, V.: Untersuchungen zur Sicherung von historischem Mauerwerk durch Vernadelung. Berlin: Deutscher Ausschuß für Stahlbeton, 1988. – In: Beiträge zum 20. Forschungskolloquium des Deutschen Ausschusses für Stahlbeton am 24. Und 25. März 1988 an der Universität und Gesamthochschule Kassel, S. 45-50, 1988
5.
Schürholz, M.: Zur Tragfähigkeit von historischem Natursteinmauerwerk durch Vernadelung – Verbunduntersuchungen. Increasing load-carrying capacity of historical masonry through tie reinforcement - bond investigations. Aachen, Technische Hochschule, Fachbereich 3, Institut für Bauforschung, Diplomarbeit, 1999. - (unveröffentlicht)
6.
Barlet, U.: Verbund zwischen Stahl und Mörtel im bewehrten Mauerwerk. München, Technische Universität, Diss., 1989
7.
Schießl, P; Schwarzkopf, U.: Verbundverhalten von feuerverzinkten Betonrippenstählen in Mauerwerk. In: Betonwerk + Fertigteiltechnik 51 (1985), Nr. 11, S. 735-740, 1985
8.
Rehm, G.: Über die Grundlagen des Verbundes zwischen Stahl und Beton. – In: Schriftenreihe des Deutschen Ausschusses für Stahlbeton (1961), Nr. 138, Berlin, Ernst & Sohn, 1961
9.
Meyer, U.: Zur Rißbreitenbeschränkung durch Lagerfugenbewehrung in Mauerwerkbauteilen. In: Aachener Beiträge zur Bauforschung (1996), Nr. 6, Technische Hochschule Aachen, Diss., 1996
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ACTUAL TRENDS IN CHEMICAL FIXINGS: FROM CAPSULE TO INJECTION SYSTEMS Joachim Schätzle fischerwerke Artur Fischer GmbH & Co. KG, Germany
Abstract This paper compares the applications and properties of chemical fixings based on glass capsule systems and injection systems. Glass capsule systems have been on the market for nearly 40 years. They have been continuously improved during that time and have reached a very high performance level. The younger injection systems, initially used only in minor applications, have reached meanwhile the same performance. Due to their higher flexibility they replace more and more capsule systems.
1. Historical background Chemical fixings, so called bonded anchors are well known and established on the market for a long time. The first product, which was already introduced in 1962, was based on a glass capsule system. In a cylindrical drill-hole a threaded rod has to be installed by an impact drilling machine with an impact rotational process. Since 1962 several new generations of capsule type anchors have been introduced on the market with improved properties: Second generation capsule anchors: The unsaturated polyester resins used in the first generation capsule anchors have been replaced by vinyl ester resins. Long-term tests of unsaturated polyester type bonded anchors have shown considerable loss of bond strength in wet concrete due to an alkaline attack (Saponification) on to the ester linkage1). Vinyl esters are very insensitive against saponification.
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Third generation capsule anchors: In generation 1 and 2, the solvent styrene is used as a reactive thinner. Meanwhile styrene is suspected of being cancerogenic. As a consequence some manufactures have replaced styrene against other reactive thinners which are not harmful. Fourth generation capsule anchors: Bonded anchors of generation 1-3 are suitable for non-cracked concrete. They are not approved to be used in cracked concrete. In a crack of 0.3 mm width the loss of pull-put load is in the range of 50 % 2) In 1993 the first capsule bonded anchors approved for cracked concrete appeared on the market. These torque-controlled bonded anchors are installed in cylindrical holes, the load transfer is realized by mechanical interlock of cones in the bonding mortar. Currently products from all the 4 generations are offered on the market.
2. Bonded anchors based on injection systems The components used for injection systems as well as their chemical reactions are very similar to those of capsule systems. Today injection systems equivalent to all 4 generations of capsule systems are available. For a long time the only approved application for injection systems was the use in hollow bricks. In solid materials considerable problems arose in cases where the drillhole was not cleaned properly. In regions with high security levels and corresponding approval restrictions injection systems have been applied only in minor applications or in perforated bricks and hollow blocks. Meanwhile the situation has changed. Some new formulations with improved properties are on the market. As a consequence more and more applications, where traditionally capsule type anchors were used, are now realized with injection systems. Furthermore new fields have been found, where capsules systems were not suitable. In the following chapter some of these improvements of injection systems are described and the advantages of both types of bonded anchors in different applications are compared.
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3. New developments of injection systems 3.1 Behavior in not perfectly cleaned drill-holes In solid anchoring bases first generation injection systems suffered from poor adhesion in not properly cleaned drill-holes. In the case of capsule systems, drill-hole cleaning is not very essential, because the friction of the broken glass and of the quartz sand cleans the concrete surface during the rotational setting process of the anchors. Due to this fact, the traditional injection systems, based on polyester or vinylester resins are not approved in Germany for the anchorage in concrete. In the case of new developed injection systems, so called hybrid systems, the loss of adhesion, due to not properly cleaned drill-holes is considerably reduced. In the following figure the relative bond strength of a vinylester and a hybrid injection system are compared. The values are normalized to 100 under cleaned conditions.
Influence of Hole Cleaning method
Hybridsystem Vinylester resin
120 100 80 60 40 20 0 Cleaned (2xblow Uncleaned (ETA- Uncleaned (2xblow out) out, 2xbrush, Regulation) (1xblow out, 1xbrush, 2xblow out) 2xblow out)
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Hybrid systems are characterized by a four-component reactive system: In the first chamber the organic resin is mixed with cement, the second chamber contains an admixture of the organic hardener (peroxide) with water, the hardener of the cement. Due to the organic part, quick hardening, with a high end-load is achieved. The inorganic part, cement and water, improves among other things, the adhesion to the drillhole. First products with approvals for rebar applications are on the market. 3.2. Behavior at high temperature In the case of injection systems based on unsaturated polyester, the failure load is continuously reduced with increasing temperature. At 100° C the bond strength is reduced to about 20 % of initial value. In the case of pure organic vinylester systems, the reduction is less than 50 %. Due to the cement content of hybrid systems, their temperature resistance is further improved. 3.3 Rebar applications For the connection of rebars hammer capsules are applied. As the drill-hole is often very deep, several capsules have to be applied in one application. Due to the strong forces, which are necessary to break the glass and to set the rebar, a high pressure at the end of a drill-hole can destroy the concrete cover. The ratio length / diameter of the drill hole which can be realized is often below technical requirements. There are less restrictions for the new hybrid injection systems due to the lower pressure during the setting of the rebar. Consequently first approvals in Germany for rebar applications were issued for hybrid injection systems. Up to now there are no hammer capsule products approved in Germany. 3.4 Behavior in cracked concrete Up to the beginning of 2001 only capsule based bonded anchors were approved for the application in cracked concrete. Since March 2001, the first injection system is DIBtapproved for cracked concrete. Especially remarkable of this system is the low installation safety factor of γ2= 1.0 which allows the realization of high permissible loads. Another advantage of this injection system is the high flexibility. One cartridge type can be used for all anchor sizes, whereas in the case of capsule systems, for each anchor size a separate capsule is necessary.
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3.5 Other applications of injection systems Apart from the possible applications of capsule systems, injection systems can be used in a while range of additional applications. In perforated bricks and hollow blocks they can be used in connection with injection anchor sleeves due to the thixotropic behavior of the mortar. This effect can not be realized with capsule systems. In nearly all other anchoring bases injection systems have found applications among them a lot there capsule systems are prohibited.
4. References 1. 2.
Eligehausen, R. and Mallée, R., ‘Befestigungstechnik im Beton- und Mauerwerkbau’, (Ernst & Sohn, Berlin 2000). Eligehausen, R., Mallée, R. and Rehm, G., ‘Befestigungen mit Verbundankern‘, Betonwerk + Fertigteiltechnik 1984, 686-692.
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PERFORMANCE OF BONDED ANCHORS IN DEPENDENCE OF INSTALLATION CONDITIONS, STATE OF CURE - DEFORMATION BEHAVIOR AT ELEVATED TEMPERATURES G.W. Ehrenstein, A. Tome Lehrstuhl für Kunststofftechnik, Universität Erlangen-Nürnberg, Germany.
Abstract At the moment many manufactures of bonded anchors are changing the resin base from unsaturated polyester (UP) with styrene content to styrene-free reaction resins. The longterm creep behaviour at static or dynamic loads, especially after installation conditions which negatively influence the curing is not completely known yet. In this paper the creep behaviour of two different commercially available bonded anchors (capsule systems) for use in concrete are examined under normal conditions and at elevated temperatures for different installation conditions and different static loads.
1. Introduction Bonded anchors based on reaction resin, i. e. high filled duroplastic resin mortars, have played a major role in civil engineering for more than 20 years. They are used for highstrength anchoring in concrete and masonry. The first form of chemical anchoring was cementitious grounting of anchor bolts. This method is still used today. Since the middle 1970’s chemical anchoring in high-strength conditions using epoxies, nowadays unsaturated polyester, vinylester (epoxymethacrylates) or vinylesterurethanes (urethanmethacrylates) has become an increasingly popular method of anchoring. 1.1. Installation of bonded anchors There are different installation techniques for bonded anchors: • Capsule placed in the hole and anchor driven in mechanically either by machine or by hammer, Fig. 1a. • Bonding material injected or poured into the hole, the anchor inserted manually or mechanically, Fig. 1b. • Anchor inserted into the hole and bonding material introduced into the hole via the anchor or around the anchor.
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Popular anchoring devices today are the glass/plastic capsule method or prepacked injection systems with coaxial or side by side cartridges.
Resin
Filler Hardener
Capsule placed in the hole Anchor driven in by machine
Capsule
e.g. Concrete
a)
Bonded material injected in the hole Anchor rod inserted manually
Anchor Sleeve
b)
e.g. Masonry
Fig. 1:
Installation techniques for bonded anchors
Regardless of the installation techniques the installation of bonded anchors is divided into the following steps: 1. Mixing of the components resin, hardener and filler or inserting the ready-to-cure mortar into the hole (the order depends on the installation technique, e.g. capsule system or injection system). 2. Inserting the anchor rod within the working time. 3. Curing the resin mortar. 4. Applicating the load after expiration of the recommended curing time according to the manufacturers instructions. 1.2. Problems of installation and curing conditions A striking feature of composite anchors based on reaction resins is that, in contrast to other anchor materials, they are manufactured yet when the attachment is being done.
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Due to the chemical reaction the curing of resin mortars depends on the installation and curing conditions e.g. the environmental conditions and surrounding temperature. Earlier experiments showed that the curing reaction can be negatively influenced by low temperatures or wet conditions (e.g. water-filled hole), /1, 2/. This effect is measurable e.g. as lower glass transition temperatures in dynamic torsion-pendulum-tests. The degree of cure can affect numerous properties of the bonded anchors. An uncomplete degree of cure can lead to higher creep-displacements and lower chemical resistance and ageing behaviour /2/. Bonded anchors are often subjected to changing temperatures. In Western Europe temperatures between -5 °C and +40 °C in concrete or masonry are expected. In special applications the surrounding temperature can be more than 80 °C to 100 °C. So the precise knowledge of processing technique and the influence of environmental conditions (temperature, water) on the curing behaviour are necessary for a constant quality of the applicated bonded anchors.
2. Experimental 2.1. Testing the curing behaviour and degree of cure of resin mortars Three test procedures for checking the reactivity and the degree of cure of resin mortars have be proved to be useful /1/. • The temperature measuring while installing and curing the resin mortar is used to get statements on the resin reactivity, on the influence of surrounding temperatures, of concrete or components of the bonded anchor (capsule, anchor rod, concrete) and on the different curing behaviour at different places in the hole. • The dynamic torsion-pendulum-test (DMA) is used to measure the glass transition temperature and the mechanical behaviour by interpreting the temperature dependent stiffness and mechanical damping. In addition different degrees of cure and the influence of e.g. water/moisture on the mechanical behaviour can be distinguished. • The differential scannig calorimetry (DSC) is used to determine the degree of cure by evaluating the reaction enthalpy. This analyses leads to very exact results for resins and other polymeric materials without water content. In case of a water/moisture content the resolution of the measurement (exothermic peak) is negatively affected by the endothermic peak of the water and therefore not recommended. 2.2. Testing the mechanical behaviour The mechanical behaviour of bonded anchors is usually determined by short-time pullout tests, long-term creep-tests and dynamic tests e.g. with the hysteresis method. In addition the installation safety under critical conditions must be verified by tests. To evaluate the dependence of the mechanical behaviour on the curing conditions these tests must be carried out under different installing and surrounding conditions.
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3. Experimental 3.1. Glass transition temperature The glass transition temperatures Tg were measured with specially manufactured specimens (rectangular shape) made from the content of the capsule. The curing conditions were kept equal as far as possible to the installation conditions. The measurement was done by DMA MK III in bending mode with a heating rate of 2 °C/min and a frequency of 10 Hz. The glass transition temperature Tg was taken as half height of the modulus step. Again, we only discuss the relative differences not the absolute values of the glass transition temperature in dependence of the „installing conditions“. 3.2. Materials and concrete Two different commercially available bonded anchors (capsule systems) for use in concrete were used for the tests. The one bonded anchor (specimen B) is based on unsaturated polyester with styrene-content, the other bonded anchor (specimen A) is a newly developed styrene-free system based on vinylester-methacrylates. In Germany the allowed characteristic load of bonded anchors size M12 is 7 kN in concrete B15 and 12 kN for a higher compressive strength of concrete. The tests were carried out in concrete B25 with a compressive strength of 21 MPa and a gross density of 2.2 kg/m3 (size 200 x 200 x 200 mm). 3.3. Test Procedure The anchors were installed and cured as specified by the manufacturer. The examined installation conditions are „normal condition“ (23 °C, reference), „low temperature“ (-5 °C) and „wet condition“ (water-filled hole, 23 °C). The specimens „low temperature“ were annealed at 23 °C for 12 h after expiration of the recommended curing time at – 5 °C. In a force test unit with heating cabinet the static loads (12 kN, 18 kN and 24 kN) were applied at normal conditions (23 °C/50% r.m.) and at elevated temperatures (40 °C, 60 °C and 80 °C) while the creep-displacement was measured. Depending on the characteristic load the chosen static loads while creeping are up to a factor of 3 to the allowed characteristic load. 3.4. Evaluation The characterization of the creep behaviour of bonded anchors in dependence of installing conditions, applied static loads and surrounding temperature was carried out in comparison with „normal conditions“ (installing condition 23 °C) at each tested surrounding temperature and applied static loads. The rating only refers to the differences in the creep behaviour of bonded anchors which are installed under „normal condition“ to critical conditions e.g. „low temperature“ and „wet condition“. Regarding the large creep-displacements at the beginning and the following increase a measuring time of 50 h was chosen. The data-points were extrapolated to larger time-ranges with the Findley-approximation. Then we can discuss the principal influence of the installing
464
condition at ambient temperature and at elevated temperatures. We cannot rate the absolute creep-displacements, because the test results are single-experiment data, so that there is no statistical exclusion.
4. Results and Discussion 4.1. Glass transition temperatures / loss in stiffness The glass transition temperatures Tg depend on the installation conditions, table 1. The estimated Tg for specimen A are in the range above 85 °C, for specimen B about 30 °C below. The very low Tg of specimen B under „wet condition“ might be due to the effects to the preparation a specially manufactured specimen with a water content of 10% in weigth. The loss in stiffness can be characterized at one hand by the temperature T50% at which 50% of the stiffness at –100 °C occur. On the other hand, the relative stiffness E* at ambient temperature (25 °C) refered to the stiffness at –100 °C characterizes the residual relative stiffness at ambient temperature. Specimen A (sytrene free) shows a significant decrease of T50% as well as E* under critical installation conditions (wet and low temperature). Therefore the temperature dependent stiffness of the resin seems to be reduced. Specimen B (styrene containing) is susceptible to "wet conditions", low temperatures seems not to affect the stiffness very critical. Altogether, the loss in stiffness as discussed for T50% and E* is more distinctive at specimen B (styrene containing) than specimen A (styrene free). These effects are strongly determined by the chosen resin mortar and should not be generalized. "normal conditions" Tg
≈
loss in stiffness E* T50% 70 °C 75%
"wet conditions" Tg
≈
loss in stiffness E* T50% 9 °C 45%
"low temperature" Tg
≈
loss in stiffness E* T50% 25 °C 48%
90 °C 85 °C Specimen A 95 °C (styrene free) Specimen B 50 °C 42 °C 72% -10 °C -10 °C 14% 50 °C 46 °C 75% (styrene containing) Table 1: Glass transition temperature and loss in stiffness of the examined resin mortars. Tg: glass transition temperature in °C (DMTA); T50%: temperature at 50%stiffness decrease refer to –100 °C; E*: relative stiffness at 25 °C refer to stiffness at –100 °C Additionally to table 1, the DMA-curves of both reaction resins are illustrated in Figure 2. In the relevant temperature range (–5 °C up to +40 °C) Specimen B shows a more distinctive decrease in stiffness than specimen A.
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Fig. 2: DMTA-curves for the different state of cure of specimen A, top, and B, bottom 4.2. Creep-behaviour in dependence of the installing conditions The left side of Figure 3 shows the creep-displacement as function of time of specimen A (styrene-free resin mortar) for the examined installation conditions at 23 °C and 80 °C testing temperature (static load 24 kN). The creep-displacements are especially under „wet condition“ but also under „low temperature“ significant bigger than under „normal condition“. In addition the creep-speed, which correlates with the gradient of the creepcurve, is much higher. This effect is at a surrounding temperature of 80 °C, lower figure,
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much stronger than at ambient temperature, upper figure. The estimated glass transition temperatures of specimen A are in the range above 80 °C, that means at surrounding temperatures of 80 °C the glass transition temperatures were not exceeded but almost reached. For the high temperature the „wet condition“ leads to creep-displacements up to 5 mm in the first 5 hours. The measured creep-displacements do not exceed the critical values under ambient temperature and at 80 °C for „normal condition“ and „low temperature“ for static loads up to a factor of 3 referring to the characteristic load. In comparison the creep-displacement of specimen B (styrene content resin mortar) at testing temperature 23 °C is more critical at installing condition „low temperature“, figure 3 right. At „wet condition“ the creep displacement is even less critical than „normal condition“. This is not in advance with the low glass transition temperature found in DMA measurements and has to be investigated further. At testing temperature 80 °C (glass transition temperatures are exceeded 30 °C) the applied load of 24 kN leads to creep-displacements up to 5 mm in the first hour. This bonded anchor is much overloaded at these surrounding conditions for all installation conditions.
1.5
"Normal Condition" 23oC/Dry/20min
0.5
0 10 20 30 40 50 0
23oC Specimen B - M12 F = 24 kN Conctrete C20
4
"Wet Condition" 23oC/Water/40min "Low Temperature" -5oC/Dry/5h
1
0
5
23oC Specimen A- M12 F = 24 kN Concrete C20
Creep Displacement [mm]
Creep Displacement [mm]
2
3 2 1 0
2000 4000 6000 8000 10000
"Low Temperature" -5oC/Dry/5h "Normal Condition" 23oC/Dry/20min "Wet Condition" 23oC/Water/40min
0 10 20 30 40 50 0
Time [h]
5
80oC Specimen A - M12 F = 24 kN Concrete C20
1.5
Creep Displacement [mm]
Creep Displacement [mm]
2
"Wet Condition" 23oC/Water/40min
1
"Low Temperature" -5oC/Dry/5h
0.5
0
"Normal Condition" 23oC/Dry/20min
0 10 20 30 40 50 0
2000 4000 6000 8000 10000
"Low Temperature" -5oC/Dry/5h
4
"Wet Condition" 23oC/Water/40min
3
"Normal Condition" 23oC/Dry/20min
2 80oC Specimen B - M12 F = 24 kN Concrete C20
1 0
0
0.5
1 0
2000 4000 6000 8000 10000
Time [h]
Time [h]
Fig. 3:
2000 4000 6000 8000 10000
Time [h]
Creep-displacement of Specimen A (left) and Specimen B (right) for different installing condition at ambient temperature (top) at elevated Temperature (bottom)
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4.3. Dependence of the applied load at elevated temperatures Figure 4, left, shows the dependence of the creep-displacement for different applied loads for bonded anchors which are all installed under „normal condition“ and tested at 80 °C. Specimen A shows a minor influence between the creep-displacement at applied loads up to 18 kN, although the creep speed (curve gradient) seems to be smaller for an applied load of 12 kN. An applied load of 24 kN leads to larger creep-displacements and creep-speeds. Specimen A is even for applied loads of 12 kN overloaded at 80 °C. 4.4. Dependence of the surrounding temperature With a reduction of the surrounding temperature the creep-displacement and the creepspeed can be reduced rapidly even for high applied loads (24 kN), especially in the range of 60 to 40 °C for specimen A, figure 4 right. The closer the surrounding temperature gets to the range of glass transition temperature the stronger are the creep displacements. Specimen B as already shown in figure 3 is overloaded for that kind of applied load at temperatures above ambient temperature. 2
80 oC Specimen A - M12 "Normal Condition" 23oC/Dry/20min Concrete C20
1.5
Creep Displacement [mm]
Creep Displacement [mm]
2
24 kN
1 18 KN
0.5 12 kN
0
0 10 20 30 40 50 0
2000 4000 6000 8000 10000
Time [h]
Fig. 4:
24 kN Specimen A - M12 "Normal Condition" 23oC/Dry/20min Concrete C20
1.5
1
80oC 60oC
0.5 40oC 23oC
0
0 10 20 30 40 50 0
2000 4000 6000 8000 10000
Time [h]
Creep-displacements of specimen A for different load levels (left) and different surrounding temperatures (right).
5. Conclusions It was shown, that the installation condition influence the creep behaviour of the examined bonded anchors. At surrounding temperatures of 23 °C the creep displacement of the installation conditions „low temperature“ and „wet condition“ exceed the creep displacement under normal conditions by a factor of up to 3. The styrene-containing bonded anchor (specimen B) is more sensitive to the installation conditions than the styrene-free system (specimen A). Its creep behaviour increases strongly at elevated temperatures. This effect correlates with the measured glass transition temperatures. While the creep-displacement of specimen A close below its estimated glass transition temperatures is stronger than at ambient temperatures, the creep-displacement of specimen B about 30 °C above its glass transition temperature is rapidly increased. Specimen B is much overloaded at that kind of temperatures even for reduced static loads.
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Therefore the long-term temperature should not exceed about 40 °C for the examined styrene-containing (specimen B) and not exceed about 80 °C for the styrene-free bonded anchors (specimen A). Otherwise the load has to be reduced significantly. If these results are transferable to other available bonded anchors with styrene-free or styrenecontaining needs to be characterized in further examinations.
6. References Journal article: Bittmann, E., Tome, A., Ehrenstein, G.W. Aushärtung und Tauglichkeit von Verbundmörtelsystemen für Dübel // Bauingenieur 72 (1997), P. 433 - 437 Book: Bittmann, E., Ehrenstein, G.W. Duroplaste - Aushärtung, Prüfung, Eigenschaften // Carl Hanser Verlag, München 1997 Paper in proceedings: Letsch, R. On the behavour of deformation of epoxy-resin mortars at steady and nonsteady temperatures // ICPIC ‘84 „Polymere in Beton“, September 1984, Darmstadt
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STUDY ON THE PERFORMANCE EVALUATION OF THE NEW CAPSULE TYPED BONDED ANCHOR Masayuki YONETANI*, Akira FUKUOKA*, Yasuhiro MATSUZAKI** *Asahikasei Corporation ,Japan **Science University of Tokyo, Japan
Abstract In Japan, after Hanshin earthquake disaster in 1995, the post-installed bonded capsule anchor is used widely, specially to reinforce against the earthquake. And that reliability and durability have been recognized . To show more performance of anchor, we found the relation of resin composition and the anchor tensile strength. And moreover, we attained the capsule composition which is satisfied that resin performance. We consider the safety in use, and developed the newtype bonded capsule anchor. We report the excellent performance of this anchor. Moreover, we developed high speed and low noise diamond core drill , and we checked also about the performance when this drill bores.
1. Examination of Resin Detailed examination was performed about the composition of resin in development of the new-type capsule anchor. Optimum composition of resin was considered, we use the epoxy acrylate resin (vinyl ester resin) which has strong durability of resistance to concrete alkali as the base polymer. In this examination, we could get especially interesting knowledge there is the big correlation of the the physical properties (share strength ) of the resin hardening thing and tensile strength of the bonded anchor. It found out that this share strength was high correlation with the molecular structure of base resin and the structure of the reactive monomer, concentration and the viscosity. Based on the above mentioned result, we attained completing optimum composition of a reactive monomer, a polymerization prohibition agent, a catalyst, etc.
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2.Development of the new-type capsule anchor The conventional bonded anchor took double glass tube structure, the hardener in inner tube ,resin and aggregate were enclosed with the outside glass tube. And resin contained the ingredient of which we are anxious about toxicity and inflammability, such as styrene. The following subjects occurred in this capsule. (1) Badness of handling and danger by using glass tube (2) Dispersin in the tensile strength due to un-uniformity hardening by inclination of hardening agent (3) Danger and harmful by using styrene monomer In order to solve these subject, the following measures attained us to the development of new-type capsule anchor. (1) film foil type (2) 1 chamber structure where hardening agent was distributed in resin (3) Adoption of resin which contain the high molecule weight monomer The structure of the new-type capsule anchor is shown in Fig. 1. a.【resin】 viscous ○ c.【hardening agent】
d.【vessel】 plastic film ● b.【aggregate】 ［expressio
HP-10～ AR CHEMICAL
HP-○ ○ ASAHIKASEI
L HP-22～ AR CHEMICAL
HP-○ ○ ASAHIKASEI
L
Fig. 1 Structure of the new-type capsule anchor
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3.The basic performance of the new-type capsule anchor The basic performance of the new-type capsule anchor developed this time is shown below. (1) Tensile strength (Fig. 2) (2) Inbedding Resistance (Fig. 3) (3) Inflammability (Fig. 4) The performance which was excellent also in which performance as compared with the conventional glass pipe type was shown.
Past type (glass tube） M24
M22
M20
M16
M12
M10
Tensile strength (KN)
350 M10 M12 M16M20M22M24 300 従来タイ プ 38 (ガラ 57ス 96 164 ## 311.3 250 ー タイ 47プ 71 (フィ 122 ル 217 ## 313 ニュ 200 150 100 50 0
New-type (film foil）
bolt size
Fig. 2. Tensile strength
M16 M30 従来タイ プ (ガラ ス 135 720 600 ニュ ータイ プ (フィ 117 ル 610 800
200
Past type
bolt size
M30
0
Past type
(glass tube） New-type
(film foil）
Fig. 3. Inbedding Resistance
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Explosion 80℃
(glass tube）
New-type
400
M16
Inbedding resistance
Inbedding time×load
Burn 90℃
(film foil）
Fig. 4.Inflammability
4. Evaluation on the actual use conditions The evaluation results on the actual use conditions are worked up too. The tendency of the performance was the same as that of the conventional glass tube type. An example is shown below. ①Relation with concrete compression strength (Fig.5) ②Relation with bore hole depth (Fig.6)
96 5.18 6.07
Tensile strength（ton）
14 12
354 9.92 10.34
477 11.7 12.2
10 8 6 4 2
Past type (glass tube) New-type (film foil)
0 0
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Fig.5
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249 7.96 8
Relation with concrete compression strength
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10 M ボル
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異形 棒鋼
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130 (標準 ） 6.5 10.8 break 8.7 11.2
160 14.4 M bolt 11.9 D bar
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Fig.6 Relation with bore hole depth
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5. Combination with Boring Machine 5.1 Introduction of SS Drill The boring becomes the very important element in the bonded anchor to stable precisely and to make it show that performance. Although the hammer drill has generally been conventionally used for anchor construction, the hammer drill is not applicable to boring, while recent years are, since noise and vibration are large. Conventional diamond core drill which are low noise and low vibration on the other hand, had a slow boring speed, its working efficiency was very bad. Now, we succeeded in the development of SS drill with low noise, low vibration ,in addition , with a quick boring speed. Boring speed and noise is shown in Fig. 7. The following development has attained this performance. (1) Adoption of small direct current motor (2) Adoption of durable super thin edge bit
’ Ｓ
BORING
TIME
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ＤＲ Ｉ
100 TIME MAXMUM NOISE
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SUMMARY OF 80 STANDAR NOISE（ｄ ｂ／ ３ REVOLUTIONS TIME （ｒ ｐ 60 BOREHOL NO MINIMU MAXMU （ｓ NOON ｅ CATALOG ５２ ×63 ０ 65 70 16 ## － － ＳＳ φ ２ φｎ ５２ ２ ×80 ０ 78.0 81 ## ## ## 1100 70 Ｈａ ｋｅ ｋ 40 STAND B+BTEC φ２ ５２ ×81 ０ 79 83 74 ## ## － φ２ ５２ ×80 ０ 80 86 45 ## ## 2400 60 ＨＩ ＬＴ Ｉ 20 ×64 １ ０ 71 73 20 ＳＳ φ ２０ HANDY ＨＬ ＩＴ Ｉ φ２ ０１ ×79 ０Ｄ79 80 28 0 50 φ２ ５１ ×61 ０５ 76 80 53 SONOR ＳＳ SS HAKKEN B+BTEC HILTI HAMMER DRILL DRILL
HANDY HITACHI φ２ ５２ ×79 ＤＨ ０－84 89 52 ## ## 370 Fig. 7. Boring time and noise of SS drill
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NOISE（dB/3m）
120
5.2 Ttensile strength of new-type capsule Anchor in SS Drill Boring The tensile strength of new-type capsule anchor when SS drill borings was checked. Although it was thought that the bond strength of the bonded anchor became low, since the unevenness of hole wall was small ,when a core drill generally bored. It was contrary to anticipation and bond strength was the value with the biggest case of SS drill boring.(Fig. 8)
SS drill Hammer drill
10 5
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Ｄ１
Ｄ１
0 Ｄ１
Tensile strength(ton)
機種 項目 Ｄ１ Ｄ１ Ｄ２ Ｄ２ 25Ｄ１ SSﾄﾞﾘﾙ 平均5 9 13 11 21 Ｒ20 2 0 0 4 1 平均 ﾊﾝﾏｰﾄﾞﾘﾙ 15 4 9 12 10 19 Ｒ 0 1 3 3 0
D bar size
Fig. 8. Comparison of anchorman adhesion intensity 5.3 The Feature of SS Drill Boring Wall The following points have been checked from the observation result of hole wall bored with SS drill. (1) although the boring wall in SS drill has small unevenness , the aggregate part of concrete put up inside the hole. It is presumed, since a bit was a thin edge and this avoided the aggregate part. (2) although unevenness of hole wall bored by the conventional core drill or hammer drill is large, protrusion is not specialization of aggregate and cement part cannot be performed. This is persumed to appear in the result with high bond tensile . Moreover, boring in SS drill is excellent in the degree of true circle, and linearity, and it was checked that the uniform hole is bored. It is thought that it was connected with the result which this makes reduce the variation in the hardening situation of adhesives, i.e., the variation of tensile strength.
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6. Conclusion The relation of resin composition and anchor strength was newly found out this time. Based on the result, it succeeded in development of the new-type capsule anchor. The capsule anchor is the bonded anchor new capsule type which also considered the safety on use further, and has checked the performance which was excellent in each performance. Moreover, it checked about the newly developed diamond core drill, and the original feature of the high speed and low noise has been checked.Furthermore, it has checked that it demonstrated the performance which was excellent also in respect of tensile strength , when boring using this core drill bores the new type capsule anchor.
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SEISMIC BEHAVIOR OF CONNECTIONS BETWEEN STEEL AND CONCRETE James O. Jirsa Department of Civil Engineering, The University of Texas at Austin, USA
Expanded Abstract The poor performance of many structures in recent earthquakes has resulted in the development of an important new area of structural design—the repair and strengthening of structures. The designer is often faced with meeting conditions that do not need to be considered in the design of new structures. These may include: • performance required by the owner or occupant may not be well defined • the condition of the structure must be assessed if there has been earthquake or other damage to the system • construction options may be limited by the need to maintain occupancy or to avoid interference with neighboring structures • time to completion may a prime factor • modifications to the structure must not lead to new zones of weakness or create operational problems in the use of the structure For concrete structures, these constraints often lead to the selection of steel elements to achieve the changes needed for meeting the performance requirements of the rehabilitated structure. Steel elements attached to concrete require connections between the two materials that will permit the modified element to reach desired strength, deform sufficiently to allow inelastic response of the element and/or structure, and be constructed economically. Because concrete and steel have very different stiffness characteristics, it is imperative that the designer consider those differences in evaluating local, as well as global response of the rehabilitated element or structure.
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The purpose of the paper is to identify several rehabilitation systems that involve the use of steel attached to concrete: • addition of steel bracing to concrete frames that have low lateral capacity and/or ductility • jacketing of elements to improve shear capacity or confinement in columns or beams that have inadequate confinement or splice details • addition of steel straps to provide additional tension capacity in beams or to transfer shear forces between elements. In each case, the connection between the concrete and the steel must be carefully detailed to ensure that the desired performance is achieved. Slip between the steel element and the concrete must be minimized. Anchors used for connecting steel elements to the concrete must be anchored adequately and the shear stiffness and strength of the connector must be evaluated. In the presentation, the use of various strengthening techniques will be described using field examples. Laboratory tests used to assess the performance of the strengthening elements and to provide design guidance will be discussed.
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TESTS ON CONNECTORS FOR SEISMIC RETROFITTING OF CONCRETE AND MASONRY STRUCTURES IN MEXICO Sergio M. Alcocer*, Leonardo Flores** *Director for Research, National Center for Disaster Prevention and Research Professor, Inst. of Engineering, Universidad Nacional Autónoma de México **Researcher, Structural Engineering and Geotechnical Area, National Center for Disaster Prevention, Mexico
Abstract The performance of inexpensive fasteners to connect reinforced concrete or mortar jacketings to existing masonry walls subjected to earthquake-type loading is discussed. The experimental variables were the type of masonry, amount of steel mesh reinforcement, the wall jacket material, as well as the type, amount and distribution of fasteners. Results clearly indicated that wall jacketing is an excellent option for improving earthquake performance and for avoiding total or partial collapse of brittle construction, provided that fasteners are properly designed and installed.
1. Introduction Mexico is located in one of the most active seismic zones in the world. An assessment of earthquake damage over the past 20 years indicates that yearly average losses amount for 305 people killed and 230 million US dollars in direct and indirect damages (Bitrán, 2000). This study indicates that the housing sector, with both urban and rural construction, and the telephone facilities outstand as two of the most hardly hit sectors in the economy. One of the determining factors for the large seismic risk of housing and phone facilities has been its high vulnerability. Indeed, Mexico has a vast inventory of existing structures that were designed and constructed using codes and material standards that pre-date current stringent requirements for seismic resistant construction. Moreover, a large portion of those structures, particularly houses in rural areas, was informally built, that is without the intervention of engineers or architects, and using local, typically weak, materials. Adobe housing is a prime example of rural construction. Wall jacketing is one of the rehabilitation techniques most often used to improve earthquake performance. Wall jacketing consists of a mortar or concrete cover reinforced
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with a steel welded wire mesh (SWWM) or a “chicken wire” mesh that is attached to the existing walls. For this scheme to work it is indispensable that earthquake-induced shear forces be transferred to the jacket by means of fasteners, shear keys or a combination thereof. Aimed at understanding the role of connectors in wall jacketing and to develop analysis, design and construction recommendations, three experimental programs were undertaken at the National Center for Disaster Prevention, CENAPRED. A complete discussion of the experimental data can be found elsewhere (Alcocer et al. 1996; Alarcón & Alcocer 1999; Flores et al. 1999). In each program, large-scale specimens were built and tested under a constant vertical axial load and cyclic lateral loads. In all cases, the cost of fastening technology was kept as low as possible. This was especially the case for the application to low cost housing, both for rural and urban structures.
2. Wall Jacketing of Adobe Housing Adobe construction in Mexico is typically found in small villages, mainly in the countryside. Adobe houses are commonly one-story buildings, with a rectangular plan of 4x8 m. The structural system consists of perimeter load-bearing walls, 3-m high and 300-to-600-mm thick. Walls are made of adobe blocks joined by mud mortar. Although roof systems vary, a typical roof consists of timber trusses that support shingles and clay tiles. Earthquake damage of this type of construction may be generally attributed to the low tensile strength of adobe masonry, aging and lack of maintenance. The most common damage patterns in this type of construction are schematically shown in Fig. 1.
Figure 1. Damage patterns in Mexican adobe houses
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Previous studies on rehabilitation schemes of Mexican adobe houses (Hernandez 1979) have indicated that the construction of a perimeter tensile chord on top of the walls or jacketing a wall with a mortar cover reinforced with a gage 14 wire (1,9-mm diameter) were viable options for reducing the likelihood of collapse. To further evaluate the efficiency of connectors and mesh size on wall jacketing, three full-scale adobe loadbearing walls were built and tested. The control specimen, A1, was an unreinforced adobe wall. After tested, A1 was repaired with a “chicken wire” mesh covered with mortar, and was retested (specimen A1R). Specimens A2 and A3, of similar geometry to A1, were strengthened without prior damage by means of a mortar jacket. In A2, jacket reinforcement consisted of SWWM’s made of gage-10 wire (3,43-mm diameter) with nominal yield stress of fy = 490 MPa and equally spaced at 150 mm in orthogonal directions. In wall A3, a “chicken wire” mesh was used. “Chicken wire” mesh is made of gage-20 wire spaced at 50 mm, fy = 640 MPa. In all cases, commercially available galvanized steel staples were used for fastening the jacket SWWM’s. Staples are made of gage-9 wire (3,76-mm diameter), with fy = 390 MPa, and were installed at 300-mm spacing (10 staples/m²). Staples used were 38-mm long. Cover mortar had a 1½:4½ volume ratio of portland cement and sand. Mortar jackets were, on the average, 30-mm thick and were hand-placed on both wall faces. Strengthening guidelines have recommended fastening the SWWM’s on both wall faces by means of steel cross ties placed through the wall thickness in holes perforated with hand drills (UNDP 1983). Such holes are thereafter filled with some epoxy or cementbased mortars. This recommendation is suitable for urban adobe construction, where drill hammers and trained labor are readily available. Due to the limited applicability of this fastening technology in Mexican rural houses, a simple and inexpensive solution, yet technically sound, was searched for. Steel staples were then found to be easy to install (just by hammering into the adobe wall) and very inexpensive (0.16 USD a piece). The evaluation of its technical feasibility was part of the study. The measured axial compressive strength of adobe blocks was fp* = 2,65 MPa; the compressive strength of adobe prisms was fm* = 0,62 MPa; and the diagonal compressive strength of adobe walls obtained was vm* = 0,03 MPa. The dimensions of the specimens were 2,5? 2,5? 0,35 m. Walls were constructed according to the local practice in the Mexican state of Michoacán. The horizontal reinforcement ratios, ph, of specimens A1R, A2 and A3, based on adobe wall area, were 0,007%, 0,035% and 0,007%, respectively. In one face of all rehabilitated walls, the SWWM was fastened directly in contact with the adobe wall and then covered with mortar. On the other face, the SWWM was fastened after a first 10-mm mortar cover was placed on the wall; the mesh was then finally covered with mortar until it reached the final 30-mm thickness. Specimens were tested under a constant vertical stress of 0,07 MPa. Final crack patterns and hysteresis loops are shown in Fig. 2. In A1, one inclined shear crack following the mortar joints controlled the behavior. Hysteresis loops were quite
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stable and with good energy dissipation capacity. Strength was reached at over 0,4% drift ratio, for a corresponding shear stress of 0,034 MPa. After repair, A1R was retested. Failure mode was changed to sliding of the wall as a rigid body. This occurred at a shear stress of 0,05 MPa (based on adobe area) that in turn, corresponded to a static friction modulus of 0,76. To fail the specimen, horizontal and vertical loads were then monotonically applied to simulate a large diagonal compression test. Strength was reached at a diagonal stress of 0,2 MPa (six times the original strength).
Figure 2. Crack patterns and hysteretic behavior of adobe walls Similarly to A1R, specimens A2 and A3 were initially tested under cyclic loads. Prior to sliding of the walls, specimens were then tested monotonically through a diagonal compression load. Measured strengths were equivalent to diagonal stresses of 0,28 and 0,27 MPa, respectively (based on the adobe area only). Strengths attained corresponded to large cracks on the mortar and the yielding of SWWM’s. A more uniform distribution of cracks was observed in wall faces where a first mortar cover was placed prior to fastening the SWWM. In both faces, staples remained anchored to the wall, even in locations close to the large diagonal cracks.
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3. Wall Jacketing of Hand-Made Clay Brick Masonry Clay brick masonry has been the most popular construction material in urban areas in Mexico. Typically, the structural system consists of load-bearing walls confined through vertical and horizontal RC tie-columns and bond-beams. Such system has performed excellently under very intense earthquakes only when adequately spaced, detailed and built confinement elements existed, as well as when sufficient lateral strength and stiffness were available. However, it is quite usual to find houses of this material where current requirements for seismic resistance are not fulfilled. For such cases, wall jacketing is one rehabilitation technique suitable for improving its lateral strength, stiffness and toughness. To better understand the resistance mechanisms and to develop design and construction guides, one two-story, three-dimensional confined masonry structure was repaired. Also, a series of four full-scale isolated confined masonry walls were tested. Specimens were built with hand-made burnt clay bricks joined with a portland cement mortar. Specimen dimensions, reinforcement details and mechanical properties of materials are presented in Fig. 3. All specimens were designed to fail in shear.
Figure 3. Characteristics of clay brick walls Specimen 3D was firstly tested by applying lateral displacements controlled by drift angle. Consistent with actual damage patterns observed after earthquakes, distress was concentrated in the ground story walls. Therefore, only such walls were repaired.
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Crushed and spalled tie-column concrete was removed and replaced by concrete with similar mechanical characteristics. Largest masonry cracks were filled with mortar and brick debris. Finally, the exterior side of the walls was jacketed with a mortar and a SWWM. The specimen was retested using the same displacement history (Alcocer et al. 1996). Common steel nails for timber construction, 50-mm long and made of gage-10 wire were used to fasten the SWWM’s. Fasteners were placed by carefully hammering them into the wall, of the grid intersections. The nail head was then bent around the wire intersection to secure the mesh in position. Fastener density was 9/m². The meshes were placed in the mid-thickness of the mortar cover, so that a 7-mm spacer was used between the wall and the mesh. This has been a typical fastening technology used in Mexican practice. In the isolated wall series, M0 was the control specimen. M1 to M3 were undamaged confined masonry walls strengthened with wall jackets on both faces, in which the horizontal reinforcement ratios were 0,072, 0,147 and 0,211%, respectively. In M1 and M2, with meshes made of gages-10 (3,43 mm) and -6 (4,88 mm) wire respectively, same fasteners in 3DR were used. However, no spacers were provided, so that the mesh was placed against the masonry wall. The amount of fasteners was different in the two faces, namely 5 and 11/m². For M3, where a steel mesh with a 6,35 mm wire diameter was used, Hilti ZF-51 fasteners were installed. This 51-mm long nail made of gage-10 wire was used in combination with a 36-mm diameter metal washer also supplied by Hilti. Fasteners were powder driven at the intersection of vertical and horizontal mesh wires with the DXE72 tool. The washer was intended to clamp the vertical and horizontal wires at the intersection. Again, no spacers were used. During construction it became evident that this fastening technology was installed faster and is more reliable than the typical hand-driven nails. The speed of installation offset the higher cost of the Hilti-type fasteners as compared to the inexpensive nails. Final crack patterns and hysteresis loops are shown in Fig. 4. Jacketed specimens exhibited a very uniform distribution of cracks and increased strength as compared to those in the control specimens (3D and M0). At same drift levels, crack widths in jacketed specimens were smaller than those recorded in control structures. In 3DR, at drifts to 0,46%, it became apparent that fasteners had been pulled out. This was attributed to the increased shear flexibility of the nail-spacer system and the reduced anchorage length of the nail into the masonry, when compared to the same nail without spacer used in M1 and M2. M1 failed after fracture of SWWM horizontal wires that led to shearing off the lower ends of the tie-columns.
4. Wall Jacketing of Concrete Masonry Infills In the aftermath of the 1985 Mexico City earthquakes, the country’s telephone infrastructure was severely damaged. The two buildings that handled international and domestic long distances suffered structural and equipment damage, rendering to a total loss of the country's capability of long distance service (Teléfonos 1988). To improve
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system redundancy and reduce building vulnerability, the company has carried out a very successful strategy of rehabilitation of their most critical facilities. One of the techniques used to improve performance has been the addition of new RC walls attached to both the existing RC frame and concrete masonry unit (CMU) infills at the perimeter of the building. Note that infills and perimeter frames are flush so that, for concrete placement, they would act as forms for one side of the new wall. To achieve a positive shear transfer and monolithic behavior between the new and existing elements, dowel bars have been used; however, detailing, number and distribution varied depending upon the design office and the contractor. Some required epoxied dowels in both the masonry infill and the RC frame; others only in the frame. In some cases, dowels in the walls were just epoxied at the mortar joints, whereas in other instances the dowels passed through the walls and were welded to small 6,4-mm thick steel plates inside the building. This variety of solutions had, evidently, very different costs.
Figure 4. Final crack patterns and hysteresis curves of jacketed clay brick walls To assess the effectiveness of this upgrading scheme, as well as the performance of different solutions for fastening, four specimens were built and tested (Fig. 5). Structures
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represented 1:1.3 scaled models of a one bay of a prototype building. T0 was the control specimen. In the strengthened (undamaged) specimen TP, epoxied dowel bars were placed in the perimeter RC frame, whereas in TD, dowel bars were distributed both in the frame and in the infilled masonry wall. Preliminary studies on isolated small specimens indicated that dowels with welded steel plates on the back of the wall performed as well as epoxied dowel bars placed in the mortar joint and embedded 80 mm into the wall thickness (Flores et al. 1999). Moreover, the latter solution was evidently more cost-effective. A two-component commercial epoxy resin was used to install the dowel bars. In TH, Hilti ZF-72 powder driven fasteners with a 25-mm spacer were installed. The spacers, made of a steel square tube, were provided to locate the SWWM in the mid-thickness of the concrete jacket. In the design of fasteners of all structures tested, it was assumed that transfer of forces between the existing and new elements would be developed through shear friction.
Figure 5. Characteristics of RC frames infilled with CMU’s Final crack patterns and hysteresis loops are shown in Fig. 6. Damage in T0 was controlled by shear-compression of the masonry infill. Specimens TP and TD showed a very similar behavior in terms of their uniform crack distribution and hysteretic curves. Failure was triggered by shear—compression cracking and crushing of the infill. Analysis of strain gage data indicated that strains in the dowel bars on the masonry infill were negligible, thus suggesting that their participation in transferring forces was minimal. Indeed, shear transfer was accomplished through shear friction between the wall and the RC frame (where dowels were actually strained), and by means of bond between CMU’s and the RC jacket (Flores et al. 1999). Fasteners in TH did not perform as intended, since at drifts to 0,4%, it was apparent that the anchorage was lost and that further shear transfer was impaired. Substandard performance was a combination of the excessive shear flexibility of the fastener due to the spacer, as well as of its reduced anchorage depth. During installation, part of the energy released by the powder charge was rebound due to the elastic deformation of the spacer, thus leaving the remainder energy to actually drive the fastener into the infill.
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Figure 6. Final crack patterns and hysteresis curves of jacketed concrete masonry infills
5. Conclusions and Recommendations Based on the observations made during the tests, and on the analysis of the instrumentation, the following conclusions and recommendations regarding the design and installation of fasteners were developed. Recommendations are applicable to existing structures with similar material characteristics as those reported herein. Wall jacketing proved to be a technically viable option for improving earthquake performance of existing structures. Its cyclic behavior strongly depends on the ability to transfer forces between new and existing elements through an adequately designed and installed fastening technology. For adobe rehabilitation, steel staples, 38-mm long, made of gage-9 wire and hammered into the adobe wall, proved to be a strong and stiff fastening system. Prior to the installation of the staples, it is recommended to place a 10-mm thick mortar cover on the adobe wall. Final mortar thickness should be of the order of 25-to-30 mm. In clay brick masonry, for light gage meshes (up to 4,11-mm wire diameter), 50-mm long steel nails driven into the wall can be used as fasteners. However, powder-driven
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connectors are most cost-effective and reliable. Nine connectors per m² are recommended. In clay brick construction, SWWM’s should be installed directly against the masonry wall without using spacers. The addition of a new RC wall connected to existing infilled RC frames through epoxied dowel bars performed satisfactorily. Moreover, it was found that dowel bars located uniformly on the masonry infill do not significantly participate in the shear transfer mechanism, since most shear is taken by dowels on the frame and bond between the new concrete and the existing infill. To connect a new RC wall, it is recommended to design the fasteners using a “capacity design approach”. Therefore, epoxied dowel bars should have strength, based on a shear friction model, of 1.5 times the maximum shear force expected to be resisted by the jacketed wall.
References 1. Bitrán, D., 'Características e Impacto Socioeconómico de los Principales Desastres Ocurridos en México en el Periodo 1980-1999', Centro Nacional para la Prevención de Desastres, Mexico, September 2000. 2. Alcocer, S.M., Ruiz, J., Pineda, J.A. and Zepeda, J.A., 'Retrofitting of Confined Masonry Walls with Welded Wire Mesh', Proceedings of the Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, June 1996, paper no. 1471. 3. Alarcón, P. and Alcocer S.M., 'Ensayes Experimentales sobre Rehabilitación de Estructuras de Adobe', (in Spanish) Proceedings, XII Congreso Nacional de Ingeniería Sísmica, Morelia, Mich., Mexico, Vol. I, (1999) 209-217. 4. Flores, L.E., Marcelino, J., Lazalde, G. and Alcocer, S.M., 'Evaluación experimental del desempeño de marcos con bloque hueco de concreto reforzado con malla electrosoldada y recubrimiento de concreto', Centro Nacional para la Prevención de Desastres, Mexico, IEG/03/99, October 1999. 5. Hernández, O., Meli, R. and Padilla M., 'Refuerzo de vivienda rural en zonas sísmicas'; Institute of Engineering, UNAM, Mexico, (1979) 45 pp. 6. UNDP/UNIDO, 'Repair and strengthening of reinforcing concrete, tone and brick masonry buildings', RER/79/015, Building Construction under Seismic Conditions in the Balkan Regions Vol. 5, ONU, Industrial Development Programme, Viena, Austria, (1983). 7. Teléfonos de México, 'Reto Sísmico: Incrementar la Seguridad y Mantener el Servicio de las Centrales Telefónicas', México, (1988) 290 pp.
Acknowledgements The participation of J. Pineda, A. Otálora, P. Alarcón, J. Marcelino, G. Lazalde, P. Olmos and C. Olmos is gratefully acknowledged. The support of CENAPRED, Universidad Michoacana de San Nicolás de Hidalgo and Teléfonos de México is recognized.
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DESIGN AND CONSTRUCTION OF HEAVY INDUSTRIAL ANCHORAGE FOR POWER-PLANTS Peter J. Carrato, William F. Brittle Bechtel Power Corporation, USA
Abstract Fossil fueled power-plant projects provide many design and construction challenges for connection of steel to concrete. Heavily loaded anchorages are required to support building structures and hold down machinery and equipment. Column bases for coal fired boiler support structures can transmit loads in the order of 4000 kN of tension and 2000 kN of shear. This magnitude of tension load requires groups of high strength bolts 100mm and larger in diameter. Shear loads are resisted using hot rolled structural shapes or heavy plate (up to 50mm thick) as shear lugs. Power-plant equipment such as turbo-generators, condensers, stacks, fans and pumps require precision placement of anchor bolts and shear lugs, often in the vicinity of congested reinforcing steel and embedded pipe and conduit. Construction consideration for column bases and equipment foundations often have a significant impact on the structural design.
1. Introduction Construction of a power generating facility involves a variety of applications of anchorage to concrete. Literally truckloads of anchor bolts are used in the construction of these facilities as can be seen in Figure 1. This paper describes some of the wide variety of connection to concrete found in a typical, natural gas fired power plant.
Figure 1 - Truckload of bolts
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Special emphasis is given to seismic resistant applications from projects being constructed in Taiwan, Turkey and California, as well as, high precision anchorage of turbine generator sets. In a fossil fuel fired power plant, most connections to concrete are made in cast in place foundations. These connections can be categorized into those that support structures and those that anchor equipment. Structural support include typical column base plates for turbine halls (Figure 2), pipe racks, water treatment buildings, etc, and more exotic bases, some of which allowing for thermal expansion at columns that support heat recovery steam generator (HRSG) boilers (Figure 3). Anchoring of tanks for fuel, water, and chemicals presents a unique structural application due to the large numbers of bolts required for a single foundation. Figure 4 shows a template used to set a stack. Figure 2 Turbine Hall
Figure 3 HSRG
Figure 4 Stack
Equipment anchorage is characterized by the need to resist dynamic loads using precisely located fasteners. Rotating equipment such as turbine generators, pumps and fans may require pre-loading anchor bolts to meet requirements given by their
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manufacturer. Non-rotating equipment like condensers and valves can present unique applications due to transient or operating conditions.
2. Machinery Foundation – Turbine Generators The turbine generators (T/G) are those pieces of equipment, which turn mechanical energy into electricity. It is often the most expensive component part of a power plant. As such, the anchorage of this equipment is given special attention. Anchoring devices used for turbine generators include not only those to secure the equipment in its final locations, but also those required to precisely position the machine. It is common to see anchor bolts 100 mm in diameter that must be placed with tolerances as tight as ± 3 mm to ± 1 mm. Critical design considerations for these applications include a variety of static and dynamic loads. The most significant design loads are those due to postulated machine malfunctions. Specifically the loss of a turbine blade or the short circuit of a generator can produce anchor bolt loads as high as 500 kN. The structural design of T/G anchorage also requires careful consideration of the thermal growth experienced by the machine as it heats up during normal operation. It is common for the temperature of the turbine casing to increase by 200 °C as the machine goes from cold shut down to full operation. Some of the larger loads transferred to a T/G foundation are those associated with aligning the machines. The shafts of the turbine and generator must be in perfect alignment. Embedded structural steel profiles (hot rolled shapes) called jacking posts are used as reaction points for hydraulic jacks used to position the machines in a horizontal plane as shown in Figure 5. Jacking post forces are often as high as 150 kN.
Figure 5 Jacking Posts
A number of different techniques are used for vertical alignment. These include grout pads and shims, jacking bolts and shims, and patented positioning devices. The choice of vertical alignment method depends on weight of the machine and the experience of the contractor performing
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Figure 6 Grout Pad
the installation. In the grout pad method (Figure 6), small pillars of grout are formed on which shims may be set, if needed, to achieve the final vertical position of the machine. The base plate is then set. Jacking bolts are threaded into the base plate and thus allow the plated Figure 7 Jacking Bolt position to be adjusted by turning the bolt. This is illustrated in Figure 7. Once the final location is achieved, the plate is shimmed and then grouted. Patented positioning devices consist of small screw or hydraulic jacks that are placed in a pocket in the concrete foundation. After the jacks have positioned the machine the device is grouted in place. Figure 8 shows a Fixator brand of positioning devices being used to set a generator. To position and anchor a T/G set while allowing for thermal growth, requires a wide variety of anchoring devices. Jacking posts, positioning devices and anchor bolts have already been mentioned. In addition to these fasteners, sole plates, center line guides, and stop blocks are also used. A sole plate is an embedded bearing plate on which the machine rests and/or slides during thermal growth. Center line guides are positioned along the shaft of the machine and control the direction of thermal expansion. Stop blocks are Figure 8 Positioning Device employed to limit the extent of thermal growth. These steel blocks are precisely positioned at the end of sole plates and restrain the machine after a predetermined amount of movement. Holding down a turbine or generator often requires 20 or more anchor bolts. To accurately cast this number of bolts into a concrete foundation typically requires one of two possible construction methods. Either the bolts must be designed so that their position may be adjusted after the concrete has set or the entire bolt group must be placed using a template that assures their precise location. Use of through bolts or an adjustable sleeve, will allow bolt positions to be adjusted after placing concrete. For
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elevated concrete decks, through bolts in oversized holes are recommended. When access to the underside of the slab is not available then an adjustable sleeve and pocket arrangement may be used. Both of these applications, shown in Figure 9; allow the bolts to be tensioned after setting the machine. When the anchor bolts are not to be preloaded after setting the machine a template may be used to position the bolt group. Templates are typically made from structural steel. The template should be fully welded or bolted together before drilling holes for the anchor bolts. The holes should only be 2 mm larger than the diameter of the bolts. Templates should be firmly supported preferably from existing concrete. It is not advisable to support a template from concrete formwork or rebar as the forms or rebar may shift during placement and consolidation of the Figure 9 Bolt Sleeves concrete. Templates are intended to fix the location of the top of the anchor bolts. For long bolts the lower portion of the bolt should be tied to the reinforcing steel thus assuring that the bolts will plumb.
3. Structural Anchors Structural anchors in power generating facilities present many challenges ranging from fastening a one half horse power pump to a 200 mm thick concrete pad to anchoring a column carrying 5000 kN of force to a 2 meter thick slab. Each of these various applications has its own unique concerns with designing the anchorage, positioning the bolts, installing the base plate and grouting the final assembly. By far, the most interesting designs are those associated with a combination large shear and uplift forces. In high seismic zones such as those found in Turkey, Taiwan and California large lateral loads must be transmitted from the superstructure to the foundation. Often these high lateral seismic loads can produce overturning moments on the structure that create uplift
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at these anchorage points. Connections such as these that must resist both uplift and large lateral forces are the most challenging to design. In these cases, an arrangement of anchor bolts designed to resist tension only and shear lugs designed to resist lateral loads is required.
Figure 10 Small Shear Lug
Figures 10 and 11 show column base plates designed for such loads. Figure 10 shows a shear lug consisting a single 18 mm thick plate that is designed to resist moderate levels of lateral load (75 to 10 kN).
Figure 11 shows an H shaped shear lug made of 50 mm thick plates. This lug is designed to resist significant levels of shear, up to 400 kN
Figure 11 Large Shear Lug
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Another practical way to resist large lateral loads is to embed the lower portion of the column shaft into a pocket in the foundation. This method, shown in Figure 12, works well in thick mat foundations such as those often used in power plant structures. There is little reference material that can be used to design a shear lug such as that shown in Figure 11. The design process should specifically consider the following 1) the strength of the lug, 2) the stiffness of the lug relative to the surrounding concrete and 3) the Figure 12 Column Pocket connection of the lug to the base plate. Of these three items connection of the lug to the base plate is the least understood and has the greatest impact on the cost of the anchorage. There are two design approaches used for this welded connection. The simplest and most straight forward considers the weld to take only the shear load transferred from the base plate to the lug. This results in very economical connection typically using a fillet weld. The other design approach is to assume that the bearing pressure applied to the face of the lug results in a bending moment on the weld of the lug to the base plate. This assumption invariably leads to a full penetration weld of the lug to the base plate. Such a weld applied to a 50 mm thick lug may increase the cost of the column-base plate assembly by as much as 50%. A well documented, definitive design method for large capacity shear lugs would be beneficial to design engineers.
4. Conclusion Design and construction of power plant facilities provide a wide variety of connections between steel and concrete. This paper has discussed a number of applications associated with anchoring structures and equipment. It is important to recognize that construction issues greatly influence the final design in many cases. Precision placement of anchor bolts and shear lugs, as well as provisions for grouting the final installation often require more engineering activity than the structural design of the connection.
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DYNAMIC BEHAVIOR OF SINGLE AND DOUBLE NEAREDGE ANCHORS LOADED IN SHEAR Jennifer Hallowell Gross*, Richard E. Klingner**, and Herman L. Graves, III*** * Cagley, Harman & Associates, King of Prussia, Pennsylvania, USA., Former The University of Texas at Austin. ** Dept. of Civil Engineering, The University of Texas at Austin, Austin, Texas, USA. *** U.S. Nuclear Regulatory Commission, Washington, D.C., USA.
Abstract Under the sponsorship of the US Nuclear Regulatory Commission, a research program was carried out on the dynamic behavior of anchors (fasteners) in concrete. In this paper, the dynamic response of single and double near-edge anchors loaded in shear is described. Hairpin reinforcement significantly increases the ductility of near-edge anchors loaded in shear. For the anchor diameters, spacings, and edge distances of this research program, behavior of double anchor connections could be approximated by combining the load-displacement behavior of each anchor, evaluated independently.
1. Objectives and Scope Under the sponsorship of the US Nuclear Regulatory Commission, a research program was carried out on the dynamic behavior of anchors in concrete. The research program comprised four tasks: 1) 2) 3) 4)
Static and Dynamic Behavior of Single Tensile Anchors (250 tests); Static and Dynamic Behavior of Multiple Tensile Anchors (179 tests); Static and Dynamic Behavior of Near-Edge Anchors (150 tests); and Static and Dynamic Behavior of Multiple-Anchor Connections (16 tests).
In this paper, dealing primarily with Task 3, the behavior of single and multiple shear anchors is described. Complete results are given in References 1 and 2.
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2. Anchors, Test Setups and Procedures Based on surveys of existing anchors in nuclear applications, the tests described here involved cast-in-place anchors, one wedge-type expansion anchor (referred to here as “Expansion Anchor II”), with some tests on one undercut anchor (“UC Anchor 1”). Based on current use in nuclear applications, it was decided to test anchors ranging in diameter from 3/8 to 1 in. (9.2 to 25.4 mm), with emphasis on 3/4 in. (19.1 mm) diameter. The tests of Task 3 involved anchors with a diameter of 3/4 in. (19.1 mm). The Cast-in-Place (CIP) anchors tested in Task 3 were A325 bolts, shown in Figure 1. The Expansion Anchor II (EAII) tested in this study is shown in Figure 2. The Undercut Anchor 1 (UC1) tested throughout this study is conventionally opening, and is shown in Figure 3.
Figure 1
Typical cast-in-place anchor (A325 bolt) tested in Task 3 of this study
D
D1 D2
wedge dimple wedge mandrel (cone)
lc
Figure 2
extension sleeve
expansion sleeve
lef
Figure 3
D2
D1
cone
D
threaded shank
Key dimensions of EAII
lc
Key dimensions of UC1
An important objective of Task 3 was to determine the influence of dynamic loading on anchor capacity as governed by concrete breakout. To ensure breakout failure, 4 in. (100 mm) embedment was chosen, which is representative of the manufacturer’s standard or minimum embedment.
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Single-anchor connections were tested at an edge distance of 4 in. (100 mm). Doubleanchor connections were composed of a front anchor with a 4 in. (100 mm) edge distance, and a back anchor with a 12 in. (300 mm) edge distance. The spacing between the two anchors was 8 in. (200 mm), twice the embedment depth. Some tests were conducted with a U-shaped #6 (19 mm) reinforcing bar, referred to as a “hairpin,” restraining the anchor [3]. The hairpin was placed directly against the anchor in some tests (“close hairpin”), and at 1-1/4 in. (32 mm) from the anchor in other tests (“far hairpin”). The target concrete compressive strength for this testing program was 4700 lb/in.2 (32.4 MPa), with a permissible tolerance of ±500 lb/in.2 (±3.45 MPa) at the time of testing. The concrete used a local river-gravel aggregate. Specimens for Task 3 were cast in blocks of dimensions 87 in. x 30 in. x 14 in. (2.21 m x 0.36 m x 0.76 m) with reinforcement located at mid-depth. The test setup for Task 3 is shown in Figure 4. Tests on single anchors used the loading shoe of Figure 5; on double anchors, the loading shoe of Figure 6. As shown in Figure 6, the anchors to be tested were inserted through the hole or holes in the shoe. The shank of the anchor was surrounded by a hardened steel insert, and the anchor was tightened by a nut placed in a recessed hole in the baseplate. For CIP anchors, the critical shear plane passed through the unthreaded portion of the anchor shank. For post-installed anchors, the critical shear plane passed through the anchor threads, and did not include the anchor sleeve. Test Frame
Hydraulic Ram
Load Cell Nut
Threaded Rod
Concrete Block
Figure 4
Setup for shear tests of Task 3 9-1/2”
1-1/8” 1-1/4” 4”
2-1/8”
Figure 5 Loading shoe for singleanchor shear tests
2”
1-1/4”
17-1/2”
2”
1-1/8” 4”
8”
2-1/8”
Figure 6 Loading plate for double-anchor shear tests
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Horizontal movement of the loading shoe was equivalent to the horizontal movement of the anchor. A linear potentiometer placed against the shoe measured the displacement of the anchor. The crack opening was measured with two direct-current differential transformers (DCDT’s), placed behind the anchor and on the side of the block. The DCDT’s were attached to a steel plate glued to the surface on the concrete and reacted against a steel angle that was also glued to the surface of the concrete on the opposite side of the crack. Tests were conducted under static and dynamic loading. Static loading involved monotonically increasing loads to failure in two to four minutes. For dynamic testing, to ensure anchor failure, a ramp loading was used, with a rise time of about 0.1 seconds, corresponding to that of typical earthquake response of mounted equipment. For tests in cracked concrete, using post-installed anchors, 0.3 mm cracks were initiated using hardened steel wedges and splitting tubes. For cast-in-place anchors, sheet-steel crack initiators were used. Anchors were tightened to the torque specified by the manufacturer. To simulate the reduction of prestressing force in anchors in service due to concrete relaxation, anchors were first fully torqued, then released after about 5 minutes to allow the relaxation to take place, and finally torqued again, but up to only 50% of the specified values.
3. Test Results Behavior of Single-Anchor Connections under Shear Loading For CIP anchors, Figure 7 shows the effects of dynamic loading, cracked concrete, and far hairpins (supplementary U-shaped reinforcement placed 1-1/4 in. or 32 mm clear from the anchor) on the concrete breakout capacity of single CIP anchors loaded in shear. Under dynamic loading, the breakout capacity of CIP anchors is higher than under static loading, other conditions being the same. The increase in capacity is approximately 20% for CIP anchors, regardless of whether hairpins are used, and regardless of whether the concrete is cracked or not. Cracked concrete reduces the breakout capacity of CIP anchors by about 18%, compared with the corresponding uncracked cases. Anchors with far hairpins retain more of their original capacity. This is because the concrete between the anchor and the far hairpin is well confined, reducing the effect of cracking. In addition, the reduction in capacity due to cracked concrete is lower for dynamic loading than for static loading. This is because the additional crack opening is generally lower under dynamic loading than under static loading. Figure 8 shows the effects of dynamic loading and far hairpins on the concrete breakout capacity of EAII and UC1 anchors. For EAII, the increase in breakout capacity due to dynamic loading is 20%, similar to that for CIP anchors. UC1 has an increase in capacity of only 12%. The breakout capacity of these post-installed anchors with a far hairpin is lower than the breakout capacity of CIP anchors with a far hairpin, possibly
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because EAII is not as stiff as the CIP anchor. In a few cases, the concrete cracked during installation of UC1, reducing breakout capacity. Increases in breakout capacity due to hairpins, and decreases in breakout capacity due to cracked concrete, were similar to those observed for CIP anchors. Figure 9 shows the effect of those same factors on ultimate capacity, taken here as the highest load recorded up to a maximum displacement of 1.2 in. (30 mm). Ultimate failure of CIP single-anchor connections with no hairpin occurred at concrete cone breakout. Connections with hairpins withstood significant additional load after concrete cone breakout. The ultimate load is approximately the same for each test type. Anchors restrained by a hairpin bent around the hairpin until the anchor displaced more than 1.2 in. (30 mm), or until load-carrying capacity was reduced because the anchor either fractured, or deformed excessively. Capacity of anchors with hairpins depends on the strength of the anchor steel rather than the strength of the concrete. Therefore, the ultimate capacity is essentially independent of loading rate and cracking of concrete. Effect of Loading Rate and Cracked Concrete on Concrete Cone Breakout Load of Cast-in-Place Anchor Loaded in Shear 89.0 15.6
15.2
16.0
14.7
13.9 12.6
12.0
12.0
11.2 9.6
8.8
10.8
10.4
7.2
8.0
71.2
53.4
35.6
4.0
Maximum Load (kN)
Maximum Load (kips)
20.0
17.8
0.0
0.0 CIP Static Uncracked
CIP Dynamic Uncracked
CIP Static Cracked
CIP Dynamic Cracked
Test Type
Figure 7
Effect of loading rate and cracked concrete on concrete cone breakout load of CIP single-anchor connections loaded in shear
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No Hairpin Close Hairpin Far Hairpin
Effect of Loading Rate on Concrete Cone Breakout Load of Expansion Anchor II and Undercut Anchor 1 Loaded in Shear 12.0
53.4 10.3
Maximum Load (kips)
9.0
40.0 7.9
6.0
26.7
3.0
Maximum Load (kN)
9.6
9.2
EAII Far Hairpin UC1 Far Hairpin
13.3
0.0
0.0 Static Uncracked
Dynamic Uncracked
Test Type
Figure 8
Effect of loading rate on concrete cone breakout load of EAII and UC1 single-anchor connections loaded in shear
The ultimate capacity of EAII and UC1 with a far hairpin are shown in Figure 10. The dynamic capacity of EAII is 14% higher than the static capacity, because the anchor tended to pull out as it displaced under static loading, but not under dynamic loading. As with CIP anchors with hairpins, the ultimate capacity of UC1 depends on the anchor steel, and is not significantly affected by loading rate.
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Effect of Loading Rate and Cracked Concrete on Ultimate Load of Cast-in-Place Anchor Loaded in Shear 30.0
133.4 24.1 22.9
20.0
18.0
18.0
17.3
111.2
22.1
21.4
89.0
16.1
15.0
66.7 11.2
10.0
10.4
8.8
44.5 7.2
5.0
Maximum Load (kN)
Maximum Load (kips)
25.0
No Hairpin Close Hairpin Far Hairpin
22.2
0.0
0.0 CIP Static Uncracked
CIP Dynamic Uncracked
CIP Static Cracked
CIP Dynamic Cracked
Test Type
Figure 9
Effect of loading rate and cracked concrete on ultimate load of CIP single-anchor connections loaded in shear
The ultimate capacity of these post-installed anchors with a far hairpin is lower than the ultimate capacity of CIP anchors with a far hairpin. This is partially due to the lower stiffness of EAII, to cracking at installation of UC1, and to differences in the load transfer mechanism of each anchor. As shown in Figure 11, hairpins increase the failure displacement of near-edge CIP anchors loaded in shear by a factor between 9.5 and 14.3 for close hairpins, and between 7.5 and 13.1 for far hairpins. The largest increases in failure displacement occur for dynamic loading in uncracked concrete; the smallest, for dynamic loading in cracked concrete. Similar increases are observed for post-installed anchors. Behavior of Double-Anchor Connections under Shear Loading The objective of the double-anchor tests was to compare single- and double-anchor tests and thereby assess the extent of load sharing as well as the interaction of the two anchors. To achieve this objective, a conceptual model was developed and compared with actual test results.
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Effect of Loading Rate on Ultimate Load of Expansion Anchor II and Undercut Anchor 1 Loaded in Shear 18.0
80.1 15.1
14.8
66.7
12.0
53.4 9.8
8.6
9.0
40.0
6.0
26.7
3.0
13.3
0.0
Maximum Load (kN)
Maximum Load (kips)
15.0
EAII Far Hairpin UC1 Far Hairpin
0.0 Static Uncracked
Dynamic Uncracked
Test Type
Figure 10
Effect of loading rate on ultimate load of EAII and UC1 singleanchor connections loaded in shear Effect of Hairpin on Displacement at Ultimate Load of Cast-in-Place Anchor Loaded in Shear
16.00
Displacement Normalized by No Hairpin
14.35 13.40 13.15
13.13 11.96
12.00 9.46
8.91
Static Uncracked 7.47
8.00
Dynamic Uncracked Static Cracked Dynamic Cracked
4.00 1.001.001.001.00 0.00 No Hairpin
Close Hairpin
Far Hairpin
Hairpin Type
Figure 11
Effect of hairpin on displacement at ultimate load of CIP singleanchor connections loaded in shear
The conceptual model is based on the hypothesis that the two anchors are far enough from each other that each behaves individually, and the response of the double-anchor
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connection is therefore equal to the sum of the responses of each anchor. The model assumes a rigid baseplate, so that the displacements of the two anchors and the baseplate are all equal to each other. Figure 12 shows the load-displacement results from (A) shear tests on a single near-edge anchor, (B) shear tests on a single back anchor, (C) the summation of those two single anchor tests, and (D) shear tests on a double-anchor connection. All are for anchors under static loading with a close hairpin in uncracked concrete. The summation (C) of the curves for the single-anchor behavior and the back anchor behavior is generally close to (D) the curve for the double-anchor connection. The curve for the double-anchor connection is shifted to the right slightly compared to the curve for the summation of the two anchors because the baseplate slipped during the double-anchor test. In all cases, the results for the summation of the responses of the near-edge single-anchor connection and the back anchor are quite close to the response of the double-anchor connections. Slight differences exist due to differences in slip of the baseplate; as seen in Figure 12, however, the curves have the same slope, and the change in curvature (which is used to determine the concrete cone breakout load) occurs at essentially the same load. It can be confidently concluded that for 3/4 in. (19 mm) diameter anchors spaced at 8 in. (200 mm), the shear behavior of a connection with two anchors will be equal to the summation of the behavior of each individual anchor. For anchors located closer to each other than 8 in. (200 mm) and diameters greater than 3/4 in. (19 mm), this conclusion may not hold. Evaluation of Double-Anchor Model for Anchors Loaded in Shear Static Loading, Close Hairpin, Uncracked Concrete Displacement (mm) 0.0
5.1
10.2
15.2
20.3
25.4
Load (kips)
50.0
266.9 (C) Summation of SingleAnchor and Back Anchor
(D) Double-Anchor Connection (5SCR5706)
40.0
222.4 177.9
30.0
133.4 (B) Back
20.0
89.0 (A) Single-Anchor Connection (1SCR5706)
10.0 0.0 0.00
Load (kN)
60.0
Slip of Double-Anchor Connection 0.20
0.40
0.60
44.5 0.0
0.80
1.00
Displacement (in.)
Figure 12
Evaluation of double-anchor model for anchors loaded in shear for the case of static loading, close hairpin, uncracked concrete
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4. Conclusions and Recommendations Single Near-Edge Anchors Loaded in Shear 1. In uncracked concrete, all anchors show an increase in concrete breakout capacity under dynamic loading as compared to static. Increases range from 20% for CIP and EAII anchors, to 12% for UC1 anchors. 2.
All anchors show a decrease in concrete breakout capacity due to cracking, as compared to the uncracked case. The decrease is 18% for CIP anchors, and similar for post-installed anchors.
3.
For all anchors, far hairpins (spaced 1-1/4 in. or 32 mm clear from the anchor) increase concrete breakout capacity by 30% to 40%. Similar increases were observed for CIP anchors with close hairpins (placed directly against the anchor). While similar increases would probably have been observed for post-installed anchors as well, it is generally not possible to install close hairpins around postinstalled anchors.
4.
Ultimate capacity, evaluated at a displacement of 1.2 in. (30 mm), is obviously increased for all anchors by hairpin reinforcement. Dynamic loading and cracked concrete have essentially no effect on ultimate capacity, which depends on a failure mechanism involving the restrained anchor only. Hairpin reinforcement confers significant ductility. For CIP anchors with a close hairpin the displacement at ultimate failure is increased by 9.5 to 14.3 times over the ultimate displacement with no hairpin. CIP anchors with a far hairpin have a slightly lower increase of 7.5 to 13.1 times. Similar results were obtained for postinstalled anchors with a far hairpin.
5.
Double-Anchor Connections Loaded in Shear The behavior of a double anchor connection consisting of 3/4 in. (19 mm) diameter CIP anchors embedded 4 in. (100 mm) with the front anchor at a 4 in. (100 mm) edge distance and the back anchor at a 12 in. (300 mm) edge distance can be determined by superimposing the load-displacement behaviors of each anchor. This conclusion is specific to this test program and may not hold for larger anchors, smaller embedments, or closer spacing.
5. Acknowledgment and Disclaimer This paper presents partial results of a research program supported by the U.S. Nuclear Regulatory Commission (NRC) (NUREG/CR-5434, “Anchor Bolt Behavior and Strength during Earthquakes”). The technical contact is Herman L Graves, III, whose support is gratefully acknowledged. The conclusions in this paper are those of the authors only, and are not NRC policy or recommendations.
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6. References 1.
Hallowell 1996: Hallowell, J. M., “Tensile and Shear Behavior of Anchors in Uncracked and Cracked Concrete under Static and Dynamic Loading,” M.S. Thesis, The University of Texas at Austin, August 1996.
2.
Klingner et al. 1998: Klingner, R. E., Hallowell, J. M., Lotze, D., Park, H-G., Rodriguez, M. and Zhang, Y-G., Anchor Bolt Behavior and Strength during Earthquakes, report prepared for the US Nuclear Regulatory Commission (NUREG/CR-5434), August 1998.
3.
Malik et al. 1982: Malik, J. B., Mendonca, J. A., and Klingner, R. E., “Effect of Reinforcing Details on the Shear Resistance of Short Anchor Bolts under Reversed Cyclic Loading,” Journal of the American Concrete Institute, Proceedings Vol. 79, No. 1, January-February 1982, pp. 3-11.
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POST-INSTALLED REBAR CONNECTIONS UNDER SEISMIC LOADING Isabelle Hofacker and Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract This paper presents results of monotonic and cyclic tests with post-installed reinforcing bars performed at the research laboratory of the University Stuttgart. The main objective was to study the behavior of post-installed rebar connections in uncracked concrete under cyclic loading. Varied was the type of mortar and the peak displacements during reversed cyclic loading between constant displacements. The results show that the behavior of post-installed rebars under cyclic loading depends on the failure mode under monotonic loading. If pullout is caused by a bond failure between mortar and bar, the cyclic behavior of post-installed rebars is much the same as for cast-in-place rebars. On the contrary if pullout is caused by a bond failure between mortar and concrete then the bond behavior of post-installed rebars under reversed cyclic excitations maybe rather poor. In the paper the tests and the evaluation of the results are presented.
1. Introduction 1.1. General The requirements in earthquake resistant structures usually lead to the need for large seismic energy input absorption and dissipation through large but controllable inelastic deformations of the structure. To meet these requirements, the sources of potential structural brittle failure must be eliminated and degradation of stiffness and strength under repeated loadings must be minimized or delayed long enough to allow sufficient energy to dissipate through stable hysteric behavior. In reinforced concrete, one of the sources of brittle failure is the sudden loss of bond between reinforcing bars and concrete in anchorage zones, which has been the cause of severe damage to, and even collapse of, many structures during recent strong earthquakes. Even if no anchorage failure occur, the hysteric behavior of reinforced concrete structures, subjected to severe seismic excitations, is highly dependent on the
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interaction between steel and concrete (bond-stress-relationship) [2]. Therefore the behavior of cast-in place rebars under seismic excitations has been studied extensively [1] and design recommendations have been formulated in codes of practice. In practise many structures have to be strengthened to increase their seismic resistance. This is often done by deformed reinforcing bars, which are bonded by a special mortar into a predrilled hole. Previous investigations with post-installed rebars in pull-out tests and overlap splices under monotonic loading have shown that the bond behavior of post-installed rebars is much the same as that of cast-in rebars provided the injection mortar is suitable [3], [4]. This statement is valid for the failure modes pullout and splitting. In contrast, the behavior of post-installed rebars under cyclic loading representing seismic excitations is not known. However, this knowledge is needed so that postinstalled rebars can safely be used in structures in seismic active areas. Therefore pullout tests have been carried out to study the cyclic behavior of post-installed rebars. Varied were the type of injection mortar (product A and product B) and the peak displacement during reversed cyclic loading (smin=± 0.2 mm to smax=± 2.0 mm (product B) and smin=± 0.2 mm to smax=± 4.0 mm (product A)).
2. Experimental Program 2.1. Test Specimen Pullout tests were performed with deformed reinforced bars (ds= 20 mm, fy= 900 MPa) installed in a concrete slab (h= 400 mm). The embedment depth was hef = 10ds. In the tests the tested rebars were produced from one lot. To avoid concrete splitting large edge distances (c≥ 250 mm) and spacing (s≥ 500 mm) were used. Two concrete slabs were made having a concrete compressive strength of about fcc~ 30 MPa (measured on cubes with a side length of 200 mm). 2.2. Injection Systems Two types of injection systems were used in the tests. Product A is a hybrid system which employs styrene-free vinylester and cement as binding material. For the cleaning of the holes newly developed special equipment was used. First the hole was cleaned 3 times by compressed air using a special lance. Then the hole was brushed 3 times by a special steel wire brush which was installed in the drilling machine. Afterwards the hole was again air lanced 3 times with compressed air.
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Product B uses unsaturated polyester as binding material. The hole was also cleaned by 3 times blowing, 3 times brushing and 3 times blowing. However the blowing was done using a hand pump and the brushing was done by hand with a steel wire brush. With both products the components of the mortar (binding material, hardener, supplement) are separately preserved. While injecting the mortar the components are automatically mixed in the mixing nozzle.
Figure 1. Cleaning process
2.3. Rebar installation Holes (d0= 25 mm) were drilled by rotary hammer drilling. After cleaning them carefully according to manufacturers recommendations (see Section 2.2) the mortar was injected using an injection tool, the holes were filled from the bottom of the hole up to about 2/3 of the embedment depth. Afterwards the rebars were installed under slight turning with the required embedment depth. All tests were performed 3 hours after rebar installation. The curing time was larger than the curing time required by the manufacturer. The temperature of the specimen was about 19° C. Different methods were used to install the rebar in concrete. All specimen tested in monotonic loading were installed in a hole with a depth of h0= 200 mm (Figure 2).
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The results of the cyclic tests should be compared with the results of tests described in [1]. In these tests a contact pressure at the bar end under compression loading was excluded. To achieve the same condition in the cyclic tests with post-installed rebars, the hole was first Figure 2. Test specimen Figure 3. Test specimen (cyclic drilled through the entire depth of the (monotonic loading) loading) slab. After cleaning the hole a wire sleeve (length 80 mm) with the closed end first was installed from the lower end of the slab (Figure 3). Then the hole was injected with mortar and the bar was installed. In this way the correct embedment depth (hef =200 mm) was ensured and no contact pressure could build up. After the tests the wire sleeve, which could easily be removed from the hole, showed indentations resulting from the displacements of the rebar under cyclic compression loading. 2.4. Experimental Setup and Testing Procedure Each specimen was attached to a specially designed testing apparatus and was loaded by a hydraulic servo-controlled cylinder. The tests were run under displacement control by subjecting the free end of the bar to the force needed to induce the desired displacement. The displacement was simultaneously measured on either side of the load application using two LVDTs; the average of the two displacements was used to control the loading. It was necessary to prestress the loading frame to the ground to apply a compressive load to the test specimen during cyclic loading (see Figure 4). No upwards movement of the test setup was observed during the tests. For monotonic tests, the specimens were tested in tension so no prestressing was applied. In all other respects the testing apparatus for monotonic and cyclic tests was the same.
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Figure 4. Test setup 2.5. Test Program The program for the monotonic tests is given in Table 1. Besides post-installed rebars cast-in place rebars were tested for comparison. The program for cyclic tests is given in Table 2. Only tests with post-installed rebars were performed. Five identical tests were carried out in each test series to account for the inevitable scatter of results. The main parameters studied in the tests are as follows: (1) Type of mortar. Two different types of mortar were used with the corresponding cleaning method. (2) Loading history in the cyclic loading tests. The main parameters were the peak displacement values ∆s between the peak values of displacement between which the specimen was cyclically loaded (∆s1=±0.2 mm, ∆s2=±0.4 mm, ∆s3=±0.8 mm, ∆s4=±2.0 mm and ∆s5=±4.0 mm (only product A)). The number of cycles was 10. After cyclic loading a monotonic tension test was performed.
Type Product/ Cleaning Method Number of Tests
Series A
Series B
Series C
Post-Installed Rebar Product A/ Machine Cleaning 5
Post-Installed Rebar Product B/ Hand Cleaning 5
Cast-In-Place Rebar -
Table 1. Test program for tests in monotonic loading
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5
Type Product/ Cleaning Method Peak Slip ∆s [mm] Number of Cycles Number of Tests
Series A
Series B
Post-Installed Rebar Product A/ Machine Cleaning 0.2 0.4 0.8 2.0 4.0 10 10 10 10 10 5 5 5 5 5
Post-Installed Rebar Product B/ Hand Cleaning 0.2 0.4 0.8 2.0 10 10 10 10 5 5 5 5
Table 2. Test program for tests with reverse cyclic loading
3. Experimental Results For reason of clarity only the averaged bond stress-displacement curves are given in the following diagrams. Each series was averaged by a computer program named Origin. The bond strength τ was calculated according to Equation (1):
τ=
N π ⋅ d s ⋅ h ef
[N/mm2]
(1)
N = measured load [N] ds = bar diameter (ds = 20 mm) hef = embedded length (hef = 200 mm) 3.1. Monotonic Loading The test results for monotonic loading are plotted in Figure 5. It shows the average bond stress-displacement curves of post-installed rebars using product A, product B and of cast-in-place rebars. In the pullout tests with rebars τ [N/mm2] post-installed with product A the 16 bond failure occurred in the post-installed bar (Product A) interface between rebar and 12 mortar. In contrast to that rebars post-installed with product B 8 failed in the interface between cast-in-place bar mortar and concrete. 4 The bond stress-displacement post-installed bar (Product B) curve of the cast-in place rebar is similar to that of the rebar post0 s [mm] installed with product A. The 0 2 4 6 8 10 12 rebar post-installed with product A reached an approximately 15% higher maximum bond Figure 5. Bond stress–displacement diagram for cast-in-place rebars and post-installed rebars in stress. The stiffness of the ascending monotonic loading.
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branch decreased gradually from its initial large value to zero when approaching the maximum bond resistance at a displacement value of approximately 1.4 mm (cast-inplace rebar) and 2.0 mm (post-installed rebar). After passing τmax, the bond resistance decreased slowly and almost linearly until it levelled off at a slip of s≈ 11 to 12 mm. This value is almost identical to the clear distance between the lugs of the bars used in the tests. The bond behavior of rebars post-installed with product B is significantly different from those of rebars post-installed with product A and of cast-in-place rebars. The initial stiffness of the bond stress-displacement relationship of rebars post-installed with product B is the same as that of the other bars. However, with product B at a rather low bond stress and corresponding small displacement the stiffness of the bond stressdisplacement and the bond strength is reached at very large displacement values (s~15 to 18 mm). The bond strength is about 60% or 45% lower than for rebars post-installed with product A or for cast-in rebars. The bond behavior of the rebars post-installed with product B can be explained as follows. The adhesion between mortar and wall of the hole overcomes at low bond stress values and the load transfer at larger displacement values is mainly due to friction because of pulling rebar with mortar through the hole with relatively rough wall. 3.2. Cyclic Loading The influence of reversed loading on the local bond stress-slip relationship of cast-in rebars has been studied intensively in [1]. These results are compared with the results of the present tests. The results of the cyclic loading tests with post-installed rebars are plotted in Figure 6a)6e) (product A) and Figure 8a)-8d) (using product B). In these bond stress-displacement diagrams, the first and the 10th cycle and the curves valid for loading to failure after 10 load reversals are plotted. Each Figure is valid for one peak displacement during reversed cyclic loading. Figure 7 (product A) and Figure 9 (product B) show the bond stress-displacement curves after cycling 10 times for all peak slip values. In all diagrams, the corresponding bond stress-displacement relationship for monotonic loadings are shown for comparison.
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2
τ [N/mm ] 16
2
τ [N/mm ] 16 12
4
4
0
-3
-2
-1
-4
-5
s [mm]
0 -4
0
1
2
3
4
-4
-3
-2
-1
5
Post-Installed Bar (Product A)
-16
4
0
1
2
3
4
-5
5
-4
-3
-2
-1
-16
1
2
3
4
d) Product A, ∆s=±2.0 mm τ [N/mm ] 16 2
τ [N/mm ] 16
monotonic
12
0,2 mm monotonic 0,4 mm
8
0,8 mm
12 8 4 0 0
1
2
3
4
4,0 mm s [mm] 5
Post-Installed Bar (Product A)
2,0 mm
4 -8 -12 -16
5
Post-Installed Bar (Product A)
-16
2
-4
s [mm] 0
-8
c) Product A, ∆s=±0.8 mm
-1
-4
-12
Post-Installed Bar (Product A)
-12
-2
2,0 mm
0
s [mm]
-8
-3
monotonic
8
0,8 mm
0
-4
5
12
4
-5
4
2
8
-4
3
Post-Installed Bar (Product A)
τ [N/mm ] 16
monotonic
12
-1
2
b) Product A, ∆s=±0.4 mm
2
τ [N/mm ] 16
-2
1
-16
a) Product A, ∆s=±0.2 mm
-3
s [mm] 0
-12
-12
-4
-4 -8
-8
-5
0,4 mm
8
monotonic
8
-5
monotonic
12
0,2 mm
4,0 mm Post-Installed Bar (Product A)
s [mm]
0 0
2
4
6
8
10
12
e) Product A, ∆s=±4.0 mm Figure 6a)-e). Bond stress-displacement Figure 7. Bond stress-displacement relationship for monotonic and reversed relationship for monotonic loading after 10 cyclic loading (product A). Only the first load reversals (product A). and the 10th cycle with subsequent loading to failure are shown.
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τ [N/mm2] 8
τ [N/mm2] 8
6
6
0,2 mm
4
2 s [mm]
0 -3
-2
-1
-2 0
1
2
-3
-2
-1
-6
Post-Installed Bar (Product B)
-8
-8
a) Product B, ∆s=±0.2 mm
1
2
3
Post-Installed Bar (Product B)
b) Product B, ∆s=±0.4 mm
τ [N/mm ] 8
τ [N/mm2] 8
2
6
6
4
monotonic
4
2
0,8 mm
2 s [mm]
0 -1
-2 0 -4
-6
-2
s [mm]
0
3
-4
-3
0,4 mm monotonic
4 monotonic
2
-2 0
1
2
monotonic 2,0 mm s [mm]
0
3
-3
-4
-2
-1
-2 0
1
2
3
-4
-6
-6
Post-Installed Bar (Product B)
-8
-8
c) Product B, ∆s=±0.8 mm
Post-Installed Bar (Product B)
d) Product B, ∆s=±2.0 mm
Figure 8a)-d). Bond stress-displacement relationship for monotonic and reversed cyclic loading (product B). Only the first and the 10th cycle with subsequent loading to failure are shown. τ [N/mm2] 8
0,2 mm 6 monotonic 0,4 mm 4 2,0 mm
0,8 mm
2 Post-Installed Bar (Product B)
0
s [mm] 0
2
4
6
8
10
12
Figure 9. Bond stress-displacement relationship for monotonic loading after 10 load reversals (product B).
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Note the different scale for the bond stresses in Figure 8a)-8d) compared to Figure 6a)6e) for the bond strength which is ±8 N/mm2 (vertical axis) and ±3 N/mm2 (horizontal axis). If cyclic loading is performed between small peak displacement values (∆s≤±0.4 mm) the bond stress-displacement curves of post-installed rebars reach the monotonic envelope for displacement values larger than the peak displacement during previous cycling. If the rebars are cycled between peak displacement values ∆s≥±0.8 mm than the monotonic envelope is not reached again. This behavior is valid for rebars post-installed with product A and product B.
In Figure 12 and Figure 13 the bond stresses after n=2 to 10 cycles at peak slip value related to the bond stress when reaching smax at the first cycle (see Figure 11) are plotted as a number of Figure 11. Graphics load cycles. Figure 12 shows the results using product A, Figure 13 those for product B. For comparison Figure 10 shows the corresponding results for cast-in rebars according to [1]. For rebars post-installed with product A the bond Figure 10. Deterioration of bond deterioration during reversed cyclic loading is resistance at peak slip as a much the same as for cast-in-place rebars function of number of cycles (compare Figure 12 with Figure 10) if cyclic is done between approximately the same values ∆s. (ds=25.4 mm, fcc~ 30 MPa)[1] In contrast to that the bond deterioration of rebars post-installed with product B is much more pronounced than that for cast-in-place rebars (compare Figure 13 with Figure 10).
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Post-Installed Bar (Product A)
Post-Installed Bar (Product B) 1
smax [mm] 0,2 0,4
0,6
2
0,8
τ(n)/τ(n=1) [N/mm ]
2
τ(n)/τ(n=1) [N/mm ]
1
0,8
0,4
2,0
0,2
0,8
smax [mm] 0,6
0,2 0,4 0,8 2,0
0,4 0,2
4,0 0
0
1
2
3
4 5 6 7 8 Number of Cycles n [-]
9
10
1
2
3
4 5 6 7 8 Number of Cycles n [-]
9
10
Figure 12. Deterioration of bond Figure 13. Deterioration of bond resistance at peak slip as a function of resistance at peak slip as a function of number of cycles (product A) number of cycles (product B) The different bond behavior during monotonic and cyclic loading of the bars installed with product A and product B can be explained as follows. Rebars installed with product A overcome the bond resistance at the interface between rebar and mortar. Therefore these rebars behave similar to cast-in-place rebars. The higher bond strength of post-installed rebars is caused by the higher compressive strength of the mortar compared to the compressive strength of the concrete. The failure of bars installed with product B occurs at the interface between mortar and concrete. After overcoming the adhesion strength at relatively small slip values (s~±0.2 mm), the load transfer is dominated by friction between mortar and concrete. This friction is reduced significantly by cyclic loading. The bond resistance of rebars post-installed with product B at small displacement values is rather low and the relatively low bond strength is reached at displacement values which in general can not be used in reinforced concrete structures. Furthermore the bond deterioration during cyclic loading is much more pronounced than for cast-in-place rebars. Therefore this product is not well suited for post-installed rebars under monotonic and cyclic loading.
4. Conclusions From the results obtained in this study, the following main observations can be made for the local bond behavior of post-installed rebars under monotonic and cyclic loading. The results show that the behavior of mortared-in bars under cyclic loading depends on the failure mode under monotonic loading. According to the test results the bond failure of deformed rebars post-installed with product A failed by overcoming the bond strength at the interface between rebar and mortar (shearing of the mortar between the lugs). Therefore the bond behavior during monotonic and cyclic loading is very similar to the bond behavior of cast-in-place rebars. On the contrary to that rebars post-installed with product B failed at the interface
519
between mortar and wall of the hole at relatively low bond stress values and corresponding low displacements. The bond behavior of these rebars under monotonic and cyclic loading was much inferior to the bond behavior of cast-in-place rebars. Therefore product B should not be used to post-installed rebars subjected to monotonic or cyclic loading. Many post-installed rebars may fail by a combination of a bond failure at the interface between rebar and mortar over a part of the embedment length and mortar and concrete over the rest of the bond length. The behavior of these rebars under monotonic loading and cyclic loading will lay in between the two extremes shown above. This behavior should be investigated in tests. The mode of failure of post-installed rebars might change with rebar diameter. Therefore with a given injection mortar, the influence of the diameter on the bond behavior should be checked by tests. In the tests described above failure occurred by pullout of the rebars. In many applications rebars will be installed with a small concrete cover and they might fail by a splitting failure. The behavior of post-installed rebars under cyclic loading in case of splitting failure should also be investigated.
5. Acknowledgement Funding for this work was made available through the Institute of Construction Materials, University of Stuttgart, Germany. Special thanks to E. Schiebelbein and F. Stockert for their encouragement in data preparation. Thanks to M. Hoehler for improving the English.
6. References [1]
Eligehausen, R.; Popov, E.P.; Bertero V.V.: Local Bond Stress-Slip Relationships of Deformed Bars under Generalized Excitations, Report No. UCB/EERC-83/23, University of California, Berkeley, California, USA, 1983.
[2]
Popov, E.P.: Mechanical Characteristics and Bond of Reinforcing Steel under Seismic Loading, Workshop on Earthquake Resistant Reinforced Concrete Building Construction, University of California, Berkeley, 1977.
[3]
Eligehausen, R.; Spieth, H.A.: Anschlüsse mit nachträglich eingemörtelten Bewehrungsstäben. Der Prüfingenieur. April 2000.
[4]
Eligehausen, R.; Spieth, H.A., Sippel, T.M: Eingemörtelte Bewehrungsstäbe – Tragverhalten und Bemessung. Beton- und Stahlbetonbau 94 (1999), Heft 12.
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AN EVALUATION OF TENSILE CAPACITY OF ANCHOR SYSTEM IN NPPS BY ACTUAL MODEL TESTS Jang Jung-Bum, Woo Sang-Kyun, Suh Yong-Pyo, and Lee Jong-Rim Nuclear Power Laboratory, Korea Electric Power Research Institute, KEPCO, Korea
Abstract The design of anchor system for fastening the equipments and piping systems, etc. to concrete structure has based on the ACI 349 code in Korean NPPs. But, CCD method of CEB code which was processed in Europe shows that anchor system design according to ACI 349 code has some of overestimated effects in the evaluation of tensile and shear capacity of the real anchor system. Also, according to US NRC SRP published in 1996, US NRC recommended that the anchor system should be designed by test results for each case until ACI 349 code will be newly revised. Moreover, Korean nuclear regulatory institute, KINS asks to follow the requirements of US NRC SRP for design of anchor system in NPPs. Therefore, in order to accurately evaluate both behavior and tensile capacity of anchor system used in Korean NPPs, actual model tests are carried out in this study. 60 test specimens with cast-in-place headed anchor system which is installed in uncracked and plain concrete test specimens, are manufactured for these actual model tests. From the results of this study, the discrepancies between the test results and these two design methods, ACI 349 code and CCD method of CEB code, are assessed and applicability of ACI 349 code for design of anchor system are evaluated.
1. Introduction The design of anchor system for fastening the equipments and piping systems, etc. to concrete structure has based on the ACI 349 code in Korean NPPs. But, CCD method of CEB code which was processed in Europe shows that anchor system design according to ACI 349 code has some of overestimated effects in the evaluation of tensile and shear capacity of the real anchor system. This discrepancy between ACI 349 code and CCD method of CEB code is due to the differences of their assumptions. That is, both ACI 349 code and CCD method of CEB
521
code assume differently for the inclination angle between the failure surface and concrete surface and concrete failure shape, etc. Also, a lot of papers related to this subject represent new movement to make some amendment to ACI 349 code or new design code based on CCD method of CEB code. According to US NRC SRP published in 1996, US NRC recognized that ACI 349 code has a some problems in design of anchor system and recommended that the design of anchor system should be performed by test results for each case until ACI 349 code will be newly revised. Moreover, Korean nuclear regulatory institute, KINS asks to follow the requirements of US NRC SRP for design of anchor system in NPPs. Therefore, in order to accurately evaluate both behavior and tensile capacity of anchor system used in Korean NPPs, KEPRI carried out the actual model tests with cast-inplace anchor system, most used in Korean NPPs. The discrepancies between the test results and these two design methods, ACI 349 code and CCD method of CEB code, will be assessed and applicability of ACI 349 code for design of anchor system will be evaluated in this paper.
2. Design Codes for Anchor System The major differences between CCD method of CEB code and ACI 349 code are as follows : ( a ) under tensile load, the inclination angle between the failure surface and concrete surface is 45 degree for ACI 349 code and 35 degree for CCD method of CEB code, ( b ) concrete tensile capacity is proportional to 2.0 power of embedment depth of anchor bolt for ACI 349 code and 1.5 power for CCD method of CEB code, and ( c ) the concrete failure shape is idealized by cone for ACI 349 code and pyramid for CCD method of CEB code. Due to above major differences between ACI 349 code and CCD method of CEB code, the prediction of concrete cone failure load is different each other. According to test results for anchor system, CCD method of CEB code well agrees with test results than ACI 349 code and ACI 349 code is shown the non-conservative design for some cases.
2.1 ACI 349 Code Under tensile load, ACI 349 code assumes that uniform tensile stress of 4φ
f c acts
on the projected area of the concrete failure cone as shown in figure 1 and the inclination angle for calculating projected area shall be 45 degree. Also, in order to avoid the reduction of concrete cone failure load, the concrete member thickness is assumed sufficiently large. For a single anchor without edge influences or over-lapping failure volume, concrete cone failure load is calculated from Eq. ( 1 )
N no = (4φ f c ) AN 0 , lb
(1)
522
where
φ
is capacity reduction factor and AN 0 is projected area of a single anchor
without any limitations and is given by Eq. ( 2 ).
AN 0 = πhef2 (1 +
du ) hef
(2)
with f c = Concrete compressive strength
d u = Diameter of anchor head hef = Effective embedment depth of anchor bolt For anchor system with edge influences ( c < hef ) or affected by other concrete breakout cones (
Nn =
s < 2hef ), the concrete cone failure load is calculated from Eq. ( 3 )
AN d 4φ f c πhef2 ( 1 + u ),lb AN 0 hef
(3)
where c is edge distance from anchor bolt to the nearest concrete edge and s is a distance between a neighboring anchor bolts. AN is actual projected area of stress cones radiating from anchor head. Effective area shall be limited by over-lapping failure volume, bearing area of anchor heads, and overall thickness of concrete member
2.2 CCD Method of CEB Code Under tensile load, the concrete failure load of a single anchor is calculated assuming an inclination angle between the failure surface and concrete surface of about 35 degree as shown in figure 2. For a single anchor in uncracked concrete without edge influences or over-lapping failure volume under tensile load, the concrete failure load N n 0 is given by Eq. ( 4 )
N n 0 = k1 f c k 2 hef2 k 3 hef−0.5 , lb where
(4)
k1 , k 2 , k 3 are calibration factors, with
k nc = k1k 2 k 3 N n 0 = k nc
f c hef1.5 , lb
(5)
523
with
k nc = 35 for post-installed anchor system k nc = 40 for cast-in-place anchor system In Eq. ( 4 ), the factor
k1 f c represents the nominal concrete tensile stress at failure 2
−0.5
over the concrete failure area, given by k 2 hef , and the factor k3hef
represents the so-
called size effect. For anchor system with edge influences or affected by other concrete breakout cones, the concrete failure load is calculated from Eq. ( 6 ).
AN ψ 2 knc f c hef1.5 AN 0 A N n = N ψ 2 N n0 AN 0 Nn =
(6) (7)
where ψ 2 is tuning factor to consider disturbance of the radial symmetric stress distribution caused by an edge, valid for anchors located away from edges and is given by Eq. ( 8 ).
ψ2 =1
if c ≥ 1.5hef
ψ 2 = 0 .7 + 0 .3
c 1.5hef
( 8.a ) if c ≤ 1.5hef
( 8.b )
3. Tensile Capacity Evaluation Tests The objectives of this study are to identify the causes of discrepancies between ACI 349 code and CCD method of CEB code and to evaluate the applicability of ACI 349 code for design of anchor system through the tensile capacity evaluation tests. This test plan intended for the cast-in-place anchor system which was most prevailed in Korean NPPs. 60 test specimens with cast-in-place headed anchors which are installed in uncracked and plain concrete test specimens, are manufactured for this actual model tests.
3.1 Test Variables In order to compare tensile capacities of anchor system estimated by two design procedures, ACI 349 code and CCD method of CEB code, with test results according to the various test variables, 5 test variables are considered. That is, these test variables are diameter of anchor bolt, embedment depth of anchor bolt, concrete compressive strength,
524
edge influence by distance between anchor system and concrete edge, and over-lapping failure volume by interaction of neighboring anchor systems. The detailed descriptions of these test variables are as follows. [1] Loading condition Anchor system is generally designed by tensile and shear load but these tests are carried out under tensile load. 100 tonf-capacity actuator is used to apply tensile load to test specimens and tensile load is gradually increased by displacement control so that displacement of anchor system occurs 0.5 mm/min. [2] Diameter of anchor bolt Diameter of anchor bolt is selected so that concrete brittle failure is occurred at test specimens under tensile load. The selected diameters of anchor bolts are cast-in-place headed anchors of 3/4, 9/8, 13/8, and 2 in. with ASTM A193 Gr B7. [3] Embedment depth of anchor bolt Referring to the existing test results related to the anchor system, both ACI 349 code and CCD method of CEB code are shown the conservative design for anchor system under about 8 in. in embedment depth of anchor bolt. But, both design codes are shown the different results for anchor system from about 8 in. up in embedment depth of anchor bolt. Therefore, this study considers the 2, 4, 8, 12, and 14 in. as embedment depth of anchor bolt. [4] Concrete compressive strength Concrete compressive strength has an less influence on concrete failure load of anchor system than the other test variables and most concrete buildings of Korean NPPs have been designed with concrete compressive strength of 4,500 psi excluding containment building. Therefore, constant concrete compressive strength of 4,500 psi is used for manufacturing the test specimens for this study. [5] Edge influence In order to examine the reduction of concrete failure load due to edge influence by distance between anchor system and concrete edge, this test variable is considered. The distances between anchor system and concrete edge are 2, 4, 6, and 7 in. with a half of embedment depth of anchor bolt so that edge influence affects the concrete failure load. [6] Over-lapping failure volume In case of anchor systems for equipments and piping system, etc. installed at NPPs, the distances between neighboring anchor bolts are very short and concrete failure load is reduced due to over-lapping failure volume by interaction of neighboring anchor bolts. In order to examine the reduction of concrete failure load due to over-lapping failure volume, anchor system which 4 anchor bolts act as single anchor system is considered and the distance between neighboring anchor bolts is determined so that it affects the concrete failure load.
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3.2 Test Specimens According to ASTM E488-96, test specimens are manufactured so that the minimum clearances between supports of test specimens are equal to or greater than 4.0 hef. Also, the test specimens are at least 2.0 hef in thickness so long as the depth is suitable for normal installation of the anchor system and does not result in premature failure at either the structural member or anchor system. Table 1 shows the test specimens manufactured for this study. The minimum of 5 tests per test number of table 1 are carried out in accordance with ASTM E488-96 and 5 test results are averaged for determining the tensile capacity of anchor systems. Figures 3 and 4 show the test specimen and view which actual model test is being carried out with 100 tonf-capacity actuator.
3.3 Test Results In case of single anchor system without over-lapping failure volume, both ACI 349 code and CCD method of CEB code are shown the conservative results in comparison with test results as shown in Figure 5(a). However, in case of multiple anchor system with over-lapping failure volume, ACI 349 code overestimated and CCD method of CEB code underestimated with test results as shown in Figure 5(b). This is probably due to the fact that their assumptions like inclination angle and concrete failure shape are different each other. That is to say, in case that over-lapping failure volume happened in anchor system, concrete failure load predicted by CCD method of CEB code is smaller than ACI 349 code because over-lapping failure volume by CCD method of CEB code is larger than ACI 349 code. Moreover, these facts are revealed in test results for examination of edge influence as shown in Figure 6. In case that concrete failure load is reduced due to edge influence by distance between anchor system and concrete edge, CCD method of CEB code well agrees with test results than ACI 349 code. Therefore, in case that anchor system for fastening the equipments and piping systems, etc. will be designed at NPPs, CCD method of CEB code turned out reasonable than ACI 349 code through this study. Figure 7 is shown the typical concrete failure shape.
526
Table 1. Test specimens for tensile capacity evaluation of anchor system
Loading No. condition
Embedment depth of anchor bolt ( in. )
1
2
2
4
3
8
4
12
5
14
6 7
Tensile load
Overlapping failure volume
Edge influence
Remarks
5 5 Single anchor
5 Center point
4 8
No. of test specimen
5 5 5
Multiple anchor
5
8
12
5
9
4
5
10
8
11
12
12
14
Single anchor
Edge point
Direct embedment type
5 5 5
Summation
60
4. Conclusions In order to accurately evaluate both behavior and tensile capacity of cast-in-place headed anchor system which is most used in Korean NPPs, actual model tests are carried out. These actual model tests are carried out for the tensile capacity evaluation of CIP anchor system as first stage of overall test plan and tests related to the shear capacity evaluation in uncracked and plain concrete, tensile and shear capacity evaluation in cracked and plain concrete will be carried out near the future as second stage. As a result of this study, CCD method of CEB code well agrees with test results than ACI 349 code and especially ACI 349 code gives the underestimated results in case of anchor systems with over-lapping failure volume and influence of edge distance. Therefore, in case that anchor system for fastening the equipments and piping systems, etc. will be designed at NPPs, CCD method of CEB code turned out reasonable than ACI 349 code.
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References [1] Fuchs, W., Eligehausen, R., and Breen, J.E.,“ Concrete Capacity Design ( CCD ) Approach for Fastening to Concrete, “ ACI Structural Journal, Vol. 92, No. 1, pp. 73 – 94, 1995. [2] Eligehausen, R. and Balogh, T.,“ Behavior of Fasteners Loaded in Tension in Cracked Reinforced Concrete,“ ACI structural Journal, Vol. 92, No. 3, 1995. [3] Hallowell, J.M.,“ Tensile and Shear Behavior of Anchors in Uncracked and Cracked Concrete under Static and Dynamic Loading,“ University of Texas at Austin, 1996. [4] Primavera, E.J., Pinelli, J.P., and Kalajian, E.H.,“ Tensile Behavior of Cast-In-Place and Undercut Anchors in High Strength Concrete,“ ACI Structural Journal, 1997. [5] ASTM E 488-96, “ Standard Test Methods for Strength of Anchors in Concrete and Masonry Elements,“ 1996.
Figure 1. Concrete failure shape by ACI 349 code
Figure 2. Concrete failure shape by CCD method of CEB code
Figure 3. Test specimen with CIP anchor system
528
Figure 4. Actual model test by 100 tonf-capacity actuator
100
100
Test Results ACI 349 Code CCD Method of CEB Code
90
80
Concrete Failure Load ( tonf )
80
Concrete Failure Load ( tonf )
Test Results ACI 349 Code CCD Method of CEB Code
90
70
60
50
40
30
70
60
50
40
30
20
20
10
10
0
0 0
2
4
6
8
10
12
14
16
18
20
Embedment Depth of Anchor bolt ( in. )
0
2
4
6
8
10
12
14
16
Embedment Depth of Anchor bolt ( in. )
( a ) Single anchor systems
( b ) Multiple anchor systems
Figure 5. Concrete failure loads by actual model test
529
18
20
100
Test Results ACI 349 Code CCD Method of CEB Code
90
Concrete Failure Load ( tonf )
80
70
60
50
40
30
20
10
0 0
1
2
3
4
5
6
7
8
9
10
Distance between Concrete Edge and Anchor system ( in. )
Figure 6. Concrete failure loads by actual model test – edge influence
Figure 7. Typical concrete failure shape under tensile load
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STRUCTURAL BEHAVIOR OF SRC COLUMN - RC BEAM JOINT UNDER MONOTONIC AND CYCLIC LOAD Sang-Hoon Lee, Young-Kyu Ju, Sung-Chul Chun and Dae-Young Kim Daewoo Institute of Construction Technology, South Korea
Abstract SRC column–RC beam joint is frequently used for the construction of underground structure in the Top-Down construction method. Various types of joint details have been proposed and implemented for the anchorage of the reinforcing bars. The types can be classified by anchoring methods as follows: (1) passing through type; (2) wing plate type; and (3) H-beam bracket type. Although these types are widely used in Korea, the structural performance is not clearly understood. For each type of joint, the structural characteristics such as strength, stiffness, energy dissipation capacity, stiffness degradation, and ductility under monotonic and cyclic loads were tested. The test results showed that the passing through type has the best structural performance. By advancing the passing through type, the wide beam type specimens were experimentally investigated for the field application. The wide beam type uses a number of reinforcing bars that are placed at the edge of the slab not to intersect a steel column without changing its sectional shape. It is concluded that the wide beam type is adequate in the SRC column-RC beam joint not only for its structural capacities, but also for its economic merits.
1. Introduction General The Top-Down method is frequently used at a downtown construction site, because it requires less construction space than other methods. Also, this method reduces construction time, noise and vibration, and prevents unequal settlement of the surrounding ground. Since its invention by Mr. Arup in 1936, characteristics, construction procedure and several details of this method have been studied to promote the construction efficiency. As one of these efforts, when deciding structural type, the composite structure is mostly preferred.1)
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In Japan, since the early recognition of the necessity of the composite structure, several beam-column joint types have been developed. Focused joint types are SRC columnSRC beam, RC column-steel beam, and SRC column-steel beam. When using SRC column-RC beam joint type, the passing through type is preferred, because of the safety from the earthquake. The reinforcing bar is anchored by making a hole at the steel column and passing through the column. SRC column-RC beam joint is usually adopted for the underground structures in Korea. However, its beam cannot maintain the continuity because of the construction characteristics. The various joint types, such as the passing through type, the wing plate type, the bracket type, and the coupler type have been proposed and implemented to settle this problem.2) In spite of frequent usage of these types, there were not comprehensive experimental bases of their structural behaviors. Research Scope In this study, the passing through type, the wing plate type, and the H-beam bracket type were considered. Although the coupler type is known for its best reliability of anchorage of the reinforcing bar, it was not considered, because it can be implemented immediately if its welding condition is proved to be good enough. First of all, the monotonic and cyclic loading experiments were conducted for each joint type to investigate the structural behaviors. Then, additional monotonic tests were performed to efficiently develop the type that showed the best performance. Special attentions were paid to investigate the efficiency of placing the tensile reinforcing bars within the effective beam width. For the field application, the wide beam type was explored by experiment.
2. Comparative Experiment Monotonic and cyclic loading tests were performed to investigate the structural capacities of three types as follows; (1) passing through type, (2) wing plate type, and (3) H-beam bracket type. Specimens were designed as the interior joint of the underground structure whose clear length of span was 790cm. The same materials were used for all specimens. The measured properties of the materials are as follows: (1) uni-axial compressive strength of the concrete (28day) was 254 kgf/cm2, (2) average uni-axial tensile strengths of the re-bars were 4,147 kgf/cm2 (D10) and 3,999 kgf/cm2 (D22), and (3) average uni-axial tensile strengths of H-beam and plate were 3,813.5 kgf/cm2 and 3,024.67 kgf/cm2, respectively.
2.1 Monotonic Loading Test General Three different types were designed and tested under the monotonic load.3, 4, 5, 6) The seismic design was not considered. The flexural failure criteria were expected to all of the specimens. Fig. 1 shows the dimensions and the details of each specimen. As shown in Fig.2, a static actuator was bound by the reaction frame to apply load to the top
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φ
(a) Passing through type
(b) Wing plate type
(c) H-beam bracket type
[Fig. 1] Dimensions and Reinforcement Details (Units in mm) of the column. The ends of the beam were supported by hinge and the ends were free to rotate only. Several transducers were placed to measure the displacement of the column and the rotation of the beam against the column. Test Results The results showed that the passing through type and the wing plate type have the satisfactory structural performances. As Table 1 presents, their ultimate strengths exceeded the design strengths by about 20% and their ductility factors also satisfy the required value of ordinary reinforced concrete structure, which is 4.0. However, the bracket type specimen did not surpass either the yield design strength or the ultimate strength. Fig. 3 shows the load-displacement relations and Fig. 4 presents the observed cracks of the specimens.
2.2 Cyclic Loading Test General Reverse cyclic loading tests were conducted to investigate the behavior of the interior beam-column joint for each type. The details of the passing through type and the Hbeam bracket type are shown in Fig. 5(a) and 5(b). The only differences from the specimen of the monotonic loading test are the length of the column and the reinforcing
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35 Passing through type 30
Pn=25.4t Load (Tonf)
25 Wing plate type 20 H-beam bracket type
15 10 5 0 0
20
40
60
80
100
120
140
Displacement (mm)
[Fig.2] Loading Method
[Fig. 3] Load-Displacement Relations
[Table 1] Monotonic Loading Test Results Specimen Type Passing Through Wing Plate H-Bracket
Yield Strength
Ultimate Strength
Design (ton)
Test (ton)
Ratio (T/D)
Design (ton)
Test (ton)
Ratio (T/D)
Displacement Ductility Factor
24.76
23.80
0.96
25.38
31.06
1.22
7.87
8.47
24.76
24.51
0.99
25.38
30.15
1.19
5.34
6.17
25.78
21.34
0.83
27.11
24.11
0.89
1.86
1.47
(a) Passing through type
Curvature Ductility Factor
(b) H-beam bracket type
[Fig 4] Observed Cracks of Specimens bars of the beam due to seismic resistance.3, 4, 5, 6) Fig. 6 shows test setup. The column was tied to the reaction frame and was allowed to rotate only. Constant axial load (150tonf), which was about 25% of the design axial strength of the column, was applied to the top end of the column during the test. In all tests, a sinusoidal displacement control wave form consisting of completely reversed cycles at the amplitude of 1δ, 2δ, 4δ, 6δ, 8δ, where δ is the displacement when the
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tensile reinforcing bar started yielding. Fig. 7 shows the detail of the location of the transducers to measure the displacements of the loading points and the rotation of the beam against the column. Prefabricated angle set was used to fix all the transducers. This angle set was attached to the specimen at the supporting point, but using ball bearings, was not affected by the movement of the specimen.
(a) Passing through type
(b) H-beam bracket type
[Fig. 5] Dimensions and Reinforcement Details
[Fig. 6] Test setup
[Fig. 7] Measuring points
Test results The measured hysteresis loops of equivalent interstory shear force(V) versus equivalent interstory drift(δ), which can be obtained using equation (1), are shown in Fig. 8(a), 8(b), and 8(c).
V = Where,
P1l1 + P2 l 2 δ + δ B2 , δ = B1 × lc l1 + l 2 lc
P1and P2 : loads applied to both beams
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(1)
l1, l2 : distance from the center of the column to the loading point lc : distance from upper supporting point to lower point of the column δB1, δB2 : displacements at the loading point of each beam The external work curve of each specimen versus cumulative displacement is shown in Fig. 8(d). Table 2 shows the equivalent inter-story shear force and energy dissipation capacity. The passing through type and the wing plate type surpassed the design strength by 14% and 27%, respectively. However, H-beam bracket type did not reach its design strength due to the premature shear failure of concrete, which resulted from the bond failure between steel and concrete. Therefore, the test was interrupted as soon as the shear failure occurred. 20 1δ
4δ
2δ
6δ
15
Equivalent Interstory Shear Force (tonf)
Equivalent Interstory Shear Force (tonf)
20
Vne Vye
10 5 0 -150
-125
-100
-75
-50
-25
0
25
50
75
100
125
150
-5 -10 -Vye -Vne
-15 -2δ
-4δ
-6δ
1δ
2δ
4δ Vne
15
Vye
10 5 0 -150
-125
-100
-75
-50
-25
0
25
50
75
100
125
150
-5 -10
-Vye
-15
-Vne -4δ
- 1δ -20
-2δ -1δ -20
Equivalent Interstory Drift (mm)
Equivalent Interstory Drift (mm)
(a) Passing through type
(b) Wing plate type 8,000
1δ
2δ
3δ
15 10 5 0 -150
-125
-100
-75
-50
-25
0
25
50
75
100
-5
-Vne -3δ
-2δ
-1δ
Wing Plate type
7,000 Vne
125
150
External Work (Ton.mm)
Equivalent Interstory Shear Force (tonf)
20
6,000 5,000 Passing through type
4,000 H-beam bracket type
3,000 2,000
-10
1,000
-15
0 0
-20
500
1,000
1,500
2,000
2,500
3,000
3,500
Cumulative Displacement (mm)
Equivalent Interstory Drift (mm)
(c) H-beam bracket type
(d) Energy dissipation curve
[Fig. 8] Cyclic Loading Test Results The passing through type specimen showed a stable behavior until 4δ. However, the deformations due to bond slippage at the panel zone became very significant, and pinching and severe degradation of stiffness were observed in the hysteresis loops at the second cycle of the 4δ. The wing plate type specimen also showed a stable behavior. Pinching and degradation of stiffness did not occur until 4δ. Because the welded area between the wing plate and the flange of the H-beam was torn out, the test was stopped at the first cycle of 6δ. In the case of the H-beam bracket type, inverse shear crack was observed during the first cycle of the loading. Several inverse shear cracks occurred as the test continued. Finally, it caused the specimen to fail.
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[Table 2] Cyclic Loading Test Results Specimen Type Passing Through Wing Plate H-Beam Bracket
Yield Equivalent InterStory Shear Force Analysis Experiment (tonf) (tonf)
Ultimate Equivalent Inter-Story Shear Force Analysis Experiment VA/VE (tonf) (tonf)
13.02
12.68
13.45
15.23
1.13
-13.02 13.02 -13.02 17.39 -17.39
-13.07 12.96 -13.04 16.10 -15.89
-13.45 13.45 -13.45 17.39 -17.39
-15.48 17.04 -17.08 16.10 -16.99
1.15 1.27 1.27 0.93 0.98
Dissipated Energy (tonf-mm) 6,081 7,058 3,254
3. Monotonic Loading Test for Wide-beam Sectional Specimens General The passing through type specimen and the wing plate type specimen satisfied the required structural performance. However, there were some problems to be solved for the field application. In case of passing through type, the thickness of the steel was the significant factor. As the thickness of column steel increased, it was difficult to make holes in thick flange and it made the passing through type less efficient for field application. In case of wing plate type, the tensile reinforcing bars of the slab were arranged in double layers and welded on and below the wing plate. It was difficult to weld the bar below the wing plate while easy to do on the plate. Therefore, additional tests for wide beam type were performed to implement these types efficiently for the field application. Special attentions were paid to investigate the efficiency of placing the tensile reinforcing bars. Five different specimens were constructed, as shown in Fig. 9, based on Chapter 10.6.6 of ACI 318-99.7) The SRC1 specimen used the reinforcing bars that were placed in two layers and welded on the wing plate for their anchorage. The design of SRC2 specimen was similar to that of the wide-beam. Only two reinforcing bars were placed in the beam and bypassed the steel column. The others were placed in the slab within the effective width of beam. Since the compressive area of the beam, which was affected by the negative moment, satisfied the required design moments, the modification of the sectional shape was not necessary. The detail of SRC3 specimen was similar to that of the SRC2, except the anchorage of the two reinforcing bars in the beam, which were welded on the wing plate. RC1 and RC2 specimens, shown in Figs. 9(c) and 9(d), were also tested to compare with SRC series specimens. During the test, the same value of the load was applied until it reached the ultimate strength. Strain gauges were attached to the reinforcing bars to evaluate the strain distributions. They were attached at the critical section that was 30cm away from the center of the column.
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Test results As shown in Fig. 11, behaviors of all the specimens were similar until they reached the yielding strength. Fig. 12 shows the strain distribution of reinforcing bars of RC1, RC2, SRC1 and SRC2 at each loading step. Since there were only two reinforcing bars in the beam section of the SRC2, the strain increment at each loading step was larger than those of the RC series. This phenomenon could be corrected by modifying the placement of reinforcing bars.
(a) SRC1
(b) SRC2
(c) RC1
(d) RC2
[Fig. 9] Dimensions and details of the specimens 35
S R C -2 R C -2
30
S R C -3 S R C -1
Load (tonf)
25
R C -1
20 15 10 5 0 0
10
20
30
40
50
60
Displacement (mm)
[Fig.10] Testing setup
[Fig.11] Load-displacement relations
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70
3000
2500
2500
2000
25 tonf
1500
20 tonf
25 tonf
2000
Strain
Strain
3000
20 tonf 1500
15 tonf
15 tonf 1000
1000
10 tonf 10 tonf
500
500
0
0
-40
-30
-2 0
- 10
0
10
20
30
-40
40
- 30
- 20
-10
(a) RC1 3000
2500
2500
Strain
Strain
20 tonf 15 tonf
1000
30
40
25 tonf
1500
20 tonf
1000
15 tonf
500
10 tonf
10 tonf
500
20
2000
25 tonf
1500
10
(b) RC2
3000
2000
0
Distance from the center (cm)
Distance from the center (cm)
0
0 -50
-40
-30
-20
-10
0
10
20
30
40
-50
50
-40
-30
Distance from the center (cm)
-20
-10
0
10
20
30
40
Distance from the center (cm)
(c) SRC1
(d) SRC2 [Fig.12] Strain distributions
[Table 4] Monotonic Loading Test Results Yield Strength Specimen Type Analysis(tonf) Experiment(tonf) SRC1 SRC2 SRC3 RC1 RC2
26.18 27.77 27.77 26.35 27.93
(a) RC1
26.58 24.09 25.42 27.00 28.58
Ratio(E/A) 1.02 0.87 0.92 1.02 1.02
(b) RC2 [Fig. 13] Observed cracks of the beam
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Experimental Ultimate Strength 27.858 30.476 28.897 29.785 28.615
(c) SRC1
50
Testing results are presented in table 4. The yield strengths of SRC2 and SRC3 were lower than the analytical value, because the experimental yield strength was evaluated when at least one of the reinforcing bars reached its yielding strain. Fig. 13 shows the cracks of the beam when the test was finished. All the cracks showed typical flexural failure mode regardless of the specimen type. The cracks of the slab of all the specimens also showed similar failure trend.
4. Conclusions In this study, monotonic and cyclic loading test were conducted to investigate the structural behavior of the several SRC column-RC beam joint types which are frequently used in the Top-Down construction method such as the passing through type, the wing plate type, and H-beam bracket type. Advanced joints for the field application, where the most of reinforcing bars were placed in the slab within the effective width of the beam, were also tested under the monotonic load. The following conclusions were made: (1) The passing through type and the wing plate type showed the satisfactory structural performance to be implemented as SRC column-RC beam joint type. Both types surpassed their analytical strengths and the required ductility. (2) When using the wide beam type, it is recommended that all the reinforcing bars bypass H-beam of the column through the slab except for the minimum number of reinforcing bars, which can be anchored to the wing plate by welding. (3) When the tensile reinforcing bars of the beam are placed within the slab, the bars work as both beam and the slab, and this method is expected to reduce the construction cost.
References 1. Daewoo Institute of Construction Technology, ‘The Development of Beam-Column Joint in Top-Down Construction Method’, DEP-009-2000, Technical Report, (2000). 2. Kim, J. H., ‘Design of Pre-constructed SRC Column-RC Beam Joint of Underground Structure Under Top Down Method’, Journal of Korean Society of Steel Construction 10(3) (June 1998) 142-150. 3. Kim, D. H., ‘Standard for Structural Calculation of Steel Reinforced Concrete Structures’ (January 1999). 4. American Institute of Steel Construction (AISC), ‘Manual of Steel Construction – Load & Resistance Factor Design’ (1994). 5. American Institute of Steel Construction (AISC), ‘Manual of Steel Construction – Allowable Stress Design’ (1989). 6. American Welding Society, ‘ANSI/AWS D1.4-92; Structural Welding CodeReinforced Steel’ (1992). 7. ACI Committee 318, ‘Building Code Requirements for Structural Concrete (ACI31899) and Commentary (ACI318R-99)’ (1999) 114.
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DYNAMIC BEHAVIOR OF TENSILE ANCHORS TO CONCRETE Milton Rodriguez1, Dieter Lotze2, Jennifer Hallowell Gross3, Yong-gang Zhang4, Richard E. Klingner5 and Herman L. Graves, III6 1 The University of Texas at Austin, Texas, USA. 2 Halfen GmbH & Co., Wiernsheim, Germany. Former, The University of Texas at Austin. 3 Cagley, Harman & Associates, King of Prussia, Pennsylvania, USA. Former, The University of Texas at Austin. 4 Han-Padron Associates, Houston, Texas, USA. Former, The University of Texas at Austin. 5 Phil M. Ferguson, The University of Texas at Austin, Austin, Texas, USA. 6 Office of Nuclear Regulatory Research, US Nuclear Regulatory Commission, Washington, DC, USA.
Abstract Under the sponsorship of the US Nuclear Regulatory Commission, a research program was carried out on the dynamic behavior of anchors (fasteners) to concrete. In this paper, the behavior of single and multiple tensile anchors is described. Under seismic loading, the tensile capacities of most anchors tested in this study were at least as high as under quasi-static loading. As a result, most anchors tested in this study, if designed for ductile behavior under quasi-static loading, would behave in a ductile manner under seismic-type loading as well. The above conclusions are not true for wedge-type expansion anchors. These tend to pull out and pull through under dynamic loading and should be evaluated individually to determine their seismic adequacy. The above conclusions are also not true for grouted anchors installed in cored holes. These tend to pull out in cracked concrete.
1. Introduction Under the sponsorship of the US Nuclear Regulatory Commission, a research program has recently been completed, whose objective was to obtain technical information to determine how the seismic behavior and strength of anchors (cast-in-place, expansion, and undercut) and their supporting concrete differ from the static behavior. As discussed in References 1 and 2, the research program comprised four tasks: 1) 2) 3) 4)
Static and Dynamic Behavior of Single Tensile Anchors (250 tests); Static and Dynamic Behavior of Multiple Tensile Anchors (179 tests); Static and Dynamic Behavior of Near-Edge Anchors (150 tests); and Static and Dynamic Behavior of Multiple-Anchor Connections (16 tests).
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2. Background The behavior of anchors (fasteners) to concrete is discussed at length in References 2 and 3. Most tests on connections have been conducted under quasi-static, monotonic loading. A few studies have investigated the effects on connections of impact loading, seismic loading or reversed loading [4, 5, 6, 7]. In most such studies, the objective was to investigate the effects of some sort of dynamic loading to low load levels, on the anchor’s subsequent load-displacement behavior to failure under monotonic load [6, 7]. Only a few investigations [8] have addressed the influence of loading rate on the entire load-displacement behavior of anchors. Relatively few tests had been conducted in cracked concrete or in high-moment regions [4, 6, 8, 9, 10].
3. Anchors, Test Setups and Procedures Based on use of existing anchors in nuclear applications, the testing program originally emphasized one wedge-type expansion anchor (referred to here as “Expansion Anchor”), with some tests on one undercut anchor (“UC Anchor 1”), and other tests on anchors in one type of cementitious grout (“Grouted Anchor”). As the testing progressed, other anchors were added: a variant on the expansion anchor (“Expansion Anchor II”); another undercut anchor (“UC Anchor 2”); and a heavy-duty sleeve-type single-cone expansion anchor (“Sleeve Anchor”). Anchors ranged in diameter from 3/8 to 1 in. (9.2 to 25.4 mm), with emphasis on 3/4 in. (19.1 mm) diameter. The Cast-in-Place (CIP) anchors tested in Task 1 were A325 bolts, shown in Figure 1.
Figure 1
Typical cast-in-place anchor (A325 bolt) tested in Tasks 1 and 3 of this study
The Grouted Anchors were A325 hex-head bolts, 3/4 in. (19 mm) diameter by 6 in. (152 mm) long. No washers were placed at the heads since the bearing area already meets the minimum requirement of ACI 349 Appendix B [11]. The Expansion Anchor II (EAII), shown in Figure 2, is a wedge-type expansion anchor.
D
D1 D2
wedge dimple wedge mandrel (cone)
lc
Figure 2
Key dimensions of Expansion Anchor II
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The Expansion Anchor (EA) tested in Task 1 of this study is an earlier version of Expansion Anchor II. It was used extensively in some existing nuclear power plants, and is no longer produced. Its dimensions are generally similar to those of EAII. Samples of EA were obtained from the manufacturer. The Sleeve Anchor tested throughout this study is a single-cone, sleeve-type expansion anchor with follow-up expansion capability, shown in Figure 3. expansion sleeve structurally funished surface cone
D
lc
lef
Figure 3
D2
plastic crushable leg
D1
spacer sleeve
Key dimensions of Sleeve Anchor
The Undercut Anchor 1 (UC1) tested throughout this study is a conventionally opening undercut anchor, consisting of a threaded rod with a steel cone at one end and an expansion sleeve (Figure 4). extension sleeve
expansion sleeve
D
lef
Figure 4
D2
cone
D1
threaded shank
lc
Key dimensions of Undercut Anchor 1
Undercut Anchor 2, tested in Task 1 of this study, is an inverted-opening undercut anchor (Figure 5). cone
expansion sleeve
D
threaded shank extension sleeve
lef
Figure 5
lc
Key dimensions of Undercut Anchor 2
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Because the failure mode of deeply embedded anchors is governed by steel yield and fracture, and is well understood, the primary objective of this testing was to examine the influence of dynamic loading on anchor capacity as governed by concrete breakout, pullout or pull-through. The embedments were shallow, either the manufacturer’s standard embedment, or the minimum recommended embedment. The target concrete compressive strength for this testing program was 4700 lb/in.2 (32.4 MPa), with a permissible tolerance of ±500 lb/in.2 (±3.45 MPa) at the time of testing. Three types of aggregate were used: a porous limestone; a river gravel; and a local granite. The test setup used for some tests of Task 1 (single tensile anchors in uncracked and cracked concrete) is shown in Figure 6. Nut
Threaded Rod
Load Cell Hydraulic Ram Steel Plate
Loading Shoe
Beam (Back-to-Back Channels)
Reaction Ring
Anchor
Concrete Block
Figure 6
Test setup for Task 1
The typical test specimen, shown in Figure 7, was a concrete block 39.5 in. (1.00 m) wide, 24 in. (0.60 m) deep, and 87.5 in. (2.20 m) long. Seven #6 (32 mm) longitudinal reinforcing bars were placed in the middle of each block to provide safety when the block was moved. This reinforcement was placed at the mid-height of the block to permit testing anchors on both the top and bottom surfaces, without interfering with anchor behavior.
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39.5 in
87
.5
in
24 in
Lifting loop
Reinforcement 7-#6
Figure 7
Typical specimen for Task 1
16 in.
6 in.
16 in.
6 in.
A specimen used for Task 1 tests in cracked concrete is shown in Figure 8. Tension tests on single anchors were conducted on concrete slabs 54 in. (1372 mm) wide by 74 in. (1880 mm) long by 10 in. (254 mm) thick. The configurations of reinforcing bars in specimens were designed differently for tests on the two sizes of anchors, to use specimens most efficiently.
6 in.
24 in.
Plan View
Elevation Reinforcement
Figure 8
Wedge Tubes
Anchors
Specimen used for tests in cracked concrete
For Task 2, anchors were loaded through a stiff baseplate accommodating two anchors. Quasi-static tests were run using a one-way actuator supplied by an electric pump. Dynamic tests were run using a servo-controller under load control, using a ramp loading, selected to ensure anchor failure. The rise time of this load (about 0.1 sec) was set to correspond to that of typical earthquake response of mounted equipment.
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For tests in cracked concrete with post-installed anchors, hammer-driven wedges and split bearing tubes of high-strength steel were used to crack the concrete specimens and to widen the crack to the desired width. For tests on cast-in-place anchors, which had to be placed in position before casting, a piece of thin steel sheet was placed directly in the plane of the anchor, to force the crack to form there. Anchors were tightened to the torque specified by the manufacturer. To simulate the reduction of preload due to concrete relaxation, anchors were first fully torqued, then released after about 5 minutes to allow relaxation, and finally torqued again, but up to only 50% of the specified value.
4. Test Results Results for Single-Anchor Tension Tests Results for single-anchor tension tests are presented in terms of normalized tensile capacity, k: k=
Pn 1.5 ef
h
fc
(1)
where: k Pn fc hef
= = = =
coefficient (normalized tensile capacity) observed tensile capacity, lb tested concrete compressive strength, lb/in.2 effective embedment, in.
The effective embedment was measured from the concrete surface to the end of the expansion sleeve or to the point of the clip in contact with the concrete (Table 1). Results are given in Reference 2, and are summarized in Tables 2 and 3. Each value is the mean of at least 5 replicates, and is associated with coefficients of variation of 5% to 8%. Results are normalized by √fc′ to a reference concrete strength of 4700 lb/in.2 (32.4 MPa).
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Table 1
Embedment and effective embedment used for each anchor
Anchor and Diameter CIP Anchor, 0.75 in. (19 mm) Expansion Anchor, 0.75 in. (19 mm) Expansion Anchor II, 0.375 in. (9.5 mm) Expansion Anchor II, 0.75 in. (19 mm)
UC Anchor 1, 0.375 in. (9.5 mm) UC Anchor 1, 0.75 in. (19 mm) UC Anchor 2, 0.75 in. (19 mm) Sleeve Anchor, 0.375 in. (9.5 mm) Sleeve Anchor, 0.75 in. (19 mm) Grouted Anchor, 0.75 in. (19 mm)
Table 2
Embedment in. (mm) 4.00 (102)
Effective Embedment in. (mm) 4.00 (102)
3.25 4.75 2.25 3.25 4.00 4.75 2.25 4.00 4.00 2.25 4.00 4.00
2.44 3.94 1.94 2.69 3.44 4.19 2.25 4.00 4.00 2.25 4.00 4.00
(83) (121) (57) (83) (102) (121) (57) (102) (102) (57) (102) (102)
(120) (100) (49) (68) (87) (106) (57) (102) (102) (57) (102) (102)
Mean normalization coefficients for tensile anchors in various conditions obtained here for CC Method Load Type and Concrete Condition
Anchor Type
Static Uncracked
Dynamic Uncracked
Static Cracked
Dynamic Cracked
Cast-In-Place
41.6
53.9
36.2
52.3
Grouted
41.2
57.0
24.5
15.5
UC1, 3/8 in. (10 mm)
37.2
44.4
35.6
41.1
UC1, 3/4 in. (19 mm)
39.4
49.0
41.7
46.2
UC2, 3/4 in. (19 mm)
43.7
53.6
28.5
45.2
Sleeve, 10 mm
37.4
38.7
29.9
29.7
Sleeve, 20 mm
44.3
55.1
35.3
39.5
EA II
36.7
37.8
29.7
28.0
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Table 3
Ratios of tensile breakout capacities (static, cracked; dynamic, uncracked; and dynamic, cracked) to static tensile breakout capacities in uncracked concrete. Load Type and Concrete Condition
Anchor Type
Static Cracked/ Static Uncracked
Dynamic Uncracked/Static Uncracked
Dynamic Cracked/Static Uncracked
Cast-In-Place
0.87
1.30
1.26
Grouted
0.59
1.38
0.38
UC1, 3/8 in. (10 mm)
0.96
1.19
1.10
UC1, 3/4 in. (19 mm)
1.06
1.24
1.17
UC2, 3/4 in. (19 mm)
0.65
1.23
1.03
Sleeve, 10 mm
0.80
1.03
0.79
Sleeve, 20 mm
0.80
1.23
0.89
EA II
0.81
1.03
0.76
Results for Multiple-Anchor Tension Tests In Figure 9, capacities of two-anchor attachments [1] are compared as a function of the relative anchor spacing (s / hef), with capacities predicted by the CC Method [12]. Calculated dynamic capacity is taken as 1.25 times the static capacity. In dynamic tests, the increase in capacity with relative anchor spacing, is nearly parallel to the calculated values. This implies that the critical anchor spacing and the critical edge distance are no smaller under dynamic load than under static load.
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260.00
240.00
220.00
Failure Load Fu [kN]
200.00
180.00
160.00
140.00
Sleeve Anchor Static UC1 Static Sleeve Anchor Dynamic
120.00
UC1 Dynamic Calculated Static
100.00
Calculated Dynamic 80.00 0
Figure 9
0.5
1
1.5 2 Relative Spacing: s / hef
2.5
3
3.5
Static and dynamic tensile capacities depending on relative anchor spacing
5. Conclusions 1) Tensile breakout capacities are well described by the CC Method. Appropriate dynamic capacity ratios (Table 3) should be used for dynamic loading. 2) Under dynamic loads, effects of anchor spacing and edge distance are about the same for dynamic as for static loading, and are well predicted by the CC Method. 3) Anchors with dynamic capacity ratios greater than 1.0, designed for ductile behavior in uncracked concrete under static loading, will probably still behave in a ductile manner in cracked concrete under dynamic loading.
6. Acknowledgment and Disclaimer This paper presents partial results of a research program supported by the U.S. Nuclear Regulatory Commission (NRC) (NUREG/CR-5434, “Anchor Bolt Behavior and Strength during Earthquakes”). The technical contact is Herman L Graves, III, whose support is gratefully acknowledged. The conclusions in this paper are those of the authors only, and are not NRC policy or recommendations.
549
7. References 1) Rodriguez, M., “Behavior of Anchors in Uncracked Concrete under Static and Dynamic Loading,” M.S. Thesis, The University of Texas at Austin, August 1995. 2) Klingner, R. E., Hallowell, J. M., Lotze, D., Park, H-G., Rodriguez, M. and Zhang, Y-G., “Anchor Bolt Behavior and Strength during Earthquakes,” report prepared for the US Nuclear Regulatory Commission (NUREG/CR-5434), August 1998. 3) “Fastenings to Reinforced Concrete and Masonry Structures: State-of-Art Report, Part 1,” Euro-International Concrete Committee (CEB), August 1991. 4) Cannon, R. W., “Expansion Anchor Performance in Cracked Concrete,” ACI Journal, Proceedings, Vol. 78, No. 6, November-December 1981, pp. 471-479. 5) Malik, J. B., Mendonca, J. A., and Klingner, R. E., “Effect of Reinforcing Details on the Shear Resistance of Short Anchor Bolts under Reversed Cyclic Loading,” Journal of the American Concrete Institute, Proceedings Vol. 79, No. 1, January-February 1982, pp. 3-11. 6) Copley, J. D. and E. G. Burdette, “Behavior of Steel-to-Concrete Anchorage in High Moment Regions,” ACI Journal, Proceedings, Vol. 82, No. 2, March-April 1985, pp. 180-187. 7) Collins, D., R. E. Klingner and D. Polyzois, “Load-Deflection Behavior of Cast-in Place and Retrofit Concrete Anchors Subjected to Static, Fatigue, and Impact Tensile Loads,” Research Report CTR 1126-1, Center for Transportation Research, The University of Texas at Austin, February 1989. 8) Eibl, J. and E. Keintzel, “Zur Beanspruchung von Befestigungsmitteln bei dynamischen Lasten,” Forschungsbericht T2169, Institut für Massivbau und Baustofftechnologie, Universität Karlsruhe, 1989. 9) Eligehausen, R., W. Fuchs, and B. Mayer, “Bearing Behavior of Anchor Fastenings under Tension,” Betonwerk und Fertigteil-Technik, No. 12, 1987, pp. 826-832. 10) Eligehausen, R. and T. Balogh, “Behavior of Fasteners Loaded in Tension in Cracked Reinforced Concrete,” ACI Structural Journal, Vol. 92, No. 3, May-June 1995, pp. 365-379. 11) “Code Requirements for Nuclear Safety Related Concrete Structures,” ACI349-90), American Concrete Institute, Detroit, MI, 1990. 12) Fuchs, W., R. Eligehausen and J. E. Breen, “Concrete Capacity Design (CCD) Approach for Fastening to Concrete,” ACI Structural Journal, Vol. 92, No. 1, January-February 1995, pp. 73-94.
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TEST METHODS FOR SEISMIC QUALIFICATION OF POST-INSTALLED ANCHORS John F. Silva Hilti, Inc., USA
Abstract The qualification of post-installed anchors for use in seismic environments in the U.S. has been addressed independently by a number of different groups, including ICBO Evaluation Service, Inc., the Structural Engineers Association of Southern California (SEAOSC), ACI, and the telecommunications industry. Some of these methods have been derived from approaches developed in the nuclear industry to account for a variety of possible events (earthquake, explosion, impact). The primary focus of most of the test methods current and proposed is the response of the installed anchor to external cyclic loading, tension and shear. With the exception of the NEBS criteria, which consists of shake-table testing, strain rate effects are not taken into account. Two methods, the Provisional Test Method developed by ACI Committee 355 and the German nuclear standard developed by the Deutsches Institut für Bautechnik (DIBt), explicitly consider damage to the concrete in the form of a static crack passing through the anchor location. The SEAOSC criteria provides a comparison of the postinstalled anchor with an “equivalent” cast-in-place headed anchor, and results in loaddisplacement information (stiffness degradation, total slip) for cyclic loading throughout the entire load range (to failure). Results are presented for one anchor tested to three of these criteria: ICBO ES AC01 Method 2, SEAOSC, and the German nuclear standard. Conclusions are drawn regarding the effectiveness of the respective test methods.
1. Earthquakes and Their Effect on Anchor Performance Strong ground motion associated with earthquakes can be defined in terms of strain rate (10-5 < ε& < 10-2) , number of cycles (typically N < 30) and displacement (from several centimeters to a meter or more). Previous studies indicate that the strain rates associated with earthquakes are not a significant factor, positive or negative, for anchor behavior. At sub-yield load levels, cycling shear loads can lead to stiffness loss; pulsing tension
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loads are generally less significant. At load levels at or near ultimate, stiffness degradation is more significant. Displacement beyond the deformation capacity of the anchor is obviously a criterion for anchor failure. Many of the documented anchor failures in the literature can in fact be characterized as resulting from excessive deformation demand, usually in shear. Inertial forces generated in structures by strong ground motion are more difficult to characterize. Historically, the design of structures for earthquake resistance has focused on collapse prevention. For this purpose, design forces were defined as a percentage of the building mass, typically at levels that are far below expected inertial forces. Implicit in this approach is an expectation of structure overload with attendant member yielding and stiffness degradation. More recently, design methods are derived from a multi-level performance concept (lifesafety, damage limitation, continued operability, etc.) that places greater emphasis on design for ‘real’ force levels. Material resistances are simultaneously derived to represent ‘real’ ultimate strengths.1 Clearly, expectations of force and displacement demands beyond the elastic range continue to form the basis for fixed base (nonisolated) seismic design of structures.
2. History The performance of post-installed anchors in earthquakes was initially a subject of concern for the nuclear industry both in Canada and the United States. Since the 1970s, attention had been focused in within the U.S. nuclear industry on encouraging ductile failure of anchorages through the design process.2 While generally practical for the design of cast-in-place anchorages, this approach is often difficult to implement in the case of post-installed anchors, most of which were/are not designed to fail in a ductile manner. A nation-wide review of as-built conditions at U.S. nuclear facilities in the early 1990s focused on best-guess estimations of anchor static capacity as a means of retroactively qualifying anchorages for seismic loads. Combined with the severe loading criteria that had been established for nuclear construction, it was believed that this approach contained sufficient conservatism to avoid further seismic qualification testing of anchors.
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60%Fy
Ns = 50%Nu tension
tension
45%Fy 30%Fy 15%Fy
30 30
80
200
Ni = 1/2(Ns-Nm)+Nm Nm = 25%Nu
cycles
10
30
100
cycles
16%Fy Vs= 50%Vu 12%Fy 8%Fy Vi = 1/2(Vs-Vm)+Vm Vm= 25%Vu
cycles
shear
shear
4%Fy
10
200 80
100
cycles
30
30 30
Figure 1 – CSA CAN N287.2 Seismic Test Cycles
Figure 2 – ICBO ES Seismic Test Cycles
Investigations in the Canadian nuclear industry centered on the response of single anchors to cyclic loading. Ontario Hydro, based on testing of then-available anchor systems, developed tension and shear cyclic loading regimens for the Canadian Standards Association that were subsequently incorporated into CSA Standard CAN3N287.2. The testing was designed to subject the anchor to a few high load cycles (60% Fy) followed by several hundred cycles to “..study the effect of fatigue on the anchor after the introduction of the initial high localized stress.” (see Fig. 1) All cycles were run with an input frequency of 5 Hz.3 On the basis of these tests, two types of anchors, heavy-duty sleeve and lead-caulking anchors, were identified as suitable for seismic loading. The other anchor types tested, drop-in and self-drill anchors, typically experienced premature bolt failure. The CSA Standard, with its emphasis on fatigue response, later served as the basis for the ICBO ES seismic qualification test. The telecommunications industry likewise began to review the seismic requirements for post-installed anchors in connection with the installation of then state-of-the-art digital switching installations in the early 1980s. Both static and shake table testing of specific
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components has since been standardized through the adoption of a synthesized waveform and corresponding set of response spectra.4 Testing of the anchors is conducted only in conjunction with a specific component, and qualification is based on a pass/fail criteria.
3. Seismic Qualification Testing in the U.S. Prior to 1997, testing of post-installed anchors for seismic performance was not common practice outside of the nuclear and telecom industries. Based on long-standing tradition, post-installed anchors were routinely listed by the International Conference of Building Officials Evaluation Service (ICBO ES) as suitable for wind and seismic loading based on static load tests in uncracked, unreinforced concrete specimens. Additionally, as late as 1987, increases in allowable loads of 33% for seismic loads were granted in conformance with applicable sections of the Uniform Building Code pertaining to shortduration loading. Connection failures in the Northridge Earthquake in January of 1994 prompted a review of this practice, however, and for the period 1995 to 1997, mechanical post-installed anchors were not permitted for seismic applications. A test criteria based loosely on the CSA Standard N287.2 was adopted in 1997,5 and listing of mechanical anchors for seismic loading resumed in 1998 with the issuance of Evaluation Reports for the Hilti HSL and Kwik Bolt II anchors. While similar to the Ontario Hydro approach (cyclic loading, descending load levels, compare Figs. 1 and 2) the test regimen used by ICBO ES differs from the Canadian approach in two significant areas: 1. 2.
The number of cycles is significantly reduced. This was done to reduce the probability of fatigue failure in the test. The peak load level was reduced to 150% of the maximum allowable design load, which in turn is limited to 133% of the static design load. Taken together, these limits typically result in a peak load on the anchor equal to twice the static allowable value, or roughly one-half of ultimate. Given that ultimate strength in tension for most post-installed anchors is limited by concrete cone breakout, this often represents a significant reduction from the CSA Standard (60% Fy, bolt).
In addition, the frequency requirement was changed from 5 Hz to a maximum of 1 Hz. In 1991 ICBO ES ceased authorizing the use of post-installed anchors for use in tensile zones. This issue was not re-visited in the context of seismic loading, and hence the seismic qualification tests for both mechanical and bonded anchors6 are performed in uncracked, unreinforced concrete specimens. Concurrent with the development of seismic qualification testing at ICBO, the Structural Engineers Association of Southern California (SEAOSC) proposed a test standard based on the assumption that the historical provisions for cast-in-place anchors in the Uniform
554
Building Code had proven adequate in past earthquakes. Accordingly, the SEAOSC Standard Method of Cyclic Load Test for Anchors in Concrete or Grouted Masonry7 requires side-by-side testing of post-installed anchors with code cast-in-place anchors (standard hex A307 bolts) of like diameter. The anchors are loaded cyclically in steps of five cycles each to failure, and the resulting load-slip curves and ultimate loads compared. Qualification of the post-installed anchor is thus based on performance equal to or exceeding that of the cast-in-place anchor. This test was subsequently adopted by the ICBO Evaluation Service as an alternate means of qualification for seismic loading.
4. Seismic Qualification Testing in Europe In 1998 the Deutsches Institut für Bautechnik (German Construction Technology Institute) issued testing guidelines for the use of anchors in nuclear power plants and nuclear installations.8 The typical loading cases (earthquake, aircraft impact, explosive shock wave) are cited. Typically, the test regimen consists of three series of tension tests, i.e.: 1. 2. 3.
monotonic tension loading to failure in 1.5 mm wide parallel crack (crack width constant over depth of test member); 15 tension load cycles ( f ≤ 1 Hz ) in 1.5 mm wide parallel crack; and 10 crack opening and closing cycles (1.0 mm to 1.5 mm) with a constant tension load applied to the anchor, followed by loading to failure with the crack width held constant at 1.5 mm.
In addition, 15 shear load cycles in a 1.0-mm parallel crack are performed, followed by shear loading to failure. The extreme crack widths required (an earlier variant required a maximum crack width of 2.0 mm) coupled with relatively severe pass/fail criteria make this the most rigorous test method currently in existence.
5. Testing of the Hilti HDA The Hilti HDA belongs to the class of self-undercutting undercut anchors (see Fig. 3). The anchor is offered in four sizes (M10, M12, M16, and M20) and two shear sleeve variants (preset and through-set, see Fig. 4). Equipped with an ISO Grade 8.8 bolt, the HDA is proportioned to exhibit bolt failure at static tension ultimate for concrete strengths greater than 14 MPa and where full development of the concrete cone breakout strength Figure 3 – HDA Self-Undercutting Anchor is afforded. The HDA was
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brought to market in 1998 and has since been tested to several criteria documenting its response to shock, fatigue, fire and earthquake in the U.S. and Europe. The results from selected earthquake/nuclear qualification tests are presented for comparison here.
6. ICBO ES AC01 Method 2 Testing of the HDA-P M12 x 100/20 per ICBO ES Acceptance Criteria AC01, Method 2, was performed at Hilti Figure 4 – HDA Setting Details laboratories using a 111-kN capacity actuator with in-line load cell and servo-controlled hydraulics. Displacement measurements were obtained with a linear variable displacement transducer (LVDT). The actuator was controlled via a digital readout device with peak hold and signal conditioners. Electronic data acquisition and control systems sampled the outputs of both the load cell and LVDTs. The HDA M12 is equipped with a 12-mm ISO 8.8 bolt and has an effective anchoring depth of 100 mm. The outside diameter of the HDA M12 is 21 mm. Five tests each in cyclic tension and shear were conducted in 22 MPa (cylinder strength) normal weight concrete. In addition, five static tension and shear tests to failure were performed to establish reference values. All testing was conducted in accordance with ASTM E488-90. Table 1 - HDA Allowable Stress Design Seismic - ICBO ES f'c = 2,500 psi Anchor
ASD Seismic T ension
ASD Seismic Shear
(k)
(kN)
(k)
HDA-P M10
3.5
15.6
2.2
(kN) 9.6
HDA-T M10
3.5
15.6
6.2
27.7
HDA-P M12
5.3
23.6
3.2
14.1
HDA-T M12
5.3
23.6
6.8
30.3
HDA-P M16
9.5
42.3
5.6
25.1
HDA-T M16
9.5
42.3
12.2
54.5
The average ultimate static tension capacity of the HDA M12 as determined in the reference tests (all tests resulted in steel failure) was 70.5 kN with a COV of 0.05%. Accordingly, the maximum test load for the seismic qualification test was set at 15.85/2 = 35.3 kN. This translates to a steel stress of approximately 418 MPa or 65% Fy (52% Fu). [Note: The allowable earthquake load for this anchor would be set at 15.85/3 = 23.5 kN.] The anchor survived the seismic test with all residual strength tests resulting in steel failure. The maximum peak displacement was 1.0 mm.
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Similarly, the average ultimate static shear capacity of the HDA-P M10 as determined in the reference tests was 41.2 kN with a COV of 9.0% (all steel failures). The maximum test load was thus set at 9.26/2 = 20.6 kN. The anchor survived the seismic test, and the mean residual strength was determined to be 36.6 kN, or 89% of the reference capacity, although all tests resulted in steel failure (COV = 1.5%). [Note: The criterion for passing is 80% of Vref.] The maximum peak displacement, at 8.8 mm, was within 23% of the allowable maximum of 10.8 mm. The resulting allowable tension and shear values for seismic loading are shown in Table 1.
7. SEAOSC (ICBO ES AC01 Method 1) Testing of the HDA per SEAOSC Standard Method of Cyclic Load Test for Anchors in Concrete or Grouted Masonry was conducted at Consolidated Engineering Laboratories in Oakland, California. Loads were applied with a 98 kN capacity hydraulic actuator equipped with an in-line load cell and servo-controlled hydraulics. LVDTs were used to measure displacement. Table 2 - HDA SEAOSC Test Result Summary Cyclic T ension Results
Mean Displacement @ Failure
Mean Ultimate T ension Load
Anchor n
(k)
(kN)
COV
(in.)
(mm)
1/2" X 4" A307
3
11.0
49.1
1.0%
0.2
5.0
HDA-P M10 x 100
5
11.4
50.8
0.4%
0.2
4.5
5/8" X 4-1/2" A307
3
17.6
78.2
4.7%
0.2
4.3
HDA-P M12 x 125
3
16.2
72.1
2.4%
0.3
7.7
5/8" X 4-1/2" A307
3
17.0
75.8
4.2%
0.2
5.9
HDA-P M16 x 190
4
20.3
90.4
0.2%
0.2
4.5
Cyclic Shear Results
Mean Displacement @ Failure
Mean Ultimate Shear Load
Anchor n
(k)
(kN)
COV
(in.)
(mm)
1/2" X 4" A307
3
5.2
23.1
7.9%
0.2
4.5
HDA-P M10 x 100
3
6.0
26.7
0.3%
0.2
5.1
5/8" X 4-1/2" A307
3
9.0
40.1
7.3%
0.3
6.6
HDA-T M10 x 100
3
15.1
67.0
0.2%
0.4
9.6
1
value limited by actuator capacity
2
bolt only
3
shear sleeve engaged
1
557
2
3
The test members consisted of concrete blocks with a cylinder compressive strength of between 20 MPa and 24 MPa at the time of testing. The blocks were cast with 1/2- (12 mm) and 5/8-inch (16 mm) A307 standard hex head bolts placed at minimum embedment per 1997 UBC Table 19D, i.e., 4 inches (102 mm) and 41/2 inches (114 mm), respectively. Block dimensions were 152 cm x 91 cm x 61 cm. They were cast vertically, with the bolts placed in the side forms to provide equivalent casting conditions for all anchors. The HDA anchors were subsequently installed in
the cured concrete blocks adjacent to the cast-in-place bolts, with sufficient spacing to allow testing per ASTM E488.
Table 3 - HDA Allowable Stress Design Seismic - SEAOSC Anchor
ASD Seismic T ension
ASD Seismic Shear
(k)
(kN)
(k)
(kN)
HDA-P M10
4.0
17.8
4.4
19.5
1
HDA-T M10
4.0
17.8
8.0
35.5
1,2
HDA-P M12
5.9
26.0
8.0
35.5
3
HDA-T M12
5.9
26.0
11.4
50.9
3,4
HDA-P M16
8.6
38.5
10.8
47.9
5
HDA-T M16
8.6
38.5
12.6
56.2
5,6
1
Equivalent to 1/2-inch A307 bolt
2
For shear, equivalent to 5/8-inch A307 bolt
3
Equivalent to 5/8-inch A307 bolt
4
For shear, assume equivalent to 3/4-inch A307 bolt
5
Assume equivalent to 1-inch A307 bolt
6
For shear, assume equivalent to 1-1/8-inch A307 bolt
According to the SEAOSC test procedure, the load steps for the cyclic loading are determined by identifying (from static test data) a First Major Event (FME), i.e., a load level at which the load-displacement of the anchor undergoes a significant change. Load steps are then established as 25% increments of the FME, i.e., 25%FME, 50%FME, 75%FME, 100%FME, 125%FME, etc. to failure. Five cycles are performed at each load step at less than 1 Hz.
Two sizes of HDA anchors, M10 and M12, were tested in cyclic (pulsing) tension. In addition, the M16 size was tested in tension to the actuator capacity of 90 kN. The rated tension capacity of the M16 is 127 kN. Both the HDA M10-P and M10-T (shear sleeve engaged) were tested in cyclic shear. All anchors were installed per manufacturer recommendations and the maximum recommended torque applied. This torque was then reduced to 50% of the maximum recommended torque prior to testing. Alternatively for some specimens, 48 hours were allowed to pass prior to testing, which resulted in a residual pre-tension value approximately equal to 50% torque. All tests resulted in steel failure at ultimate, with the exception of the HDA M16 anchors, which were not tested, to failure. Test results are provided in Table 2. Sample load-displacement curves are shown in Fig. 5, and the allowable loads implied from the test data are given in Table 3.
8. German Nuclear Qualification Testing of the HDA for structural applications in German nuclear facilities was conducted at the University of Stuttgart according to the DIBt Guideline For Evaluating Anchor Fastenings For Granting Permission In Individual Cases According To The State Structure Regulations Of The Federal States. Tests were conducted with three HDA sizes, M10, M12 and M16. Three types of tension tests were conducted:
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Table 4 - HDA - German Nuclear Standard Tension Test Result Summary f cc
Anchor T ype
Crack Width
T est T ype
Mean Ult. T ension
Displ. @ Mean Ult.
(MPa)
Load
Crack
(mm)
n
(kN)
COV
HDA-T M10x100
25.0
monotonic
static
1.5
5
40.9
14%
5.0
HDA-T M10x100
28.8
monotonic
static
1.5
5
46.1
7%
3.2
HDA-T M10x100
25.0
cycl. tension
static
1.5
5
40.1
13%
1.6
HDA-T M10x100
25.0
cycl. tension
static
1.5
5
37.0
13%
1.3
HDA-T M10x100
30.8
monotonic
moving
1.5
5
48.2
1%
3.1
HDA-T M12x125
25.0
monotonic
static
1.5
5
64.4
9%
4.4
HDA-T M12x125
27.1
cycl. tension
static
1.5
5
64.4
13%
2.5
HDA-T M12x125
28.3
cycl. tension
static
1.5
5
67.6
9%
2.6
HDA-T M12x125
25.0
monotonic
moving
1.5
5
67.6
4%
4.6
HDA-T M16x190
25.0
monotonic
static
1.5
5
119.7
5%
5.5
HDA-T M16x190
25.0
cycl. tension
static
1.5
5
113.3
12%
3.6
HDA-T M16x190
25.3
cycl. tension
static
1.5
5
122.8
11%
3.6
HDA-T M16x190
27.3
monotonic
moving
1.5
5
125.8
8%
6.3
1. 2. 3.
(mm)
static tension tests in parallel cracks pulsing tension tests in parallel cracks static tension tests in opening and closing cracks
Crack widths in all cases were 1.5 mm. Cyclic shear tests were conducted in 1.0-mm cracks with both the P and T versions of the HDA. Tension test results are presented in Table 4. A representative load-displacement curve is shown in Fig. 6. Table 5 - HDA Category A Allowable Loads - German Nuclear Standard C20/25 concrete Anchor
NRk,p
VRk,s
(kN)
(kN)
HDA-P M10
16.5
16.8
HDA-T M10
16.5
33.3
HDA-P M12
23.5
22.4
HDA-T M12
23.5
41.3
HDA-P M16
47.1
48.0
HDA-T M16
47.1
80.0
An evaluation of the test data resulted in recommended working loads as shown in Table 5.
9. Comparison of Test Methods It is remarkable that, with respect to the determination of allowable loads for tension, all three methods arrive at roughly the same values for allowable stress design, albeit by very different means (compare Tables 1, 3 and 5). It should be noted that this result is likely unique to undercut-type anchors that do not suffer dramatic capacity reductions in cracked concrete. Anchors that do not exhibit such behavior may not achieve a similar
559
Steel Failure
k 12 11 10
HDA M10
kN
9 8
1/2” A307 std hex bolt
7
HDA M10
6 5 4 3 2 1
0 0
0.05
0.10
0.15
0.20
0.25 in
Figure 5 – Sample SEAOSC Seismic Test LoadDisplacement Curves
mm
Figure 6 – DIBt Tension Cycle in 1.5 mm Crack
result. The greatest differences in the allowable loads occur in shear, whereby the increased number of cycles associated with the ICBO ES Method 2 test restricts the shear value, essentially as a function of low-cycle fatigue. As discussed above, this is true to the original concept of the Canadian standard on which the ICBO test is based. Of greater interest, however, is the information to be derived from the test aside from simple pass/fail results. Figure 5 shows typical load-slip curves derived from the SEAOSC seismic cycle. Note that it is possible to derive stiffnesses from this data throughout the entire load range that reflects a realistic numbers of cycles. While the German standard provides similar information (see Fig. 6), the information provided regarding the response at near-ultimate load levels is limited.
10. Conclusions Seismic qualification of anchors is based on various and disparate philosophies regarding the appropriate conditions to be simulated in testing. ICBO ES continues to use a low-cycle fatigue standard, while the German nuclear standard focuses heavily on the effects of base material damage on anchor behavior. The SEAOSC approach, while concentrating on comparisons with cast-in-place anchors, allows for development of
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stiffness behavior necessary for the employment of advanced anchor design methods. Clearly, an argument can be made for a combination of the SEAOSC approach with a realistic approximation of base material damage (cracking).
11. Future Test Methods Documented anchor failures in past earthquakes are likewise in many cases attributable to shear overload, as opposed to pullout. Clearly, the response of anchors to earthquake-induced loads is dependent on several factors; nevertheless, four critical parameters can be identified: 1. 2. 3.
load direction and magnitude displacement demand deformation constraints 4.
FEQ
Fy FEQ
a.
Mp
b. Figure 7 – Anchor Design Concepts a. ductile anchor b. yielding element
earthquake-induced damage to the base material (cracking)
It can be argued that factors 1 through 3 are controlled by and, in most cases, a byproduct of, the design process. That is, load and deformation demands on the anchor are dependent to a large extent on connection detailing. Inertial loads as derived in analysis are typically based on assumptions regarding induced accelerations. While they may serve as a starting point for the correct proportioning of the load path, static lateral loads rarely lead to a correct estimation of the actual force/deformation requirements for the anchor in the event of a significant (design level) earthquake. For this reason, newer design codes have adopted language that encourages a stiffness/ductile design approach to anchorage. The 2000 International Building Code section on anchorage9 contains provisions that require the anchorage design to satisfy either a ductile anchor criterion, or to establish a yielding mechanism elsewhere in the load path (see Fig. 7). This second approach ensures that the anchor is not the weak link in the load path. In the case of
561
predominantly shear loading, provision of such a yielding ‘fuse’ is the only sensible way to protect the anchor from catastrophic overload. Critical for an anchorage design that considers stiffness and material interaction in the detail design is understanding the likely response history of the components being considered. In the case of the anchor, such information can only be provided from testing that mimics the essential components of strong motion and measures the required response parameters in a way that is useful for design.10 While the recently published ACI 355.2-00 test method11 includes cracking and is therefore a dramatic improvement over previous criteria, it continues to be based on a low cycle fatigue loading regimen. Consideration should therefore be given to seismic qualification criteria that include stepwise cyclic loading (with three to five cycles at each load step) as described in the SEAOSC method, with the following modifications: a) conduct the tests in static cracks*, and b) report the load-slip behavior, in the form of a characteristic envelope curve, along with the other design parameters.
12. Summary Three methods for qualification of anchors for seismic loading are currently in use in the U.S. and Europe. Taken together, these methods encompass the effects of cyclic loading, base material damage, and anchor overload. An undercut anchor has been tested using the three standards, and the results provide a limited basis for evaluation of the test methods. A test method that combines the best elements of the three current methods is required to meet the requirements of future design codes.
References 1. 2. 3.
4.
FEMA Publication 273, ‘NEHRP Guidelines for the Seismic Rehabilitation of Buildings’, Building Seismic Safety Council, Washington D.C., October 1997. ACI Committee 349, ‘Code Requirements for Nuclear Safety Related concrete Structures (ACI 349-85)’, American Concrete Institute, Detroit, 1985. Senkiw, G. A., ‘Qualification Tests on Concrete Anchors for CANDU Nuclear Power Plants’, ACI Symposium on Anchorage to Concrete, Phoenix, Arizona, March 1984. Bell Communications Research, ‘Generic Requirements GR-63-CORE, Network Equipment-Building System (NEBS) Requirements: Physical Protection’, Bellcore Customer Research, Piscataway, New Jersey, Issue 1, October 1995.
*
It should be noted that a cycling crack test would more closely approximate the conditions associated with a structure subjected to strong ground motion, although the practical implications of such a test have not been adequately explored to date.
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5.
ICBO ES, ‘AC01, Acceptance Criteria for Expansion Anchors in Concrete and Masonry Elements’, ICBO Evaluation Service, Inc., Whittier, California, January 2001. 6. ICBO ES, ‘AC58, Acceptance Criteria for Adhesive Anchors in Concrete and Masonry Elements’, ICBO Evaluation Service, Inc., Whittier, California, January 2001. 7. SEAOSC, ‘Standard Method for Cyclic Load Test for Anchors in Concrete or Grouted Masonry’, Structural Engineers Association of Southern California, Whittier, California, April 1997. 8. DIBt, ‘Verwendung von Dübeln in Kernkraftwerken und kerntechnischen Anlagen, Leitfaden zur Beurteilung von Dübelbefestigungen bei der Erteilung von Zustimmungen im Einzelfall nach den Landesbauordungen der Bundesländer’ (Use of Anchors in Nuclear Power Plants and Nuclear Technology Installations, Guideline For Evaluating Anchor Fastenings For Granting Permission In Individual Cases According To The State Structure Regulations Of The Federal States), Deutsches Institut für Bautechnik, Berlin, September 1998. 9. ICC: International Building Code, 2000 Edition, Whittier, CA 90601, Sec. 1916, pp. 469-477. 10. Silva, J., Eligehausen, R., ‘The Concrete Capacity Design Method for Anchors in Concrete’, Proceedings 69th Annual Convention Structural Engineers Association of California, August 2000, p. 10. 11. ACI Committee 355, ‘Evaluating the Performance of Post-Installed Mechanical Anchors in Concrete (ACI 355.2-00)’, Concrete International, February 2001, pp. 108-136.
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SAFETY CONCEPT FOR FASTENINGS IN NUCLEAR POWER PLANTS Thomas M. Sippel*, Jörg Asmus*, Rolf Eligehausen** *Engineering Office Eligehausen and Sippel, Stuttgart, Germany **Institute of Construction Materials, University of Stuttgart, Germany
Abstract In nuclear power plants post-installed fastenings are often used. A decisive criteria for the use of fastenings in safety critical applications is the proper functioning of fasteners under special conditions such as impact loading and earthquake excitations and cracks in concrete with a width ≥ 0.5 mm due to earthquake loadings. Such special conditions are not covered by Technical Approvals according to [1]. Therefore, in Germany a guideline for the assessment of fasteners in nuclear power plants has been published [3]. This guideline is valid for undercut anchors with an embedment depth hef ≥ 80 mm, which are approved according to [1]. In this paper the concept of the guideline is explained. Details of the required suitability tests and the tests to determine admissible service conditions are given. Furthermore, results of tests with different types and sizes of undercut anchors are shown.
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1. Introduction In nuclear power plants post-installed fastenings are often used. A decisive criteria for fastenings in safety relevant applications of nuclear power plants is their proper functioning under special conditions, which may occur during the service life of the plant. Such conditions include impact loading, earthquake excitations and cracks in the concrete with a width ≥ 0.5 mm due to earthquake loading. These special conditions are not covered by Technical Approvals according to [1]. Therefore, a guideline for the assessment of fasteners intended for use in nuclear power plants has been published in Germany [3]. This guideline gives tests methods and assessment criteria. Furthermore modifications to the design method (CC-method) described in [1] and [2] are given. This paper describes the concept of the guideline [3]. It gives details of the test program, the assessment criteria and the modification of the CC-method. Furthermore results of tests with undercut anchors are shown.
2. Safety concept 2.1. General Post installed fasteners are often used in nuclear power plants to fasten pipe systems which are critical for the safe operation of the plant. Therefore the fasteners must safely transfer the loads acting on the base plate, even under extreme conditions which may occur during the service life of the nuclear power plant. These conditions include e.g. impact loading, earthquake excitations and cracks in the concrete with a width ≥ 0.5 mm due to earthquake loading. They are not covered by Technical Approvals according to [1]. Therefore according to [3] additional tests are necessary to check the suitability (proper functioning) of the fastener and to deduce allowable conditions of use under the above mentioned conditions.
565
2.2. Use Categories and related partial safety factors For the design of fasteners in nuclear power plants the safety concept of partial safety factors is used. It must be shown that the design actions Sd are not larger than the design resistance Rd (Eq. (1)). Sd ≤ Rd
(1)
In the simplest case (permanent load Gk and one variable load Qk acting in the same direction as Gk) the design actions are calculated according to Eq. (2). Sd = γG · Gk + γQ · Qk with
γ G, γ Q
(2)
= partial safety factors for permanent or variable load resp.
The design resistance is given by Eq. (3). Rd = Rk/γM with
Rk γM
(3)
= characteristic resistance (5%-quantile) = material safety factor
For fastenings in nuclear power plants, three different use categories (A, B and C) have to be considered [4]. These three categories assume different expected frequencies of the loading within the service life of the power plant (see Table 1). In category C the same loadings and requirements as in normal buildings are considered. Therefore the partial safety factors given in [1] and [2] must be used (see Table 1). In category A it is assumed that the loading will occur only once during the service life of the structure. Examples are the maximum expected earthquake, the hitting of the containment by a plane or explosions. Under these conditions it must be ensured that the nuclear power plant can be safely shut down. Because cooling water is needed for the shut down, fasteners of the corresponding cooling pipes must function properly. Therefore the safety factors γG = γQ = 1.0 and γMc = 1.7 are used. In category B a frequency of loading n ≤ 10 during the service life of the structure is assumed, such as "normal" earthquakes. The partial safety factors are in between the values valid for category A and C.
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Table 1: Use categories and corresponding safety factors for fastenings used in nuclear power plants according to [3] use category A B C >> 10 frequency during service life 1 ≤ 10 crack width [mm] ≤ 0.5 mm ≤ 0.3 mm ≥ 0.5 mm concrete class acc. to [7] C20/25 to C50/60 max. long term temperature ≤ 80°C partial safety factors 1.0 1.2 1.4 action γG = γQ 1.7 1.9 2.1 resistance (concrete) γMc = γMp
3. Requirements on Fastenings 3.1. General In use category C cracks with a width wk ≤ 0.3 mm or wk ≤ 0.5 mm under the quasipermanent or allowable service load of the structure are assumed. Therefore only fasteners with a Technical Approval according to [1] may be used. In use category A (e.g. maximum expected earthquake) large cracks may occur in the concrete in the most stressed areas due to yielding of the reinforcement. The width of cracks have been evaluated based on the design actions in nuclear power plants. According to the evaluation in general the width of cracks running in one direction is wk ≤ 1.0 mm. Only in extreme cases the crack width may be wk ≤ 1.5 mm. Outside the most stressed regions where the reinforcement is strained below the yield strain the crack widths are much smaller. During an earthquake cyclic loading on the structure and on the fastenings is induced simultaneously. Due to this the width of the cracks will vary between a minimum and a maximum value and the fastenings will be loaded cyclically. These conditions must be taken into account in the test regime (see Section 4). 3.2. Fasteners As a principle, only fasteners with a Technical Approval for use in cracked and non cracked concrete according to [1] should be used for safety relevant fastenings in nuclear power plants. The width of cracks under seismic excitations can not be assessed very accurately but some variations may occur. Therefore only undercut anchors with a sufficiently large undercut are allowed, because their behaviour will not be influenced significantly if even larger cracks than given above may occur. Undercut anchors (Fig. 1) transfer the load by mechanical interlock into the concrete. After producing of the cylindrical hole by drilling, the undercutting is produced in a second operation before installation of the anchor (Fig. 1a and b) or during installation of the anchor (Fig. 1c). The use of torque controlled expansion anchors is not allowed in [3] because their proper
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functioning may be impaired significantly if they are anchored in a crack with a width larger than anticipated. For safety relevant fasteners an effective anchorage depth hef ≥ 80 mm is required. Anchors with an effective anchorage depth hef ≥ 40 mm are allowed only if very small loads must be transferred into the concrete (adm F ≤ 0.4 kN).
a) Fig. 1: Undercut anchor systems
b)
c)
3.3. Concrete Concrete classes B25 to B55 according to DIN 1045 [5] or C20/25 to C50/60 according to EN 206 [7] are covered in the guideline [3]. 3.4. Protection against fire, corrosion and atomic radiation For the resistance against fire and corrosion the regulations in the Technical Approval for normal applications are valid. The influence of atomic radiation on the load-bearing behaviour can be neglected. 3.5. Installation The guideline [3] is valid only for fasteners, which are installed by skilled workers according to the installation instruction of the manufacture and additional requirements in the guideline. The correct installation must be controlled by independent personnel. Therefore, tests to investigate the sensibility of fasteners to installation inaccuracies (installation safety) can be omitted (see Section 4). 3.6. Design concept Fastenings in nuclear power plants for safety related applications should be designed in such a way that they are ductile. The ductility can be ensured by the attachment, the fixture or the anchors. According to [3] in general in the design of the fastening consisting of attachment, fixture and anchors the failure mode concrete cone failure should not be decisive.
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The design of fasteners in nuclear power plants closely follows the design model according to [1] or [2] (CC-method). However, the characteristic resistance for concrete cone failure is calculated according to Eq. (1).
with
1,5 0 N Rk,c = k ⋅ fcc ⋅ h ef k = 6.0 fcc = concrete cube strength = effective embedment depth hef
(1)
The factor k = 6.0 is approximately 15% lower than the value according to [1] or [2] for cracked concrete with a crack width w = 0.3 mm. The lower value k considers the influence of larger cracks (w = 1.0 mm) on the ultimate load for concrete cone failure. Furthermore, the failure load VoRk,c for concrete edge failure is reduced by about 15% compared to [1], [2]. The characteristic resistance for pull-out failure and steel shear failure is evaluated from the results of relevant tests.
4. Required Tests for Use Category A The required suitability tests and tests for evaluating allowable conditions of use are summarised in Table 2. Tests under monotonic loading are performed with normal loading rate, because the results of tests in [9] and [10] showed that anchor behavior is not negatively influenced by loading rates typical for earthquake excitations. The tests will be conducted with a crack width w1 = 1.0 mm (reference tests) and w2 = 1.5 mm. In tension tests with w = 1.5 mm the failure load should reach ≥ 0.8times the average value valid for tension tests with w = 1.0 mm (reference failure load) to take into account that the probability of occurrence of such wide cracks is relatively low. Furthermore tests with cyclic tension load on the anchor (n = 15 cycles) must be performed. The upper load is equal to Nmax = NRk/γMc with NRk = characteristic resistance evaluated from results of tests according to Table 2, line 4 and γMc according to Table 1 for use category A. The minimum load is N = 0. This loading represents the cyclic excitations of the fastening due to an earthquake or other dynamic loadings. During the test no failure of an anchor is allowed and the average failure load in the subsequent test to failure must be at least 70% of the reference failure load. To model the influence of cyclic excitations of the structure on anchor behaviour tests in opening and closing cracks are required. During the test the anchors are loaded with a
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constant tension load Nmax as given above. The crack widths are varied 10 times between w1 = 1.0 mm and w2 = 1.5 mm. After this the crack is opened to w2 = 1.5 mm and the anchor is loaded monotonically to failure. During the tests no anchor may fail and the average failure load in the tension tests must be at least 70% of the reference failure load. During an earthquake the anchors may be cyclically loaded in tension or shear. If reversed cyclic shear loading occurs the anchor may fail by steel rupture due to low cyclic fatigue. To check this, tests in cracked concrete (w = 1.0 mm) with 15 reversals of the shear load between Vmax = ± VRk,s/γMs (VRk = characteristic shear resistance for steel failure for monotonic loading and γMs = partial safety factor = 1.5 for anchor steel with normal ductility) must be performed. The shear load is applied in direction of the crack. During the load reversals no anchor failure may occur and the average failure load in the subsequent test to failure must be ≥0.9times the reference value valid for monotonic loading. Table 2: Suitability tests and tests for admissible service conditions for use category A n Line Purpose of test load ∆w N V α = u or u 2) dir. mm
N u,0
1)
4
Suitability tests monotonic tension loading N 1.5 ≥5 load cycles nL = 15 N 1.5 ≥5 crack movements nR = 10 N 1.5/1.0 ≥5 Admissible service conditions monotonic tension loading N 1.0 ≥5
5
monotonic shear loading
V
1.0
≥5
6
load cycles nL = 15
V
1.0
≥5
1 2 3
1) 2)
3)
α ≥ 0.8 α ≥ 0.7 3) α ≥ 0.7 3) reference ultimate load for tension tests reference ultimate load for shear tests α ≥ 0.9 3)
N = tensile load, V = shear load Nu (Vu) = average failure load in tension (shear) tests, Nu,0 (Vu,0) = reference average ultimate load in monotonic tension (shear) tests with w1 = 1.0 mm no failure during cyclic loading or crack moving
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Vu,0
5. Test Results In the following typical test results of different types and sizes of undercut anchors performed according to the above described concept of the guideline [3] are shown. Tension tests have been performed in line cracks with a width w = 0.3 mm to 1.7 mm. In general, with the investigated fasteners concrete cone failure was observed. Fig. 2 shows typical load displacement curves of undercut anchors tested in cracks with a width w = 1.5 mm. The behaviour is not significantly different compared to tests in w = 0.3 mm; only the anchor stiffness is reduced and the scatter of the test results may be somewhat larger. In Fig. 3 the ratio of measured to calculated failure loads in cracked concrete are plotted as a function of crack width. It demonstrates that the measured ultimate loads exceed the characteristic resistance for concrete cone failure according to Eq. (1). Furthermore, with increasing crack width no significant reduction of failure loads can be observed up to a crack width w ≈ 1.7 mm. The tension behaviour of anchors in cracks with constant width may be influenced by cyclic loads on the anchor. Therefore tests under repeated loading have to be carried out in cracked concrete (w = 1.5 mm) applying 15 load cycles. Fig. 4 shows a typical loaddisplacement curve of an anchor subjected to repeated loading with subsequent tension loading to failure. During cyclic loading the anchor displacement increase, however the failure load is generally not much influenced by the previous load cycles. Typical results of tests with opening and closing cracks using different types and sizes of undercut anchors are shown in Fig. 5. In Fig. 5 the average displacement of 5 test per series with anchors in line cracks loaded with a constant tension load Np = 0.6 to 0.7 N0Rk,c (N0Rk,c according to Eq. (1)) is plotted as a function of the number of crack openings. In the tests the maximum crack width amounts to w2 = 1.5 mm and the minimum crack width was about 1 mm. With increasing number of crack openings the displacements increase. This increase depends mainly on the load bearing area of the undercut system, the magnitude of the constant tension load on the anchor and the number of crack openings. During the crack openings none of the tested anchors failed. However, anchors with an insufficient load bearing area may be pulled out after a small number of crack openings. In general the increase of displacements during tests with opening and closing cracks is larger than in the tests with cyclic loading on anchors located in a crack with a constant width (compare Fig. 5 with Fig. 4).
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140 120 Test 1 Test 2
100
Load [kN]
Test 3 Test 4
80
Test 5
60 40 undercut anchor M16, type 1 embedment depth hef = 190 mm fcc = 28.5N/mm²; w = 1.5 mm
20 0 0
5
10
15
20
25
30
35
40
45
50
Displacement s [mm]
Fig. 2: Load displacement curves for an undercut anchor M16 in cracked concrete w = 1.5 mm Ratio Nu,test/N
o Rk,c
(cracked concrete)
2,50 2,25 2,00 1,75 1,50 1,25 1,00 o Rk,c
N
0,75 0,50
1,5
(cracked concrete) = 6,0 * hef
1,5
* fcc
crack
undercut anchor, type 1 undercut anchor, type 2 undercut anchor, type 3
0,25
anchor
0,00 0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
Crack width w [mm]
Fig. 3: Ratio measured to calculated failure load as a function of crack width (line cracks)
572
60
undercut anchor M10, type 3
55 50
Nmax = 0,59 NoRk,c
45
Load [kN]
40 35 30 25
Nmax
20 15 10 5 0 0
5
10
15
20
25
Displacement s [mm] Fig. 4: Load-displacement behaviour of an undercut anchor M10 in cracked concrete (w ≈ 1.5 mm) under repeated loading with subsequent tension loading to failure average displacement d [mm] 20 undercut anchor, type 1, M10 undercut anchor, type 1, M12 undercut anchor, type 1, M16
18
undercut anchor M12, type 2 undercut anchor M20, type 3
16 14
wmax = 1,5 mm wmin = 1,0 mm
12
Np = 0,6 ... 0,7 NoRk,c with NoRk,c = 6 x hef1,5 x fcc0,5
10 8 6 4 2 0 1
number of crack openings
10
Fig. 5: Average displacements of different undercut anchors in tests with opening and closing cracks as a function of the number of crack openings
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If fasteners are located sufficiently far from edges and loaded in shear, steel failure may occur. Under seismic excitation the fastener may be subjected to large shear loads with changing load directions. Therefore, in [3] tests under reversed cyclic shear loading in cracked concrete w = 1.0 mm are required. In Fig. 6 typical shear load shear-displacement curves for undercut anchors tested under reversed shear loads in cracked concrete (w = 1.0 mm, loaded in direction of the crack) are plotted. The behaviour in these tests is significantly influenced by the maximum load Vmax and the number of load cycles. Furthermore, the type of fastener (throughpositioning anchor or pre-positioning anchor) is decisive. Fig. 6a and 6b show the displacement behaviour for different shear load levels. A regular behaviour with relatively small displacements after 15 shear load cycles can be seen in Fig. 6a. The peak shear load at the load cycles was about 45% of the average shear load measured in monotonic tests. After cyclic loading, the shear load was increased monotonically up to failure. The anchor failed by steel rupture. When increasing the amplitude of the shear load by about 40% for the same anchor type, steel failure occurred after 4 load cycles (Fig. 6b). 120
120
110
undercut anchor M12, type 3
100
100
90
90
80
80
70
70
Load [kN]
Load [kN]
110
60 50
60 50
40
40
30
30
20
20
10
10
0
undercut anchor M12, type 3
0 -40-35-30-25-20-15-10 -5 0 5 10 15 20 25 30 35 40
-40-35-30-25-20-15-10 -5 0 5 10 15 20 25 30 35 40
Displacement s [mm]
Displacement s [mm]
a) b) Fig. 6: Shear force – shear displacement curves for an undercut anchor M12 (throughpositioning anchor) tested in cracked concrete (w = 1.0 mm) a) repeated maximum shear load Vmax = ±47.5 kN and subsequent shear test to failure b) repeated maximum shear load Vmax = ±66.4 kN; steel failure after 4 load cycles
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6. Summary In nuclear power plants post-installed fasteners are often used. A decisive criteria for the use of fastenings in safety critical applications is the proper functioning of fastener under special conditions such as large dynamic loadings and large cracks (w ≥ 0.5 mm) due to earthquakes. Such special conditions are not covered by Technical Approvals according to [1]. Therefore, in Germany a guideline for the assessment of fasteners in nuclear power plants has been worked out [3]. In this paper the concept of the guideline is explained. Details of the required suitability tests and the tests to determine admissible service conditions are given. Furthermore, results of tests with different types and sizes of undercut anchors are shown.
7. References [1]
[2]
[3] [4] [5] [6] [7] [8]
[9]
[10]
„Guideline for European Technical Approval of Anchors (Metal Anchors) for Use in Concrete“; Mitteilungen des Deutschen Instituts für Bautechnik; Sonderheft Nr. 16; 31.Dezember 1997. Deutsches Institut für Bautechnik: Bemessungsverfahren für Dübel zur Verankerung im Beton (Design Concept for Fasteners fastened in Concrete); Berlin, Juni 1993 Deutsches Institut für Bautechnik, Berlin: Verwendung von Dübeln in Kernkraftwerken und kerntechnischen Anlagen. Ausgabe 9/98. DIN 25449: 1987-05: Auslegung der Stahlbetonbauteile von Kernkraftwerken unter Belastung aus inneren Störfällen DIN 1045: Tragwerke aus Beton, Stahlbeton und Spannbeton, Bemessung und Konstruktion DIN 1055: Lastannahmen für Bauten ENV 206: Beton; Eigenschaften, Herstellung, Verarbeitung und Gütenachweis. Eligehausen, R.; Mallée, R.: Befestigungstechnik im Beton- und Mauerwerkbau (Fastening Technique to Concrete and Masonry Structures). Ernst & Sohn, 2000. Eibl, J.; Keintzel, F.: Behavior of expansion anchors and undercut anchors under dynamic loads. Institut für Massivbau und Baustofftechnologie, Universität Karlsruhe, 1989 Eibl, J.; Keintzel, F.: Behavior of expansion anchors and undercut anchors under high impact and alternate loads. Institut für Massivbau und Baustofftechnologie, Universität Karlsruhe, 1989
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EXPERIMENTAL STUDY ON SEISMIC PERFORMANCE OF BEAM MEMBERS CONNECTED WITH POST-INSTALLED ANCHORS Reiji Tanaka* Koichi Oba** *Tohoku Institute of Technology, Japan **Hilti (Japan), Ltd.
Abstract In Japan, post-installed anchors are not allowed to connect beams or columns of buildings. The reason is that cyclic loads are applied to the connection of beams or columns due to earthquakes. If post-installed anchors are capable of connecting beams or columns, building construction work gets quite easy and its advantage is enormous. This report investigated the dynamic behavior of bonded anchors and the seismic performance of beams through an experiment of cyclic loading simulating earthquake that is applied to beam specimens connected with bonded anchors. This study aims for the feasibility of bonded anchors for beam connection.
1. Objective Post-installed anchors are currently used mainly for fastening of equipments and very seldom for connection of structural members in Japan. But in seismic reinforcing works, many of them are being used for connection of structural members like existing buildings and added shear walls. This indicates that post-installed anchors are usable for structural applications. If post-installed anchors can connect structural members in building structural design process, then flexibility of design will quite increase and its merits are unpredictable. Since Japan is a seismic country, enough mechanical performance both in elastic region and also plastic region is required, if structural post-installed anchors are utilized for connecting beams and columns, etc. During seismic loading, cyclic loads are applied to beams and columns, and therefore post-installed anchors connecting these members also should have enough mechanical performance against cyclic tension, shear and combined loads both in elastic and plastic regions. Thus this study plans to conduct cyclic loading experiments simulating seismic loads and investigate the feasibility of bonded anchors for structural applications.
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2. Outline of experiments 2.1 Specimen types Table 1 shows the overall specimen types. Specimen quantity is 6 altogether. They are divided into 2 series of anchor rod diameter: D13 series and D16 series. Both series include monolithic specimens for comparison purpose. Effect of embedment depth is studied by changing it from standard value of manufacturer’s specification (l = 1h) to twice of standard value (l = 2h). Other parameters are the same. Table 1 Specimen No.
Specimen name
Specimen types
Bonded anchors Dia.
D13 series
D16 series
Quantity
Main rebars/ anchor rods embedment depth (l)
1
BN-4D13
monolithic specimen for reference
2
BN-4D13-H1
D13
3
BN-4D13-H2
4
BN-4D16
monolithic specimen for reference
5
BN-4D16-H1
D16
6
BN-4D16-H2
4
Rebar dia.
Minimum sectional area (mm2)
D13
127
D16
199
1h (110 mm) 2h (220 mm)
4
1h (125 mm) 2h (250 mm)
< Common items > Beam section: 200 mm × 200 mm Stirrup: 2—D6φ @50 (Pw=0.64%) Column concrete strength : σB =20.1 N/mm2
- Main rebar:
SD295A
- Beam concrete strength: σB =22.8 N/mm2
2.2 Shape and size of specimens, and rebar arrangement Fig. 1 shows the shape and size of specimen, and rebar arrangement. As for beams, shape and size are common for all specimens ant its cross section size is B×D = 200 mm× 200 mm. This is a cantilever beam with test section a = 600 mm (shear span ratio a/D =3.0) Main rebar quantity is 4 for both D13 series and D16 series. Anchor rod length is l = 750 mm and anchor rods work as beam rebar without any connection parts. Shear reinforcing bars are 2 – D6φ＠50. Column simulates the existing concrete, and its size is B×D×L = 700mm×400mm× 700mm for embedment parameter 1h, and B×D×L = 900mm×400mm×1,200mm for embedment parameter 2h assuming some cone failure. 2.3 Material used 1) Bondeed anchors Bonded anchors used are of capsule type (2 types for D13 and D16). Fig.2 shows its details.
577
700 200
250
250(350)
700(900) 250(350) ( )BC-4D13-H2, 200 BC-4D16-H2
150
250
400
bonded anchor
Pc steel rod
↓
↓
2-D10@100
a)monolithic specimen
Fig. 1
2-D6@50
2-D19 4-D19
130 Stub
2-D10@100
b)anchor specimen
35
Pc steel rod
4-D19
2-D13 or 2-D16
2-D6@50
4-D13 or 4-D16
130 35 200
2-D13 or 2-D16
600 1,150
Ｑ
embedment depth
Ｑ
130 35 200 35 c)beam section (common for all specimens)
Shape and size of specimens, and rebar arrangement ｌ ｌe Existing concrete Anchor rod
Bonded anchor capsule
Fig.2
ｄa
ｌ：embedment depth ｌe：effective embedment depth ｄa：main rebar diameter
Details of bonded anchors
2) Rebars The material of main rebars and anchor rods D13, D16 is SD295A. The mechanical property is given in Table 2.
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Table 2
Mechanical property of main rebars and anchor rods
Location
Rebar type
Rebar dia.
Sectional area as (mm2)
Anchor rods / main rebars Shear reinforcing bar
SD295A
D13 D16
127 199
320 332
SD345
D6
32
404
Tensile strength σmax (N/mm2)
Young’s modulus Es×105 (N/mm2)
0.183 0.184
450 479
1.75 1.80
0.232
504
1.76
Yield point Strain Strength εy σy (%) (N/mm2)
3) Concrete Ready mixed concrete was cast in two steps. First column section was cast, and anchors were installed after curing. Then beam section was cast. The mechanical property of concrete is given in Table 3. Table 3 Mechanical property of concrete Location
Beam member Column member
Maximum strength (N/mm2)
σB
Strain εB (%)
22.8 20.1
0.221 0.248
Young’s modulus 1/3Ec×104 (N/mm2) 1.99 1.75
2.4 Loading method Alternating flexural shear loads were applied to cantilever beams as shown in Fig.1. Loading was conducted in such a way that load value was controlled until yield point, and then displacement was controlled after yield point. Load was applied with manual hydraulic jack (300 kN), and load value was measured with load cells (100 kN). 2.5 Measuring method of displacement and rebar strain Displacement was measured with electric transducers. We took measurement of both relative displacement (1/200 mm accuracy) of loading point above column surface (600 mm) and upheaval of column surface (1/500 mm accuracy). Strains of main rebars at beam end and shear reinforcing bars are measured with wire strain gauge (capacity 2 mm).
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3. Test result and review 3.1 Maximum load, joint translation angle at maximum load, failure mode and Q-R curve Table 4 shows the maximum loads, joint translation angles at maximum loads, and failure modes of all specimens. Fig.3, Fig,4 and Fig.5 give the comparison of maximum loads of all specimens, crack patterns at maximum loads, and load – joint translation angle curve ( Q-R curve) respectively. Next comments are derived from Table 4 and Fig.3～5. ① With D13 series, all specimens did not give any anchor failure, and same performance as monolithic specimen was recognized until joint translation angle at maximum load R= 7.5/ 100 rad. The hysteresis loop had a spindle shape with excellent stable flexural performance. This means that D13 series did not have any influence of embedment depth of bonded anchors. ② With D16 series, concrete cone failure caused drastic resistance reduction in case of standard embedment (1h). But specimens with embedment 2h showed similar performance to monolithic one in terms of resistance and displacement. This means that the performance against cyclic loading after yielding of beams depends on the embedment depth. Table 4 Test result No .
Specimen name
D13 series
1 2 3 4 5 6
Joint translation angle at max.load
BN-4D13 BN-4D13-H1 BN-4D13-H2 BN-4D16 BN-4D16-H1
26.6 26.5 26.9 41.7 36.1
7.5 7.7 8.0 7.8 1.5
BN-4D16-H2
41.4
6.5
Failure mode Flexural yield Flexural yield Flexural yield Flexural yield Flexural yield failure Flexural yield
50 40 30
D16 serise D13 serise
10
name Fig.3 ComparisonSpecimen of max. loads
580
BC-4D16-H2
BC-4D16-H1
BN-4D16
●：Cone failure specimen BC-4D13-H1
0
BC-4D13-H2
20
BN-4D13
D16 series
Maximum load (kN)
max. load (kN)
Series
and
cone
D 1 3 serie s
2)BC －4D13 －H1
3)BC －4D13 －H2
4)BN －4D16
5)BC －4D16 －H1
6)BC －4D16 －H2
D 1 6 serie s
1)BN －4D13
Fig.4
Crack pattern at max. loads of each specimen
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30 Ｑ
Ｑ
20
(kN)
10
15
0
0
-10
-15
-20
-30
-30 -8
▼：at max. load
▲
-6
▼
BN-4D16
30
Ｒ
(kN)
45 Ｑ
▼
BN-4D13
-4
-2
0
2
4
6
-45▲ -8
8
▼：at max. load -6
-4
-2
0
2
4
Ｒ (1/100rad)
30
8
Ｑ
20
45
BC-4D16-H1
Ｑ
▼
BC-4D13-H1
6
Ｒ (1/100rad)
▼
30
(kN)
(kN)
10
15
0
0
-10
-15
-20
-30
-30 -8
▲
▼：at max. load
▲
-6
-4
-2
0
2
4
6
-45 -8
8
-6
-4
-2
▼：at max. load 0
2
4
Ｒ (1/100rad)
30 Ｑ
20
45
▼
30
(kN)
(kN)
10
15
0
0
-10
-15
-20
-30
▼：at max. load
▲
-30 -8
8
BC-4D16-H2
Ｑ
▼
BC-4D13-H2
6
Ｒ (1/100rad)
-6
-4
-2
0
2
4
6
-45 -8
8
▼：at max. load
▲
-6
-4
-2
0
2
Ｒ (1/100rad)
b) D16 series
a) D1 3 series
Fig.5
4
6
Ｒ (1/100rad)
Q-R curve of each specimen
582
8
3.2 Comparison of test result and calculated values In this experiment, anchors receive both tensile and shear loads at the same time, and the calculation should include both loads in priciple. But this test result gives the fact that concrete cone failure was predominant caused by tension. Thus we focus on just tension. 1) Tensile resistance evaluation equation of bonded anchors in Japan *1 In Japan, tensile resistance of bonded anchors is decided from the minimum value of the calculated ones by equations (1), (2) and (3). Equations (1), (2) and (3) give tensile yield strength of anchor rods, concrete cone failure strength and bond strength respectively. T1 = σy・a0-------------------(1) T2 = 0.23 σB ・Ac----------(2) T3 = τa・π・da・le--------(3) τa = 10 σB / 21 ---------(4) σy: nominal yield point of anchor rod (N/mm2). The values in Table 2 was adopted for calculation. a0: Minimum sectional area of anchor rods (mm2) σB: Compressive strength of base material (N/mm2) Ac: Effective projected area of concrete cone failure (mm2) calculated by equation (5). Ac =π・le・(le +da)----------(5) le: Effective embedment depth of anchor rods (mm) da: Anchor rod diameter (mm)
here
In this experiment, anchor spacing is 130 mm as shown in Fig.1, Effective projected area overlaps as shown in Fig.7. In such case, the effective projected area can be calculated as the oblique line area in Fig.7.
45゜
Ｄa
Ａc＝ πｌa （ ｌa＋ ｄa）
130
cone failure surface
130
ｌ
ｄa ｌa
ｄa
π Ａ0＝ ・ ｄa2 4
(a)Projected area for D13 ｌa ｄa
(b)Projected area for D16
ｌa
Fig.6 Effective projected area of bonded anchors
Fig.7 Effective projected area by anchor diameter
583
2) Review on condition of resisting cyclic loading after flexural yield In order to study the condition where anchor rods can resist to cyclic loading after flexural yield, we introduced the index of reserve ratio of cone failure strength given by equation (6). Reserve ratio of cone failure strength = calculated cone failure strength ／ calculated anchor rod yield strength---------(6)
Reserve ratio of cone failure resistance(T2/T1)
Fig.8 shows the relationship between effective embedment depth and reserve ratio calculated with equation (6). The followings are derived from Fig.8. ① When the reserve ratio of cone failure strength exceeds 2.0, all specimens in both D13 and D16 series can resist well to cyclic loading after flexural yield. ② When the reserve ratio of cone failure strength is below 1.0, D13 beam specimen can resist well to cyclic loading after flexural yield, but D16 beam specimen gave cone failure and can not resist to cyclic loading. ③ Summarizing the above, future additional investigation seems necessary in terms of performance against cyclic loading after flexural yield, when the reserve ratio of cone failure resistance is below 1.0.
3.0
D13 series
2.0
D16 series
1.0
●：Cone failure Fig.8
0.0 0
5 10 15 20 Effective embedment depth/anchor rod dia. (ｌ e/ｄa)
Reserve ratio of cone failure resistance and performance against cyclic loading after flexural yield
584
4. Conclusion We have obtained the following facts from this experiment. 1) Connection of beam members with bonded anchors gave substantial mechanical performance resisting to cyclic loading after flexural yield. 2) Beam members with reserve ratio of cone failure resistance above 2.0 can resist well to cyclic loading after flexural yield. 3) We must pay careful attention to the beam members with reserve ratio of cone failure resistance below 1.0 that sometimes show cone failure due to cyclic loading after flexural yield.
6. Reference *1 Architectural Institute of Japan ,“Design Recommendations for Composite Construction”, 1985
585
SHALLOW SHEAR ANCHOR BOLTS FOR STRUCTURAL SEISMIC STRENGTHENING OF COLUMNS WITH WING WALL Yasutoshi Yamamoto*, Yuriko Hattori**, Tadaki Koh***, Mitsuharu Kato**** *Dept. of Architecture, Shibaura Institute of Technology, Tokyo **Shibaura Institute of Technology, Tokyo ***Dept. of Architecture, Graduate School of Science and Technology, Meiji Univ., Tokyo **** Dept of Architectural Engineering, Yahagi Construction Co. Ltd., Nagoya
Abstract An improved method of seismic strengthening of existing R/C buildings using reinforced exterior members has been developed. This method shortens the construction period and makes it possible to use the building while under construction. The method, called Concrete Member Included Plate (CMIP), has been used and it performed well with school buildings and public service buildings. The next aim is expanding its use with apartment buildings which wing walls and non-structural walls become integral parts of columns. The reinforced member must not obstruct any part of the building and must be thinner and lighter than other presented methods. Thus anchor bolts shallowly embedded are used to connect existing R/C member to the reinforced member. This paper presents mechanical behavior and transmits shear load capacity of adhesive post-installed anchor bolts embedded in thin R/C wall. The pilot tests for these anchors are reported and the shear capacity and the failure mechanism described. And furthermore, a new style of anchor bolt is proposed for the thin R/C wall.
1. Introduction Low- and middle-rise Japanese apartment buildings utilizing R/C frame structure built in the 60s and 70s, are insufficiently seismically resistant. As a result, great damage occurs, as has been clearly reported since the Hyogo-ken Nanbu earthquake. Typically, seismic strengthening methods have not allowed the residents to continue living in their units. For this reason most buildings are left in their present condition without being reinforced. CMIP allows the use of building under construction. The construction method is shown in Fig.1. The most important concept developed as a component of this method is an adhesive post-installed anchor bolt for shear reinforcement. Each anchor bolt connects a very thin reinforcing R/C wall and the existing member.
586
30
Existing R/C wall Headed anchor bolt Grouted mortar Steel plate
90 120
55or80 20
R/C column CMIP member
Wing wall
Wire mesh Sprayed mortar
Flange Anchor bolt
Fig.1. CMIP method Several experimental studies of anchors made of short bolts embedded in concrete have already been published. However, there has not been enough research about headed anchor bolts in concrete subjected to shear. The objectives of this paper are to investigate appropriate shear capacity and failure mechanism of single-headed anchor bolts in the existing member and secondarily to address anchor bolts in the reinforced member.
2. Description of specimens The type of threaded headed studs required by Japanese Industrial Standard (JIS) and Japan Stud Association*1 is determined by the diameter of the anchor shank and its length. The specimen details are shown in Fig.2. 120mm wall thickness is in common use in Japan and 12mm to16mm anchor bolt diameters are suitable or recommended, and the reinforced member generally has a thickness of 80 to 100mm.
a) KP-55 series
150 150 300 M12,M16 Threaded anchor PL-2.3 80
60 100
75 150 75 300
hole
75 150 150 150 75 600
75 150 150 150 75 600
150 150 300
55
40 100
The tests were performed with 3 different types of anchors. As shown in Fig. 2, Type A featured threaded bolts with a nut, Type N featured nuts with a head and steel plate, and Type W had one of the nuts welded with a steel plate (W-type).
75 150 75 300
Mortar
a) KP-80 series Fig.2 Specimens and anchor type
587
Nut Type A Nut Type N Welded Nut Type W
The end of 100 mm anchor is subjected to shear, and it transmits loads to the specimen through the bolt which goes through the hole (bolt diameter + 10mm) into the plate.
3. Material properties 3.1 Properties of anchor bolts Mechanical properties of anchor bolts are shown in Table 1. The yield point σy was determined by using the intersection between the Q-ε curve and 0.2% shifting the strain. Table 1 Properties of steel bolts Type and disignation M12 JIS G3101(SS400) M16 JIS G3101(SS400)
Effective area Modulus of elasticity Yield strength Max. strength Elongation Es×105[MPa] σy[MPa] σmax[MPa] [%] eas[mm]
Diameter da[mm]
12
83.4
2.16
412.8
434.7
5.32
16
157.0
1.91
386.2
431.6
5.63
3.2 Mortar Mortar was used for fixing embedded anchor bolts. The curing properties of compound mortar are shown in Table 2. Table 2 Properties of mortar Concrete weight of unit volume Mortar compressive strength 2 σM[MPa] γ[kN/m ]
20.9
Split tensile strength 2 σSP[N/mm ]
Modulus of elasticity 4 EM ×10 [MPa]
2.58
2.37
33.6
4. Description of tests 4.1 Setting up of the specimen The application of shear load to the specimens is shown in Figure 3. Single anchor bolt in specimens were subjected to monotonic lateral loading.
Anchor bolt
Load cell
Load direction Testing stand
Displacement measurement
Shear block
Fig.3 Test set up
588
Oil jack
4.2 Measurement of load and displacement Lateral loads and shear displacements were measured using the shear block indicated in Fig.3. The crack pattern was observed after the test without setting.
5. Test results 5.1 Behavior under monotonic loading Experimentally derived shear force (Q) - deformation (δH) diagrams are shown in Figures. Specific differences were not observed in KP-12 series to correspond initial rigidity and maximum load. Moreover the KP-A-12 series expresses the similar deterioration of strength after the peak load. On the other hand KP-16 series expresses that Type A has the highest initial rigidity. 50 Q[kN] KP-A-12-55 40
KP-N-12-55 KP-W-12-55
KP-N-12-80 KP-W-12-80
KP-A-12-80
30 2
1
20
3
3
4
10
4
2
2
1
0
δH[mm] 4 6
2
2 1
2
1
1
1
2
a) KP-12 Series
50 Q[kN]
3
2
40 2
1
30
1 4
20
0
2
2 3
10
KP-A-16-55
2
4
1
1
1 1
δH[mm] 6
KP-N-16-55 KP-W-16-55
2
2
4
KP-A-16-80
KP-N-16-80 KP-W-16-80
a) KP-16 Series Fig4 Load–deformation diagram
5.2 Failure mode and crack Pattern The decisive failure mode for the entire specimen is given by steel shear cutting. Embedded bolts are not influenced by lateral pressure against mortar. The final crack patterns of the thickness of 55mm mortar are shown in Fig.5. No cracks in the 80mm specimens were observed.
589
Loading direction A-12-4
W-12-1
A-12-3
W-12-2
A-12-2
N-12-1
Loading direction A-12-1
A-16-4
N-12-1
W-16-1
a) KP-12-55 Series
A-16-3
W-16-2
A-16-2
N-16-1
A-16-1
N-16-1
b) KP-16-55 Series Fig5 Crack patterns
Cracks in mortar were observed in KP-12-55 and KP-16-55 series; it was more extensive in KP-16-55 series. It is shown that as the strength increases, the crack increases with the steel diameter. Cracks were also observed in the perpendicular direction. Based on the observation, it is estimated that mortar suffers from lateral pressure and tensile strength derived from flexural moment of reinforced member action.
6. Discussion of test data 6.1 Thickness of mortar effects The crack in the surface occurred in both M12 and M16 in thickness of 55mm mortar. Differences among specimens in initial rigidity and deterioration of strength are relatively insignificant for seismic sufficiency. No crack occurred on the mortar surface in both M12 and M16 specimens in thickness of 80mm mortar. Comparing KP-12 and KP-16, it is recognized that different mortar thickness did not give severe influence with regard to maximum strength and deformation. 6.2 Effects of diameter of the bolt The experimental data are summarized in Table 3. Comparing KP-12-55 and KP-12-80 series based on the experimental data, the former specimens surpass 1.08 to 1.16 times of the strength on average. In the tests, as the maximum load amount to the value, the deformation increases. It is considered that anchor bolts in shear rotate to form cracks; these cracks actually improve shear deformation. Although the notion of small deformation at maximum strength is preferred, the test data recognized that anchor bolts of this ductile design surpass in terms of energy absorbing capacity. Therefore the data of KP-12-80 series showed unfavorable effect on earthquake resistance.
590
Table 3 Summary of test data Designed Max. Shear Failure Ratio of Mortar Head Embedded shear Deformation Ave. shear Reference test Diameter stress mode actual / thickness diameter length capacity load no. design da[mm] t [mm] dH[mm] le [mm] Qm[kN] τm[MPa] Qc[kN] δH[mm] [mm] 22 40 24.1 12 55 KP-A-12-55-1 28.1 337.1 Steel 1.17 4.48 3.74 *6 -2 27.0 323.6 Steel 1.12 4.43 -3 26.3 315.7 Steel 1.09 3.40 -4 26.1 312.4 Steel 1.08 2.64 KP-N-12-55-1 26.1 312.4 Steel 1.08 3.81 3.41 -2 25.9 310.1 Steel 1.07 3.00 KP-W-12-55-1 25.2 302.2 Steel 1.05 3.63 3.33 -2 25.5 305.5 Steel 1.06 3.02 12 22 60 80 KP-A-12-80-1 22.9 274.0 Steel 0.95 2.62 3.02 -2 22.7 271.7 Steel 0.94 3.23 -3 24.2 289.7 Steel 1.00 3.60 -4 23.1 277.3 Steel 0.96 2.63 KP-N-12-80-1 22.9 274.0 Steel 0.95 2.63 2.52 -2 24.9 298.8 Steel 1.03 2.41 KP-W-12-80-1 24.8 297.6 Steel 1.03 3.62 3.52 -2 22.1 265.0 Steel 0.92 3.41 55 40 16 27 42.5 KP-A-16-55-1 36.6 233.0 Steel 0.86 4.61 4.26 *6 -2 43.3 275.5 Steel 1.02 4.61 -3 43.5 277.3 Steel 1.02 4.40 -4 45.1 287.5 Steel 1.06 3.43 KP-N-16-55-1 43.4 276.7 Steel 1.02 5.61 4.81 -2 42.7 271.9 Steel 1.00 4.00 KP-W-16-55-1 40.4 257.5 Steel 0.95 4.41 3.92 -2 43.3 275.5 Steel 1.02 3.43 27 60 16 80 KP-A-16-80-1 43.5 277.3 Steel 1.02 4.41 3.98 -2 42.5 270.7 Steel 1.00 4.20 -3 45.3 288.7 Steel 1.07 4.22 -4 41.3 262.9 Steel 0.97 3.08 KP-N-16-80-1 41.8 266.5 Steel 0.98 3.62 3.93 -2 42.1 268.3 Steel 0.99 4.23 KP-W-16-80-3 44.1 280.9 Steel 1.04 4.41 3.81 -2 39.8 253.3 Steel 0.94 3.20
From the test data, the strength is higher and the deformation is lesser on the average in KP-A-16-80 series than in KP-A-16-55 series. Moreover Types N and W were inferior to the strength and deformation slightly. With regard to steel sizes, the maximum strength of KP-16-55 series exceeds the value of KP-12-55 series 1.57 to 1.86 times on average. And KP-16-80 series exceeds the strength in the efficiency of embedment length 1.76 to 1.86 times. The deformation at the maximum load also increases. The value of strength (as × σy) of M12 to M16 is expressed 34.4 : 60.7[kN] =1 : 1.76 from the test result. It is recognized that the M12 threaded anchor bolt surpasses the M16 bolt in strength in regard to the shear stress. Although both 12mm and 16mm embedded bolts are appropriated for earthquake resistance, M12 threaded anchor bolts are slightly efficient.
591
6.3 Pilot tests 6.3.1 Anchor bolts in reinforced members under lateral monotonic loading Results from the aforementioned test showed that anchor bolts failed in the reinforced members because of the failure of the steel bolt. On the other hand, it is desirable that the strength of the anchor bolts in the existing members remains equal to that in the reinforced member. In additionally in Table 4 and 5 are shown the pilot test data under monotonic lateral loading. In Japan, existing non-structural walls are approximately 120mm thick, hence the embedment length is less than 100mm. Table 4 Summary of test results of M16 anchor Max. Ratio of Designed Anchor type Reference Concrete Embedded shear Shear Failure actual / shear DeforDiameter thickness length load stress mode design capacity mation Ave. designation test no. Qc[kN] δH[mm] [mm] da[mm] t [mm] le [mm] Qm[kN] τm[MPa] M16 HY150-S-1 43.5 277.1 Steel 0.87 16 120 88 49.8 14.73 10.48 *6 JIS B1051 -2 41.5 264.3 Steel 0.83 8.56 Grade 4.6 -3 45.4 289.2 Steel 0.91 8.16
σ y = 455 .7[ MPa ], E S = 1.91 × 10 5 [ MPa ], e a s = 157 .0[ mm ], σ B = 30 .6 [ MPa ], E C = 2.06 × 10 4 [ MPa ]
From Table 3, 4 and 5, the ratio of maximum shear strength (Qm) / designed shear capacity (Qc) for M16 threaded anchor bolts are 0.86-1.06 and 0.87-0.91, and for D19 is 0.75-0.97. Moreover it is pointing out that the shear strength slightly surpasses in M16 anchor bolts embedded in the existing member. In comparison with the value of shear stress (τm) is 265.0-337.1 in M12 specimens, 233.0-288.7 and 264.3-289.2 in M16 specimens and 189.5-263.9 in D19 specimens. The shear stresses of M16 anchors are poor in reinforced member. In studying Tables 3 and 4, it is recognized that the failure mode is defined in regard to the strength of M16 anchor bolts in the reinforced member. Table5 Summary of test results of D19 anchor Anchor type designation D19 G3112 SD345
Max. Ratio of Designed Concrete Embedded shear Shear Failure actual / shear DeforReference Diameter thickness length load stress mode design capacity mation Ave. test no. da[mm] t [mm] le [mm] Qm[kN] τm[MPa] Qc[kN] δH[mm] [mm] A15-100S-1 61.0 212.9 Concrete 0.84 19 250 100 72.5 12.00 12.23 -2 58.7 204.9 Concrete 0.81 *6 12.00 -3 54.3 189.5 Concrete 0.75 12.70 A21-100S-1 71.0 247.8 Concrete 0.91 78.0 16.10 15.40 -2 75.6 263.9 Concrete 0.97 *6 16.00 -3 58.7 204.9 Steel 0.75 14.10
σ y = 389 .1[ MPa ], E S = 1.92 × 10 5 [ MPa ], e a s = 286 .5[ mm ] σ B = 20 .4[ MPa ], EC = 1.96 × 10 4 [ MPa ], σ B = 25 .7[ MPa ], EC = 2.48 × 10 4 [ MPa ]
6.3.2 Suggestions for a new type of anchor Based on the experimental study discussion and present papers*2,3,4,5 according to the numerous experimental studies calculating shear capacity in anchors of different sizes, a new type of anchor bolt is suggested. The main factors are as follows: a) embedment
592
length of anchor bolts, b) diameter of anchor-bolt shaft, c) yielding strength of anchor bolts, and d) concrete compressive strength. a) Effect of embedment length of anchor bolts Fig. 6 shows the relationship of shear strength (Qm) and shear stress (τm) to embedment length (le) based on present experimental data. In general, the thicknesses of anchors embedded in existing members are thinner and in reinforced member as well. The following values of shear stress from the data are scattered in 200 to 550 [MPa] regions that indicate the shear stress is not dependent on embedded length. From the diagram, it indicates the possibility of strengthening the shear capacity when embedment length of anchor bolts over 3da. The value of shear strength of anchor bolts under 16mm diameter distributed low strength region. 200
600 τm [MPa]
Qm [kN]
150 400 100 200
50 Embedment length [da]
0
2
4
6
8
Embedment length [da]
0
○ anchor in existing member (da≦16mm) △ anchor in reinforced member (da≦16mm)
2
4
6
8
● anchor in existing member (da＞16mm) ▲ anchor in reinforced member (da＞16mm)
Fig.6 Q and τ- le relationship b) Effect of anchor bolt diameter In Fig.7, shear strength (Qm) and shear stress (τm) are shown in relation to the anchor bolt diameter (da). Shear strength is directly proportional to the diameter of anchor bolt and shear stress shows proportional tendency to the diameter of anchor bolt. Therefore it is essential to strengthen the shear strength when steel diameter increases. 200
Qm [kN]
600
τm [MPa]
150 400 100 200
50 diameter [mm]
0
4
8
12
16
20
diameter [mm]
0
4
Fig.7 Q and τ- da relationship
8
12
16
20
c) Effect of yielding strength of anchor bolts In Fig.8 are given the shear strength (Qm) and shear stress (τm) to the yield strength (σy).
593
From these diagrams, the shear strength is unrelated to the yield strength of anchor bolts with under 16mm diameter. It is recognized that a high value of yielding strength is more effective. However, the shear strength does not increase when anchor bolt governed by bearing concrete. 200
Qm [kN]
600
τm [kN]
150 400 100 200
50
σy [MPa]
σy [MPa]
0
100
200
300
400
500 0
100
200
300
400
500
Fig.8 Q and τ - σy relationship d) Effect of concrete compressive strength In Fig.9 are given the shear strength (Q) and shear stress (τ) to the concrete compressive strength (σB). It is clear from these diagrams that the shear strength increases with the concrete compressive strength when the diameter of anchor increases. 200
600
Qm [kN]
150
τ m[MPa]
400
100 200 50 σB [MPa]
0
10
20
30
0
40
σB [MPa]
10
Fig.9 Q and τ -σB relationship
20
30
40
e) Suggestion toward a new anchor bolt From these experimental data, a preferable style of anchor bolt is recommended and described in Fig.10. Existing R/C wall Grouted mortar 50 30 Steel plate 70
90 120
80 20
Sprayed mortar
32~36 20~22 12 Shallow anchor bolt JIS B1051-1985 8.8 grade
Fig.10 New anchor bolt
594
7. Conclusion and recommendation Seismic strengthening of columns with thin wing walls in apartment buildings requires strong shallow anchor bolt for shear. The recommended diameter of anchor bolt was 12-16mm for walls approximately 120mm thick. As the results of the experimental data and diagrams, higher strength and larger diameter of anchors are recommended, and a new type of anchor bolt is suggested. The experimental research of this program will be continued in the future and more recommendations will be developed.
8. Acknowledgments The tests were sponsored by Science Frontier Research Project in Graduate School of Science and Technology, Meiji University, Tokyo. This experiment is supported by Yahagi Construction Co. Ltd. and Hilti Japan Co. Ltd. The authors would like to acknowledge the assistance, support, and efforts of S.I.T. students.
9.
References
1. 2.
‘Welding Stud’, Japan Stud Association, Sep. 1982, pp48-49 R.E.Klingner, et al, ‘Shear Capacity of Short Anchor Bolts and Welded Studs: A Literature Review’, ACI JOURNAL, Technical Paper, Sep.-Oct. 1982, pp339-349 Nihon Decoluxe, ’Test of Chemical Anchor in Shear and Tension’, Technical Paper, Feb.1982 Sugaya,S. et al, ‘Experimental Study on Anchors for Equipment and Plumbing’, Proceedings of Architectural Institute of Japan,Sep.1981, pp1567-1568 Tsusai,H. et al, ‘Shear Strength of Wedge Anchor Bolts under Reversed Cyclic Loading’, Proceedings of Japan Concrete Institute, vol.5, pp1983,233-236 ‘Post-installed Anchor –Design and Construction ’, Okada, T. et al, pp1990 59-73 Design Recommendations for Composite Constructions, Architectural Institute of Japan, 1998, pp244-245
3. 4. 5. 6. 7.
10. Appendix The following anchor steel strengths calculation for predicted shear capacity has been used. *6,7 Q c = min [Q c 1 , Q c 2 ] Q c 1 = 0 .7 s σ y s a e
governed by steel failure
Q c 2 = 0.4 E c σ B s a e governed by concrete failure s
a e : effective area of the anchor bolt
595
SEISMIC RESPONSE OF MULTIPLE-ANCHOR CONNECTIONS TO CONCRETE Zhang, Yong-gang*, Richard E. Klingner**, and Herman L. Graves, III*** * Han-Padron Associates, Houston, Texas, USA. ** Dept. of Civil Engineering, The University of Texas at Austin, Austin, Texas, USA. *** U.S. Nuclear Regulatory Commission, Washington, D.C., USA.
Abstract Under the sponsorship of the US Nuclear Regulatory Commission, a research program was carried out on the dynamic behavior of anchors (fasteners) in concrete. As part of that program, full-scale seismic tests were conducted at dynamic loading rates on 16 multiple-anchor connections to concrete. Test variables included anchor type, loading history, and the presence of cracks. Multiple-anchor connections designed for ductile behavior in uncracked concrete under static loading, in general behaved in a ductile manner in cracked concrete under dynamic loading.
1. Background A few studies have investigated the behavior of connections under impact loading, seismic loading and reversed loading [1, 2, 3, 4]. Loading patterns primarily involved dynamic loading far below the anchor's ultimate capacity, followed by monotonic loading to failure [3, 4]. Only a few investigations [5, 6, 7] have studied the influence of loading rate on the overall load-displacement behavior of anchors. Some tests have been conducted in cracked concrete or in high-moment regions [1, 3, 5, 8]. To the best of the authors’ knowledge, the testing program described here is the first published testing on multiple-anchor connections under seismic loading.
2. Anchors, Test Setups and Procedures Based on their use in nuclear applications, this research program involved one wedgetype expansion anchor (“Expansion Anchor II”), with some tests on one normally opening undercut anchor with large bearing area (“UC Anchor 1”). Anchors were 5/8 in. (16 mm) diameter, installed with an effective embedment of 7 in. (178 mm) to develop ductile response. Expansion Anchor II (EAII) is described in Figure 1. Undercut Anchor 1 (UC1) is described in Figure 2.
596
D
D1 D2
wedge dimple wedge mandrel (cone)
lc
Figure 1
Expansion Anchor II
extension sleeve
threaded shank
expansion sleeve
lef
D2
D
D1
cone
lc
Figure 2 Undercut Anchor 1 The target concrete compressive strength for this testing program was 4700 lb/in.2 (32.4 MPa), with a permissible tolerance of ±500 lb/in.2 (±3.45 MPa) at the time of testing. Aggregate was river gravel. The overall test setup for Task 4 is shown in Figure 3. Reversed cyclic loads were applied to the connection through a loading attachment, shown in Figure 4. The stiff baseplate was 2 in. (51 mm) thick; the flexible one, 1 in. (25 mm). Both baseplates had stiffeners. External load on the connections was measured with a load cell. Tension in each anchor was measured with a force washer placed between the normal washer and the baseplate. Slip of the baseplate was measured with a potentiometer placed against the back of the baseplate, and displacement of the vertical beam was measured at 12 in. (305 mm) from the surface. Loading Attachment
Load Cell
DCDT
Hydraulic Actuator
Clamping Beams
Concrete Specimen
Reaction Frame
--- Lab Floor ---
Figure 3
Tie-Down Rods On Floor
Test setup for multiple-anchor tests of Task 4
597
The prescribed displacement history that simulated earthquake loading 10 in. was developed by idealizing the 6 in. attachment as a bilinear singledegree-of-freedom (SDOF) system with a concentrated mass at 12 in. 9 in. 12 in. Stiffeners (305 mm) above the concrete 12 in. surface, sufficient to give a realistic period of vibration, and to produce Plan View yielding of the attachment under the 14 in. selected ground motion. The Elevation response of the SDOF system was Figure 4 Loading attachment used for Task 4 calculated using as input the earthquake history of El Centro 1940 (NS component). The most significant portion, consisting of the first 6.0 sec. of that record (Figure 5), was used as the prescribed displacement history. D isplacem ent Input
0.8
Displacement (in.)
0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0
2
4
6
8
10
12
14
Time (sec.)
Figure 5
History of estimated attachment displacements for seismic tests
Some specimens had cracks with an initial width of 0.012 in. (0.3 mm), introduced using wedge-type splitting tubes of high-strength steel. Anchors were installed to the torque specified by the manufacturer. To simulate the reduction of prestressing force in anchors in service due to concrete relaxation, anchors were first fully torqued, then released after about 5 minutes to permit relaxation, and finally torqued again, but only to 50% of the specified torque. For multiple-anchor shear tests, two separate cracks were initiated parallel to the loading direction. Crack widths were monitored during tests, but not controlled.
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For static tests, the load was applied slowly and monotonically under displacement control. For dynamic tests, the loading pattern was dynamic reversed cyclic loading (Figure 5), applied under displacement control. During tests, the loading sequence was first applied with a maximum displacement of 0.6 in. (15.2 mm). If the connection did not fail, loading sequences were applied with maximum displacements of 1.0 in. (25 mm) and then 1.5 in. (38 mm). Further cycles, to a maximum displacement of 15 in. (38 mm), were applied until failure. Before each loading sequence, the anchors were finger-tightened to eliminate any initial lack-of-fit, which would have increased the displacement required to reach any particular load level. Tests are listed in Table 1. For all tests, the edge distance was 5 in. (127 mm), and the embedment was 7 in. (178 mm). Table 1 Test 4101 4102 4203 4204 4205 4206 4307 4308 4309 4310 4411 4412 4513 4514 4615 4616 4617
Test matrix for eccentric shear tests on multiple-anchor connections Description static, 4-anchor group, rigid baseplate, uncracked concrete, e = 12 in. (305 mm) static, 4-anchor group, rigid baseplate, uncracked concrete, e = 18 in. (457 mm) dynamic, 4-anchor group, flexible baseplate, uncracked concrete, e = 12 in. (305 mm) dynamic, 4-anchor group, rigid baseplate, uncracked concrete, e = 12 in. (305 mm) dynamic, 4-anchor group, rigid baseplate, uncracked concrete, e = 12 in. (305 mm) dynamic, 4-anchor group, rigid baseplate, uncracked concrete, e = 18 in. (457 mm) dynamic, 4-anchor group, rigid baseplate, cracked concrete, e = 12 in. (305 mm) dynamic, 4-anchor group, rigid baseplate, cracked concrete, e = 12 in. (305 mm) dynamic, 4-anchor group, rigid baseplate, cracked concrete, e = 18 in. (457 mm) dynamic, 4-anchor group, rigid baseplate, cracked concrete, e = 18 in. (457 mm) static, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, no hairpins, e = 12 in. (305 mm) static, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, no hairpins, e = 18 in. (457 mm) dynamic, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, no hairpins, e = 12 in. (305 mm) dynamic, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, no hairpins, e = 18 in. (457 mm) static, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, close hairpins, e = 12 in. (305 mm) dynamic, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, close hairpins, e = 12 in. (305 mm) dynamic, near-edge, 4-anchor group, rigid baseplate, uncracked concrete, close hairpins, e = 18 in. (457 mm)
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Anchor UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) EAII 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) EAII 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) EAII 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm) UC1 5/8 in. (16 mm)
3. Test Results In Figures 6 and 7, the load-displacement envelopes of dynamic tests under eccentric shear at 12 in. (305 mm) and 18 in. (457 mm) respectively, are compared with the static tests on the same configuration (Test 4101 versus Test 4203, and Test 4102 versus Test 4206). The following observations can be made: 1) The dynamic load-displacement curves follow the static load-displacement curves over most of the displacement range, differing only near the ultimate load. 2) The maximum dynamic capacity was close to the maximum static capacity. It was 7% higher at a 12 in. (305 mm) eccentricity, and 7% smaller at an 18 in. (457 mm) eccentricity. Due to the small number of tests, however, this observation is not definitive. 3) The most significant effect of dynamic reversed cyclic loading is the increase in total displacement, due to spalling of the concrete in front of the anchors, to the gaps between the baseplate and the anchors and between the anchors and the concrete, and to the larger tensile displacement of the anchors under dynamic cyclic loading. Seismic tests on a connection with EAII under dynamic reversed cyclic loading (Test 4307) showed large displacements of about 1 in. (25.4 mm) measured at 12 in. (305 mm) above the concrete, although there is no corresponding static test with which this can be compared. In Figures 8 and 9, load-displacement curves for tests with dynamic loading in cracked concrete (Tests 4308 and 4309) are compared with the corresponding curves for tests with static loading in uncracked concrete (Tests 4101 and 4102). The dynamic load-displacement envelopes for these tests also follow the static load-displacement curves well, except near the ultimate load. Horizontal Displacement at 12 in. (305 mm) (mm) -38.1
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Figure 6 Static versus seismic load-displacement curves, multiple-anchor connections, UC1 Anchors, at 12 in. (305 mm) eccentricity (Tests 4101 and 4203)
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Horizontal Displacement at 12 in. (305 mm) (mm) -63.5 -50.8 -38.1 -25.4 -12.7
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Figure 7
Comparison of static and seismic load-displacement behaviors of multiple-anchor connections with UC1 Anchors under shear at 18 in. (457 mm) eccentricity (Tests 4102 and 4206 respectively) Horizontal Displacement at 12 in. (305 mm) (mm) -63.5 -50.8 -38.1 -25.4 -12.7
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Figure 8
Comparison of seismic load-displacement behavior of multipleanchor connections with UC1 Anchors at 12 in. (305 mm) eccentricity in cracked concrete (Test 4308) with static behavior in uncracked concrete (Test 4101)
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Comparison of Test Results and Analytical Predictions Test results were compared with predictions of BDA5, a macro-model program developed at the University of Stuttgart for the static analysis of multiple-anchor connections loaded by eccentric shear [9]. It requires as input data a complete set of load-displacement curves of the anchor under oblique loading at angles from 0 to 90 degrees, and assumes a rigid baseplate. Comparisons were reasonable, and are discussed in more detail in Zhang [10]. Horizontal Displacement at 12 in. (305 mm) (mm) -38.1
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Figure 9
Comparison of seismic load-displacement behavior of multipleanchor connections with UC1 Anchors at 18 in. (457 mm) eccentricity in cracked concrete (Test 4309) with static behavior in uncracked concrete (Tests 4102)
Comparison of Test Results with Plastic Analysis Methods The Plastic Method [11] and the Modified Plastic Method [7] predict the capacity of multiple-anchor connections with large edge distances, loaded in shear and failing by steel fracture. For the connection with a loading eccentricity of 18 in. (457 mm), the capacities calculated by the Plastic Method and the BDA5 program are very close to the test results. The Modified Plastic Method [7], however, underestimated the static capacity by as much as 10%. For the connection with a loading eccentricity of 12 in. (305 mm), both the Plastic Method and the BDA5 program overestimated the static capacity. The Modified Plastic Method [7] was very close to the test results.
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4. Conclusions and Recommendations 1) Multiple-anchor connections in uncracked or cracked concrete, with or without edge effects, and with or without hairpins, loaded dynamically under reversed cyclic loading histories representative of seismic response, behaved consistently with the results of previous single- and double-anchor tests of this study. Previous observations regarding the load-displacement behavior, and failure mechanisms of single and double anchors, were applicable in predicting the behavior of complex, multiple-anchor connections under simulated seismic loading. The implications of this are clear. Multiple-anchor connections designed for ductile behavior in uncracked concrete under static loading, will probably still behave in a ductile manner in cracked concrete under dynamic loading. 2) Anchors that show relatively good performance when tested individually in cracked concrete (CIP headed anchors, UC1, and 20 mm diameter Sleeve) will probably also show relatively good performance in multiple-anchor connections subjected to seismic loading. Anchors that show relatively poor performance when tested individually in cracked concrete (Grouted Anchor, EAII, and 10 mm diameter Sleeve) will probably also show relatively poor performance in multiple-anchor connections subjected to seismic loading. 3) Cyclic load-displacement behavior of multiple-anchor connections is accurately bounded by the corresponding static load-displacement envelope, and also by the static load-displacement envelope predicted by the BDA5 program. Dynamic cycling does not significantly influence the fundamental load-displacement behavior of multiple-anchor connections. 4) Under dynamic reversed cyclic loading in both uncracked and cracked concrete, the load-displacement envelopes of multiple-anchor connections with the UC1 Anchor basically follow the static curves in uncracked concrete over most displacements, differing only near the ultimate load. Dynamic reversed loading did not significantly affect the maximum dynamic capacity. In uncracked concrete, the connection had larger displacements under reversed dynamic than under static loading. Under dynamic reversed loading, connections in cracked concrete had slightly larger displacements than those in uncracked concrete. 5) Under dynamic reversed cyclic loading, multiple-anchor connections with Expansion Anchor II had very large displacements. In both uncracked and cracked concrete, the connections loaded at 12 in. (305 mm) eccentricity failed by steel fracture. The test in cracked concrete had a larger displacement and smaller capacity than that in uncracked concrete. The connection loaded at an 18 in. (457 mm) eccentricity experienced gross pull-out failure of the anchors.
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6) The capacity of multiple-anchor connections at large edge distances was predicted with reasonable accuracy by the plastic design procedures [7, 10, 11]. 7) Capacities were reasonably predicted by the BDA5 program [9].
5. Acknowledgement and Disclaimer This paper presents partial results of a research program supported by the U.S. Nuclear Regulatory Commission (NRC) (NUREG/CR-5434, “Anchor Bolt Behavior and Strength during Earthquakes”). The technical contact is Herman L Graves, III, whose support is gratefully acknowledged. The conclusions in this paper are those of the authors only, and are not NRC policy or recommendations.
6. References 1.
Cannon, R. W., “Expansion Anchor Performance in Cracked Concrete,” ACI Journal, Proceedings, Vol. 78, No. 6, November-December 1981, pp. 471-479.
2.
Malik, J. B., Mendonca, J. A., and Klingner, R. E., “Effect of Reinforcing Details on the Shear Resistance of Short Anchor Bolts under Reversed Cyclic Loading,” Journal of the American Concrete Institute, Proceedings Vol. 79, No. 1, January-February 1982, pp. 3-11.
3.
Copley, J. D. and E. G. Burdette, “Behavior of Steel-to-Concrete Anchorage in High Moment Regions,” ACI Journal, Proceedings, Vol. 82, No. 2, March-April 1985, pp. 180-187.
4.
Collins, D., R. E. Klingner and D. Polyzois, “Load-Deflection Behavior of Cast-in Place and Retrofit Concrete Anchors Subjected to Static, Fatigue, and Impact Tensile Loads,” Research Report CTR 1126-1, Center for Transportation Research, The University of Texas at Austin, February 1989.
5.
Eibl, J. and E. Keintzel (1989): “Zur Beanspruchung von Befestigungsmitteln bei dynamischen Lasten,” Forschungsbericht T2169, Institut für Massivbau und Baustofftechnologie, Universität Karlsruhe, 1989.
6.
Rodriguez, M., “Behavior of Anchors in Uncracked Concrete under Static and Dynamic Loading,” M.S. Thesis, The University of Texas at Austin, August 1995.
7.
Lotze, D. and Klingner, R. E., “Behavior of Multiple-Anchor Connections to Concrete From the Perspective of Plastic Theory,” PMFSEL Report No. 96-4, The University of Texas at Austin, March 1997.
8.
Eligehausen, R. and Balogh, T., “Behavior of Fasteners Loaded in Tension in Cracked Reinforced Concrete,” ACI Structural Journal, Vol. 92, No. 3, May-June, 1995, pp. 365-379.
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9.
Li, L., BDA: Programm zur Berechnung des Trag- und Verformungsverhaltens von Gruppenbefestigungen unter kombinierter Schragzugund Momentenbeanspruchung (Programmbeschreibung), The University of Stuttgart, June 1994.
10. Zhang, Yong-gang, “Dynamic Behavior of Multiple-Anchor Connections in Cracked Concrete,” Ph.D. Dissertation, Dept. of Civil Engineering, The University of Texas at Austin, August 1997. 11. Cook, R. A. and Klingner, R. E., “Ductile Multiple-Anchor Steel-to-Concrete Connections,” Journal of Structural Engineering, ASCE, Vol. 118, No. 6, June 1992, pp. 1645-1665.
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SMEARED FRACTURE FE-ANALYSIS OF REINFORCED CONCRETE STRUCTURES – THEORY AND EXAMPLES Joško Ožbolt Institut of Construction Materials, University of Stuttgart, Germany
Abstract In the present paper the smeared fracture concept for the nonlinear finite element analysis of concrete and reinforced concrete structures is discussed. After a short introduction into the problems related to the smeared crack approach, a brief theoretical background of the finite element code MASA is presented. The code has been developed at the Institute of Construction Materials, University of Stuttgart, and is aimed to be used for the nonlinear smeared fracture finite element analysis of concrete and reinforced concrete structures. The used constitutive law (microplane model for concrete) and the so called localization limiters, which assure mesh objective results, are described. To demonstrate the ability of the code to realistically predict the ultimate capacity and failure mode of concrete and reinforced concrete structures, several examples are shown and briefly discussed.
1. Introduction In recent years a significant progress in modeling of concrete like materials for general stress-strain histories has been achieved. Presently available models for concrete can roughly be classified in two categories: (i) Macroscopic models, in which the material behavior is considered to be an average response of a rather complex microstructural stress transfer mechanism and (ii) microscopic models, in which the micromechanics of deformations are described by stress-strain relations on the microlevel. No doubt, from the physical point of view microscopic models are more promising. However, they are computationally extremely demanding. Therefore, in practical applications macroscopic models have to be used. At the macro scale the model has to correctly describe microstructural phenomena such as cohesion, friction, aggregate interlock and interaction of microcracks. Traditionally,
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macroscopic models are formulated by total or incremental formulation between the σij and εij components of the stress-strain tensor, using the theory of tensorial invariants [1][2]. In the frame work of the theory there are various possible approaches for modeling of concrete, such as theory of plasticity, plastic-fracturing theory, continuum damage mechanics, endocronic theory and their combinations of various form. Due to the complexity of concrete these models can not realistically represent the behavior of concrete for general three-dimensional stress-strain histories. Therefore, to formulate a more general and relatively simple model significant effort has recently been done in further development of the microplane model for concrete [3][4][5][6]. Some of the latest results [6] confirm that the model is able to realistically simulate response of concrete structures for arbitrary load histories. Cracking and damage can principally be modeled in two different ways: (i) discrete (discrete crack model) and (ii) smeared (smeared crack model). The classical local smeared fracture analysis of materials which exhibit softening (quasi-brittle materials) leads in the finite element analysis to the results which are mesh dependent [7]. As well known, the reason for this is the localization of strains in a row of finite elements and a related energy consumption capacity which depends on the element size, i.e. if the finite element mesh is coarse the energy consumption capacity will be larger than when the mesh is fine. Consequently, the model response is mesh dependent. To assure mesh independent results, total energy consumption capacity has to be independent of the element size, i.e. one has to regularize the problem by introducing a so-called localization limiter. Currently two different approaches are in use. The first one is relatively simple crack band method [8] and the second ones are the so called higher order methods: Cosseratcontinuum [9] and nonlocal continuum approaches of integral type [10][11] or gradient type [9]. Compared to the crack band method the higher order procedures are rather complex, but more general. Mesh independent result can alternatively be obtained by the use of the discrete crack approach [12]. The main drawback of this approach is the need for continuous remeshing, which is a rather complex and time consuming procedure. Moreover, some stress-strain situations (for instance compression) are difficult to model in a discrete sense. To overcame the problems related to the smeared crack modeling and to avoid complex re-meshing when discrete crack approach is employed a new type of the finite elements has recently been employed [13]. These elements are based on the discontinuous strain field (embedded crack). The background of the method is the discrete crack approach, however, the cracks are here treated at the finite element level with no need for continuous re-meshing. In the concept there are still a number of theoretical difficulties which need to be solved (more than one crack per element, three-dimensionality and other). Presently available numerical examples are restricted to theoretical case studies.
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Therefore, a considerable amount of work need to be done before the concept is going to be used as a robust tool for the analysis of structures in engineering practice. The finite element code for the "every-day" use in engineering practice has to be based on the realistic material model for concrete, i.e. the concrete response should be realistically predicted for arbitrary load history. Moreover, the solution strategies have to be robust, what is from the view point of complexity of the material behaviour not a simple task. In spite of a number of difficulties mentioned above, the smeared crack approach is currently still one of the most general and reliable concept for realistic analysis of concrete and reinforced concrete structures, at least for the practical engineering applications. In the present paper a brief overview of the finite element code which is based on the smeared crack concept and microplane model for concrete is given. On a several numerical examples is demonstrated that the code is able to realistically predict failure mode and resistance of concrete and reinforced concrete structures.
2. Smeared fracture finite element analysis 2.1 General The finite element (FE) code employed in the present study (MASA) is aimed to be used for the nonlinear smeared fracture analysis of concrete and reinforced concrete structures [14]. It is based on the microplane model and a smeared fracture concept. As regularization procedures the standard or improved crack band approach (stress relaxation method) can be used. Alternatively, the nonlocal integral approach can be employed as well. The concrete is discretized by four-node quadrilateral elements (plane analysis) or by four to eight-node three-dimensional elements. The reinforcement is represented by truss elements. Optionally, it can also be modeled in a smeared way, i.e. smeared inside a row of concrete elements. Besides these standard elements, special linear or nonlinear contact elements are available as well. The analysis is incremental with a standard solution procedure based on the constant stiffness method (explicit approach). The tangent (Newton-Raphson) or secant stiffness approach can also be employed. 2.2 Constitutive law for concrete – microplane material model In the microplane model is for each integration point of the finite element the material characterized by a relation between the stress and strain components on planes (microplanes) of various, in advance defined, orientations (see Fig. 1). These "monitoring" planes may be imagined to represent the damage planes or weak planes in the microstructure, such as contact layers between aggregates in concrete. In the model the tensorial invariance restrictions need not to be directly enforced. They are automatically satisfied by superimposing the responses from all microplanes in a suitable manner. The basic concept behind the microplane model was advanced in 1938 by G.I. Taylor [15]. Later the model was extended by Bažant and co-workers for modeling of quasi-brittle materials which exhibit softening [3][4][5][6].
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The advanced version of the microplane model for concrete was recently proposed by Ožbolt et al. [6]. It is based on the so called relaxed kinematic constraint concept. In the model the microplane (see Figure 1) is defined by its unit normal vector of components ni. Normal and shear stress and strain components (σN, σTr; εN, εTr) are considered on each plane. Microplane strains are assumed to be the projections of the macroscopic strain tensor εij (kinematic constraint). Based on the virtual work approach, the macroscopic stress tensor is obtained as an integral over all microplane orientations:
σ ij =
3 3 σ N n i n jd Ω + ò 2π 2π Ω
ò
Ω
σ Tr (n i δ rj + n jδ ri ) dΩ 2
(1)
To realistically model concrete, the normal microplane stress and strain components have to be decomposed into volumetric and deviatoric parts (σN=σV+σD, εN=εV+εD; see Figure 1), which leads to the following expression for the macroscopic stress tensor: σ ij = σ V δ ij +
3 3 σ D n i n j dΩ + ò 2π 2π Ω
ò
Ω
σ Tr (n i δ rj + n jδ ri ) dΩ 2
(2)
For each microplane component, the uniaxial stress-strain relations are calculated as: σ V = FV (ε V ,eff ) ; σ D = FD (ε D,eff ) ; σ Tr = FTr (ε Tr ,eff )
(3)
From known macroscopic strain tensor, the microplane strains are calculated based on the kinematic constraint approach. However, in (3) only effective parts of these strains are used to calculate microplane stresses. Finally, the macroscopic stress tensor is obtained from (2). The integration over all microplane directions (21 directions) is performed numerically. To model concrete cracking for any load history realistically, the effective microplane strains are introduced. They are calculated as: ε m,eff = ε m ψ
(4)
where subscript m denotes the corresponding microplane components (V, D, Tr) and ψ is a so called discontinuity function. This function accounts for discontinuity of the macroscopic strain field (cracking) on the individual microplanes. It "relaxes" the kinematic constraint which is in the case of strong localization of strains physically unrealistic. Consequently, in the smeared fracture type of the analysis the discontinuity function ψ enables localization of strains, not only for tensile fracture, but also for dominant compressive type of failure. For more detail see [6].
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The model was implemented into the finite element code and a rather broad experience has been gained with it so far. Some of its characteristics are: (1) The main advantage of the model is its conceptual simplicity, i.e. only a set of uniaxial stress-strain curves on the microplane need to be defined and the macroscopic model response comes automatically out as a result of the numerical integration over a number of microplanes; (2) The model covers full three-dimensional range of applicability; (3) It is relatively easy to account for initial anisotropy; (4) The comparison between test data and model response for different stress-strain histories shows good agreement; (5) Unlike to most macroscopic models, in the presented microplane model there is smooth transition from hardening to softening, without unnatural sharp discontinuities. This is very important feature which in the finite element analysis leads to significant reduction of the mesh sensitivity and assure better convergency of the solution; (6) Implementation in the finite element code and a number of numerical studies that have been carried out indicated the capability of the model in realistic prediction of concrete behavior for different stress-strain histories [16].
a)
b)
z z
ε εT εK
x
Integration point y (finite elemen)
εN
εM
y
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x
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Figure 1. The concept of the microplane model: a) discretization of the unit volume sphere for each finite element integration point (21 microplane directions) and b) microplane strain components.
2.3 Localization limiter As mentioned above, to obtain mesh objective results the so-called localization limiter has to be used. In the following, two possible approaches are briefly described – crack band approach and nonlocal integral method.
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2.3.1 Crack band method The main assumption of the crack band method is the localization of damage (crack) into a row of finite elements. To assure a constant and mesh independent energy consumption capacity of concrete (concrete fracture energy GF) the constitutive law needs to be modified such that:
G F = A f h = const.
(5)
where Af = the area under the uniaxial tensile stress-strain curve and h = average element size (width of the crack band). Principally, the same relation is valid for uniaxial compression with the assumption that the concrete compressive fracture energy GC is a material constant: G C = A fc h = const.
(6)
in which Afc = area under the uniaxial compressive stress-strain curve. It is assumed that GC is approximately 100 times larger than GF (GC ≈ 100 GF). From (5) and (6), it is obvious that the constitutive law for concrete needs to be adopted to the element size. Although the crack band method provides results which are independent of the element size, they can still depend on the form and orientation (alignment) of the finite elements. This is especially true when the mesh is relatively coarse or the material is extremely brittle. To reduce this dependency and to keep the simplicity and a relatively low computational effort of the crack band method, a new so called "Stress Relaxation Method" [17] was developed. The method is a combination of the crack band approach and the nonlocal approach of integral type. Due to the low computational costs and, compared to the standard crack band approach, reduced sensitivity to the shape of the mesh the method is appropriate tool for practical applications. 2.3.2 Nonlocal integral approach The nonlocal integral continuum approach offers a more general possibility to avoid spurious mesh dependency in the smeared fracture analysis of quasi-brittle materials. An effective form of the approach, in which all variables which control the softening are nonlocal and all others are local (nonlocal strain approach), was proposed by PijaudierCabot and Bažant [10]. The key parameter in this approach is the so-called characteristic length l. This length controls the size of the representative volume in which the local quantities are averaged.
In the nonlocal continuum concept the stress at a point depends not only on the strain at the same point but also on the strains in the (in advance) defined domain V of the point. In general, the local variable which controls damage needs to be replaced by its nonlocal counterpart obtained by weighted averaging over a spatial neighborhood of each point. If
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f(x) is the local variable, which controls the material model response, then the corresponding nonlocal variable is defined as:
f (x ) =
1 ò α( x, s) f (s) dV(s) = ò α' ( x, s) f (s) dV(s) VR ( x ) V V
(7)
The bar overscript denotes the averaging operator; α(x) = nonlocal weighting function; x and s are coordinate vectors of the averaging and contributing point, respectively; V = volume of the entire structure and VR = the representative volume calculated as: VR ( x ) = ò α( x, s) dV(s) ,
α ' ( x , s) =
V
α( x , s) VR ( x )
(8)
The nonlocal weighting function is often taken as the Gauss distribution function: α(r ) = exp(−
r2 2l 2
),
r = s−x
(9)
where l is the internal (characteristic) length of the nonlocal continuum. Another possible choice is the bell-shaped function: 2 ìæ 2 ö r ÷ 0≤r≤R ïïç1 − α(r ) = íç R 2 ÷ è ø ï ïî0 R≤r
(10)
where R (radius) is the parameter related, but not equal to the characteristic length. The variable, which is to be averaged, must be chosen such that the nonlocal solution exactly agrees with the local solution as long as the material behavior remains in the elastic range. Furthermore, for homogeneous stress-strain field the nonlocal solution must be identical with the local one. Principally, the choice of the variable which is to be averaged is rather arbitrary. However, practically the choice depends on the type of the constitutive law, e.g. plasticity theory, damage theory, microplane model, etc. It was first assumed that l is a material property related to the maximum aggregate size da (l = 3da). However, it turned out that the characteristic length generally depends not only on the composition of concrete. Namely, it has been found that the optimum value of l/da depends on the stress-strain state. This means that the characteristic length is not a material constant. Therefore, to improve the concept, a new nonlocal approach of integral type which finds the physical background in the interaction of microcracks has
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been proposed by Bažant [18] and implemented into a finite element code by Ožbolt and Bažant [11]. In the here presented finite element code the both above mentioned nonlocal approaches are implemented. Theoretically, they are more general than the relatively simple crack band approach. Using these approaches the results of the analysis are mesh independent. However, according to the experience made in the last years there are still a number of problems which make the use of nonlocal approaches in practical applications for concrete and reinforced concrete structures difficult. The results are realistic only for relatively fine meshes. Consequently, the computational costs are often too high and the approach can not practically be used. This is especially true for three-dimensional simulations of reinforced concrete structures.
3. Numerical examples The discussed finite element code was in the last few years employed in a number of theoretical and practical studies. In the following the capability of the code is demonstrated on several numerical examples. Considered is one rather complex theoretical case of the mixed mode fracture as well as two practical applications, pull-out of a headed stud from a concrete block and shear failure of a slender reinforced concrete beam with and without shear reinforcement. In all case studies the spatial discretization of concrete is performed by 8-node isoparametric finite elements (three-dimensional analysis) or by 4-node elements (axisymmetrical analysis). The reinforcement is modeled by 2-node truss or beam elements assuming an ideally elasto-plastic stress-strain relationship. To assure mesh objective results the crack band approach is employed. As a solution strategy the secant stiffness approach with direct or indirect displacement control was used. 3.1 Double edge notched specimen The Double-Edge-Notched specimen tested by Nooru-Mohamed [19] was analyzed. The geometry and the test set-up are shown in Figure 2a. The specimen was first loaded by shear load S. Subsequently, at constant shear load, the vertical tensile load T was applied up to failure. The load control procedure was used by moving the upper loading platens in horizontal and vertical direction, respectively. The rotation of the loading platens was restricted. During the application of the horizontal load S, the vertical load was kept zero (T = 0). By subsequent tensile loading the shear force was kept constant. The bottom (support) platens were fixed and, the same as the upper (loading) platens, glued to the surface of the specimen. Three case studies were carried out, i.e. S = 5 kN, S = 10 kN and S = Smax. The finite element discretization is performed by the three-dimensional eight node solid finite elements with eight integration points (see Figure 2b). The width of the finite element model was 5 mm (the actual width of the specimen was 50 mm). The material properties are taken as: Young’s modulus E = 32800 MPa, Poisson’s ratio
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ν = 0.2, tensile strength ft = 3.0 MPa, uniaxial compressive strength fc = 38.4 MPa and concrete fracture energy GF = 0.11 N/mm. a)
b)
S
P
100
50
T
N
65
5
M
N' 100
M'
50
P'
25 30
150
25 30
Figure 2. a) Geometry of the DENS specimen and b) three-dimensional finite element mesh.
a)
b)
c)
Figure 3. Crack patterns observed in the experiment and in the analysis: a) for S = 5 kN, b) for S = 10 kN and c) for S = Smax.
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As discussed in more detail by Ožbolt and Reinhardt [20], although the results were not optimized they exhibit very good agreement with the experimental results. For illustration the corresponding crack patterns (maximal principal strains) are plotted in Figure 3. The crack patterns obtained in the experiment are shown as well. It can be seen that the present finite element code correctly predicts the crack propagation for mixedmode fracture, i.e. the calculated and observed crack patterns are for all three load histories almost identical. As shown by di Prisco et al. [21] this was not possible to obtain by using smeared crack models which are based on the tensorial formulation (classical plasticity formulation, nonlocal damage model or gradient plasticity model), especially for the case S = Smax. 3.2 Pull-out of a headed stud In practice headed studs are used to transfer loads into concrete members. Extensive experimental and numerical studies have shown that tensile load can be transferred into unreinforced concrete member [22]. If the steel strength of the stud is large enough, the failure of the stud is caused by the formation of a concrete cone. The failure mechanism is controlled by the tensile resistance of concrete, the cracking is stable and therefore the concrete fracture energy can effectively be utilised [23].
a)
b)
Figure 4. Pull-out of a headed stud: a) Formation of the concrete cone (principal strains, dark areas) analysed by the use of the axisymmetrical version of the code and b) crack pattern observed in the experiment.
For a better understanding of the failure mode as well as to investigate the resistance of the headed stud anchors of various embedment depths, a large number of numerical studies were carried out [22][23]. The numerical simulations based on the axisymmetrical FE-code show good agreement with the test results. Some typical calculated and observed crack patterns for a headed anchor with an embedment depth hef = 450 mm are shown in Figure 4. As can be seen, the calculated crack pattern agrees well with the crack pattern obtained in the test. The concrete pull-out failure load of a headed stud relies only on the tensile resistance of concrete. To design safe and economical anchorage it is important to know how the
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2
4
6
8
10
Concrete cone pull-out failure fcc= 33 MPa, GF= 0.1 N/mm
8
Test data
6
1
LEFM - Design code
Calculated
4
Nominal strength [MPa]
2
embedment depth influences the failure capacity of the fastenings (size effect). In Figure 5 the nominal strength of the headed stud (σN = PU/(hef2·π); PU = ultimate load) is plotted as a function of the embedment depth. Test results are compared with the numerical results. Furthermore, the prediction by a design formula, which is based on the linear elastic fracture mechanics (CC-method), is plotted as well. Figure 5 indicates that the nominal pull-out capacity decreases with the increase of the embedment depth, i.e. there is a strong size effect on the pull-out capacity. This important effect is correctly predicted by the smeared fracture FE analysis as well as by the proposed design formula.
10
2
3
4
5
6 7 8 9
100
2
3
4
5
6 7 8 9
1000
Embedment depth [mm] Figure 5. Size effect on the concrete cone pull-out load.
The comparison between numerical and test results confirms that the finite element code is able to correctly simulate failure mechanism and ultimate resistance of headed anchors. 3.3 Shear failure of reinforced concrete beam Three-dimensional finite element analysis of reinforced concrete beam loaded in threepoint-bending was carried out. The beam failed in the so-called diagonal shear failure mode. Two cases were studied: (a) the beam without shear reinforcement and (b) the beam with shear reinforcement. The geometry of the beam and material properties are shown in Figure 6. The test results for case (b) were obtained after the numerical results were published [24]. The test results for case (a) are not yet available.
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y Frames φ 8, 100mm apart 2 500mm
B
A
C
x
5 000mm
Concrete: E = 37 272 MPa ν = 0.2 ft = 3.9 MPa fc = 38.3 MPa GF = 110 J/m² Reinforcement:
y
20 + 8 + 8/2 = 32mm
20 + 8 + 8/2 = 32mm
2 HA8
500mm
z 2 HA32
20 + 8 + 32/2 = 44mm 200mm
E = 200 000 MPa σy = 400 MPa ET = 3245 MPa
20 + 8 + 32/2 = 44mm
Figure 6. Calculated and measured load-displacement curves: (a) beam without shear reinforcement and (b) beam with shear reinforcement.
a)
b) 300
300
Beam without stirrups
250
Analysis
Total vertical load [kN]
Total vertical load [kN]
250 200 150 100 50
200 150
Beam with stirrups
100
Analysis (before test) 50
0
Test
0 0
10 20 30 40 50 Vertical midspan displacement [mm]
60
0
10 20 30 40 50 Vertical midspan displacement [mm]
Figure 7. Calculated and measured load-displacement curves: (a) beam without shear reinforcement and (b) beam with shear reinforcement.
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60
a)
b) 450.
Y
450.
Y
300.
300.
150.
150.
0.
0.
0.
X
150.
Y
Z
X
0.
150.
Y
X
Z
X
Figure 8. Calculated crack pattern (maximum principal strains): (a) beam without shear reinforcement and (b) beam with shear reinforcement.
a)
b)
Figure 9. Localization of strains in reinforcement: (a) beam without shear reinforcement and (b) beam with shear reinforcement.
In Figure 7 are shown the calculated and measured (case b) load-displacement curves. The comparison for case (b) shows good agreement. The beam without shear reinforcement fails in diagonal shear failure mode. The crack pattern is shown in Figure 8a (maximum principal strains). At peak load no yielding of reinforcement was observed. The overall behavior of the beam is relatively brittle, what is a typical for this kind of failure mechanism. On the contrary, the beam with stirrups shows rather ductile response (see Fig. 7b). The calculated failure mode after peak load is shown in Figure 8b. The same as in the experiment, the beam fails in the so-called compressive shear failure mode. After ductile response caused by yielding of bending reinforcement, sudden compressive failure took place. Figure 9 shows the strains in the main reinforcement and in the stirrups after peak load. As can be seen, in the main reinforcement as well as in the stirrups there is a localization of strains (yielding). It is obvious that the finite element model is able to account for the activation of the shear reinforcement. Consequently, the failure load compared to the beam without shear reinforcement increases by about 20%, what is in good agreement with design codes.
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4. Conclusions In the present paper some theoretical aspects as well as aspects related to the application of the smeared fracture concept in engineering practice are discussed. In spite of a number of difficulties which can arise when the smeared fracture concept is used in the analysis of concrete and reinforced concrete structures, it is shown that the code which is based on the microplane constitutive law for concrete is able to realistically predict behavior of concrete and reinforced concrete structures. The discussion of the theoretical aspects and the comparison between calculated and test results lead to the following conclusions: (1) The smeared fracture analysis is reliable only if a realistic material model is coupled with an efficient localization limiter; (2) The localization limiter based on a higher order method is computationally expensive and, if the finite element mesh is not fine enough, it may lead to unrealistic results. For most practical problems the crack band method can reasonably well predict behavior of concrete structures; (3) It is demonstrated that the used finite element code is able to realistically predict structural behavior of a rather complex practical cases. From the computational point of view the important feature of the employed constitutive model is the fact that in the model there is no sharp discontinuity which can cause convergency problems and strong mesh dependency; (4) Using a realistic numerical tool a number of phenomena can be explained and, what is important, the amount of expensive experimental work can be reduced.
5. Acknowledgement This work was partly supported by the DFG and by the following companies: Fischerwerke, Hilti, Halfen and Würth. The support is very much appreciated. 6. References 1.
2. 3.
4.
K.J. Willam and E.P. Warnke, 'Constitutive model for triaxial behaviour of concrete', Seminar on Concrete Structures Subjected to Triaxial Stresses, International Association of Bridge and Structural Engineering Conference, Bergamo, Italy, (1974). M.A. Ortiz, 'A constitutive theory for the inelastic behaviour of concrete', Mechanics of Materials, 4, 67-93, (1985). Z.P. Bažant and P.C. Prat, 'Microplane model for brittle-plastic material - parts I and II', Journal of Engineering Mechanics, ASCE, Vol. 114(10), 1672-1702, (1988). J. Ožbolt and Z.P. Bažant, 'Microplane model for cyclic triaxial behaviour of concrete', Journal of Engineering Mechanics, ASCE, 118(7), 1365-1386, (1992).
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5.
6.
7. 8. 9.
10. 11.
12.
13.
14. 15. 16.
17. 18. 19.
20.
I. Carol, P. Prat, and Z.P. Bažant, 'New explicit microplane model for concrete: theoretical aspects and numerical implementation', International Journal of Solids and Structures, 29(9), 1173-1191, (1992). J. Ožbolt, Y.-J Li and I. Kožar, 'Microplane model for concrete with relaxed kinematic constraint', International Journal of Solids and Structures, 38, 26832711, (2001). Z.P. Bažant and L. Cedolin, 'Blunt crack band propagation in finite element analysis', Journal of Engineering Mechanics, ASCE, 111, 381-389, (1979). Z.P. Bažant and B.-H. Oh, 'Crack band theory for fracture of concrete', Materials and Structures, 16(93), 155-177, (1983). R. de Borst, 'Continuum models for discontinuous media', Proceedings of the International RILEM/ESIS Conference on “Fracture processes in concrete, rock and ceramics”, Ed. by van Mier, Rots and Bakker, E & FN Spon / Chapman & Hall, Noordwijk, The Netherlands, 601-618, (1991). G. Pijaudier-Cabot and Z.P. Bažant, 'Nonlocal Damage Theory', Journal of Engineering Mechanics, ASCE, 113(10), 1512-1533, (1987). J. Ožbolt and Z.P. Bažant, 'Numerical smeared fracture analysis: Nonlocal microcrack interaction approach', International Journal for Numerical Methods in Engineering, 39(4), 635-661, (1996). A. Hillerborg, M. Moder and P.E. Petersson, “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements.” Cement and Concrete Research, 6, 773-782, (1976). M. Jirásek, 'Embedded crack models for concrete fracture', Computational Modelling of Concrete Structures, de Borst, Bićanić, Mang & Meschke (eds), Balkema, Rotterdam, 291-300, (1998). J. Ožbolt, 'MASA – MAcroscopic Space Analysis', Internal Report, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, (1998). G.I.Taylor, 'Plastic strain in metals', Journal of the Institute of Metals, London, (62), 307-324, (1938). J. Ožbolt, U. Mayer, H. Vocke and R Eligehausen, 'Das FE-Programm MASA in Theorie und Anwendung', (Finite Element Code MASA in the Theory and Applications), Beton- und Stahlbetonbau, 94, Heft 10, 403-412, (1999). J. Ožbolt, 'Nonlocal fracture analysis - stress relaxation method', Internal Report, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, (1999). Z.P. Bažant, 'Why continuum damage is nonlocal: micromechanics arguments', Journal of Engineering Mechanics, ASCE, 117(5), 1070-1087. (1991). M.B. Nooru-Mohamed, 'Mixed-mode fracture of concrete: an experimental approach', Doctoral thesis, Delft University of Technology, Delft, The Netherlands, (1992). J. Ožbolt and H.W. Reinhardt, 'Numerical study of mixed-mode fracture in concrete', submitted for possible publication in International Journal of Fracture, (2001).
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21.
22. 23. 24.
di Prisco, M., Ferrara, L., Meftah, F. Pamin, J., De Borst, R. Mazars, J. and J.M. Reynouard, 'Mixed mode fracture in plain and reinforced concrete: some results on benchmark tests', International Journal of Fracture (103), 127-148, (2000). J. Ožbolt, R Eligehausen and H.W. Reinhardt 'Size effect on the concrete cone pull-out load', International Journal of Fracture, 95, 391-404, (1999). J. Ožbolt, 'Maßstabseffekt in Beton- und Stahlbetonkonstruktionen', Postdoctoral thesis, IWB-Mitteilungen 1995/2, Universität Stuttgart (1995). EDF- MECA benchmark, 'Three dimensional non linear constitutive models for fracture of concrete', Comparison Report#1, edited by EDF R&D, (2001).
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NUMERICAL AND EXPERIMENTAL INVESTIGATIONS OF THE SPLITTING FAILURE MODE OF FASTENINGS Jörg Asmus*, Joško Ožbolt** *Ingenieurbüro Eligehausen und Sippel, Stuttgart, Germany **Institute of Construction Materials, University of Stuttgart, Germany
Abstract In the present paper the numerical results for the splitting failure mode which is typical for fastening elements that are used too close to the member edges or in a narrow concrete members are presented and discussed. To investigate the influence of the size and geometry on the splitting failure, three-dimensional FE analysis was carried out. In the analysis the nonlocal mixed formulation of the microplane model for concrete was used. The splitting fracture is generated by imposing controlled concentrated radial displacement in the hole of the anchorage element. Geometrical parameters of a concrete specimen (width and thickness), the size of the relatively small loading area (diameter and height) as well as the embedment depth of the fastening element are varied. The analysis shows a strong size effect on the ultimate pressure at splitting failure and good agreement with experimental observations.
1. Introduction Failure of fasteners can be caused by a rupture of steel, anchor pull-out or by a concrete cone failure. In the past these failure modes have been intensively investigated and their failure load can be predicted using known design equations [1]. However, when the fasteners are pulled out from a concrete member in the anchorage zone rather high radial splitting forces are generated. These forces may cause splitting failure. The splitting failure load is lower than concrete cone failure. Therefore. it has to be considered on the design of fasteners. To calculate the splitting failure load no general equation is available. It mainly depends on the dimensions and the material properties of the concrete member and the fastening system.
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In a 3D-analysis using the nonlocal microplane model numerical investigations with such radial forces acting in the anchoring zone of the concrete specimen with given nodal displacements were carried out. The applied microplane material model [6] is a general macroscopical three-dimensional material model for friction-cohesive, quasi-brittle materials. The model is macroscopical i.e. it does not model the material on the microstructural level. In order to prevent a localization of damage into a zero volume, the model was coupled with a so called localization limiting procedure (nonlocal concept). In the present paper a part of the numerical results for a single fastener are presented and discussed.
2. Numerical analysis 2.1 Geometry, material properties and FE discretization The aim of the FE analysis was to study the influences of the dimensions of concrete member and of the load bearing area of a fastener. The detailed investigated influences are as follows: • •
Concrete member member thickness h member width b or edge distance c respectively
• • •
Fastener embedment depth hef drilled hole diameter dB height of the load transfer zone hLE
The study was carried out for a double symmetric concrete strip with a drilled hole in the mid of it. The specimen was loaded by controlling the radial displacement applied over a relatively small load transfer zone of the fastener. The analysis was performed by the use of the eight node solid finite elements based on the linear strain field assumption (eight integration points). The mesh size and form for different FE models was in the crack initiation zone of the same shape and size. The volume close to the load transfer zone is modeled by finer mesh (element size of approximately 2.5 - 3 mm). The size of the elements increased moving away from the area of the load transfer zone (see Fig. 1). The following material properties for concrete were used: uniaxial tensile strength ft = 2.2 MPa, uniaxial compressive strength fc = 34 MPa, fracture energy GF = 0.05 N/mm, initial modulus of elasticity E = 25500 MPa and Poisson’s ratio ν = 0.18. To assure the objectivity of the analysis with respect to the mesh size and orientation the non-local integral approach (micro-crack interaction approach; [5]) was employed. Besides the concrete constitutive law, the governing parameter in the nonlocal analysis is the so-called characteristic length [5]. In the present study the characteristic length was set to lch = 5 mm. The splitting force is calculated as:
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Sp =
ò p dA
(1)
A
where p= pressure over the loading area and A= area of the loading zone. Note, that this force is actually the total radial force which generates splitting failure of the specimen. More details of the numerical investigations are given in [3]. 2.2 Comparison between two different discretizations All here presented numerical results are obtained by modeling only a quarter of the concrete plate, i.e. two symmetry planes are assumed (Model A, see Fig. 1a). Two a)
Z
X Y
b)
Y
X Z
Figure 1. Crack pattern in terms of maximal principal strains close after the peak load: a) model A and b) model B.
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additional calculations using the model where only one plane of symmetry is considered (model B, see Fig. 1b) served as a comparison to see whether the model with two symmetry planes could realistically predict splitting failure mode. In this comparison two different member width were used (b = 160 and 640 mm) and all other parameters were kept constant. No doubt, the model B is closer to reality, however, from the computational point of view it is more time consuming. The failure modes close after the ultimate load are plotted in Fig. 1 in terms of the maximal principal strains. The dark zones indicate damage (cracks). Obviously, both models correctly predicted the splitting of concrete block. The model A with two planes of symmetry seems to be reliable and therefore it was used in all subsequent calculations.
3. Numerical results 3.1 Influence of the member width To find the influence of the member width on the splitting failure load altogether three calculations were carried out. The member height (h = 160 mm) and the embedment depth (hef = 80 mm) were kept constant, while the member width was varied (b = 160, 320 and 640 mm). 150 Variation of the member width (Model A) h= 160 mm, hef= 80 mm
radial force [kN]
125 100 75 50
b= 160 mm b= 320 mm
25
b= 640 mm
0 0.0
0.2
0.4
0.6
0.8
1.0
displacement [mm] Figure 2. Load-Displacement curves for three different member width.
The L-D curves for the three investigated cases (b = 160, 320 and 640 mm) are shown in Fig. 2. For all three cases the failure is due to splitting of concrete. When small concrete members split the typical failure is brittle and there is no indication or warning before it happens. On the contrary, the failure of larger concrete members is more ductile. The
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reason for this is higher local damage of concrete in the zone where the load is applied since in larger specimen the total radial force is also larger. In Fig. 3 the relationships between the average ultimate pressure (p = Sp/A) normalized to the uniaxial compressive concrete strength is plotted as a function of the member width. As expected, when the member width increases the ultimate splitting strength increases as well and reaches for b = 640 mm value that is approximately pcrit = 7fc. Fig. 4 shows the nominal splitting strength calculated as the ultimate splitting force divided by the cross section area of the concrete member (Sp/(b⋅h)). The increase of the specimen width leads to the decrease of the nominal splitting strength. A similar trend is observed for the relative crack length wr at peak load (see Fig. 4). It is calculated as wr = wa/l where wa = the distance of the crack front measured perpendicular to the load surface area and l = the length of the splitting crack at failure. Obviously, with increase of the specimen width the critical crack length decreases i.e. the cracking is less stable and consequently the nominal strength decreases.
10
relative pressure (p/fc)
Variation of the specimen width h= 160 mm, hef= 80 mm
8
analysis: p = Sp,ult/ (π dBLhLE) approx.: p = 101.23 (b/hef)0.36
6
4
2
0 0
2
4
6
8
10
relative member width (b/hef) Figure 3. Relative pressure as a function of the width of the concrete member.
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relative crack length (wr)
1.0 Relative crack length (peak load) hef= 80 mm, h= 160 mm
0.8
calculation, wr= wa/ l Approx. wr= 0.7 (b/hef)-0.36
0.6
0.4
b
0.2
0.0 0
2
4
6
8
10
relative member width (b/hef) Figure 4. Relative crack length at peak load as a function of the relative member width.
Before the splitting failure is reached a small volume of concrete close to the loading zone is in a high 3D compressive state. The reason is relatively small area of the load transfer zone and strong lateral confinement. Above and under this compressed volume zone high tensile strains (damage zones) localize in the radial as well as in the splitting direction (splitting crack). This can be seen from Fig. 5 which shows the splitting crack front over the specimen depth at peak load in terms of principal stresses. The dark zones indicate the crack front. In front of this zone there is a hardening of the concrete and behind of it the softening (cracked area). By further increase of radial displacement (loading) the softening zones above and below the compressed concrete zone come together what result in a splitting failure. The splitting crack localizes in the weakest vertical plane which propagates under an angle of approximately 450 measured to the longitudinal axis of the test specimen (see Fig. 1a). The damage zones are the result of the non-homogeneous strain field which develops as a consequence of the nonuniform boundary conditions. The relative non-homogeneity of smaller concrete specimen is higher what result in a more brittle failure. This strain nonhomogeneity decreases with increase of the specimen size. As a result, the behaviour under ultimate conditions for wider plates is more ductile since it is much harder to produce the non-homogeneity of strains that would result in splitting failure.
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Z
Y X
Figure 5. The front of splitting crack in terms of max. principal stresses.
3.2 Influence of the concrete member height A series of FE calculations using a constant member width (b = 320 mm), member length (l = 640 mm) and embedment depth (hef = 80 mm) with a variable member height of h = 120, 160 and 240 mm were carried out to investigate the influences of the member height on the splitting failure load. 10
relative pressure (p/fc)
Variation of the member height b= 320 mm, hef= 80 mm
8
analysis: p = Sp,ult/(πdBhLE) approx.: p = 111.8 (h/hef)0.42
6
4
2
0 0
1
2
3
4
5
relative member height (h/hef) Figure 6. Relative pressure as a function of the relative member height.
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The resulting L-D curves are similar as obtained for the variation of the specimen width i.e. thinner members show a more brittle behaviour. As expected, the numerical analysis shows that with an increase of the member height the ultimate pressure increases as well (see Fig. 6). However, if the member is thicker than h = 2hef only a minor increase of the ultimate relative pressure was observed i.e. for an increase of the embedment depth from h = 2hef to h = 3hef the pressure increases only for about 6%. Only two of the investigated cases (b = h and 2h) showed a clear splitting failure with a localized splitting crack. For h > 2hef the specimen tends to fail not in the splitting failure mode but rather in a combined failure where the side concrete cone failure tends to dominate. This tendency agrees well with results in experimental investigations [2]. 3.3 Influence of the embedment depth To investigate the influence of the embedment depth on the splitting failure load a series of calculations were carried out by varying the embedment depth between hef = 40, 80, 160 and 320 mm. The ratios h/hef = 2 and b/hef = 4 were kept constant. Furthermore, the size of the hole diameter as well as the height of the loading zone were kept constant as well (dB = 18 mm and hLE = 10 mm). 15
relative pressure (p/fc)
Variation of the embedment depth b= 4hef, h= 2hef
12
analysis: p = Sp,ult/ (π dBhLE) approx.: P = 5.13 (hef)0.76
9
local concrete compr. failure
6
3
0 0
50
100
150
200
250
300
350
embedment depth hef [mm] Figure 7. Relative pressure as a function of the embedment depth.
Similar as in previous calculations the L-D curves indicate more brittle response for concrete specimens with smaller embedment depths. For embedment depths hef = 40, 80 and 160 mm the resulted failure mode was splitting. In the case of hef = 320 mm a local compression failure took place. In Fig. 7 the relationships between embedment depth and the relative ultimate pressure is shown. It can be seen that up to approximately hef = 200
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mm the ultimate pressure increases proportionally with the embedment depth. However, for larger embedment depth a local concrete compression failure occurs. The relative pressure at which this takes place was observed to be about 9fc. 3.4 Influence of the load bearing area For all the results shown above the diameter of drilled hole and the height of load transfer zone were kept constant. Experimental investigations showed that the height of the loading zone influence the splitting failure load [2]. Therefore, to investigate this in more detail a series of calculations for a concrete member of constant size (hef = 160 mm, h = 2hef and b = 4hef) were carried out. In these calculations the diameter as well as the height of the loading zone were scaled proportionally with the specimen size (diameter: dB = 18 and 72 mm; the height of the load transfer zone: hLE = 10 and 40 mm). The analysis principally shows that the failure load increases with increase of the loading area. Furthermore, smaller loading areas promote a more ductile behaviour. For all calculated cases a splitting failure was observed.
ultimate radial force Sp,ult. [kN]
900 dB= 18 mm (constant), hLE= 10 mm (constant), f (hef)0.76 dB= 18 mm (constant), hLE= varied, f(hef)1.43
750
dB= varied, hLE= 10 mm (constant), f(hef)1.59 dB= 0.25hef, hLE= 0.45hef, f(hef)1.94
600 450 300 150 0 0
40
80
120
160
200
embedment depth hef [mm] Figure 8. Ultimate load for different geometrical configurations as a function of embedment depth.
In Fig. 8 the calculated results are summarized. The failure load is for different geometrical configurations plotted as a function of the embedment depth (characteristic size). The largest increase of the ultimate load is observed if the geometry, including the hole diameter and the height of the loading zone, is scaled proportionally. For this case the ultimate load is approximately proportional to the square of the embedment depth i.e.
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there is no size effect on the ultimate load. In contrast to this, the lowest increase of the ultimate load is observed for the case where the specimen geometry was scaled proportionally but the size of the loading area was kept constant.
4. Discussion of the numerical results The presented results show that the splitting failure load of a concrete block loaded by inside pressure depends on the size and geometry of the concrete specimen. When plotting the calculated data of section 3.4 as a relative pressure (p/fc) versus the relative load area (d = loading area divided by the splitting failure area), as shown in Fig. 9, then can be seen that for the size range of practical importance all calculated data are well fitted by the Bazant size effect formula [6]. Furthermore, a fit of the calculated data by the power function yields to an exponent of n = -0.42. The so called characteristic size resulting from the Bazant’s size effect formula is very small (d0 = 0.03). This shows that the size effect on the relative ultimate pressure is strong and close to that predicted by the linear elastic fracture mechanics size effect formula. The theoretical limit for the relative pressure in case of d → 0 is approximately 30fc. The numerical results are in good agreement with the experimental experience for partly loaded concrete areas [7]. 20 Splitting failure relative pressure (p/fc)
16
Calculated Bazant SEL, p= B fc(1+d/do)-0.5; B=29.24, do = 0.03 Power fit: p=159 d-0.42; d= rel. load surface [%]
12
8
4
0 0
1
2
3
4
5
(load surface / failure surface) x 100
Figure 9. Relative pressure as a function of the relative load area – size range of practical interest.
Furthermore, the extrapolation of the calculated results to the maximal size of d = 100 should theoretically yield to the relative strength of one (p/fc = 1) i.e. the compressive splitting strength should coincide with the uniaxial concrete compressive strength. In Fig. 10 is this extrapolation plotted for the Bazant size effect formula and for the power function from Fig. 10. Having on mind that both curves are obtained by fitting the
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calculated data of a very limited size range, the agreement with the lower theoretical limit is relatively good. This confirms that the numerical results are reliable.
8
relative pressure (p/fc)
7
Splitting failure
6
Calculated
5
Bazant SEL, p= B fc(1+d/do)-0.5; B=29.24, do = 0.03 Power fit: p=159 d-0.42; d= rel. load surface [%]
4 3 2 theoretical limit: p= fc
1 0 0
20
40
60
80
100
(load surface / failure surface) x 100
Figure 10. Relative pressure as a function of the relative load area – full size range.
5. Conclusions In the present paper the numerical results of the 3D finite element study for the splitting problem of a concrete block caused by a concentrated internal pressure are presented and discussed. The aim of the study was to better understand the failure mechanism as well as to investigate the influence of the member geometry and the load bearing area of a fastener on the ultimate splitting failure load. The results show that the ultimate pressure at splitting failure strongly depends on the size and geometry of the specimen as well as on the size of the loading area. When the structure geometry and the loading area is scaled proportionally, the ultimate load increases approximately proportionally as well i.e. no size effect on the failure load is observed. However, if the structure size is scaled proportionally but the size of the loading area is kept constant, there is an strong size effect on the ultimate load. The reason is localization of damage and consequently decrease of the peak resistance by increase of the size. The size effect on the average ultimate pressure related to the relative loading area is strong and close to the prediction according to the linear elastic fracture mechanics. When the relative loading area yields to the maximal possible value (one) the extrapolation of the ultimate pressure results approximately to the uniaxial concrete compressive strength. The numerical results are in good agreement with the experimental observations [2] as well as with the theoretical
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and experimental studies for concrete members loaded by locally applied compressive forces [7].
6. References 1. 2. 3.
4.
5. 6. 7.
R. Eligehausen and R. Mallee, ’Befestigungstechnik im Beton- und Mauerwerksbau’, Ernst & Sohn, Berlin, Germany, (2000). J. Asmus, ’Bemessung von zugbeanspruchten Befestigungen bei der Versagensart Spalten’, Dissertation, Universität Stuttgart, Germany, (1998). J. Ožbolt, J. Asmus, and K. Jebara, ’Dreidimensionale-Finite-Elemente-Analyse zur Versagensart Spalten durch Befestigungsmittel’, Report Nr. 16/22-97/23, IWB, Universität Stuttgart, Germany, (1996). J. Ožbolt, Y.-J Li and I. Kožar, 'Microplane model for concrete with relaxed kinematic constraint', International Journal of Solids and Structures, 38, 26832711, (2001). J. Ožbolt and Z.P. Bažant, ‘Numerical Smeared Fracture Analysis: Nonlocal Microcrack Interaction Approach’, IJNME, 39(4), p. 635-661, (1996). Z.P. Bažant, ‘Size Effect in Blunt Fracture: Concrete, Rock and Metal’, JEM, ASCE, 110(4), p. 518-535, (1984). K.-H. Lieberum, ’Das Tragverhalten von Beton bei extremer Teilfächenbelastung’, Dissertation, Technische Hochschule Darmstadt, Germany, (1987).
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THREE DIMENSIONAL MODELING OF AN ANCHORAGE TO CONCRETE USING METAL ANCHOR BOLTS Hocine Boussa, Ghassan Mounajed, Bruno Mesureur & Jean-Vivien Heck CSTB, Marne La Vallée, cedex 02, France
Abstract Modern construction is now using steel anchor bolts in order to assure the connection between different building components and to allow loads transmission in-between different elements of a structure. Over the past twenty years, much research work has been carried out on anchors in different countries of the world. The majority of the design models and methods proposed for this type of anchorage are based on a statistical empirical approach. Practice and tests have shown that they are not always predictive for a shear force although the values obtained are on the safe side. This research work deals with the study of the behavior under shear loading of a single steel bolt anchored in concrete close to the edge or the corner of the concrete slab. The aim is to predict the failure modes and the failure load. The study is based on a numerical resolution using the finite element method. Different types of non linearity are considered in the model: non-linear behavior laws for steel and concrete, geometrical non linearity due to the large displacements and non linearity due to the change in the limit conditions i.e. contact.
1. Introduction Modern construction is now using metal anchor bolts in order to assure the connection between different building components and to allow loads transmission in-between different elements of a structure. Over the past twenty years, much research work has been carried out on anchors in different countries of the world2,3,5,6,7,8,9. The majority of the design models and methods proposed for this type of anchorage are based on a statistical empirical approach. Practice and tests have shown that they are not always predictive for a shear force although the values obtained are on the safe side. The origin of this problem is that different failure modes can arise in relation to the values of the different parameters involved (the characteristics of the anchors and their support, the spacing between anchors, the distance to edges and the direction of the
637
applied force). The current available models are only predictive for a restricted range of parameters and by introducing certain factors whose physical significance is open to criticism. Consequently, it appeared necessary to restudy the behavior of anchorage subjected to shear loads using scientific criteria. This research work deals with the study of the behavior under shear loading of a single steel bolt anchored in concrete close to the edge or at the corner of the concrete slab. The aim is to predict the failure modes, the failure load and the global load-displacement behavior. The study is based on a numerical resolution using the finite element method. Different types of non linearity are considered in the model: non-linear behavior laws for steel and concrete, geometrical non linearity due to the large displacements and non linearity due to the change in the limit conditions. The different parts of the anchorage are explicitly modeled, i.e. screw, and sleeve, expansion cone, fixture, concrete substrate and the initial prestressing force is applied. Today, the qualification of anchors is currently made by testing following a relevant test regime. Such a procedure is of course time consuming and does not provide us with a completely satisfying description of the anchor behavior. Indeed, it does not seem reasonable to perform a complete test program combining all the possible influencing parameters. The idea of testing the anchors in concrete by computer simulation has raised some years ago at the CSTB. The project is called “Virtual Laboratory for anchors in concrete”. The present paper represents the second step of this project. The first one was described in a paper1 published by the ACI (American Concrete Institute). Eventually, the aim of this study is to take account of the virtual tests in the evaluation procedure, decrease, if possible, the number of pre qualification and qualification tests and improve the design code.
2. Current design of anchorage subjected to shear loads The shear failure mode of steel, or the concrete failure mode at the slab edge or by pryout, is influenced by the distance to free edges, the anchorage depth and the stiffness of the anchor. Shear generally causes greater displacements than those due to tensile forces. This can be explained by the bending in the threaded part of the bolt due to the second order effect of displacement and to the local damage in the concrete in the front of the fixture. The different failure modes observed under shear loading are: steel failure, concrete pryout failure and concrete edge breakout failure. 2.1. Steel Failure Steel failure is generally accompanied by large relative displacements and is more frequent in the case of deep anchors and high anchor stiffness. The failure mechanism is generally characterized by the failure of the anchor in the plane of the applied tangential load. It is due to shear and bending stresses in the bolt. Local damage in the concrete can
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also be present, but it does not significantly influence the ultimate resistance of the anchor. Indeed, when the anchor comes in contact with the concrete surface, stress redistribution takes place along the full anchoring depth, developing by a flexing in the shank. In general, increasing the applied load leads to a form of spalling. This mode of concrete surface damage causes an increase in the bending moment acting on the shank and a decrease in the pry-out effect at the base of the anchor. In the case of a deep anchor, the applied shear load can continue to increase until total failure of the anchor steel under the combination of shear, bending and tensile stresses. The characteristic resistance of an anchor is given by the following formula:
VRk,c = 0.5 × A s × fuk
(1)
AS is the stressed section of the thread and fuk is the characteristic tensile resistance of steel. When the shank is predominantly subjected to bending and tension stress the failure can even occur beneath the concrete surface, in the reduced section of the anchors above the expansion cone. Of course, in this case, this formula does not apply any more. 2.2. Pry-Out Failure Pry-out failure is frequent in the case of short and stiff anchors and it occurs on the opposite side of the applied shear load. The shear force causes a pressure at the rear of the anchor. This pressure leads to uplift in the concrete, in the opposite direction of the applied force. The corresponding characteristic resistance is given, for first analysis, by the equation:
VRk,cp = k × NRk,c
(2)
NRk,c is the tensile resistance of the anchor. This model is on the safe side but is rarely predictive since the value for k must be determined by tests for each type of anchor. 2.3. Concrete edge breakout failure When the anchor gets close to free edges, the hydrostatic confinement pressure of concrete and the concrete failure resistance decrease. Several failure modes can exist depending on the direction of the applied force, the number of anchors and the distance to edges. For anchors group, it is assumed that the closest anchors to edges are those that determine the characteristic resistance of the concrete. However, if these anchors are very close to the edge, an oblong hole can be arranged in the fixture so that transmission of the shear force takes place only, at least at the limit service condition, through the anchors that are placed furthest from the edge. In the case of an anchor or a group of anchors placed alongside an edge, only the anchors, which act most unfavorably, have to be taken into account to determine the characteristic resistance:
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0 VRk,C = VRk ,C ×
0 VRk ,c
A C, V A 0C, V
= 0.45 × dnom
× ψ S, V × ψh, V × ψ α, V × ψ ec,N × ψ ucr, V æ l ö × çç f ÷÷ è dnom ø
(3)
0,2
× fck,cube × c11,5
(4)
This is the initial value for the characteristic resistance of an anchor placed in cracked concrete and stressed perpendicular to the edge without being influenced by the spacing, the distances to the other edges and the thickness of the concrete slab. Unless the effective length lf is clearly defined the equation is not actually predictive and tests are needed to assess the value of this parameter. ψ α,V is a factor which takes account of the angle αV between the applied load and the direction perpendicular to the free edge. The model given in the ETAG4 for concrete edge failure gives satisfactory results (although it cannot be considered as fully predictive) when the shear load is directed towards the free edge. However, it is not predictive when the force is directed towards the center of the slab, and this in spite of the introduction of coefficient ψ α,V . The experience shows that there is not a good match between the model and the experimentation. The difference may be significant in the case of an anchor group of 4 anchors.
3. Anchorage modeling The tests have shown that the fracture of an anchorage under shear loading is governed by the geometry and by the mechanical properties of the anchor and its support. For a semi-infinite medium implantation, the failure may occur with concrete damage (pry-out for small embedment length) or steel rupture accompanied by spalling at the concrete surface. The concrete fracture is governed by the non-linear behavior laws under tensile loading. It may be crushed under high compressive stresses and locally damaged when subjected to contact phenomena with steel interfaces. The anchors are placed in a C20/25 concrete (i.e. fck=20 MPa on cylinders). The concrete is made of normal weight aggregates from the Seine River. The anchor has the following dimensions: Table 1 : anchor dimensions External diameter: Effective embedment Angle of the Thickness of depth: hef expansion cone fixture: tfix dnom [mm] [mm] [°] [mm] 21.5
125
30
640
25
the
3.1. Mesh generation and material properties The three dimensional finite elements chosen to mesh the anchor and the concrete are 8nodes isoparametric hexahedral elements. Additional 4-nodes isoparametric tetrahedral elements are added to the configuration in order to take account of the semi-infinite medium of concrete. In order to capture correctly the higher stress gradient around the anchor, we used a high mesh density in this area. The complete finite element model consists in 12,670 nodes and 25,506 elements. Among these elements, 8,594 are 8-nodes hexahedral elements and 16,805 are 4-nodes tetrahedral elements. Figure 2 shows the principal parts of the mesh.
Figure 2 : anchor mesh
Figure 1 : global mesh
The shear force is simulated by a horizontal displacement applied, along X-axis, on the backside of the fixture. The concrete properties are given below: Table 2 : concrete properties Ultimate tensile Young’s modulus strength : f’t : Ec [N/mm²]
[Gpa]
Poisson’s ratio: νc [-]
3
30
0.2
Mass density: ρc [Kg/m3]
fracture energy : Gf
2500
65
[J/m²]
The steel properties are given below: Table 3 : steel properties Young’s modulus : Poisson’s ratio : νs Es [GPa]
[-]
Mass density : ρs [Kg/m3]
210
0.28
7800
641
Plasticity : Von Mises, Isotropic Hardening σs = 640 MPa
The behavior of concrete far from the anchor is assumed to be purely elastic. The concrete that is located in the cracking zone around the anchor is modeled using the fixed smeared crack approach. When the anchor is placed near the edge or at the corner of the slab, the plasticity of concrete is not taken into account in the computation because the failure is due to concrete edge failure, i.e. a relatively brittle failure. To solve such complex non-linear problem, the Newton Raphson’s method for large displacements is used. The convergence is tested on relative displacements and the tolerance is equal to 0.5%. The computation is carried out in transient dynamic in order to regularize the contact solution. 3.2. Concrete model-smeared crack approach Concrete exhibits a non-linear stress strain behavior mainly because of progressive micro-cracking and void growth. The development of micro cracks results in a degradation of elastic stiffness. Generally they are oriented with respect of applied stress history and the degraded elastic operator becomes gradually anisotropic due to cracking. For our modeling, the cracking progress in concrete is modeled using the multidirectional smeared crack approach with three orthogonal cracks. The model is based on the decomposition of the total strain vector into two vectors - as given in the following equation : ∆ε = ∆εco +∆εcr
(5)
∆εco is the strain of the solid part (concrete) and ∆εcr is the strain of the crack part. The global crack strain vector is given by the equation:
∆ε cr = N ⋅ ∆e cr
(6)
Where ∆e cr is the local crack strain vector and N is the transformation matrix reflecting the orientation of the crack. A fundamental feature of the present concept is that N is assumed to be fixed upon crack formation (fixed crack concept). For uncracked concrete: ∆σ = Dc 0 ∆ε c 0
(7)
For cracked concrete, the vector of incremental tensions across the crack is given by: ∆t cr = D cr ∆e cr
(8)
cr
Where D is a diagonal matrix (DI, DII, DIII), DI, DII and DIII are the I-mode, II-mode and III-mode stiffness moduli for a smeared single crack respectively. It is assumed that direct shear-normal coupling is not decisive. Distinction between II-mode and III-mode is not relevant, so that the mode II will be mentioned only. The overall relation between global stress and strain is given by the equation10 : −1 ∆σ = éD c 0 − D c 0N D cr + N T D c 0N NT D cO ù ⋅ ∆ε (9) êë úû Assuming that Ec is the initial elastic modulus, DI is the cracking stiffness modulus:
[
DI =
ft'2 ⋅ h 2 ⋅ Gf
]
DII =
β⋅G 1− β
(10)
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The II-mode response and the III-mode response are related to the initial shear modulus G. A constant value of the crack shear modulus DII corresponds to a linear ascending relation between shear stress and shear strain across the crack. This may increase the shear stress indefinitely, and, hence, cause the rotation of the principal stresses in the cracked elements. An improvement of the model may be obtained by making the shear stiffness after cracking a decreasing function of the crack normal strain10. Despite this improvement, many authors have noticed a stress locking. In order to overcome this problem, we have chosen to reduce the shear components in the local axis to zero when a crack initiates. The objectivity of the model is ensured by adjusting the size of the crack bandwidth h during crack progress. It takes account of the element dimensions and the crack normal direction. 3.3. Contact problem : solver constraint method The present study takes account of the contact phenomena between steel and concrete interfaces on the one hand and between anchor components on the other hand. The contact is assumed to be perfect (without friction). In the presence of large relative displacements between solids in contact (e.g. in the case of steel and concrete) the problem becomes highly non-linear. The main difficulties encountered in contact problems come from the fact that the boundary conditions linked to the contact are not previously known because of the large displacements. Different methods are used for numerical contact resolution. We used the solver constraint method. In this method, no additional parameters are added to the overall system matrix as it is the case in the penalty method or in the Lagrange multipliers method. When the contacting body touches the contacted body, a normal reaction force is developed perpendicular to the contacted surface element. 3.4. Results By comparing the test results and the numerical simulations we can show that our FE model based on the smeared crack approach provided us with numerical results that are in agreement with the tests results. In particular, the peak loads and the displacements at the peak comply with the experimental results. Nevertheless the simulations show a stiffer behavior during the initial stage. This deviation may be caused by the following reasons: plasticity of concrete has been neglected, a few mechanical properties of the concrete have not been accurately identified by testing (e.g. fracture energy and tensile strength). It must be pointed out that after the peak the experimental load decreases strongly and numerical convergence problems logically appear.
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Figure 3 : edge failure (CSTB test At 100 mm from the edge) and simulation 40 35 30
Load (KN)
25
Experiment Simulation
20 15 10 5 0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Displacement (mm)
Figure 4 : Load displacement curves : edge failure experimental and simulation results
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Figure 5 : corner failure for α = 0° (CSTB Figure 6 : corner failure for α = 0° test at 190 mm from the edge) (simulation) 90 80 70 Sim ulation Experiment
Load (KN)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
Displacem ent (m m )
Figure 7 : Load displacement curves : corner failure for α =0 experimental and simulation results
4. Conclusion The three-dimensional modeling of an anchorage to concrete using metal anchor bolts has been achieved. The numerical problems encountered in the past are now solved: i.e. inter-penetration between contacted bodies, control of the convergence algorithms and a too stiff behavior due to the non-respect of the gaps between bolt and fixture.
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A modified smeared crack model used for concrete behavior law has recently been implemented by a “CSTB-MARC” team on the MSC-MARC software. Now taking account of the fracture energy, the model ensures the objectivity of the results with regards to the mesh. Despite the fact that shear stress components have been reduced to zero in the local axis of the cracks in order to avoid stress locking, the formulation provides us with simulation results that fit the experimental results quite nicely. These encouraging results have invited us to develop another formulation, which can correctly take account of the shear behavior in the local axis of the cracks. Implemented in the general 3D finite element code SYMPHONIE-CSTB, this model is likely to simulate the cracking behavior of concrete and predict the rupture with sufficient reliability. The future developments will aim at improving the model and enlarging its field of application, in particular by adding plasticity. It will be the topic of another paper in the next future. This research work was carried out by the CSTB in cooperation with HILTI Aktiengesellschraft, Business Unit Anchor Division (Schaan, Principality of Liechtenstein).
5. References 1.
El Dalati, R.; Mounajed, G.; Mesureur, B. et Berthaud, Y. Three dimensional modeling of anchorage subjected to shear loads, American Concrete Institute, 2000 2. Cook, R.; Collins, D.; Klingner, E. and Polyzois. Load-eflection Behavior of cast in place and retrofit concrete anchors. ACI Str. J. Title 89-S60, 1992, pp. 639-649. 3. Eligehausen, R. and Lehr, B. Shear capacity of anchors placed in non cracked concrete with large edge distance. Univ. Stuttgart, Rep. N° 10/20 E-93/11E, 1993. 4. ETAG. « Guideline for European Technical Approval of Anchors (metal anchors) for use in concrete ». Annex C: Design Methods for anchorage, 1997. 5. Hawkins, N. « Strength in shear and tension of cast-in-place anchor bolts ». Anchorage to concrete, American Concrete Institute, SP 103, 1987, pp. 233-257. 6. Klinger, R.E & Mendonca, J.A. « Shear capacity of short anchor bolts and welded studs : A literature review ». ACI Journal. No. 79-34, 1982, pp 339-347. 7. Ohlsson , U. & Olofsson, T. «Mixed-mode fracture and anchor bolts in concrete. Analysis with inner softening bands». J. of Eng. Mech., 1997, pp. 1027- 1033. 8. Ozbolt, J.& Eligehausen, R. « Bending of anchors, Final Element Studies », Universität Stuttgart, Report n° 10/23-94/6, IWB, 1994. 9. Fuchs, W. « Tragvelhaten von Befestigungen unter Querlast in ungerissenem beton (Bearing behavior of fastenings under shear loads in uncracked concrete) », dissertation Universität Stuttgart, IWB-Mitteilugen 1990/2, 1990. 10. Rots, J.G. and Blaauwendraad, J. « Crack models for concrete: Discrete or smeared ? Fixed, multi-directional or rotating? ». Heron, Vol. 34, No.1, 1989.
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INFLUENCE OF BENDING COMPRESSIVE STRESSES ON THE CONCRETE CONE CAPACITY Markus Bruckner, Rolf Eligehausen, Joško Ožbolt Institute of Construction Materials, University of Stuttgart, Germany
Abstract In the present paper the influence of bending compressive stresses on the concrete cone failure load of anchor bolts used to anchor a column into a foundation was investigated. The compressive stresses spread from the column base conically toward the foundation base and can influence the concrete cone failure capacity. To investigate the problem a column-foundation connection was designed and analyzed with the nonlinear FE program MASA. The distance between the resulting compressive force and the anchor tensile force was varied. Usually anchorages are designed using the CC-method (Concrete Capacity Method) neglecting this positive influence of compressive stresses on the concrete cone failure load. In order to take this effect into account the numerical results are compared with the CC-method and a multiplication coefficient is suggested. The multiplication coefficient is dependent on the relation between the internal lever arm of the column and the effective embedment depth.
1. Introduction In the last years the use of headed reinforcement increased strongly. The reason for this could be found in the extensive use of prefabricated elements and the advantages which are achieved by the application of this reinforcing alternative. The main advantages of the anchorage of tension forces by headed reinforcement are the shorter load introduction length, the very small slip values and the simple reinforcement arrangement. In the case of a column-foundation connection a precast concrete column or a steel column is often attached to a cast-in-place concrete foundation using headed reinforcement. For a connection at least four headed bars are used. Depending on the structural system the column is stressed by a normal force, a shear force and a bending moment. The bending moment is initiated over a couple of forces (tension and compression) into the foundation. The tension force is transferred by the anchors which are located in the tensile zone. The compressive force is transmitted directly into the
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foundation and spreads conically toward the foundation base (Figure 1). Depending on the distance between the resultant compressive force and the pulled anchors the head of the pulled anchors could be situated inside the compressed volume. This has an influence on the concrete cone failure load. In this paper this influence is studied on the basis of a numeric parameter study. The calculations are performed with the finite element (FE) code MASA3 and the results are compared with the CC-method [1] since this method represents the common calculation model for the design of anchorages with headed bars.
a) b) Figure 1: a) Anchorage exposed to normal and shear forces as well as a bending moment, b) top view of the base plate Anchorages with headed bars loaded by a tensile force and a bending moment have been already examined by Zhao [2]. He conducted tests far away from edges of a concrete member under an eccentric tensile load. These tests are taken here as a basis to develop an equation for a multiplication coefficient ψmoment. This coefficient represents the relation between the measured concrete cone failure load of an eccentrically loaded anchorage group to the concrete cone failure load calculated according to the CC-method neglecting the influence of compression stresses under the base plate due to the applied moment. The equations proposed by Zhao [2] are presented in equation (1) and equation (2). The test setup is shown in Figure 2a. In Figure 2b the multiplication coefficient is plotted as a function of the quotient of the anchor spacing to the anchorage depth according to equation (1) and equation (2). The experimental values are shown as well.
648
ψ moment =
hef
ψ moment = 1
s
for 0 ≤
s ≤ 0.5 2 ⋅ hef
for 0,5 <
(1)
s ≤ 1.0 2 ⋅ hef
(2)
a) b) Figure 2: a) Test set-up, b) experimental values and curve according to equation(1) and (2), after Zhao [2] Note that the multiplication factor ψmoment depends on the internal lever arm z (distance between tension anchors to centroid of compression force). For reason of simplicity this distance has been assumed as the distance between the headed anchors by Zhao [2]. The results of Zhao [2] are compared with the results of the FE calculations and the use of the proposed equations to design column-foundation connections is discussed.
2. Finite element analysis 2.1. Geometrical and material properties The numerical studies are performed for a steel column attached to a reinforced concrete foundation using headed reinforcement. As concrete strength the concrete cylinder strength fc,cyl = 25 MPa has been assumed. The dimensions of the foundation are l / h / b = 10m / 1m / 1.8 m (length / height / width). The height of the column is hS = 10 m. The steel column is assumed as HEB profile. The headed bars have a diameter of ds = 40 mm and are manufactured from ripped reinforcing bar with fy = 500 MPa. The head was formed by a hydraulic press. The anchorage depth is taken as hef = 500 mm. The bending reinforcement of the foundation is designed according to [3] and is inserted in an upper and a lower position into the foundation. The reinforcement (fy = 500 MPa) is not staggered along the length of the foundation. A
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transverse reinforcement along the foundation width is used. Linear elastic behavior was assumed for the anchors and the bending reinforcement to exclude steel failure. The base plate (cf. Figure 1) that is used to attach the column to the foundation and the distance between the pulled and compressed anchors are varied. These dimensions are given in Table 1. Table 1: Dimension of the base plate and spacing of the anchors No. 1 2 3 4 5
Base plate [mm x mm] 300 x 300 400 x 400 500 x 500 600 x 600 1100 x 1100
Spacing of anchor [mm] 200 300 400 500 1000
The load is applied by a horizontal translation at the top of the column. Using this cantilever arm the anchorage is loaded by a bending moment and only by a relatively small horizontal force. No vertical (normal) force is applied because this would unload the pulled anchor. Modeling the material of the foundation the dead weight is taken into account. 2.2. Finite-Element-Code MASA The used finite element code is based on the microplane model. It can be used for two and three-dimensional analysis of quasi-brittle materials. The model allows a realistic prediction of the material behavior in case of three-dimensional stress - strain states. The smeared crack approach is employed. To ensure mesh independent results the crack band approach is used. In the microplane model the material properties are characterized separately on planes of various orientations within the material. On these microplanes there are only a few uniaxial stress and strain components and no tonsorial invariance requirements need to be considered. The constitutive properties are entirely characterized by relations between the stress and strain components on each microplane in both, normal and shear directions (Figure 3). It is assumed that the strain components on the microplanes are projections of the macroscopic strain tensor (cinematic constraint approach). Knowing the stress-strain relationship of all microplane components, the macroscopic stiffness and the stress tensor are calculated from the actual strains on the microplanes by integrating the stress components on the microplanes over all directions. The simplicity of the model is due to the fact that only uniaxial stress-strain relationships are required for each microplane component and the macroscopic response is obtained automatically by integration over the microplanes. More details related to the used model can be found in Ožbolt et al. [4].
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ε
z
z
n
x
εT
εN εM
y
εK
y
Microplane Mikroeben
x
a) b) Figure 3: Concept of the microplane model: a) unit volume sphere – integration point and b) strain components 2.3. Spatial discretization The modeling of the system and the evaluation of the results are performed by the commercial program FEMAP [5]. The concrete and the soil are modeled with 8-node elements (hexaeder) and the headed reinforcement as well as the reinforcement of the foundation are modeled with 2-node elements. The material representing the soil is assumed in the way that only compressive forces and no tension forces could be transmitted. Two crossing bars Figure 4: Simplification headed bars in the simulate the head of the anchors (Fig. numerical analysis 4). Wagner [6] has shown the applicability of this simplification in detail. The material behavior of the headed bars, the bending reinforcement and the column is assumed to be linear elastic. 2.4. Results of the analysis All numerically examined configurations failed by a shear failure of the concrete. A diagonal crack from the anchor head towards the compression zone of the column base and an almost horizontal crack in the opposite direction are formed. In Figure 5a and 5b the maximum principal strains ε11 of the system with an anchor spacing s = 300 mm at maximum load and behind post peak load are shown. In Figure 6 the anchor tensile force at the top of the column base is plotted against the deflection of the anchor at this point. It shows that the maximum anchor load decreases with increasing anchor spacing. This can be explained with the conical distribution of the bending compressive force. In the area of the pulled anchor it comes to an overlay of tensile and compressive stresses. With
651
increasing distance of the pulled and compressed anchors and thus with increasing internal lever arm, the influence of the bending compressive stresses on the concrete failure load decreases (cf. Figure 1).
a) b) Figure 5: Maximum principal strains ε11 of the system with an anchor spacing s = 300 mm. a) maximum load, b) post peak
652
Figure 6: Anchor force versus anchor-displacement of column-foundation connections with different anchor spacing
In order to get more information about the behavior of the investigated structure, the maximum anchor tensile force is plotted over the quotient between anchor distance (approximation for the internal lever arm) and effective anchorage depth (Figure 7a). Apart from the results of the FE analysis the concrete cone failure load calculated according to the CC-method is shown as well. The concrete cone failure load is calculated using equation (3) and (4).
N u ,c = with
Ac , N 0 c, N
A
⋅ψ s , N ⋅ N u0,c
(3)
Ac , N = ( s + 3hef ) ⋅ 3hef
c ≤ 1.5hef
(3a)
Ac , N = b ⋅ 3hef
c > 1.5hef
(3b)
0 c, N
A
= (3 ⋅ hef )
2
(3c)
ψ s , N = 0.7 + 0.3 ⋅ c 1.5h ≤ 1.0 ef
(3d)
N u0,c = 15.5 ⋅ f cc0.5 ⋅ hef1.5
(3e)
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c = 0.5 ⋅ (b − s ) b = const. = 1800 mm hef = 500 mm f cc = 28.5 MPa N u ,anchor = 0.5 ⋅ N u ,c
(4)
Because of the constant width of the foundation (b = 1800 mm) there is an edge effect 0
for s ≥ 300 mm (s/hef ≥ 0.6). Therefore for s ≥ 300 mm the quotient Ac , N Ac , N = const. = 1.2 and the calculated failure load decreases because of a decreasing factor ψs,N. Fig. 7a shows that the peak anchor forces obtained by the numerical analysis are higher then the failure loads calculated according to the CC-method. However, for c = 2 hef the difference is very small (~ 1%). In the CC-method the radius of the failure cone on the concrete surface is assumed as r = 1.5 hef. Furthermore the resultant of the compression force is assumed to coincide with the location of the anchors at the compressed side of the base plate. Thus for an anchor spacing s/hef ≥1.5 (s ≥ 750 mm) no significant influence of the compression force between baseplate and foundation on the concrete cone failure load should be expected. For s/hef ≥ 1.5 the numerically obtained peak anchor tension forces are about 1,6% higher than the values calculated according to the CC-method. For increasing anchor spacing the numerically obtained peak anchor loads decrease in the same proportion as the values according to the CC-method (Nu (FE-analysis)/Nu (CC-method) = 0.99 for s = 2 hef). This reduction of the failure load is caused by the edge effect. For spacings s < 1.5 hef the failure loads obtained numerically increase. This is partly caused by the reduced edge effect and partly by the influence of the compression force. Therefore in Fig. 7b the failure loads obtained numerically and calculated according to the CC-method are normalized to the values valid for s = 1.5 hef. For s < 1.5 hef the related failure loads obtained numerically are much higher than the values calculated according to the CC-method. This is due to the restraint of the formation of the concrete cone due to compression stresses between base plate and concrete surface. In Fig. 8 the relation between numerically obtained relative failure loads (see Fig. 7b) and relative values calculated according to the CC-method are plotted as a function of the ratio s/hef. They can be approximated by equation (5) which was found by non-linear curve fitting. This equation is also plotted in Fig. 8.
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a) b) Figure 7: a) Ultimate anchor forces acc. to FE-analysis and CC-method versus s/hef, b) relative ultimate anchor forces versus s/hef
ψ moment =
1
(5)
h 1 − 0.15 ⋅ ef s
Equation (5) describes the influence of the compression stresses between base plate and concrete surface on the concrete cone capacity of fastenings. In Fig. 8 the test results by Zhao [2] and his proposal for ψmoment (Equ. (1) and (2)) are plotted as well. It can be seen, that according to Zhao and the present investigation the values ψmoment increase with decreasing ratios s/hef. However the increase predicted by Zhao is larger than found in the present investigation. This might be due to several reasons e.g. different conditions in the test by Zhao (tensile forces and bending moment compared to mainly bending in the present study, smaller anchorage depth). This is currently investigated further. In the present evaluation it is assumed that the magnitude of the internal lever arm coincides with the spacing of the anchors. This might be incorrect, especially if higher
655
normal compression forces act on the fastening. Therefore the ratio s/hef should be replaced by z/hef (z = internal lever arm) in equation (5). Equation (5) yields values ψmoment = ∞ for s/hef = 0.15. Fastenings with such small spacing loaded by a bending moment have never been investigated. Therefore it is proposed to use Equ. (6) in design which gives almost the same results as Equ. (5) for z/hef ≥ 0.4 but conservative values for ψmoment for ratios z/hef < 0.4. It is proposed to add the factor ψmoment according to Equ. (6) into Equ. (3) to take account of the beneficial effect of a bending moment acting on the base plate of a fastening on the concrete cone failure load. Equ. (6) (as Equ. (1)) is valid for fastenings with one anchor row at the tensioned side of the base plate and for a moment acting in one direction. In practice fastenings with more than one row of tensioned anchors as well as bending moments in two directions might occur. Further studies are needed to check whether Equ. (6) is valid also for these cases.
Figure 8: Multiplication coefficient ψmoment as a function of s/hef
ψ moment = 2 − ψ moment = 1
z hef
for 0 ≤ for
z <1 hef
(6a)
z ≥1 hef
(6b)
z = internal lever arm (distance between resultant of compression and tensile force)
656
3. Conclusions In the present paper the results of a numerical analysis on column-foundation connections with headed reinforcement are presented. It is demonstrated that there is a relatively strong influence of the bending compressive force on the concrete cone failure load. Until now this influence is not taken into account in the CC-method, which is commonly used for the design of anchorages. In order to account for this influence a multiplication coefficient ψmoment acc. to Equ. (6) is introduced which may be used with the CC-method. The presented studies were conducted with a constant anchorage depth hef = 500mm and a variable anchor spacing. To investigate the problem in more detail, further studies with variable anchorage depths need to be carried out. Furthermore fastenings with more than one row of tensioned anchors loaded by normal forces and bending moments in one ore two directions should be studied.
4. References 1.
2. 3. 4.
5. 6.
Fuchs, W., Eligehausen, R., Breen, J.E., ‘Concrete Capacity Design (CC) Approach for Fastenings to Concrete’ ACI Structural Journal, Vol. 92, No. 6, 1995, 794-802, Zhao, G., ‘Tragverhalten von randfernen Kopfbolzenverankerungen bei Betonausbruch’, IWB Mitteilungen, Universität Stuttgart, 1994 DIN 1045-1, ‘Tragwerke aus Beton, Stahlbeton und Spannbeton’, Teil 1: Bemessung und Konstruktion, Februar 1997 Ožbolt, J., Li, Y.-J., Kožar, I., ‘Microplane model for concrete with relaxed kinematic constraint’, International Journal of Solids and Structures, 38, 2001, 2683-2711 FEMAP, ‘High Performance CAE For The Desktop’, Structural Dynamic Research Corp., Exton, 2000 Wagner, Gunter, ‘Numerische Untersuchungen an Rahmenecken mit KopfbolzenBewehrung’, Diplomarbeit am Institut für Werkstoffe im Bauwesen, Universität Stuttgart, Februar 2000
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ATENA - AN ADVANCED TOOL FOR ENGINEERING ANALYSIS OF CONNECTIONS Vladimír Červenka, Jan Červenka and Radomír Pukl Červenka Consulting, Czech Republic
Abstract Advanced constitutive models implemented in the finite element system ATENA serve as rational tool to explain behavior of connection between steel and concrete. Three nonlinear material models available in ATENA are described: crack band model based on fracture energy, fracture-plastic model with non-associated plasticity and microplane material model. Nonlinear simulation using these advanced constitutive models can be efficiently used to support and extend experimental investigations and to predict behavior of structures and structural details.
1. Introduction Structural response of anchoring elements can be simulated by a nonlinear finite element analysis. This is a general approach based on principles of mechanics and should provide an objective tool for all types of geometry, material properties and loading. Such simulation is recently used to supplement experimental investigations, where it significantly increases the value of experimental data. The goal of this approach is to provide a tool more general than simple design formulas, which are usually valid for very limited range of parameters. The scope of application for complex nonlinear analysis is aimed to the development of new technical solutions of anchors, special loading types and investigation of failure cases. It is not aimed at the normal design, which can be accomplished by simple design formulas. An algorithm for nonlinear analysis is based on three basic parts: Finite element technique, constitutive model and non-linear solution methods, which should compose a balanced approximation. Nevertheless, the constitutive models decide about the material behavior, and therefore they are treated here more extensively, while the finite elements and non-linear solution are mentioned only briefly. With reference to renewed research authorities in the field of concrete mechanics and materials, such as RILEM, FIB,
658
FRAMCOS, it is recognized, that the most important effects to be included is the constitutive model of concrete are tensile fracturing and compressive confinement. Several constitutive models covering these effects are implemented in the computer code ATENA, which is a finite element package designed for computer simulation of concrete structures. The graphical user interface in ATENA provides an efficient and powerful environment for solving of many anchoring problems. ATENA enables a virtual testing of structures using computers, which is a present trend in research and development world. Several practical examples of ATENA utilization for simulation of connections between steel and concrete are presented in paper [1].
2. Material models Program system ATENA offers variety of material models for different materials and purposes [2]. For metals von Mises plasticity can be used, for rock and soil DruckerPrager plasticity with associated or non-associated flow rule is available, for steel reinforcement multilinear uniaxial model with cycling is determined. Nonlinear and contact springs for supports can be used, for interfaces Mohr-Coulomb friction is available. In some cases the use of isotropic elastic material law can be advantageous. Nevertheless, the most important material models in ATENA are the material models for concrete. These advanced models take into account all the important aspects of the real material behavior in tension and compression. Three nonlinear material models for concrete are available in ATENA: crack band model based on fracture energy, fractureplastic model with non-associated plasticity, and microplane material model. These three material models are described bellow in more detail. 2.1 Crack band model The basic constitutive model in ATENA is based on the smeared crack concept and the damage approach. Concrete without cracks is considered as isotropic and concrete with cracks as orthotropic. The material axes of cracked concrete, the axes of orthotropy, can be defined by two models: rotated or fixed cracks (refer [2] or [3] for details). In the rotated crack model the crack direction always coincides with the principal strain direction. In the fixed crack model the crack direction and the material axes are defined by the principal stress direction at the onset of cracking. In further analysis this direction is fixed and cannot change. An important difference in the above approaches is in the shear model on the crack plane. In the fixed crack model, a strain field rotation generates shear stress on the crack plane. Consequently the model of shear becomes important. In the case of the rotated cracks a shear on the crack plane never appears and the shear model need not to be employed. The stress response is based on a damage concept and it is defined by means of the equivalent uniaxial stress-strain law. This law describes the development of distinct material variables and their damage and covers the complete material behavior under monotonically increasing load including pre- and post-peak softening in compression
659
and tension. In the case of a uniaxial stress state it reflects the experimentally observed uniaxial behavior. In a biaxial state, the equivalent strain is calculated using the current secant inelastic elastic modulus. In the uncracked concrete the material is considered as isotropic and one elastic secant modulus is defined corresponding to the lowest compressive stress. In the cracked concrete, which is orthotropic, two moduli are defined, the first one for compressive and the second one for tensile material axes respectively. The effect of a stress state on the compressive and tensile strengths is considered by modifying the peak stresses using the failure functions based on Kupfer’s experiments.
Fig.1 Stress - crack opening law according to Hordijk [7] The method described above is applicable for the pre-peak response and unfortunately, cannot be simply extended in the post-peak range. It is known from material research, that the post-peak softening is structure-dependent and a simple strain-based model is not objective, but dependent on the finite element mesh due to strain localization in softening. In order to avoid this problem, localization limiters should be employed. Therefore, fracture mechanics approach (see [4]) based on the crack band model [5] and fracture energy is implemented. Such model substantially reduces the mesh sensitivity. In this model discrete cracks and compression failure zones, which represent discontinuities, are modeled in the finite element displacement fields by means of strain localization within bands. The model is based on an assumption of equal energy dissipation. Unified approach is used for tensile and compressive softening. The behavior of a crack in concrete is idealized by the model of a cohesive fictitious crack according to Hillerborg [6] where the crack opening law is governed by three parameters: tensile strength, fracture energy, and the shape of the softening curve. The exponential shape experimentally derived by Hordijk [7] is used for descending branch, Fig.1.
660
The unloading path of the stress-strain law is considered to the origin. This is certainly an approximation, which can be accepted in the case of a monotonic loading history. However, even if the load is increased monotonically, in certain material points the stresses are unloading. For example, in the process of crack formation distributed cracks are initiated in large material volumes, and then some cracks open while many other cracks close. Consequently, the unloading law is essential for the strain localization. The unloading material modulus describes a material damage due to mechanical loading. In this respect, the model described above is similar to the damage theory. Shear of the cracked concrete is important for the fixed crack model, as already mentioned in the context of crack models. Many researchers found, for example Rots [8], that a simple reduction of shear resistance by a constant factor (a constant shear retention factor), does not work well. Therefore, the presented model utilizes the variable shear retention factor, in which the crack shear resistance is decreasing with the crack opening. Decrease of compressive strength in the cracked concrete may be important in some types of failure. It was introduced by Collins [9] and is now being used in design. This model describes a reduction of concrete compressive due to lateral cracking. In the present model the exponential formula based on the Collin’s experiments is employed. The amount of the maximal reduction is given as a parameter in order to enable a control of this effect. The constitutive model described above can be used for plane stress analysis of normal, as well as high strength and steel fiber reinforced concrete. For these concrete types, special modifications of the descending branch are available. 2.2 Fracture-plastic model This three-dimensional constitutive material model for concrete combines plasticity with fracture. For detailed description of the model please refer [2], [10], [11]. The fracture is modeled by an orthotropic smeared crack model based on Rankine tensile criterion. Hardening-softening plasticity model based on Menétrey-Willam [12] three-parameter failure surface is used to model concrete crushing. The presented model differs from the other published formulations by ability to handle also physical changes like for instance crack closure, and it is not restricted to any particular shape of hardening/softening laws. Also within the proposed approach it is possible to formulate the two models (i.e. plastic and fracture) entirely separately, and their combination can be provided in a different algorithm or model. The method of strain decomposition as it was introduced by de Borst [13] is used to combine fracture and plasticity models together. Both models are developed within the framework of return mapping algorithm. This approach guarantees the solution for all magnitudes of strain increment. From an algorithmic point of view the problem is then transformed into finding an optimal return point on the failure surface. The return-
661
mapping algorithm for the plastic model is based on predictor-corrector approach as is shown in Fig.2 (for details see ref. [11]).
Fig.2 Plastic predictor-corrector algorithm according to [11] The combined algorithm must determine the separation of strains into plastic and fracturing components, while it must preserve the stress equivalence in both models. The algorithm is based on a recursive iterative scheme. It can be shown that such a recursive algorithm cannot reach convergence in certain cases such as, for instance, softening and dilating materials. For this reason the recursive algorithm is extended by a variation of the relaxation method to stabilize convergence. 2.3 Microplane model The basic idea of the microplane model is to abandon constitutive modeling in terms of tensors and their invariants and formulate the stress-strain relation in terms of stress and strain vectors on planes of various orientations in the material, now generally called the microplanes. This idea arose in G.I. Taylor’s pioneering study from 1938 of hardening plasticity of polycrystalline metals. Proposing the first version of the microplane model, Bažant [14], in order to model strain-softening, extended or modified Taylor’s model in several ways (in detail see [15]), of which the main one was the kinematic constraint between the strain tensor and the microplane strain vectors. Since 1984, there have been numerous improvements and variations of the microplane approach. A detailed overview of the history of the microplane model is included in [15]. Sketch of the fundamental concepts of the microplane model is shown in Fig.3.
662
Fig.3 Fundamental concepts of the microplane model In the microplane model, the constitutive equations are formulated on a plane called microplane with an arbitrary orientation characterized by its unit normal ni . The kinematic constraint means that the normal strain ε N and shear strains
εM ,εL
on
the microplane are calculated as the projections of the macroscopic strain tensor:
ε N = ni n j ε ij , 1 ( mi n j + m j ni ) ε ij , 2 1 ε L = ( li n j + l j ni ) ε ij 2
εM =
where mi and li are chosen orthogonal vectors lying in the microplane and defining the shear strain components. The constitutive relations for the microplane strains and stresses can be generally stated as:
663
σ N (t ) = Fτt=0 [ε N (τ ), ε M (τ ), ε L (τ ) ] σ M (t ) = Gτt =0 [ε N (τ ), ε M (τ ), ε L (τ ) ] σ L (t ) = Hτt =0 [ε N (τ ), ε M (τ ), ε L (τ ) ] where F , G and H are functionals of the history of the microplane strains in time t. For a detailed derivation of these functionals please refer [16]. The macroscopic stress tensor is obtained by the principle of virtual work that is formulated for a unit hemisphere Ω. After the integration, the following expression for the macroscopic stress tensor is recovered:
σ ij =
Nm 3 6 s d Ω ≈ wi sij( µ ) ∑ ij ∫ 2π Ω µ =1
sij = σ N ni n j +
σM 2
(m n i
j
+ m j ni ) +
σL 2
(l n i
j
+ l j ni )
where the integral is approximated by an optimal Gaussian integration formula for a spherical surface. The microplane model M4 derived above is implemented into the finite element package ATENA. For details about the implementation and applications refer [17].
3. Software package ATENA ATENA is a commercial finite element software package for nonlinear simulation of concrete and reinforced concrete structures. Based on advanced material models, described above, it can be used for realistic simulation of structural response and behavior. ATENA works under MS Windows operating system and its code is written in MS Visual C++. It heavily uses MFC and ATL libraries, thereby ensuring high productivity in code development and high compatibility with other third-party PC-based software. The code has object-oriented architecture. It is created in hierarchical manner and each SW layer has its own DLL library (or libraries). Code and associated data are arranged in objects together, (in i.e. C++ classes). ATENA system consists of several dynamically linked libraries (DLLs) and a few control programs (Fig.4). It is believed that architecture and build up of ATENA system supersedes usual finite element packages.
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C++ libraries
MFC
ATL
CCUtils_MFC CCRealMatrix AtenaDLL
CCFEModel CCStructures CCElements_2D_Basic
AtenaGUI
CCElements_2D_Extended
AtenaWin
CCStructuresCreep CCStructuresTransport
AtenaConsole PollutTransport CCElements_3D_Extended
Modeln
CCMaterials_Basic
FEMAP
CCMaterial_Microplane4
CCMaterials_Extended_A
Fig.4 Layered structure of ATENA system ATENA offers user-friendly graphical interface, which enables an efficient solving of engineering problems including anchoring technology and reinforcing of concrete [1]. Native ATENA GUI is available for 2D and rotationally symmetrical problems. It supports the user during pre- and postprocessing, and enables real-time graphical tracing and control during the analysis. ATENA preprocessing includes an automatic meshing procedure, which generates Q10, isoparametric quadrilateral and triangular elements. Reinforcement in ATENA can be treated as smeared reinforcement, reinforcing bars or prestressing cables. The discrete reinforcement is independent on the finite element mesh. The graphical postprocessing can show cracks in concrete, with their thickness, shear and residual normal stresses. User-defined crack filter is available for obtaining of realistic crack patterns. Other important values (strains, stresses, deflections, forces, reactions etc.) can be represented graphically as rendered areas, isoareas, and isolines, in form of vector or tensor arrow fields. All values can be also obtained in well-arranged numerical form. The interactive solution control window (Fig.5) enables graphical as well as numerical monitoring of the actual task, and supports user interventions during the analysis (user interrupt, restart). For the 3D pre- and postprocessing, professional third party software FEMAP in combination with alphanumerical ATENA Console window is employed. ATENA enables to load the structure with various actions: body forces, nodal or linear forces, supports, prescribed deformations, temperature, shrinkage, pre-stressing. These loading cases are combined into load steps, which are solved utilizing advanced solution methods: Newton-Raphson, modified Newton-Raphson or arc-length. Secant, tangential
665
or elastic material stiffness can be employed in particular models. Line-search method with optional parameters accelerates the convergence of solution, which is controlled by residua-based and energy-based criteria. This is only a concise survey of ATENA features. All of the described features support the user by engineering analysis of connections between steel and concrete and computer simulation of its behavior.
Fig.5 ATENA real-time graphical window
4. Conclusions The nonlinear finite element package ATENA is based on advanced constitutive models. Crack band approach employed for tensile and compressive softening avoids the finite element mesh sensitivity of solution. ATENA is able to predict and explain behavior of steel reinforcement as well as steel anchors in concrete structures in a consistent way. It can be effectively used to support and extend experimental investigations for innovative solutions in the field of connections between steel and concrete.
Acknowledgment This paper is related to the research topics supported by grant of Grant Agency of Czech Republic (GAČR) No. 103/99/0755. The financial support is greatly appreciated.
References 1.
Pukl, R., Červenka, J. and Červenka, V., 'Simulating a response of connections', Proceedings of the RILEM Symposium on Connections between Steel and Concrete, Stuttgart, Germany, September 2001.
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2. 3. 4. 5. 6.
7. 8. 9.
10.
11.
12. 13. 14.
15.
16. 17.
'ATENA Program Documentation, Part 1 - Theory', Červenka Consulting, Prague, Czech Republic, 2000. Červenka, V., 'Simulating a Response', Concrete Engineering International, 4 (4) (2000) 45-49. Margoldová, J., Červenka, V. and Pukl, R., 'Applied Brittle Analysis', Concrete Engineering International, 2 (8) (1998) 65-69. Bažant, Z.P. and Oh, B.H., 'Crack band theory for fracture of concrete', Materials and Structures, 16 (1983) 155-177. Hillerborg, A., Modéer, M. and Peterson, P.E., 'Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements', Cement Concrete Res., 6, (1976), 773-782. Hordijk, D.A., 'Local Approach to Fatigue of Concrete', Ph.D. Thesis, Delft University of Technology, The Netherlands, 1991. Rots, J.G., 'Computational Modelling of Concrete Fracture', Ph.D. Thesis, Delft University of Technology, The Netherlands, 1988. Vecchio, F.J. and Collins, M.P., 'Modified Compression-Field Theory for Reinforced Concrete Beams Subjected to Shear', ACI Journal, 83 (2) (1986) 219231. Červenka, J., Červenka, V. and Eligehausen, R., 'Fracture-plastic material model for concrete, application to analysis of powder actuated anchors', Proceedings of the International Conference on Fracture Mechanics of Concrete Structures FraMCoS 3, Gifu, Japan, 1998 (Aedificatio Publishers, Freiburg, Germany, 1998) 1107-1116. Červenka, J. and Červenka, V., 'Three Dimensional Combined Fracture-Plastic Material Model for Concrete', Proceedings of the 5th U.S. National Congress on Computational Mechanics, Boulder, Colorado, USA, August 1999. Menétrey, P. and Willam, K.J., 'Triaxial failure criterion for concrete and its generalization', ACI Structural Journal, 92 (3) (1995) 311-318. de Borst, R., 'Non-linear analysis of frictional materials', Ph.D. Thesis, Delft University of Technology, The Netherlands, 1986. Bažant, Z.P. , 'Microplane model for strain controlled inelastic behavior', Chapter 3, Proceedings of Conference Mechanics of Engineering Materials, University of Arizona, Tucson, January 1984, Eds. C.S. Desai and R.H. Gallagher (J. Willey, London, 1984), 45-59. Bažant, Z.P., Caner, F.C., Carol, I., Adley, M.D., and Akers, S.A., 'Microplane model M4 for concrete: I. Formulation with work-conjugate deviatoric stress', J. of Engrg. Mechanics ASCE 126 (9) (2000), 944—953. Caner, F.C. and Bažant, Z.P., 'Microplane model M4 for concrete: II. Algorithm and calibration', J. of Engrg. Mechanics ASCE 126 (9) (2000), 954—961. Bažant, Z.P., Červenka, J. and Wierer, M., 'Equivalent Localization Element for Crack Band Model and as Alternative to Elements with Embedded Discontinuities', Proceedings of the International Conference on Fracture Mechanics of Concrete Structures FraMCoS 4, Paris, France, 2001.
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A COMPUTATIONAL MODEL FOR DOUBLE-HEAD STUDS André Haufe* and Ekkehard Ramm** *Department of Civil Engineering, University of Calgary, Canada **Institute for Structural Mechanics, University of Stuttgart, Germany
Abstract The advantages of so called double-head studs over conventional stirrups in concrete, namely the employment of the full yield strength immediately behind the anchorage, more efficient confinement near the surface and ease of placement are the main reasons for the increasing number of their applications ([2], [3] & [5]). Their development has been mainly driven through experimental investigations. This paper will outline the approach that will be followed in a numerical study that is currently in progress at the University of Calgary. The research is mainly focused on the local anchoring effects and the confinement provided by the double-head studs. A three dimensional finite element analysis is chosen as a suitable means to model the studs and the surrounding concrete. Classical plasticity theory will be used to take into account the different material properties of concrete and steel in a phenomenological sense. A common remedy to mesh sensitive results in finite element analysis occurring from the use of softening material formulations will be shortly addressed.
1. Motivation The mechanical behavior of double-head studs as possible replacement for traditional cross ties in concrete columns has been investigated in various test series at the University of Calgary. Here straight studs with mechanical anchors at each end have been used. It should be noted that the area of the head has been chosen equal to 10 times that of the stem to ensure that yielding of the stem can be developed without appreciable slip of the anchor. In particular, it has been found that with this setup the double-head studs remarkably increase the ductility and the energy dissipation of the structure, which is of course a preferable design criteria in areas with a high seismic activity (see Fig. 1). While the experimental investigations clearly show the aforementioned superior behavior over classical cross ties [17], efforts towards numerical simulation of the local and global load carrying capacity
2500 cross-ties only
load [kN]
2000
vertical bars and cross-ties double-head studs only vertical bars and double--head studs
1500 1000 500 0
placement of studs
failure mode of column
0
5 10 15 20 strains [10 --3]
experimental results
Fig. 1: Double-head studs as replacement of cross ties in concrete columns (Dilger & Ghali [3]) of double-head studs are in progress. In this paper the principle constitutive models that are applied will be presented. For the numerical analysis, a three dimensional finite element discretization of the doublehead studs and the surrounding concrete is made. Linear kinematics are assumed in the first step. The materially nonlinear analysis is performed within a standard incremental-iterative Newton-Raphson framework. All presented constitutive models are based on rateindependent classical plasticity using Backward-Euler integration schemes.
2. Constitutive Model for Concrete 2.1
General overview
For the concrete constitutive model a multi-surface plasticity formulation is applied which was originally proposed by Menrath [11] for two dimensional structures and later expanded to the fully three dimensional stress space by Haufe [7]. The proposed model uses an associated plastic potential (normality rule) for all regular yield surfaces g i = F i ∀ i ∈ [1, 2, 4] and associated evolution laws that are based on the work hardening principle. Furthermore it features only very few material parameters that can be easily identified using EC2 [4] or CEB-FIP [1] recommendations. The failure surface depends on the two stress invariants I 1 and J 2 = 12 |s|2 and is built up of two regular Drucker-Prager cones, F 1 and F 2. Furthermore it is limited in the equitriaxial compressive stress space by a spherical cap F 4 (see Fig. 2). A third inverted cone F 3 is introduced at the apex solely to assure a proper stress projection within the local integration algorithm. Their defining equations read as follows: F i(s, I1, Á i) = |s| + α i I 1 −
23 f (Á ) ,
F 3(s, I1, Á 1) = |s| + α 3 I 1 −
i
i
23 f (Á ) 3
1
i = 1, 2
(1) (2)
|s| + 19 (I − I
F 4(s, I1, Á 2) =
1
(Á 2))2 − R(Á2)
(3)
1,m
The regular Drucker-Prager cones in eqn. (1) depend on the evolution laws for tension σ 1(Á1) and compression σ 2(Á2) which are introduced via f i(Ái) = β i σ i(Ái). Here the β i as well as the α i in eqn. (1) define the yield surface in the invariant stress space according to: α1 =
23 γγ ff
α2 =
23 2γγ −−11
1
cm
1
cm
− f ctm + f ctm
2
and
β1 =
2 γ1 f cm γ1 f cm + f ctm
(4)
and
β2 =
γ2 2 γ2 − 1
(5)
2
The inverted cone (see eqn. (2)) also depends on the tensional evolution law thus its parameters α 3 and f 3 are obtained from geometrical considerations at the apex: α3 = − 1 3α 1
f3 = − 1 2 f1 3α 1
and
(6)
The spherical cap is C 1-continuously fixed to the second Drucker-Prager cone F 2. Therefore two additional functions I 1,m(Á2) and R(Á 2), defining the midpoint of the sphere on the hydrostatic axis and its radius respectively, need to be defined. They allow for kinematic hardening or softening according to F 2: I 1,m(Á2) = − 54 α 2 + 2 γ2σ 2(Á2)
and
R(Á 2) =
23 + 6α
2 2
γ2 σ 2(Á 2)
(7)
The evolution laws σ 1(Á1) and σ 2(Á2) itself are functions of the equivalent plastic strains in tension Á 1 and compression Á 2 and are defined as follows (see Fig. 3):
Á σ(Á 1) = f ctm exp − À 1 tu
with
À tu =
Gt l crs f ctm
(8)
2J 2 = |s| F2 F3
R(Á 2)
F1 2 − γ 2σ 2(Á2) 3
1 I (Á ) 3 1,m 2
F4
I1 <0 3
Fig. 2: Multisurface-model in the I1 -J2 -invariant stress space
Á Á f cm γ3 + 2(1 − γ 3) À2 − (1 − γ 3) À2 e e σ 2(Á2) =
f cm
Á −À 1 − À 2 − Àe cu e
where
2
for Á 2 < À e (9)
2
À e = γ4
for À e ≤ Á2 < À cu
f cm Ec
and
À cu =
3 Gc + Àe 2 h f cm
(10)
Here G t and f ctm represent the fracture energy and the strength of concrete in tension, respectively, while G c and f cm are the corresponding values for compression. h represents a characteristic finite element length and l crs the effective average crack spacing. Furthermore four additional model parameters γ 1 ÷ γ 4 are needed to define the shape of the yield surface and of the evolution law in compression. It has been shown by Menrath [11] that γ 1 = 3.0 and γ 2 = 1.2 satisfactorily represent the failure envelope of Kupfer and Gerstle [10]. Furthermore for standard grade concrete the parameters for the evolution law in compression are chosen to γ 3 = 0.3 and γ 4 = 1.33 (Haufe et al. [6]). 2.2
Algorithmic aspects
In the following the algorithmic aspects for the concrete model, excluding the spherical cap F 4 due its complexity, are summarized. A more detailed discussion can be found in the references [11] and [12]. The mean stress state of cracked reinforced concrete σ rc is decomposed into two parts, the stress contribution of the concrete, σ c and of the reinforcing steel, σ s: σ rc = σ c + σ s (11) The contribution of the so-called tension stiffening effect, which occasionally is introduced as a third stress component, is negligible in this local study. Furthermore the stress tensor σ s is only used to model smeared meshtype reinforcement. The strain tensor is additively decomposed into a reversible elastic part Á e and a nonreversible inelastic part Á ie ≡ Á pl, where the latter is understood as plastic in a phenomenological sense. Making a)
b)
σ1
Gt l crs
f ctm
σ2 f cm
Gc h
γ 3 fcm Á2
Á1 À tu
À e(γ4)
Fig. 3: Evolution laws in tension (a) and compression (b)
À cu
use of Koiter’s rule [9] for multisurface plasticity models within the incremental iterative procedure, the plastic strain increment for loadstep n+1, ∆Á pln+1, can be calculated by 3
∆Á pln+1 =
c
i
∆λ i,n+1
i=1
∂g i ∂σ
g i = Fi
with
(12)
where only active yield surfaces (c i = 1) contribute to the plastic strains. For inactive yield surfaces the algorithmic parameter is set to zero (c i = 0). The increment of the plastic multipliers is restricted to ∆λ i ≥ 0. The loading and unloading conditions are determined by the well known Kuhn-Tucker-conditions. An ’elastic predictor-plastic corrector’-stress integration algorithm is applied. Within the Backward-Euler-scheme the consistency condition is fulfilled at the end of the time step. For the presented two-invariant model this approach leads to the radial-return-algorithm: Á pln+1
= Á pln + ∆Á pln+1
(13)
q n+1
= q n + ∆qn+1 = q n + ∆λ n+1
(14)
σ * n+1 = C : (Á n+1 − Á pln)
(15)
= C : (Á n+1 − Á pln+1) = σ * n+1 − C : ∆Á pln+1 = σ * n+1 − ∆σ pln+1
σ n+1
(16)
Here C is the elastic constitutive tensor; σ * n+1 represents the elastic trial stress and q n+1 is the vector of the internal variables q i = Ái based on the work hardening hypothesis. By consistent linearization of this incremental equations we finally arrive at 3
dσ n+1 = H : (dÁ n+1 −
c
i
dλ i,n+1
i=1
∂g i ) = H : (dÁ n+1 − Udλ ) ∂σ
(17)
where the modified elastic tangent H reads
3
H= C
−1
+
i=1
∂g i c i dλi,n+1 ∂σ ∂σ
−1
(18)
and the symbols of a generalized formulation composed of dλ = [dλ 1, dλ2, dλ 3] and
U = c1
∂g 1 ∂g 2 ∂g 1 ,c ,c ∂σ 2 ∂σ 3 ∂σ
(19)
have been introduced. Making use of the consistency condition in a modified form dF i = c i
∂F∂σ : dσ + ∂F∂q : dq + (1 − c ) dλ i
i
i
3
i
where
and introducing the components of the hardening matrix ∂F j E ij = − c i c j q − (1 − c i) δ ij , i we can write
dq =
c dλ i
i
(20)
i=1
(21)
dλ = E V dσ −1
T
with
∂F ∂F ∂F ,c ,c V = c ∂σ ∂σ ∂σ 1
1
2
2
3
3
T
.
(22)
By inserting eqn. (22a) into eqn. (17) and using the Sherman-Morrison-formula to avoid time consuming numerical inversion of the resulting 6x6-matrix we arrive finally at
−1
dσ n+1 = H − HU E + V THU V TH
n+1
: dÁ n+1 .
(23)
Here the expression in square brackets is known as algorithmic elastoplastic tangent operator C ep,alg . It should be noted that the obvious difference in the third column between n+1 eqn. (19) and eqn. (22b) is due to a nonassociated choice of the plastic potential for the third yield function F 3. Here the plastic potential has been chosen to g 3 = g 1 . This results eventually in a nonsymmetric tangent operator for stress paths that activate the inverted cone. When applying softening materials, eventually the underlaying differential equation changes its type from elliptic to hyperbolic which is known as loss of ellipticity. This leads to results that are strongly dependent on the finite element mesh size and also on the mesh orientation. All appropriate strains due to softening will eventually localize into one element band. A popular yet easy remedy is to adjust the softening modulus to a characteristic length of the actual size of the finite element mesh h.Thus the maximum amount of fracture energy that can be released in a single integration point becomes a function of the discretization. For plain concrete the effective average crack spacing (see eqn. (8b)) is equal to the characteristic length l crs = h, while for reinforced concrete it is chosen to be l crs = min [l c, h]. Here l c is the average crack spacing as defined for example in [1]. Introducing this concept to the aforementioned concrete model leads to the dependency of À tu and À cu on the characteristic length h (compare eqns. (8b) and (10b)). However, it should be noted that while the dependency on the mesh size is significantly lower, it has been found that the results are still influenced by the mesh orientation. In defining the characteristic length h, which not only depends on the mesh size but also on the Ansatz-functions of the finite elements used, the proposals by Rots [14] are followed.
3. Constitutive Model for Studs And Reinforcement The von Mises-criteria (i. e. classical associated J2 --plasticity) with nonlinear kinematic and isotropic work-hardening has been chosen as yield surface for the steel studs. The evolution laws can either be of Ramberg-Osgood-type or given as multilinear data. Further constructive mesh-type reinforcement can be modeled as smeared additional stiffness in the reinforced direction (see eqn. (11)). Since this approach is straightforward the reader is directed to the comprehensive textbooks of Hofstetter & Mang [8] or Simo & Hughes [16].
4. Concrete-Stud Interface 4.1
Overview of Element Formulation
The stress transfer between the profiled stems of the studs and the surrounding concrete has a significant influence on the degree of confinement provided by the studs. Therefore 2D interface elements not having a physical thickness and incorporating a nonlinear constitutive relationship will be used to model the bond slip, see Schellekens [15]. For the three dimensional simulation they consist of 8 nodes for 8 node brick elements or of 16 nodes for 20 node brick elements (see Fig. 4). This leads to the following element nodal displacement vector v for the 8 node interface element v = v 1r , , v 8r , v 1s , , v 8s , v 1t , , v 8t
T
(24)
which is related to the continuous displacement field u via T
u = u ur, ulr, u us, uls, u ut, u lt = H N v .
(25)
Here the superscripts u and l indicate the upper or lower surface of the element and r, s, t the directions of the tangential coordinate system with t being the normal direction. The matrix H N contains the interpolation functions in the submatrices N1x4 in diagonal form H N = diag[N, N, N, N, N, N ] which can be rearranged using the constant operator matrix --1 +1 0 0 0 0 L = 0 0 --1 +1 0 0 (26) 0 0 0 0 --1 +1
to obtain the relative displacement vector ∆u = L u = L H N v = Bv. The relative displacement-nodal displacement matrix B and the elastic constitutive tensor read
--N +N 0 0 0 0 B = 0 0 --N +N 0 0 0 0 0 0 --N +N
d = 0 0
r
and
C
el
d
0 0 dr 0 0
(27)
t
respectively. Thus the traction vector t can be calculated according to t = C el ∆u . Assembly of the stiffness matrix K = BCB TdS, derived from the principle of virtual work, is a)
upper surface
b)
§ £
¦ ¢
v 6t ¤ ¡ lower surface
¥ v 6r
v 6s ©
Fig. 4: Exemplary setup of a 16 node (a) and 8 node interface element (b)
a)
b) F Coul
tr Ô(À)
c
c(À)
tt
c0
(< 0)
ts
dc = k c dÀ
À
Fig. 5: a) Yield surface of Coulomb’s friction law b) Bilinear cohesion law straightforward. However since the physical behavior of the bond requires a very stiff response in the elastic regime that is subsequently followed by yielding once the yield or “slip” condition is satisfied. These extremely high stiffness contributions to the global stiffness matrix may cause traction oscillations in the adjacent elements. It has been shown by Menrath [11] and Schellekens [15] that they can be significantly lowered by alternative integration techniques e. g. Newton-Cotes- or Lobatto-schemes. For linear or quadratic interpolation functions both schemes are identical. 4.2
Constitutive Model
To account for the nonlinear behavior of the interface, which is characterized by bond and subsequent slip, a nonlinear constitutive formulation based on Coulomb’s friction law (see Fig. 5a) is used. The yield surface depends on the tractions t = [t r, t s, t t], the cohesion c as function of the internal variable À and the friction angle Ô: F Coul = t 2r + t 2s + t t tan Ô − c(À) = 0
∆u. plr t
À=
where
2
(28) . pl 2
+ ∆us dτ
(29)
t=0
In cases where the normality rule is not applicable the friction angle Ô is replaced by the dilatancy angle ψ in the plastic potential g Coul thus resulting in a nonassociated formulation. The incremental traction-relative displacement relation can be derived according to [16] as
dt n+1
=Θ
Θ Coul
−
∂g Coul
∂FCoul ∂t
∂t T
∂FCoul
Θ
∂t
∂g Coul ∂t
+ k
T
Θ
d(∆u) n+1 .
(30)
n+1
Again the expression within the brackets is known as algorithmic elastoplastic tangent opwhere the modified elastic tangent is defined as erator C ep,alg Coul Θ Coul =
C
el −1
∂ 2g Coul ∆λ ∂F Coul + ∆λ + ∂À k ∂t 2
∂g Coul ∂t
∂À ∂∆u pl
T
∂ 2g Coul ∂t 2
−1
. n+1
(31)
k represents the usual hardening/softening parameter. In the general case of friction and cohesion hardening/softening, thus Ô = Ô(À) and c = c(À), it reads t n ∂ tan Ô ∂c ∂F + = − k Ô + kc . k = − Coul = − (32) ∂À ∂À ∂À However in the present study the friction angle is not dependent on the evolution parameter thus eqn. (32) simplifies to k = k c = ∂c∕∂À (see Fig. 5b).
5. Summary The approach towards a detailed three dimensional numerical simulation of double-head studs has been described. For the concrete model presented the main objective has been to use a simple yet robust and effective formulation which uses only a small number of readily available material parameters. It is based on classical plasticity and uses the fracture energy to define softening/hardening characteristics within the framework of a multisurface yield criterion. The number of material parameters (fc , fctm , Gt , Gc ) has on purpose been kept as low as possible to simplify their identification according to EC2-standard or CEB-FIP rules. A formulation for continuous interface elements has been presented. In order to circumvent oscillation problems within the traction-profiles a Newton-Cotes- or Lobatto-integration scheme is employed. The constitutive relationship of the presented interface elements are based on Coulomb’s friction law which can be treated as a standard plasticity problem. Linear hardening or softening characteristics are so far taken into account for the evolution laws. The steel of the studs is modeled by standard von Mises-plasticity with multi-linear or nonlinear Ramberg-Osgood type of hardening. The constitutive models as well as the interface element are being implemented into the finite element program system CARAT of the Institute of Structural Mechanics, University of Stuttgart [13]. Since the research project started in March 2001 no numerical examples are available at the time of writing this paper. However the proposed approach will be followed and preliminary numerical results will be presented at the conference.
6. Acknowledgement The financial support for this research project by the German Academic Exchange Service (DAAD) is greatly appreciated. Furthermore the first author likes to express his deepest gratitude to Dr. Ghali for providing advice and resources at the Department of Civil Engineering at the University of Calgary.
7. References 1. 2.
CEB-FIP -- Model Code 1990, Bulletin d’Information CEB, 1990. Birkle, G., Dilger, W. H., Ghali, A., Schäfer, K. (2001), ’Doppelkopfstäbe in Konsolen’, Beton- und Stahlbetonbau, Vol. 96, No. 2, pp. 82-89.
3.
Dilger, W. H. and Ghali, A. (1997), ’Double-Head Studs as Ties in Concrete’, Concrete International, Vol. 19, No. 6, pp. 59-66.
4.
Eurocode 2 (1992), ’Planung von Stahlbeton- und Spannbetontragwerken’, DIN V 18932 (10.91), DIN ENV 1992-1-1 (06.92).
5.
Ghali, A. and Dilger, W. H. (1998), ’Anchoring with Double-Head Studs’, Concrete International, Vol. 20, No. 11, pp. 21-24.
6.
Haufe, A., Menrath, H. and Ramm, E. (2000), ’Numerical Simulation of High Strength Steel--High Strength Concrete Composite Structures’, In: Conference Proceedings of the 6th ASCCS Conference on Steel and Concrete Composite Structures 2000, Eds.: Y. Xiao and S. A. Mahin, Los Angeles, CA, USA, March 22-24, 2000.
7.
Haufe, A. (2001), ’Dreidimensionale Simulation bewehrter Flächentragwerke aus Beton mit der Plastizitätstheorie’, Ph.D.-Dissertation , Report Nr. 35, Institute for Structural Mechanics, University of Stuttgart.
8.
Hofstetter, G. and Mang, H.A. (1995): ’Computational Mechanics of Reinforced Concrete Structures’, Vieweg & Sohn, Braunschweig/Wiesbaden.
9.
Koiter, W. T. (1953), ’Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface’, Quart. of Appl. Mech., Vol. 11, pp. 350-354.
10. Kupfer, H. B. and Gerstle, K. H. (1973), ’Behavior of Concrete Under Biaxial Stress’, Journ. Eng. Mech. Div., ASCE, EM4, pp. 853-866. 11. Menrath, H. (1999), ’Numerische Simulation des nichtlinearen Tragverhaltens von Stahlverbundträgern’, Ph.D.-Dissertation , Report Nr. 29, Institute for Structural Mechanics, University of Stuttgart. 12. Menrath, H., Haufe, A. and Ramm, E. (1998), ’A Model for Composite Steel-Concrete Structures’, Proceedings of the EURO-C 1998 Conference on Computational Modelling of Concrete Structures, Eds.: De Borst, R., Bicanic, N., Mang, H. A., Meschke, G.; Badgastein/Austria, A. A. Balkema Publishers, Rotterdam, Volume 1, pp. 33-42. 13. Programmsystem CARAT (2000), ’CARAT: Eingabebeschreibung und Dokumentation’, Institute for Structural Mechanics, University of Stuttgart. 14. Rots, J. G. (1988), ’Computational Modeling of Concrete Fracture’, Ph. D.-Dissertation, Delft University of Technology, The Netherlands. 15. Schellekens, J.C.J. (1990), ’Interface Elements in Finite Element Analysis’, Ph.D.Dissertation, Report Nr. 25-2-90-5-17, TU-Delft, The Netherlands. 16. Simo, J. C. and Hughes, T. J. R. (1998), ’Computational Inelasticity’, Springer-Verlag New York, Inc. 17. Youakim, S. A. and Ghali, A. (2001), ’Seismic Behavior of Concrete Columns with Double-Head Studs as Cross Ties’, Proceedings of the 29th Annual Conference of CSCE, Victoria/Canada.
BEHAVIOR AND DESIGN OF FASTENINGS WITH HEADED ANCHORS AT THE EDGE UNDER ARBITRARY LOADING DIRECTION Jan Hofmann, Joško Ožbolt, Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract In the present paper the theoretical aspects and the application of the non-linear finite element program MASA for analysis of anchorages placed at an edge of a concrete block are discussed. After an introduction the structure of the finite element (FE) code is briefly described. The results of the simulations are shown and compared with experimental data. They confirm that the FE code is able to simulate realistically the behaviour of anchorages.
1. Introduction The failure load of anchorages with headed studs may be calculated according to the CC-Method by Fuchs, Eligehausen, Breen (1995). In order to understand the behaviour of headed studs very close to an edge under tension and shear loading in more detail and possibly to improve the CC – method, a numerical investigation was carried out with the non-linear FE code MASA. It is based on the microplane model. The program is able to analyze the three-dimensional nonlinear behaviour of concrete. In the present paper it is shown that the program MASA is able to predict realistically the behaviour of fastenings with headed anchors close to an edge.
2. Finite-Element-Ccode MASA 2.1. General The used finite element code is based on the microplane model. It can be used for the two and the three-dimensional analysis of quasi brittle materials. The model allows a realistic prediction of the material behavior in case of three-dimensional stress - strain states. The smeared crack approach is employed. To ensure a mesh independent crack development a so-called "localization limiter " is used. This is realized by the crack band
678
approach or by a generalized nonlocal integral method. For the analyses discussed in the present paper, the improved crack band approach was used. The material model is described in detail in Ožbolt et al. (2001) The concrete is discreted by 8-node brick elements. The reinforcing bars are modelled with bar elements or smeared within the concrete elements. Beside the standard finite elements special contact elements are available. They allow a simulation of the contact between concrete and headed stud. The analysis is incremental. For simple handling of the program as well as for the pre and post processing the commercial program FEMAP (1997) is used. 2.2. Constitutive law – Microplane model In the microplane model the material properties are characterized separately on planes of various orientations within the material. On these microplanes there are only a few uniaxial stress and strain components and no tonsorial invariance requirements need to be considered. The constitutive properties are entirely characterized by relations between the stress and strain components on each microplane in both, normal and shear directions (Fig. 1). It is assumed that the strain components on the microplanes are projections of the macroscopic strain tensor (kinematic constraint approach). Knowing the stress-strain relationship of all microplane components, the macroscopic stiffness and the stress tensor are calculated from the actual strains on the microplanes by integrating the stress components on the microplanes over all directions. The simplicity of the model is due to the fact that only uniaxial stress-strain relationships are required for each microplane component and the macroscopic response is obtained automatically by integration over the microplanes. More details related to the used model can be found in Ožbolt et al. (2001).
ε
z
z
n
x
εT
εN εM
y
εK
y
Microplane Mikroeben
a)
b) x
Figure 1. Concept of the microplane model: a) unit volume sphere – integration point and b) strain components.
679
3. Comparison between experimental and numerical results in case of blow out failure To verify the suitability of the finite element program MASA for the numerical simulation of headed studs placed close to the edge of a concrete block a numerical study was carried out and the results are compared with experimental results. 3.1. Geometry and discretization The geometry of the modelled anchorage structure is shown in Figure 2a. A concrete slab with a width of b = c + 400 mm (c = concrete cover), a length of 800 mm and a height of 380 mm is analysed. The material properties are adapted to the properties known from the experiments and are summarized in Table 1. Figure 2 also shows the finite element mesh used in the analysis. The existing symmetry plane was used to reduce the analysis time. The mesh was refined within the area of the headed stud. The modelled test specimen is restrained in vertical direction at a distance of 85 mm from the anchor (Fig. 2b). The numerical analysis considers the same boundary conditions as in the experiment (Furche, Eligehausen 1991). The discretization of the concrete slab was per-formed by eight - node solid elements. The microplane model was used. Linear elastic material behavior was assumed for steel elements. 400 mm
400 mm 400 mm
restraint
load
380 mm
400 mm
85 mm
stud
c head Headed stud d = 25 mm a)
b)
Figure 2. Dimensions of the FE – model.
680
Between the steel elements of the headed stud and the concrete elements contact elements were placed. These elements have a thickness of 0.5 mm. They where modelled that only compressive stresses between concrete and anchor could be taken up. The load was applied by displacement control at the nodes of the headed stud. The displacement was in-creased by 0.05 mm in each step. concret Gf
fctm
EBeton
geometry βw
hef
a
γ
steel c
EStahl
fy
[Mpa] [Mpa] [Mpa] [Mpa] [mm] [mm] [°] [mm] [Mpa] [Mpa] 0,075
2,5
35000
35
400
7,5
90
60
20000
2000
Table 1 : Material properties assumed in the analysis.
3.2. Numerical results and comparison with test results In both the experimental and the numerical investigations a characteristic blow out failure could be observed. The damage zone obtained in the analysis is shown in Figure 3 as maximum principal strains. The dark areas are the areas of strain localization (damage). The comparison shows a good agreement between the failure mode observed in the experiments and the analysis.
c = 60 mm load N
c = 80 mm
c = 60 mm
c = 40 mm
c = 40 mm
c = 80 mm
Figure 3. Post peak crack pattern, hef = 400 mm (embedment depth), c = 60 mm (edge distance), a = 7,5 mm (head shoulder). Experiment made by Furche, Eligehausen, 1991.
The displacements and the anchor forces were taken at the head of the stud. At maximum load the displacement measured in the experiment is slightly larger than in the
681
load N [N]
load N [N]
simulation. This is due to the complex conditions when local damage at the head of the stud takes place. Figure 4 shows a comparison between the ultimate loads measured in the experiments and obtained from the analysis. In all cases failure was caused by blow-out. The numerical results show a good agreement with the experimental results
displacement [mm]
edge distance [mm]
displacement of concrete surface s [mm]
Figure 4. Influence of edge distance on failure load. Experimental results taken from Furche, Eligehausen, 1991. numerical simulation
N
test
s
force at head [N]
Figure 5. Displacement of concrete surface close to the head perpendicular to the surface. Test results are taken from Furche, Eligehausen, 1991.
In Figure 5 the lateral deformation of the concrete surface close to the head of the stud is plotted as a function of applied load. The numerical result agrees sufficiently well with
682
the experimental results. The lateral displacements increase fast after the maximum load is reached, indicating the failure of the concrete close to the head.
4. Comparison between experimental and numerical results in case of edge failure 4.1. Geometry and discretization The geometry of the modeled structure is shown in Figure 6. A concrete slab with a height of 420 mm, a length of 740 mm and a width of c +270 mm (c = concrete cover) was modeled by eight node solid elements. Between the steel elements of the headed stud and the concrete elements a contact layer with a thickness of 0.5 mm was placed. The material properties were adapted to the material properties obtained from the experimental investigations of Wüstholz (1999). The head stud was loaded in shear towards the edge. The supports were selected (Fig. 6) as in the experiment with a distance of four times the edge distance. In the analysis the available symmetry was used.
370 mm c + 270 mm
Restraint 270 mm
Restraint
c
Shear load
Headed stud Restraint 2·c
Figure 6. Geometry and finite element mesh of the test specimen loaded in shear towards the edge.
683
4.2. Numerical simulations of shear load with not restraint anchors A typical shear failure mode occurred in the numerical analysis as well as in the experiment. It is shown in Figures 7 and 8. The crack pattern obtained in the analysis shows a good agreement with the crack pattern observed in the test. The influence of the edge distance on the failure load is shown in Figure 9. For edge distances of 60 mm and 100 mm a good agreement of the calculated maximum loads with the experimental data was reached. For an edge distance of 160 mm a local failure in front of the anchor occurred in the FE – simulation, which was not observed in the tests. load Q
load Q
failure coin
failure coin
load Q test test
analysis
Figure 7. Post peak crack pattern (hef = 130 mm, c = 100 mm, shear load).
Failure coin
Local failure in front of the anchor Figure 8. Influence of the edge distance on the failure load.
684
4.3. Influence of a restraint moment to the failure load In the numerical simulations of the shear tests different load displacement behaviours occurred. This is probably caused by different boundary conditions. In the finite element model the real restraining at the loading point must be simplified in the following some calculations are analysed to show the influence of an end moment at the loading point. Test specimen In the experimental tests the anchor bolts were loaded towards the edge. Therefore a steel plate is fixed with a washer and a screw nut. Normally there is a clearance between anchor shaft and the hole of the steel plate. The anchor is able to rotate at small displacements because of this clearance (Figure 9b) when increasing the displacement the anchor is not able to rotate anymore and an end moment develops at the fixing point (Fig. 9c). So the clearance between the shaft and the hole of the base plate has probably an influence on the failure load. With a large clearance a bending force will be activated at higher loads than with a small clearance. The bending moment probably will influence the failure load. anchor
s = 0 mm
s
s steel plate
loading point
a)
b)
c)
Figure 9. Fixed end moments caused by steel plate a) non deformed b) small deformation c) large deformation
Finite Element Simulation specimen The experimental test specimens are simplified for the finite element simulation. There are two possibilities to model the loaded point. The first possibility is to restrain the nodes at the anchor shaft (Fig 11a). In this way an end moment occurs while increasing the displacement of the anchor. This is a realistic boundary condition for anchors with large deformations at ultimate load or for headed anchors welded to a steel plate. The second possibility is not to restrain the nodes of the anchor shaft (Fig 11b). So no end moment occurs at the loading point. With the first possibility the ultimate load is probably overestimated but seems to be more realistic because normally the clearance between the anchor shaft and the hole of the base plate is very small and the displacements of shear-loaded anchors at ultimate load are large.
685
To show the influence of a restraint of the anchor on the behaviour under shear loading anchors with a diameter of 16 mm and an embedment depth of 130 mm are calculated.
c = 160 mm
c = 70 mm
Figure 10. Calculated shear load – shear displacement curves and tension force in the anchor (d = 16 mm, hef = 130 mm an) with an edge distance of a) c = 70 mm b) c =160 mm
Fastening with an edge distance of 70 mm and 160 mm are analysed. Figure 10a and 10b shows the calculated shear load shear displacement curves for a restraint anchor bolt and a not restraint anchor bolt. The ultimate load is about 1.6 to 2.0 times higher if the nodes are fixed at the loading point. Not only a bending moment at the loading point occurs but also always a compression force is inducted. For an edge distance of 70 mm the calculated ultimate load is about 20 kN (without restraining) and about 38 kN (with restraining). The average test load was about 26 kN. For an edge distance of 160 mm the calculated failure load is about 45 kN (without restraining) and about 75 kN (with restraining). The average test load in case of concrete coin failure is 74 kN (63 kN for concrete with fcc = 30 MPa). With an edge distance of 160 mm and a restraint at the fixing point the results of the finite element calculation are in good agreement with the test results. For an edge distance of 70 mm the test results are between the calculated results for a restraint and a not restraint anchor. This means that the effect of restraint is smaller for an edge distance of 70 mm at ultimate load. The anchorage with an edge distance of 70 mm failed at low displacements due to concrete cone failure. Therefore probably only a small bending moment developed. The anchorage with an edge distance of 160 mm failed at large displacements by a local failure in front of the anchor first and followed by concrete cone failure at high displacements. Due to the displacements a larger moment could develop.
686
The differences of shear load reaction between anchors restraint and not restraint at the fixing point are calculated and simplified in Fig. 11a/b. The shear load reaction at the same displacement is about 1.7 higher if the anchor is restraint at the fixing point. This factor could be observed in the finite element calculations. For an edge distance of 70 mm in the test a small bending moment occurred at failure. In this case the displacement was small and nearly no pressure could be introduced in front of the anchor (Fig. 11c). For an edge distance of 160 mm the displacement at failure was large and there was the possibility to introduce a pressure force in front of the anchor (Fig. 11d). s
s
s
a) Model restraint
b) not restraint
c) small edge distance
s
d) large edge distance
Figure 11. Model to describe the influence of bending and failure mechanism on the calculated ultimate loads
4.4. Comparison with test results The comparison of the results of the numerical simulations with test data is shown in Fig. 12a. While the comparison is acceptable for a small edge distance, the calculated failure load is much to small if the anchor was not restraint in the simulation. This is due to local concrete cracking in front of the anchor wich could be observed in the simulation (Fib 12b). If the anchor is not restraint at the fixing point concrete edge failure occurred (Fig 12c) and the calculated Failure load agrees reasonably well with the test results (Fig 12a).
687
c)
b)
Q
a)
Q
Without restraint moment With restraint moment at the loading point at the loading point • local failure in front of • edge failure the anchor
Figure 12. Comparison between a simulation with/without restraint moment at the loading point and test data
5. Conclusion The comparison between the results of the numerical simulations and experimental tests shows that the FE – code MASA is able to simulate the failure mechanism of headed stud anchorages placed close to edge under tensile loading as well as under shear loading. Under shear loading the calculations show that there is an influence on the anchor behavior caused by different boundary conditions of the fixing point. If the anchor is not restraint for large edge distances the ultimate load is to low and the failure load is caused by local failure in front of the anchor. Restraining the anchor the ultimate load increases and failure is caused by edge failure and splitting in front of the anchor. For this case the ultimate load is slightly overestimated. For small edge distances the results of the calculations with no restraint are close to the results of the experimental test.
6. Literature 1. 2. 3. 4.
Ožbolt, J.; Li, Y.-J. and Kožar, I. (2001). Microplane model for concrete with relaxed kinematic constraint. International Journal of Solids and Structures. Fuchs, W.; Eligehausen, R and Breen, J.E. (1995). Concrete Capacity Design (CCD) Approach for Fastenings to Concrete. ACI Structural Journal, Vol. 92, No. 6, S794-802 Furche J.; Eligehausen, R. (1991). Lateral Blouout Failure of headed Studs Near the Free Edge. In:Senkiw,G.A. ; Lancelot, H.B., SP-130 Design an Behavior . American Concrete Institute, Detroit, page 235 – 252. Wüstholz, T (1999). Tragverhalten von randnahen Befestigungsmitteln unter Querlasten bei der Versagensart Betonausbruch. Diploma theses at the Institute of construction material, University Stuttgart
688
EVALUATION OF A BRIDGE DECK STRENGTHENING WITH SHEAR CONNECTORS: FINITE ELEMENT ANALYSIS AND EXPERIMENTAL RESULTS Antônio J. Leite Salvador, Brazil
Abstract A 10 m wide and 120 m long bridge, with three simple supported 40 m spans, showed excessive vibrations under traffic. The structural system consisted of four unshored, 2.00 m depth, steel main girders, 2.50m center spaced, supporting a reinforced concrete slab 0.26m thick. To assess its dynamic performance under vehicle loads a finite element analysis and local strain measurements were carried out. It was concluded that the girders would be overstressed for the required design load combination and the deck flexibility should be properly strengthened to overcome the excessive vibrations. In order to obtain a composite action to increase the girder inertia, ∅38 mm holes were drilled from the top of the concrete slab, through its thickness, just outside both edges of the top main girders’ flanges. Shear connectors welded to squared plates were positioned within the slab holes from underneath and fixed to the concrete slab with an epoxy compound before the plates were welded to the flanges. To increase the natural frequency a complementary reinforced slab with average thickness of 150 mm was added to the top flange. The finite element analysis of the strengthened deck under the load combinations and the strain measurements on the shear connectors and on critical sections of the composite girder under loading tests showed a satisfactory behavior.
1. Introduction A 10 m wide and 120 m long bridge, with three simple supported 40 m spans (see photo in Fig. 01), showed excessive vibrations under traffic. To assess its dynamic
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performance under vehicle loads a finite element analysis and local strain measurements were carried out. It was concluded that the girders would be overstressed under the required design load combination and the deck flexibility should be properly strengthened to overcome the excessive vibrations. In order to obtain a composite action to increase the inertia of the girders, shear connectors welded to squared plates were positioned from underneath, within slab holes previously drilled, and fixed to the concrete slab with an epoxy compound. The plates were butt-welded on the top flanges from below the bridge deck. To increase the natural frequency a complementary reinforced slab with average thickness of 150 mm was added to the top flange, as the foundations and columns allowed the extra dead load. Cover plates designed to control the stress levels on the lower flange of the strengthened composite girders made them compatible with the required load combination. The finite element analysis of the strengthened deck under the load combinations and the strain measurements on the shear connectors and on the composite girder critical sections during the tests showed a satisfactory behavior. The maximum girder bottom flange strain measured was 48% proportionally to the earlier data; if we consider the four girder actual strain data summation it reaches 62%. The measured natural frequency after the pavement completion was 2.4 Hz and it is now fairly comfortable standing on the bridge deck during a loaded truck passage or under normal traffic.
Fig.1 - General view of the bridge over Buranhém River.
2. Finite element analysis The structural system consisted of four unshored, 2.00m depth, steel main girders (weathering steel; fyk= 345 MPa), 2.50 m spaced, supporting a reinforced 260 mm thick
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(fck= 20 MPa) overhanging 1.25 m the edge girders. The 210 mm structural slab was cast over a set of stay-in-place 50 mm thick precast concrete deck panels. The bridge was designed for two lanes of traffic and two extra lanes for disabled vehicles. The bridge girder-slab system was modeled using a finite elements program (1) where the loads and member properties were considered as the followings: a. Load Case 1 – girders and the 260 mm slab dead load resisted by the girders alone; b. Load Case 2 and 2A – railing dead load (LC2) and a 250 kN dump truck load (LC2A) resisted by the girder-slab composite sections; c. Load Case 3 – complementary slab dead load (150 mm average thickness) resisted by the girder-slab composite sections strengthen with bottom flange cover plates; d. Load Cases 4, 5, 6 and 6A – pavement dead load of 2.0 kN/m2 (LC4); highway live lane load of 5.0 kN/m2 (LC5); 450 kN standard truck live load (LC6) and; a 323 kN dump truck load (LC6A) resisted by the final strengthen girder-slab composite sections. A schematic of the girder and transformed mid-span cross sections for each Load Case is shown in Fig. 02 with geometric properties and maximum bottom flange strain.
Fig.2 – Load Cases’ girder geometric properties, moment and mid-span cross section bottom flange strain from finite element solution. The finite element analysis LC1 showed a tensile stress on the bottom flange of 128 MPa (37% of the fyk) due to dead load on the girder’s bottom flange mid-span critical section and a natural frequency of 0.6 Hz. Further investigations showed that the girders would be overstressed under the required design load combination and it was
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concluded the deck flexibility should be properly strengthened to overcome the excessive vibrations. The strengthening sequence started with the installation of shear connectors between the existing slab and the girders as in the LC2 section the next step was the cover plate welding on the bottom flanges as in the LC3 section and at last the cast of the complementary slab, ranged from 70 mm at the column supports to 190 mm at mid-span, added to the previous 210 mm structural slab.
3. Shear connectors How to install shear connectors after slab casting? That was the main question. The answer may show an easy way to strengthen other existing structures, taking advantage of the composite action. The difficulties of drilling holes from the top of the slab and to weld the connectors on the main girders top flange can be overcome if holes are drilled just outside both edges of the flanges. Shear connectors welded to squared plates positioned within the slab holes from underneath can be fixed to the slab with an epoxy compound after the plates are butt-welded to the flanges. The connection detail used is showed on Fig. 3; for each one of the 12 main girders (4 girders times 3 spans) 2 times 66 connectors spaced 0.60 m were installed on the top flange sides (2).
Fig.3 – Shear connection detail; connectors placed outside the girder flange.
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4. Strain measurements The field test data were recorded on a portable digital data acquisition system. Strain gages were placed on the critical sections of the main girder flanges, along the web height, on stiffeners and on connectors. The data were recorded before and after the strengthening of the bridge. The mid-span section gages were placed permanently in order to monitor and to limit the truck loads as the system is capable of triggering a camera every time the specified limit is exceeded. The comparison of the measured behavior and the load control possibilities will be mentioned next. After casting the 210 mm structural slab over the stay-in-place 50 mm thick precast concrete deck panels and after casting the railings, a test was performed with a 250 kN dump truck load at a speed of 10 km/h over the girders G1, G2, G3 and G4 consecutively. The bottom G1 to G4 flange gages at mid-span cross section showed the strain response presented in Fig. 4 when the truck was over G1.
Fig. 4 – Girder G1 to G4 bottom flange strain; 250 kN truck forward and backward. The Table 1 shows the measured bottom flange girder strains when the 250 kN truck is over each girder. Note that the summation of the 4 girders strains [εM (Total) column] due to truck load over each girder is approximately equal, ± 5% off the average, as the girders have the same inertia and the total flexural moment on the span has to be the same for the same load. The girder strains due to the finite element flexural moment for the same load are also presented in the table for comparison. The railings inertia not considered in the model lead to higher analytical than measured strain.
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Table 1: (LC2A) Measured/Analytical strains (εM and εA x10-6); Load over G1 to G4.
Load εM εM εM εM εM εA εA εA εA εA over (G1) (G2) (G3) (G4) (Total) (G1) (G2) (G3) (G4) (Total)
G1 G2 G3 G4
120 80 40 20
80 75 60 55
60 65 80 90
25 40 90 125
285 260 270 290
185 110 40 25
105 95 75 45
45 70 95 105
25 40 110 185
360 320 320 360
Another field test was performed with two 323 kN and 292 kN dump truck load after bridge strengthen completion. Fig. 5 presents the bottom strain response at mid-span G1 and G4 cross section when the 323 kN truck was over G1/G2 traffic lane.
Fig. 5 - Girder G1 and G4 bottom flange strain; 323 kN truck. Table 2 shows the measured strains when the truck is over each girder. The finite element flexural moment strains under the same load are also presented in the table. When we compare the strain average before and after bridge strengthen, see Tables 1 and 2, accounting linearly for the dump truck 250 kN and 323 kN load difference, we obtain a 62% strain decrease or an actual/original inertia equivalent ratio equal to 1.6. Adding the 323 kN and the 292 kN load truck bottom flange strain for comparison we obtain 215 and 190 x10-6 respectively, an error less than 3%. The normal traffic truck loads can be monitored accordingly with satisfactory accuracy. A research program has been proposed to the Highway State Department to monitor this bridge in order to control the average daily truck traffic and other parameters to obtain a relationship between vehicle weight and fatigue life (3). Table 2: (LC6A) Measured/Analytical strains (εM / εA x10-6); Load over G1/2 and G3/4.
Load over G1/G2 G3/G4
εM εM εM εM εA εA εA εA εA εM (G1) (G2) (G3) (G4) (Total) (G1) (G2) (G3) (G4) (Total) 75 40
55 60
50 60
35 70
215 230
694
90 10
65 40
40 65
10 90
205 205
The measured strain at G1 mid-section bottom flange and web gages [εx10-6 = 75 (bottom flange: y = 0); 50 (web: y = 695 mm) and; 15 (web: y = 1600 mm)] established the neutral axis at about the top flange indicating satisfactory composite action. The squared 25 x 25 mm and 250 mm long connectors above the top flange surface plane have 200 mm grouted inside the structural slab. Strain gages were installed on four near support connectors at the stay-in-place 50 mm thick precast concrete deck panels mid height. Fig. 6 presents the measured flexural strains on both connector faces due to two consecutive 323 and 292 kN dump truck. That might not tell us much about the quantitative ultimate shear capacity but it is a good qualitative data regarding the girderslab composite behavior.
Fig. 6 – Front and back side near support connector flexural strains for two consecutive 323 and 292 kN dump truck.
5. Dynamic behavior The original bridge finite element solution showed a 0.6 Hz natural frequency. Its value increased to 0.9 Hz for the strengthen bridge finite element solution. Unfortunately we were not able to record dynamic data for the original bridge as the roadway was not ready for traffic, just allowing low speed or static load test. After completion of the bridge strengthening, strain gage data were recorded for normal speed truck load. Fig. 7 presents the girder G1 strain data under the 323 kN truck load at
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70 km/h speed. When we count the vibration cycles in a time interval we obtain the bridge measured natural frequency which is 2.4 Hz. The massive concrete railings are not modeled like structural components and they are just considered as dead load. However as they are monolithic with the slab deck, there is a greater increase in its overall inertia and stiffness then in its mass, leading to an increase in the natural frequency as measured.
Fig. 7 Girder G1 bottom flange strain; 323 kN truck at 70 km/h.
6. Conclusions Connectors can be used to strengthen existing non-composite structures. Holes can be drilled outside the girder flange edges and shear connectors welded to squared plates positioned within slab holes from underneath can be fixed to the slab with an epoxy compound after the plates are butt-welded to the flanges. The strengthened bridge deck had a measured equivalent average inertia 60% increase. The finite element structural model analysis gives very precise results and they are used to establish the structural component ultimate capacity. However the measured strains reflect the real structure and in this particular case the railings and pavement mass and inertia not included in the model, since they are only considered as dead load, lead to lower measured strains than analytical ones. The actual portable digital data acquisition system available made the field test data recording an easy task. The bridge mid-span girder section gages were placed
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permanently in order to monitor and to limit the highway truck loads. The monitoring of all girder data in one span is essential to establish the total flexural moment. The sampled and saved data files controlled by an on-board acquisition system can be remotely downloaded and is capable of triggering a camera or a video recording device every time some specified limit is exceeded. The stress range is one of the designer’s major concern in the fatigue behavior of structures, along with the initial flaw size and the material fracture toughness: the initial flaw size is a parameter dependent upon fabrication procedures, workmanship, etc. and it is quantified through the level of reliability of the nondestructive inspection method used; the fracture toughness is established with the materials choice and; the stress range and the number of cycles can be monitored. The highway load control through the bridge strain monitoring will permit the recording of a valuable amount of data and to establish very important parameters as: average daily truck traffic, vehicle weight frequency distribution, load and strain relationship at a particular location on the structure.
7. References 1.
2.
3.
Computer and Structures Inc., SAP2000Plus program Version 7.1, 1999, “Three Dimensional Static and Dynamic Finite Element Analysis and Design of Structures”. Leite, Antônio J., ‘Strain monitoring and strengthen design of the bridge over the Buranhém River’, March 2000. Technical Report No. E60A/0300,
[email protected]. Fisher, J. W., “Bridge Fatigue Guide – Design and Details, ”American Institute of Steel Construction (AISC), New York, 1977.
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NUMERICAL ANALYSIS OF GROUP EFFECT IN BONDED ANCHORS WITH DIFFERENT BOND STRENGTHS Y.-J. Li and R. Eligehausen Institute for Construction Materials, University of Stuttgart, Germany
Abstract In recent years the failure behavior of group anchors has been investigated and the group effect for quadruple fastenings with bonded anchors has been clarified. However the performed work is available only for an average bond strength within 8 MPa to 12 MPa. No doubt, with the variation of the bond strength the group effect for bonded anchors should be influenced. In this paper the influence of the bond strength on the failure mode and the group effect is investigated. The investigation is carried out by performing a series of numerical analysis of single and quadruple fastenings with bonded anchors. In the calculation the concrete and the bond material are simulated by the improved microplane model, which is implemented in the 3D nonlinear finite element program MASA. Investigated are groups with bonded anchors (d =16 mm, hef = 96 mm) with a spacing s = 48 mm to s = 288 mm. Varied is the average bond strength (6.2, 11.1, and 22.5 MPa). From the results of the numerical study the influence of bond strength on the failure modes of groups with bonded anchors is revealed and the group effect as a function of the bond strength is clarified.
1. Introduction The bond strength plays an important role for both single and group fastenings with bonded anchors. During the last 20 years several research works on bonded anchors have been published (Eligehausen, Mallee & Rehm, 1984, 1997; Eligehausen, Lehr, Meszaros & Fuchs, 1999; Cook, Doerr & Klingner, 1993; Cook, Kunz, Fuchs & Konz, 1998) and design recommendations have been proposed both for single anchors (Eligehausen, Mallee & Rehm, 1984; Eligehausen, Lehr, Meszaros & Fuchs, 1999; Cook, Kunz, Fuchs & Konz, 1998) and for group anchors (Eligehausen, Mallee & Rehm, 1984; Eligehausen, Lehr, Meszaros & Fuchs, 1999). However a general design recommendation for groups with bonded anchors is still a challenge topic. In recent years a series of research work in this field has been performed at the University of Stuttgart. The failure behavior of group
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bonded anchors has been investigated both experimentally and numerically. The group effect for quadruple fastenings with bonded anchors has been clarified (Lehr and Eligehausen, 1998; Li, Ozbolt, Eligehausen & Lehr, 1999). However the research work is valid only for a bond strength of about 8 MPa to 12 MPa. These bond strength values are valid for most of bond materials currently available on the market. No doubt, with the variation of the bond strength the group effect of bonded anchors should be influenced. This means that with a higher or lower bond strength the load carrying capacity as well as the failure mode should be different from those of normal bond strength. The purpose of this work is to study how the group effect of bonded anchors is influenced by the variation of the bond strength. The investigation is carried out by performing a series of numerical analysis of quadruple fastenings with bonded anchors, in which the average bond strength of single anchors τu (τu = Nu /(π d hef ), Nu is the peak load of single bonded anchor) varies from 6.2 MPa to 22.5 MPa. The 3D nonlinear finite element program MASA is used for the calculation (Ozbolt, 1998), in which the newly developed microplane material model for concrete with relaxed kinematic constraint (Ozbolt, Li & Kozar, 2000) is implemented. The studied specimens are bonded anchors of the injection type based on resin mortar anchored in a concrete block and subjected to tensile loading. Both single and group bonded anchors are considered for the calculation. The concrete block and bond material are simulated by the improved microplane model and the steel bar is considered as a linear elastic material. The attention of the research is focused on the influence of bond strength on the failure mode of anchor groups and the group effect. Based on the numerical results the group effect as a function of bond strengths is clarified.
hef
S
d
S S
Fig. 1 Geometry of quadruple fastenings with bonded anchors
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2. Numerical analysis The analyzed specimen is schematically shown in Figure 1, in which d is the anchor diameter (d = 16 mm), hef is the embedment depth (hef = 96 mm) and s is the spacing between anchors. A typical finite element mesh with load and boundary conditions is shown in Figure 2. Due to symmetry, only a quarter of the specimen is simulated. The simulated system includes the steel anchors, the adhesive mortar and the concrete block. The steel anchor is assumed as a linear elastic material with Young's modulus E = 210000 N/mm2 and Poisson's ratio ν = 0.3. The concrete is modeled by the improved microplane model with relaxed kinematic constraint and the material parameters are taken as Young's modulus E = 30000 N/mm2, Poisson's ratio ν = 0.18, tension strength ft = 2.4 N/mm2, compression strength fc = 30 N/mm2 and fracture energy Gf = 0.1 N/mm. The compressive fracture energy is taken as 200 times the tensile fracture energy. The bond material is simulated by the normal microplane model with a special attention on the shear strength as τu = 6.2 MPa, τu = 11.1 MPa and τu = 22.5 MPa, respectively. In order to avoid concrete cone failure the value of high shear strength τu (22.5 MPa) is calibrated by the specimen of a confined single anchor with embedment depth hef = 100 mm, which corresponds to the dimension of the specimen used for the investigation of lateral load influence on the bond strength (Meszaros and Eligehausen, 1998). The load is applied at the top end of the steel anchor. Displacement control is used in order to get the post peak load-displacement curve. A fixed boundary condition, corresponding to the support lines in experiments, is applied on the non-symmetry edges at the loaded side of the specimen (see Figure 2).
Fig. 2 Finite element mode with boundary conditions Totally 21 cases were calculated, which include 18 anchor groups and 3 single anchors. The calculation is divided into 3 groups with 3 different bond strengths, namely high bond strength with τu = 22.5 MPa, average bond strength with τu = 11.1 MPa and low bond strength with τu = 6.2 MPa, respectively. 7 calculations were performed for each
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group, in which 6 cases are for group anchors and 1 case for single anchor. The analyzed specimens are listed in Table 1 and the calculated failure loads and failure modes are presented in the same table as well. In a preliminary study a shear failure in the concrete near the bond layer was observed in the case of a mortar with high bond strength. This seems not realistic comparing to the experimental observations for average bond strength (Lehr and Eligehausen, 1998), in which a concrete cone failure was observed for the bonded anchor specimens with shorter embedment depth. In order to avoid this shear failure the width of the elements used to simulate the bond layer is extended from 2 mm to 6 mm. The dimension of the elements near the bond layer remain constant for all of calculations. The spacing between anchors varies from 48 mm to 288 mm but the anchor diameter d and the embedment depth hef remain constant for all calculations as d = 16 mm and hef = 96 mm. The concrete material properties in all calculations are kept constant only the bond strength was varied as given above. The dimension of the simulated concrete block is 400 mm times 400 mm wide with a depth of hef + 188 mm, which has been shown enough to simulate a non-confinement pullout test (Li, Ozbolt, Eligehausen & Lehr, 1999). Table 1 Numerical results of single and group anchors with different bond strength value Spacing Bond Strength τu [MPa] s 6.2 11.1 22.5 [mm] Fu [kN] 1) FM 1) Fu [kN] 1) FM 1) Fu [kN] 1) FM 1) 2) 29.96 PO 53.78 PO 65.72 CC 0 48 20.95 CCB 25.18 CC 23.79 CC 96 24.74 FPO 31.34 CC 31.47 CC 144 28.46 PO 40.30 FPO 42.41 CC 192 28.94 PO 46.68 PO 51.95 CC 240 29.19 PO 48.01 PO 58.24 CC 288 30.05 PO 50.31 PO 59.05 CC Note: 1) Fu: Failure load; FM: Failure mode ; 2) s = 0: single anchors The load-displacement curves at the loaded side of the anchor were calculated in the analysis and the failure modes were investigated as well. In the calculations four different failure modes of anchor groups were observed namely concrete cone failure (CC), pullout failure (PO), false pullout failure (FPO) and the combination failure of concrete cone and pullout failure (CCB). The detailed description of the failure mechanism of the 4 failure modes can be found in (Li, Ozbolt, Eligehausen & Lehr, 1999). For single anchors two failure modes were observed i.e. pullout failure and concrete cone failure, which are shown in Figure 3. The pullout failure was observed in the cases with average and low bond strengths and the concrete cone failure was observed in the case with a high bond strength. This means that when the bond strength is relatively low the failure is caused by a bond failure, but when the bond strength is high the failure is caused by a concrete cone breakout. The reason of the concrete cone breakout is mainly because the resistance of the bond material is stronger than the
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resistance of the concrete cone. In fact this kind of failure occurs normally in pullout tests with headed anchor. As we know that the CC-method (Fuchs, Eligehausen & Breen, 1995) has been developed for evaluating the load capacity of headed anchors. This means that the load capacity of bonded anchors with a high bond strength could be evaluated by the CC-method. a)
b)
Fig. 3 Failure modes of single anchors: a) pullout failure with low bond strength (τu = 6.2 MPa); b) concrete cone failure with high bond strength (τu = 22.5 MPa)
s = 48 mm (τu = 6.2 MPa)
s = 144 mm (τu = 6.2 MPa)
s = 288 mm (τu = 6.2 MPa)
s = 48 mm (τu = 11.1 MPa) s = 144 mm (τu = 11.1 MPa) s = 288 mm (τu = 11.1 MPa)
s = 48 mm (τu = 22.5 MPa) s = 144 mm (τu = 22.5 MPa) s = 288 mm (τu = 22.5 MPa) (a) Failure modes of anchor groups with different bond strengths
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τu = 22.5 [MPa]
70
single anchor
30
s = 288 mm
60
s = 240 mm s = 196 mm s = 144 mm
50
s = 96 mm
Load [kN]
Load [kN]
s = 48 mm
40 30
20
τu
= 6.2 [MPa] single anchor s = 288 mm
10
20
s = 240 mm s = 196 mm s = 144 mm
10
s = 96 mm s = 48 mm
0
0
0.0
0.5
1.0
1.5 2.0 Displacement [mm]
2.5
3.0
0.0
0.5
1.0
1.5 2.0 Displacement [mm]
2.5
3.0
(b) Load-displacement curves (plotted is the load of one anchor) Fig. 4 Numerical results of anchor groups with different bond strengths The calculated failure modes for anchor groups show a strong influence by the bond strength. The selected failure modes for three bond strengths with typical spacings (s = 48 mm, s = 144 mm and s = 288 mm) are shown in Figure 4a and the load-displacement curves for all calculated spacings with high and low bond strengths are shown in Figure 4b. From Figure 4a we can see that for high bond strength (τu = 22.5 MPa) the failure modes in all spacings are concrete cone failure. But for average and low bond strengths (τu = 11.1 MPa and τu = 6.2 MPa) the failure modes vary from concrete cone failure to bond failure with increasing spacing. This indicates that for high bond strength the failure mode is dominated by concrete cone breakout, while for a relatively low bond strength the failure mode varies from concrete cone failure to bond failure with increasing spacing. From the tendency of the calculated failure modes we can image that when the bond strength is very low only bond failure might occur for groups with bonded anchors. 3.
Influence of bond strength on the group effect
For anchor groups with a spacing smaller than a critical value it is found that the failure load is reduced with decreasing spacing, which is called group effect. The critical value is called characteristic spacing scr. In our previous study the group effect in the case of an average bond strength has been investigated and a model for evaluating the load capacity has been proposed (Li, Ozbolt, Eligehausen & Lehr, 1999). In this work the bond strength has been extended to both higher and lower bond strength values to investigate if the group effect will be influenced by the value of bond strength. Figure 4 and Table 1 show that although the failure behaviors of three groups with different bond strengths are not identical the group effect exists in all three groups. For the group with high bond
704
Fu / Fu
s
strength (τu = 22.5 MPa) the calculated failure modes in all investigated cases (single anchor and groups with s ≤ 3hef) are concrete cone failure, which is caused by concrete breakout, starting at the end of the anchor rod with a common concrete cone failure for s ≤ 2hef . The failure mode and the load-displacement behavior of one anchor of the group with s = 3hef is almost identical to the behavior of a single anchor. Because of the concrete cone failure the average bond stress at peak load of the single anchor τu is only 13.6 MPa, much smaller than the bond strength value τu = 22.5 MPa, which was identified by a confined pullout test with bond failure. The group effect is caused by an overlapping of tensile stresses in the concrete of neighboring anchors. When the spacing is small the peak load taken by one anchor of the group increases with increasing spacing. The group effect vanishes at a spacing s ~ 2.5 hef to 3.0 hef . In the groups with average and low bond strengths (τu = 11.1 MPa and τu = 6.2 MPa) the calculated failure modes were shown not only as a CC failure but also as CCB, FPO and PO failure (see Figure 4 and Table 1). The concrete cone failure was obtained in the cases with s = 48 mm and s = 96 mm for average bond strength and in the case with s = 48 mm for low bond strength. The FPO failure was observed in the case with s = 144 mm for average bond strength and in the case with s = 96 mm for low bond strength. For other spacings in both groups pullout failure was observed. The reason of group effect for these two groups is caused not only by the overlapping of concrete cone ( for CC and CCB failure) but also by the reduced shear resistance of bond material due to the damage at bottom of group anchors and tensile stress between anchors (for FPO and PO failure), as described in (Li, Eligehausen, Lehr & Ozbolt, 2001).
F su : failure load of single anchor
g
4 x Fu (single)
4.0
Fg u : failure load of group anchors
3.0
u
F (group) / F (single)
4
s 4 X Fu
2.0
u
No group effect zone bond strength 6.2 MPa
Strong group effect zone
bond strength 11.1 MPa
1.0
1
bond strength 22.5 MPa
0.0 0
50
100
150 s [mm]
200
250
300
Fig. 5 Numerical results of group bonded anchors with different bond strengths
Scr[W]
Scr[M]
Scr[H]
S
Fig. 6 Group effect of bonded anchors with different bond strengths
In order to evaluate the influence of bond strength on the group effect the numerical results in all three groups are presented in Figure 5. Plotted are the ratios between the calculated failure loads of the groups and the calculated failure load of a single anchor as a function of the anchor spacing. From this figure one can see that the bond strength has
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a significant influence on the group effect of bonded anchor groups. With increasing bond strength the characteristic spacing scr increases. From the calculated results the characteristic spacing could be abstracted as scr ~ 150 mm for a low bond strength (τu = 6.2 MPa), scr ~ 200 mm for an average bond strength (τu = 11.1 MPa) and scr ~ 290 mm (s ~ 3 hef ) for a high bond strength (τu = 22.5 MPa ). This indicates that for a high bond strength the group effect exists until the spacing is larger than 290 mm, but for a low bond strength the group effect vanishes for a spacing s ~ 150 mm. The influence of the bond strength on the group effect is schematically plotted in Figure 6.
4. Conclusions In this paper the influence of bond strength on the failure mode and the failure load is investigated numerically for single and quadruple fastenings with bonded anchors (d =16 mm, hef = 96 mm = 6d). The numerical results show that the bond strength has a strong influence on the failure mode both for single anchors and for anchor groups. For single anchors, when the bond strength is low failure is caused by pullout failure. However when the bond strength is high rupture is caused by a concrete cone failure. For the investigated anchor groups, rupture is caused by the concrete cone failure for a high bond strength, but for an average and low bond strengths the failure mode varies from concrete cone failure to bond failure with increasing spacing. Furthermore, the group effect is influenced significantly by the bond strength. In the studied cases the characteristic spacing increases with increasing bond strength from scr ~ 150 mm (~9d ) for low bond strength τu = 6.2 MPa to scr ~ 290 mm (~3hef ) for high bond strength τu = 22.5 MPa.
5. Reference 1. Eligehausen, R., Mallee, R. and Rehm G. (1984) “Befestigungen mit Verbundankern.” Betonwerk + Fertigteil-Technik, Heft 10, 686-692; Heft 11, 781-785; Heft 12, 825829 2. Eligehausen, R., Mallee, R. and Rehm G. (1997) “Befestigungstechnik (Fastening technique).” Betonkalender 1997, Ernst & Sohn, Berlin 3. Eligehausen, R., Lehr, B., Meszaros, J. and Fuchs, W. (1999) “Behavior and design of anchorage with bonded anchors under tension load.” Proc. of Int. Conference on Anchorage & Grouting towards the new Century, 6-9 Oct. 1999, Guangzhou, China, Zhongshan University Publisher, pp 93-105 4. Cook, R. A., Doerr, G.T. and Klingner R.E. (1993) “Bond stress model for design of adhesive anchors.” ACI Structural Journal, 90 (5): 514-524 5. Cook, R. A., Kunz, J., Fuchs W. and Konz R. (1998) “Behavior and design of single adhesive anchors under tensile load in uncracked concrete.” ACI Structural Journal, 95(1): 9-26
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6. Lehr, B. and Eligehausen, R. (1998) “Centric tensile tests of quadruple fastenings with bonded anchors.” Internal research report, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, not published 7. Li, Y.-J., Ozbolt, J., Eligehausen, R. and Lehr, B. (1999) “3D numerical analysis of quadruple fastenings with bonded anchors.” CD-Rom Proc. of 13th ASCE Engineering Mechanics Division Conference, 13-16 Jun. 1999, Baltimore, USA. 8. Ozbolt, J. (1998) “MASA - Finite element program for nonlinear analysis of concrete and reinforced concrete structures.” Internal research report, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, not publish 9. Ozbolt, J., Li, Y.-J. and Kozar, I. (2000) “Microplane model for concrete with relaxed kinematic constraint.” International Journal of Solids and Structures, in press 10. Meszaros, J. and Eligehausen, R. (1998) “Ausziehversuche mit injektionsdübeln HIT-HY 150 bei gleichzeitiger Zweiaxialbelastung des Ankergrundes.” Internal research report, Institut für Werkstoffe im Bauwesen, Universität Stuttgart, not published 11. Fuchs, W., Eligehausen, R. and Breen J. B. (1995) “Concrete capacity design (CCD) approach for fastening to concrete.” ACI Structural Journal, 92(1): 73-94 12. Li, Y.-J., Eligehausen, R., Lehr, B. and Ozbolt, J. (2001) “Fracture analysis
of quadruple fastenings with bonded anchors.” Accepted on the 4th Int. Conference on Fracture Mechanics of Concrete Structures, May 28-June 2, 2001, Cachan - France
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SIMULATION OF FASTENING SYSTEMS UTILIZING CHEMICAL AND MECHANICAL ANCHORS Jürgen Nienstedt*, Richard Mattner*, Ute Nestler** and Chongmin Song* *Hilti AG, Corporate Research, Schaan, Principality of Liechtenstein **Hilti Inc., Technical Services Department, Tulsa, USA
Abstract Numerical simulation is becoming more commonly used also for applications in fastening technology. Especially the finite element method based numerical simulation has already been successfully applied in the product development process for several years. This was only possible by introducing a reliable material model suitable for every stress state into the finite element code. The simulation of complex fastening structures generally requires a three dimensional modelling. Typical examples of these applications are the anchoring close to an edge of the concrete base material and/or the application of a shear force on the structure. The understanding of the load transfer mechanisms and the loading state occurring in the base material caused by the influence of a nearby edge is an essential input also for the evaluation of design rules. The insight into the material behaviour serves as the basis which is required for the development of excellent products.
1. Introduction The simulation technique of the finite element method is becoming part of the daily business also in the field of fastening technology. The finite element method allows an insight into the material behaviour and its stressing state. The state at every location of the calculated structures can be considered. This detailed knowledge of the anchoring mechanism can be utilized during the product development process. Over the last years simulation has been proven to be a beneficial tool and an excellent supplement to the experiment [1, 2].
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The development of more sophisticated and robust material models for concrete considering general stress states like tensile, compressive and mixed stress states offers a widespread range of applications suitable for simulation possibilities. Anchoring applications close to an edge of the base material and/or subjected to shear loads are of special interest in the development process as well as for the evaluation of design rules. The different working principles of anchors have been investigated by simulation and verified by experiments. Two working principles – the bonding mechanism of chemical anchors and the frictional principle for expansion anchors – are shown in this paper. The representatives for the working principles chosen here are a threaded rod set in HIT HY 150 for the bonding mechanism and a Kwik Bolt II for the frictional principle. Both types of anchors are loaded by axial tensile loads as well as shear loads. Due to the different load transfer mechanisms from the anchor into the base material the influence of the edge distance differs significantly for both types of anchors. The comparison with experiments is shown as an example for the expansion anchor under shear loading.
2. Material modeling The simulation of anchoring systems close to the edge of concrete base material requires a realistic modelling of tensile stresses and the cracking process after reaching the tensile strength of the material. An essential part of the material description is the modelling of the fracturing that is generally caused by mode I fracture mechanics failure. Hence the fracture energy necessary to develop a crack must be modelled consistently. A widely distributed approach to describe the mode I cracking for brittle material and especially for concrete is the so-called smeared crack approach [3]. The rotating smeared crack concept is integrated here into an uni-axial stress-/strain environment. Figure 1 illustrates schematically the stress-strain behaviour under uni-axial loading conditions.
σ ε
Figure 1 Constitutive law for uni-axial loading conditions
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To consider the influence of multi-axiality of the stress states, hence the changed material behaviour resulting from that effect, an interaction between the stress state and the stress-strain relationship in the corresponding integration point has been introduced. This is especially necessary in the regions of load transfer into the base material. This constitutive model has been proven for several applications to be very robust and easy to handle for the development engineer in his/her daily business for several applications. Comparisons between simulated results and the corresponding experimental results show very good agreement within the scatter of the experiments.
3. Numerical simulation The working principles, the loading of the base material and the failure mechanism for anchors close to an edge are illustrated with two representative anchors: the Kwik Bolt II for expansion anchor fastenings and the HAS in HIT mortar for adhesive fastenings. As an example one of the loading conditions is compared with experimental results. 3.1 Expansion anchor The Kwik Bolt II is utilized as the representative example for an expansion anchor. Figure 2 shows this type of expansion anchor. During the setting process of the anchor the wedge with its three sleeves expands over the cone and thus transfers the force from the anchor into the depth of the borehole.
Figure 2
Expansion anchor
The finite element model of the anchor and the considered structure are shown in figure 3. The darker left side of the structure indicates the free edge. The working principle of friction requires a corresponding expansion force acting radial from the anchor axis onto the base material. The load transfer from the anchor to the base material is locally concentrated between wedge and concrete base material at least during the setting process.
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Figure 3
Finite element mesh of the Kwik Bolt II expansion anchor and the simulated structure
3.1.1 Axial pull-out loading The distribution of the maximum principal stresses in figure 4 clearly shows the locally concentrated load transfer in the depth of the borehole. The areas without any iso-lines indicate the domain of compressive stresses. The tensile iso-lines show a small influence of the free edge on the stress field in the base material.
Figure 4 Distribution of the maximum principle stresses The corresponding maximum principal strains are shown in figure 5. The figure especially well illustrates the crack initiation, which can be seen on the symmetry plane to the right of the anchor.
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Figure 5 Distribution of the maximum principle strains 3.1.2 Shear loading towards the edge The stress field of the maximum principal stresses in figure 6 shows the large compressive domain neighbouring the anchor in the direction of the shear load. A small compressive domain can be seen at the bottom of the borehole. The stresses already indicate the concrete cone failure at the free edge with stresses in the softening domain of the material.
Figure 6
Distribution of the maximum principle stresses
This is supported by a more detailed view (see figure 7) of the maximum principal strains distribution. The strain iso-lines describe the existing crack line creating a concrete failure cone and a splitting of that concrete cone along the symmetry plane. Experimental results performed with the same boundary conditions utilized in the simulation show a maximum load varying from 9700 N to 16200 N with a mean value of 13400 N. The maximum force calculated using numerical simulation is 12500 N. That is in good agreement with the experimental results.
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Figure 7
Distribution of the maximum principle strains
3.2 Adhesive anchor The adhesive anchor investigated here is a threaded rod. This rod is set into mortar HIT HY 150 which previously has been injected into the borehole. The geometry of the considered structure is shown in figure 8. For illustrative reasons one quarter (the right front part) is deleted. The right side shows the free edge of the structure. The structure is subjected to two load cases: axial pull-out force and shear loading towards the edge.
Figure 8
Geometry of the HAS fastening
3.2.1 Axial pull-out loading The working principle of the adhesive anchor under tensile loading conditions is characterized by a large area of load transfer along the embedment depth of the anchor. The load is mainly introduced into the base material by utilizing the shear mechanism along the interface layer between the mortar injected into the borehole and the concrete. Figure 9 shows the distribution of the maximum principal stresses in the base material before failure.
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Figure 9
Distribution of the maximum principle stresses shortly before failure load
As it is clearly indicated the region of iso-stresses deviates from the symmetrical stage caused by the edge influence. Nevertheless the edge distance is of minor influence on the maximum load and failure criterion which is also shown in figure 10 describing the maximum principle strains as a measure for the occurring cracks.
Figure 10 Distribution of the maximum principle strains shortly before failure load Only iso-lines of smaller strains deviate in the direction of the free edge. The remaining failure criterion is the bonding failure with a small concrete cone at the upper part of the embedded rod.
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3.2.2 Shear loading towards the edge The loading of the anchor with shear acting towards the free edge completely changes the behaviour compared to that in concrete without any edge influence. The distribution of the maximum principle stresses clearly illustrates the stress state shortly before the concrete cone breaks out (see figure 11).
Figure 11 Distribution of the maximum principle stresses shortly before failure load The region of compressive stresses can be seen along the upper half of the embedment depth in the direction of the free edge.
Figure 12 Distribution of the maximum principle strains shortly before failure load The strains at that stage of loading are displayed in figure 12. The observed strains are a direct measure for the occurring cracks.
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4. Conclusions Numerical simulation enables us to calculate the structural behaviour of anchoring fastenings also for complex applications and loading conditions. Different failure mechanisms like e.g. concrete failure or bond failure can be investigated. The knowledge of the structural behaviour and the basic mechanisms in the base material can be used within the development process for new products. The insight understanding of the basic principles is the basis for a successful and high quality product. The available finite element code to date is at a development level, which also allows the simulation of complex applications as a beneficial tool for the design engineer. Different failure mechanisms with their corresponding load carrying capacity can be evaluated, thus giving the designer a better understanding of load distribution, stress states and weakest points in their design applications.
5. References 1. Nienstedt, J. and Dietrich, C., ‘Application of the finite element method to anchoring technology in concrete’, in ‘Fracture mechanics of concrete structures’, Proceedings of the Second International Conference on Fracture Mechanics of Concrete Structures, Zürich, July, 1995 (Aedificatio Publishers, Freiburg/Breisgau, Germany, 1995) 1909-1914. 2. Nienstedt, J., Mattner, R. & Wiesbaum, J. 1999. Constitutive modelling of concrete in numerical simulation of anchoring technology. In ‘Structural engineering in the 21st century’, Proceedings of the 1999 Structures Congress, New Orleans, April, 1999 (American Society of Civil Engineers, Reston/Virginia, USA) 211-214. 3. Hillerborg, A., Modeer, M. and Petersson, P.P., ‘Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements’, Cement and Concrete Research 6 (1976) 773-782.
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HEADED STUD ANCHOR - CYCLIC LOADING AND CREEP-CRACKING INTERACTION OF CONCRETE Joško Ožbolt, Jan Hofmann and Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract It is well known that the ultimate resistance of a concrete member under sustained load compared to the resistance of the same member loaded by instantaneous load can be considerably smaller. One of the reasons for this is creep-cracking interaction which for a sustained load causes an increase of damage zone and reduction of ultimate capacity. This effect is stronger if the structure was previously loaded by cyclic loading. In the present paper is demonstrated that the microplane model for concrete which is coupled in series with the linear creep model (Maxwell chain model) is able to account for the above phenomena. The three-dimensional finite element analysis of concrete specimen loaded in uniaxial compression and the analysis of a headed stud anchor loaded by monotonic and cyclic shear load was carried out. It is shown that the shear resistance of the anchor under sustained load reduces by 15%. Moreover, the reduction of the loadcapacity increases if the anchor has previously been loaded by cyclic load.
1. Introduction Two important aspects of durability of fastening elements in concrete and reinforced concrete structures are the effect of repeated loading and the interaction between concrete cracking and creep of concrete. It is well known that the ultimate resistance of a concrete member under sustained load compared to the resistance of the same member loaded by instantaneous static load could be considerably smaller. One of the reasons for this is creep-cracking interaction which for a constant load leads to an increase of damage zone and reduction of the ultimate capacity. This effect is stronger if the structure was previously loaded by cyclic load.
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During the last two decades significant progress in modelling of fracture and damage of concrete-like materials has been done. However, how to describe creep rupture of concrete theoretically has not been dealt with until recently. In the present paper a threedimensional finite element model which accounts for cracking and nonlinear behavior of concrete (microplane model) is coupled in series with the creep model (Maxwell chain model). To investigate whether the model is able to qualitatively predict the effect of creep of concrete on the reduction of the failure load, three-dimensional parameter studies of concrete specimen loaded by sustained uniaxial compressive load were carried out. Moreover, a three-dimensional finite element analysis of a headed stud loaded by monotonic and cyclic shear load and subsequently loaded by sustained load of different levels was performed.
2. Modelling of creep fracture of concrete It is well known that the concrete deformation and strength under sustained load are influenced by the material and geometrical defects, i.e. larger initial flaws lead to lower strength at sustained load. Following this argument, the main assumption of the present approach is that the non-linear creep of concrete is a consequence of the redistribution of stresses due to creep and with this related increase of damage. The redistribution takes place between stronger (less damaged) and weaker (more damaged) zones of the material. Their existence depends on the inhomogenity of concrete, on the structural geometry as well as on the loading. When such zones do not exist (homogeneity of the stress-strain field), no redistribution of stresses is possible and consequently there is no non-linear creep. When the constitutive law accounts for the existence of these zones then the coupling of such a constitutive relationship with the linear creep law should be able to predict the effect of non-linear creep. To confirm the above discussed assumption, in the present paper the microplane model for concrete is coupled in series with the Maxwell chain model (see Figure 1). In an incremental iterative procedure, at time tr the stress increment ∆σr is calculated from the known total strain increment ∆εr based on the microplane model as:
(
∆σ r = D r ∆ε r − ∆ε "r
)
(1)
in which ∆εr” is the creep strain increment, calculated from the linear creep law (Maxwell chain model), and Dr is the material stiffness tensor obtained from the microplane model. It is assumed that the microplane model parameters are time independent. One important point in the modelling of the non-linear creep is that the constitutive law (in our case microplane model) must be able to realistically model concrete response for cyclic loading history, i.e. realistic loading-unloading-reloading rules have to be employed. By the use of a simple secant loading-unloading rule (see Figure 2), what is
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common in the non-linear analysis of concrete and reinforced concrete structures, it is not possible to account for the effect of non-linear creep. Namely, for relatively high stress levels the unbalanced stresses of the i-th iteration step are too low in comparison to the stresses obtained from a realistic constitutive stress-strain law (compare secant and realistic unloading rule in Figure 2). In such a case it is not possible to realistically reproduce the redistribution of stresses in the structure. Consequently, the effect of nonlinear creep can not be accounted for.
σµ
σ
Eµ
ε µ=1
2
σ
m
Figure 1. Maxwell chain model.
n
Figure 2. Realistic modeling of concrete for loading-unloading-reloading stress-strain history.
2.1 Microplane model The microplane model is a three-dimensional macroscopic constitutive law. In the model the material is characterised by a uniaxial relations between the stress and strain components on planes of various orientations. At each integration point these planes may be imagined to represent the damage planes or weak planes of the microstructure. The tensorial invariance restrictions need not be directly enforced. Superimposing the responses from all microplanes in a suitable manner automatically satisfies them. The basic concept behind the microplane model was advanced in 1938 by G.I. Taylor [1]. Later the model was extended by Bažant and co-workers for modelling quasi-brittle materials which exhibit softening [2] [3]. In the present paper an advanced version of the microplane model for concrete proposed by Ožbolt et al. [4] is used. The model is based on the so called "relaxed kinematic constraint" concept. For more detail see [4]. 2.2 Rate-type creep law of ageing concrete – Maxwell chain model Creep of concrete is modelled by the Maxwell chain model (see Figure 1). It is assumed that the Poisson's ratio due to creep is the same as the elastic one. At time tr the total strain increment is decomposed into elastic (∆εrel), cracking (∆εrcr) and creep (∆εr") strain increments as:
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" ∆ε r = ∆ε elr + ∆ε cr r + ∆ε r
(2)
The elastic and damage strains are calculated from the microplane model whereas the creep strains are obtained from the Maxwell chain model. Creep deformations are calculated by the use of the algorithm for step-by-step integration proposed by Bažant and Wu [5]. For time step ∆tr the creep strain increments ∆εr" are calculated as: ∆ε "r =
{
1 m ∑ 1 − e −∆t r /τµ E "r µ =1
}σ
µ r −1
(3)
with, E "r =
m
∑ λ µr E µ r −1 / 2 + E ∞r −1 / 2
µ =1
where
E µ r −1 / 2 =
(
σ µ r = σ µ r −1 e −∆t r / τµ + λ µ r −1 E µ r −1 / 2 ∆ε r − ∆ε cr r
(
)
)
(
1 E µ r −1 + E µ r 2
) (4)
λ µ r = 1 − e −∆t r / τµ τ µ / ∆t r
in which µ denotes µ-th unit of the Maxwell chain model, τµ = ηµ/Eµ is the relaxation time of the unit, ηµ and Eµ are viscosity and modulus of the µ-th unit, respectively, σµ is the so called hidden stresses of the µ-th spring unit and Er" is pseudo-instantaneous Young’s modulus. In the present study the model with eight units is employed. The main advantage of the rate type formulation over the integral formulation is that the creep deformations are calculated only from the stresses of the previous load step whereas in the integral formulation the entire load history needs to be stored. 3. Numerical analysis of creep-fracture interaction To investigate whether the coupling of the microplane model for concrete in series with a Maxwell chain model can account for the effect of non-linear creep, three-dimensional finite element analysis of concrete compressive and tensile specimen was carried out. For both specimens the load was applied at concrete age of 28 days. The linear creep deformation at t = ∞ was taken three times larger than the instantaneous deformation (creep factor φ = 3). The smeared fracture finite element analysis was carried out by the use of the eight-node solid finite elements with eight integration points. To account for the objectivity of the analysis with respect to the size of the finite elements, the crack band approach was used [6].
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3.1 Uniaxial compression Creep of concrete under compressive load was analysed for the specimen geometry shown in Figure 3. The basic material properties were as follows: Young's modulus E = 28000 MPa, Poisson's ratio ν = 0.18, uniaxial tensile strength ft = 2.0 MPa, uniaxial compressive strength fc = 28 MPa, fracture energy GF = 0.10 N/mm and concrete compressive fracture energy GC = 100GF. The typical uniaxial tensile-compressive stress-strain curve obtained from one three-dimensional finite element, assuming a crack band width of h = 20 mm is shown in Figure 4. 10
Steel plate
Uniaxial loading-unloading-reloading rules (one 3D finite element, h= 20 mm)
15
P
0 -6 -4 Strain x 1000
-2
0
300
-10
-20
2
4
Stress [MPa]
-8
150 150
-30
horizontally free surface
Figure 3. Geometry and boundary conditions of compressive specimen (all in [mm]).
Figure 4. Constitutive law for concrete – uniaxial tensile-compressive relationship obtained from a single solid finite element. 1.25
10
Average strain (x1000)
Relative strength [fc,s* / fc* ]
Concrete under sustained compressive load 8
Load level 0.70 fc
6
0.80 fc 0.90 fc
4
2
0.75
0.50
0 0E+0
1.00
2E+3
4E+3 6E+3 8E+3 Time after loading [days]
1E+0
1E+4
Figure 5. Calculate strain-time relationship for different load levels.
1E+1
1E+2 1E+3 1E+4 Time after loading [days]
1E+5
Figure 6. The relation between the relative compressive strength and time at failure.
The load was applied over a stiff loading platen. It was used because in this way the inhomogeneity of the stress-strain field was generated and it was not necessary to introduce a week zone or to randomly generate the material properties. First, the average strength of the specimen under instantaneous load was calculated as fc* = PU/A, where
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PU = ultimate load and A = cross section area. The load was performed by displacement control. The concrete strength was obtained as fc* = 24.40 MPa (note that this strength contains the structural effects and is not the same as fc). Subsequently, the time analysis of the specimen loaded by constant compressive load of different levels (load control) was carried out. The sustained load was varied from P = 0.6PU to P = PU. The maximal duration of the loading was 10000 days. When during this period of time the specimen did not fail it was assumed that the compressive strength under sustained load fc,s* was higher.
a)
b)
c)
Figure 7. Calculated failure modes (dark zone = maximal principal strains) for: a) instantaneous load, b) P = 0.9PU and c) P = 0.7PU.
The strength under sustained load is 30% smaller than the compressive instantaneous strength (fc,s* = 0.7fc*). The three typical average deformation versus time curves (P = 0.7PU, 0.8PU and 0.9PU) are shown in Figure 5. The curves show that with increase of the load level (0.7PU to 0.9PU) the creep deformations increase and the time to failure decreases. The calculated relation between the relative compressive strength and duration of load is shown in Figure 6. The typical failure mode due to the instantaneous load is shown in Figure 7a. For comparison, Figures 7b and 7c show the failure mode of the specimen loaded by P = 0.9PU (failure after 211 days) and 0.7PU (failure after 8111 days), respectively. The above numerical results are similar to the experimental observations, except that it is believed that the compressive strength under sustained load is approximately 0.8PU and not 0.7PU as obtained in the present analysis. The reason may be due to the fact that so far no experiment has been performed over a time period of 25 years (specimen loaded with 0.7PU failed after approximately 25 years) or this may be caused by the fact that in the analysis the ageing effect, i.e. increase of the strength with time was not accounted for. It is interesting to observe that the failure mode of the specimen loaded
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with P = 0.9PU is the same as for the specimen under instantaneous load. However, the specimen loaded by P = 0.7PU fails in a different way (compare Figures. 7b and 7c). 3.2 Headed stud anchor loaded by shear load The influence of the creep fracture interaction on the load capacity of headed anchors was investigated on a single anchor placed close to the edge of a concrete block and loaded by shear load in direction perpendicular to the edge of the concrete specimen. The anchor was first loaded by monotonic or cyclic shear load, respectively. Subsequently, the sustained shear load was applied. Age of the concrete at application of load was 28 days and the creep factor was assumed to be φ = 3. The geometry of the specimen and the finite element mesh are shown in Figure 8. In the analysis the load control was used. The anchor was discretized by three-dimensional eight-node linear elastic finite elements. The contact between the anchor and the concrete was modeled by the interface elements. They could take up only compressive stresses. The material properties used in the analysis are summarized in Table 1. Table 1. Material and geometrical properties used in the analysis. Concrete [N/mm][MPa]
GF 0.07
ft 2.5
EC 30000
370 mm
Geometry [mm]
ν 0.18
fc 25
hef 120
c + 270mm
c 70
Steel[MPa]
ES 200000
Restraint
Restraint Shear load
270 mm
185 mm c Headed stud
2c
Restraint
Figure 8. The geometry and the finite element mesh of the test specimen loaded in shear towards the edge.
3.2.1 Monotonic loading To check whether the finite element model is able to predict the failure mode and resistance realistically, the anchor was first loaded by instantaneous load up to failure. The calculated results are in good agreement with the experimental evidence [7]. Similar as in experiments, two critical cracks grow from the anchor into the direction of the free edge (see Fig. 9). They propagate under an average angle of α = 300, measured from direction of loading.
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load failure cone
load failure cone
load P test
analysis
Figure 9. Post peak crack pattern (dark zone = maximal principal strains) – comparison with the experiment.
Subsequently, the anchor was loaded by sustained shear loads PS = γPU. The loading coefficient γ was varied from 0.70 to 0.90. If the anchor has not failed after 10000 days, it was assumed that the strength at sustained load is reached. The results show that the anchor resistance under sustained load is 15% lower than the resistance obtained for instantaneous load (PU,S = 0.85PU).
Figure 10. The relation between anchor topdisplacement and duration of loading for different load levels.
Figure 11. Relative resistance of the anchor under sustained load for monotonic and cyclic pre-loading history.
The typical average displacement versus time relationships, measured at the loading point, are shown in Figure 10. The curves show that with increase of load the creep deformations increase and the time at failure decreases. The calculated relationship between the ultimate sustained load and duration of loading is plotted in Figure 11. The typical crack patterns at application of sustained load (t' = 28 days, P = 0.9PU) and at failure (t-t' = 1010 days) are shown in Figure 12. As can be seen, short after begin of
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loading the damage localises into a relatively small volume close to the anchor. Due to the creep deformations (duration of load t-t' = 1010 days) the cracks propagate from the anchor into the direction of edge under an average angle of 300 (measured from the loading direction). The crack pattern is similar to the crack pattern obtained for the failure under instantaneous load (see Fig. 9). a)
b) a)
P
P
Figure 12. Crack patterns (dark zone = maximal principal strains): a) at application of load and b) at failure - 1010 days after loading with 85 % of ultimate instantaneous resistance.
3.2.2 Cyclic loading To investigate the influence of the cyclic load history on the anchor resistance under sustained load, the anchor was first loaded by three different load histories: (i) shear load PMAX = 0.8PU was applied and followed by 10 unloading-reloading cycles, (ii) the same as (i) but only six loading cycles were applied and finally (iii) the same as (i) but PMAX = 0.5PU. After applied cyclic load the anchor was loaded by sustained load of different levels. The calculated load-displacement curves for cyclic pre-loading histories and corresponding relations between displacement at the anchor top and time under loading are shown in Figures 13 and 14. Figure 13 shows that the increase of the displacement due to the cyclic loading depends on the level of loading and on the number of loading cycles. Higher the load level and larger the number of loading-unloading-reloading cycles, larger is the increase of displacement. For the load history (i) the sustained load PS = γPU was applied with γ = 0.40, 0.70 and 0.80. It turned out that after cyclic loading applied at relatively high load level (PMAX = 0.80PU) the resistance under sustained load reduces by 30% compared to the resistance under instantaneous load. For the second load history with PMAX = 0.80PU and only six loading-unloading-reloading cycles, the
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a)
a)
b)
b)
c)
c)
Figure 13. Calculated load-displacement curves for three cyclic load-displacement histories.
Figure 14. The relation between anchor topdisplacement and duration of loading.
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applied sustained load was varied with γ = 0.70 and 0.80. The results show that the resistance at sustained load is reduced by 20% (PS = 0.80PU). As expected, the higher the damage due to the cyclic loading history the larger is the reduction of the strength at sustained load, i.e. the creep-fracture interaction is stronger when damage due to the cyclic loading is higher. This confirm the results for the load history (iii) in which the resistance under sustained load was the same as for the case where the anchor was loaded only by monotonic load (PS = 0.85PU). The comparison between the strength under sustained load for two different pre-loading histories, monotonic and cyclic case (i), is shown in Figure 7. The typical crack patterns for the load history (i) (PMAX = 0.80PU) before the application of sustained load and at failure are shown in Figures 15a and 15b. In contrary to the failure mode for the loading history without cyclic loading (see Fig. 12), it can be seen that at failure two cracks from both sides of the anchor forms (see Fig. 15b). First initiates the crack which growths under an larger angle α and close before failure forms a new crack that propagates steeper from the anchor towards the free boundary of the concrete block. Moreover, the damage zone is more concentrated, what is a consequence of the damage induced by the cyclic loading. a)
b)
P
P
Figure 15. Crack patterns (dark zone = maximal principal strains): a) after 10 loading cycles with loading-unloading-reloading of 80 % of the ultimate instantaneous load b) at failure under sustained load.
4. Conclusions In the present paper the numerical model which is based on the serial coupling of the microplane model for concrete and the Maxwell chain model is used to study creepfracture interaction for the case of a single anchor applied close to the edge of a concrete block and loaded in shear. To verify the model, a three-dimensional finite element
727
analysis of concrete compressive specimen was first carried out. It is demonstrated that the model is able to predict the effect of non-linear creep, i.e. nonlinear increase of creep deformations at higher stress levels and the decrease of the concrete strength at sustained load. The compressive strength of concrete under sustained load is found to be 30% lower than the strength under instantaneous load. This is in good agreement with the experimental observations. Subsequently, the three dimensional analysis of the anchor loaded by shear force is carried out. The numerical study shows that the resistance of the anchor under sustained load compared to the resistance under instantaneous load decreases by about 15%. Moreover, it is shown that the cyclic load history significantly influence the resistance of the anchor under sustained load. The decrease of the resistance depends on the damage introduced by cyclic load history. For the studied case it turned out that the cyclic loading-unloading-reloading between zero and 80% of the resistance under instantaneous load decreased the resistance under sustained load by 30%. The decrease depends on the level of loading and on the number of loading cycles. The higher the damage induced by cyclic loading the larger is the reduction of the strength at sustained load. To investigate these effect in more detail further systematic numerical and experimental studies are needed.
5. Acknowledgement This work was supported by the following companies: Fischerwerke, Hilti, Halfen and Würth. The support is very much appreciated. 6. References 1. 2. 3. 4.
5. 6. 7.
G.I. Taylor, 'Plastic strain in metals', Journal of the Institute of Metals, London, (62), 307-324, (1938). Z.P. Bažant and P. Gambarova, 'Crack shear in concrete: Crack band microplane model', Journal of Engineering. Mechanics, ASCE, 110, 2015-2035, (1984). Z.P. Bažant and P.C. Prat, 'Microplane model for brittle-plastic material - parts I and II', Journal of Engineering. Mechanics, ASCE, 114, 1672-1702, (1988). J. Ožbolt, Y.-J Li and I. Kožar, 'Microplane model for concrete with relaxed kinematic constraint', International Journal of Solids and Structures, 38, 26832711, (2001). Z.P. Bažant and S.T. Wu, 'Rate-type creep law of aging concrete based on Maxwell chain', Materials and Structures, 7(37), 45-59, (1974). Z.P. Bažant and B.-H. Oh, 'Crack band theory for fracture of concrete', Materials and Structures, 16(93), 155-177, (1983). R. Eligehausen and R., Mallée, R., 'Befestigungstechnik im Beton- und Mauerwerkbau', Ernst & Sohn, Berlin, Germany, (2000).
728
NUMERICAL INVESTIGATIONS OF HEADED STUDS WITH INCLINED SHOULDER Peter Pivonka, Roman Lackner, and Herbert A. Mang Institute for Strength of Materials Vienna University of Technology, Austria
Abstract
Failure of steel-concrete connections such as anchor bolts strongly depends on the material behavior of steel and concrete, respectively, and the geometric properties. The latter are commonly represented by the so-called span/depth-ratio (a=d-ratio), see Figure 1(a). Hereby, the embedment depth d is equal to the distance from the anchor head to the concrete surface. The span a represents the distance from the center of the steel rod to the support.
a
a
support
d
(a)
standard headed stud with headed stud inclined shoulder (b)
Figure 1: Geometric properties of headed stud: (a) a=d-ratio and (b) shape of anchor head The aim of the investigation presented in this paper is to obtain clear insight into the structural behavior of headed studs with inclined shoulder (see Figure 1(b)). For this purpose, two constitutive models for concrete formulated in the framework of plasticity theory are considered in the numerical simulations. The rst model is a multi-surface model consisting of one Drucker-Prager surface reformulated for the description of con ned compressive stress states, and three
Rankine surfaces for the description of the tensile material behavior of concrete. The second model is a single-surface model considering the dependence of the concrete strength on the Lode angle. Both models account for the in uence of con nement on the ductile behavior of concrete. In the numerical analyses, headed studs characterized by di erent geometric properties, i.e., by di erent a=d-ratios will be considered. Moreover, the in uence of the nite element (FE) mesh and the material model on the peak load and the failure mode will be investigated. 1. Introduction
The connection of steel and concrete structures in structural engineering is generally accomplished by means of anchor devices, such as headed studs, undercut anchors, etc.. In the past, the development of anchor devices was mainly performed by means of experiments. Today, this development is intensively supported by numerical simulations. Such simulations provide insight into the load transfer from the anchor to the surrounding concrete. They allow to monitor the development of the failure mode and give an estimate for the peak load of the anchor device. Both failure mode and peak load strongly depend on the concrete strength, the geometric dimensions of the anchor device, and the steel strength (see Figure 2). A prerequisite for realistic analyses are sophisticated material models for the description of the mechanical behavior of concrete. Such material models must be capable to simulate tensile, compressive, and con ned compressive failure of concrete. (a)
P
(b)
P
(c)
P (d)
P
Figure 2: Failure mechanism of headed studs [1]: (a) concrete-cone failure, (b) pull-out failure, (c) bursting failure, and (d) steel failure In this paper, two material models for plain concrete are considered. They are applied to the analysis of a headed stud with inclined shoulder. The paper is organized as follows: In Section 2, the employed material models are brie y described. Application of these material models to the simulation of the previously mentioned headed stud is reported in Section 3. Three di erent studies will be presented:
I The rst study will focus on the in uence of the geometric properties on the load-carrying behavior. II Di erent FE meshes will be employed in the second study in order to assess the in uence of the underlying discretization on the numerical results. III Finally, the in uence of the material model for concrete on the numerical results will be investigated in the third study. Section 4 contains concluding remarks. 2. Description of material models
The rst model is based on multi-surface plasticity. It consists of four yield surfaces: a Drucker-Prager (DP) yield surface for the description of concrete subjected to compressive loading and three Rankine (RK) surfaces for the description of tensile failure. In the principal stress space, the failure criteria read p q (1) fDP ( ; qDP ) = J2 DP I1 DP with qDP = fcy qDP ;
DP
and
f
(A ; qRK ) = A qRK with qRK = ftu qRK ; (2) where the subscript "A"(A=1,2,3) refers to one of the three principal axes. ftu is the tensile strength and fcy represents the elastic limit of concrete under compressive loading. DP and DP are constant material parameters. qDP and qRK represent the hardening force of the Drucker-Prager and the Rankine criterion, respectively. The Drucker-Prager criterion is reformulated in order to account for con ned compressive stress states (for details, see [9]). The second model is a single-surface plasticity model originally proposed by Etse and Willam [3]. It is referred to as Extended Leon Model. This model accounts for the dependence of strength on the Lode angle. The loading surface is given as [9] RK;A
f
(
ELM
p
r
rg(; e) 2 3 rg (; e) (p; r; ; q ; q ) = 1 + + p f 2 f 6f q 2 p rg(; e) q 2 q + m(q ) + p = 0; f f f f 6f h
q f
h
s
cu
cu
h
cu
cu
h
s
cu
tu
s
cu
with
q = f
cu
(3)
and qs = ftu qs : (4) In Equation (3), p is the hydrostatic pressure, r is the deviatoric radius, and denotes the Lode angle. fcu and ftu denote the uniaxial compressive and tensile h
cy
q
cu
)2
h
strength, respectively. A proper representation of compressive and tensile failure of concrete is achieved by the introduction of an elliptic function in the deviatioric plane, g (; e) [12] (see Figure 3). Hereby, the eccentricity parameter e is de ned as the ratio of the distance from the tensile and compressive meridian to the hydrostatic axis, i.e., e=rt /rc [11]. It de nes the shape of the ellipse ranging from e=0.5 (triangular form of yield surface) to e=1 (circular form of yield surface). The size of the loading surface is controlled by means of the hardening/softening forces qh and qs .
1 r
c
ellipse
r
t
r
1
circle t
3
2 (a) e =
r =1 r t
c
3
2
r
c
(b) e =
r <1 r t
c
Figure 3: Extended Leon Model: in uence of the eccentricity parameter e on the shape of the yield surface in the deviatoric plane (rt and rc represent the distance from the tensile and compressive meridian to the hydrostatic axis) Cracking of concrete is characterized by a localization of deformations. The formation of localized deformations is generally accompanied by the loss of ellipticity of the underlying boundary value problem, which in turn causes the loss of objectivity of the numerical solutions obtained by the FEM. The employed material models are regularized by means of the fracture energy concept which guarantees objectivity with respect to the element size. Softening functions appearing in the formulations of both models are calibrated according to the ctitious crack concept [4] (for details, see [8]). 3. Numerical analyses of headed stud
The headed stud considered in the numerical studies is characterized by an inclined shoulder (see Figure 4). The material properties of concrete and steel employed in the numerical analyses are given in Table 1. 3.1 General remarks
In the numerical studies, the material behavior of the steel bolt is assumed to
a=200 a=200 14
1 =12 coneshaped contact surface
50
5
4
260 203.65 5.55 50.8
d=50.8
100
40
50
2 =22
334
32
334
Figure 4: Geometric dimensions (in [mm]) of headed stud with inclined shoulder considered in the numerical studies concrete
Young's modulus Poisson's ratio uniaxial compressive strength uniaxial tensile strength fracture energy: GIf fracture energy: GIfI Young's modulus Poisson's ratio
steel
30000 N/mm2 0.2 40 N/mm2 3 N/mm2 0.1 Nmm/mm2 50 GIf 210000 N/mm2 0.3
Table 1: Material parameters of concrete and steel be linear elastic. At the cone-shaped contact surface between the anchor head and the concrete (see Figure 4), no slip is considered. The analyses are performed displacement-driven. The displacements are prescribed at the top of the steel rod. Because of axisymmetry of the geometric properties and the loading conditions, the problem is solved by means of axisymmetric analyses. 3.2 Numerical study I: variation of
a=d-ratio
In order to investigate the in uence of the a=d-ratio on the numerical results, the a=d-ratio of 4, depicted in Figure 4, was reduced to 3, 2, and 1. The di erent
geometric properties considered in this study are shown in Figure 5.
(a) a=d=4
(b) a=d=3
(c) a=d=2
(d) a=d=1
Figure 5: Study I: considered geometric properties of headed stud Figure 6 shows the employed FE mesh consisting of 2695 four-node elements. A relatively ne discretization was generated in the area where failure of concrete is expected. For the remaining part, a coarser mesh was designed.
mesh1
n=2695
axis of symmetry
zoom
Figure 6: Study I: FE mesh (n: number of elements) As regards failure of headed studs in consequence of concrete failure, two di erent types of failure modes can be distinguished. On the one hand, high compressive loading of concrete at the anchor head might cause local shear failure. On the other hand, a circumferential crack initiating at the anchor head and propagating towards the support might develop, nally resulting in a cone-shaped failure surface. As already pointed out in [10], the relative displacement between the anchor head and the concrete surface, ub us (see Figure 7(a)), allows to distinguish between the two aforementioned failure modes. Whereas an almost constant value of ub us is typical for cone-shaped failure, local shear failure at the anchor head is characterized by a continuously increasing value of ub us . Figure 7(a) shows the histories of us and ub obtained from numerical analyses
with a=d=4 and 1, respectively. For a=d=4, almost identical histories are observed for us and ub . This indicates rather small deformations and, hence, rather low compressive loading of concrete over the anchor head. On the other hand, a continuously increasing value of ub us is obtained for the analysis based on a=d=1, indicating compressive failure of concrete over the anchor head. However, the value of ub us in the post-peak regime is almost constant. Hence, similar to the analysis with a=d=4, a cone-shaped failure surface nally develops, causing failure of the headed stud. Figure 7(b) shows the history of the obtained load as a function of the prescribed displacement u for the considered values of the a=d-ratio. For decreasing values of the a=d-ratio, an increase of the peak load is observed.
150
u
s
u
P [kN]
P
b
111 000 000 111
100
u 150
a=d=4 a=d=3 a=d=2 a=d=1
P [kN]
100
u u
50
b
s
0 0
0.5
1.0 (a)
u,u b
50 s
[mm] 1.5
0 0
0.5
1.0 (b)
1.5
u [mm] 2.0
Figure 7: Study I: load-displacement curves obtained from multisurface model (a) for a=d=4 and 1 and (b) for di erent values of the a=d-ratio The distribution of the internal variable of the Drucker-Pager criterion, DP , in the vicinity of the anchor head is given in Figure 8 for a=d=4 and 1 at the respective peak loads. Figure 8(a) indicates an almost elastic material response of concrete over the anchor head for the headed stud with a=d=4. Peak values of DP are observed in the region left of the upper outer corner of the anchor head. Figure 8(b) shows the distribution of DP for an a=d-ratio equal to 1. In contrast to the distribution given in Figure 8(a), peak values of DP are observed over the anchor head. The respective plastic deformations are responsible for the increasing value of the relative displacement ub us in Figure 7(a). The distribution of the minimum in-plane principal stress, min , provides insight into the load-carrying behavior of the headed stud (see Figure 9). In general, the load is transferred from the anchor head to the support ring by means of a
[ 10 2 ] 1.0 0.8
5.000e+00
0.000e+00
0.6 0.4 0.2
-5.000e+00
-1.000e+01
-1.500e+01
0.0
-2.000e+01
(a)
(b)
Figure 8: Study I: distribution of the internal hardening/softening variable of the Drucker-Prager criterion, DP , in the vicinity of the anchor head obtained for (a) a=d=4 and (b) a=d=1 at the respective peak loads compressive strut. For a=d-ratios ranging from 3 to 1, this strut can clearly be identi ed (see Figures 9(b) to 9(d)). The previously observed increase of the peak load for decreasing values of the a=d-ratio is re ected by increasing compressive stresses min in the strut. The stress distribution shown in Figure 9(a) refers to a=d=4. The compressive strut between the anchor head and the support is divided into two parts. The lower part of the strut is similar to the strut obtained from the analysis with a=d=3. It starts at the anchor head and is aligned towards the support. However, for a=d=4 it does not reach the support. It becomes almost horizontal at a distance of approximately d/2 from the concrete surface. The upper part of the strut is parallel to the concrete surface, starting at the support ring. The load transfer between the two horizontal parts of the strut from a depth of d/2 to the concrete surface is accomplished by mixed compressive-tensile loading. Insight into the failure mechanism is gained from the distribution of the maximum plastic strain in the axisymmetric plane, "pmax , depicted in Figure 10. "pmax represents the opening of circumferential cracks which nally cause cone-shaped failure of concrete. For the headed stud considered, two di erent circumferential cracks are observed. One of them is located in the previously mentioned compressive strut between the anchor head and the support ring. It is a consequence of high compressive loading in this strut. The second crack originates from the geometric properties of the anchor head. It starts from the upper outer corner of the anchor head. Depending on the geometric properties of the headed stud, de-
(a) a=d=4
3.0
5.000e+00
-13.6
0.000e+00
(b) a=d=3
-30.2
-5.000e+00
-46.8
-1.000e+01
(c) a=d=2
-63.4
-1.500e+01
-80.0
-2.000e+01
(d) a=d=1
Figure 9: Study I: distribution of minimum principal stress in the axisymmetric plane, min (in [N/mm2 ]) scribed by the a=d-ratio, the two cracks are developing di erently as regards both crack width and orientation. For the analysis with a=d=4, characterized by the compressive strut consisting of two parts, the second crack governs the structural failure. The rst crack, i.e., the one located within the compressive strut, has only slightly developed. The opposite situation is found for a=d=1. Here, the crack located in the compressive strut dominates the failure of the headed stud. The second crack is almost horizontal and, hence, has no in uence on the failure of the stud. The analyses based on a=d=2 and 3 represent transition states between the previously described two extreme cases a=d=4 and 1. The peak loads and the displacements at peak load obtained from this study are summarized in Table 2. 3.3 Numerical study II: variation of discretization
The second investigation focusses on the in uence of the underlying FE mesh on the numerical results. For this purpose three FE meshes consisting of 2695, 994, and 2676 four-node elements are considered (see Figures 6 and 11). Mesh1
[ 10 3 ]
(a) a=d=4
1.00
5.000e+00
0.78
0.000e+00
(b) a=d=3
0.56
-5.000e+00
0.34
-1.000e+01
(c) a=d=2
0.12
-1.500e+01
-0.10
-2.000e+01
(d) a=d=1
Figure 10: Study I: distribution of maximum plastic strain in the axisymmetric plane, "pmax has already been employed in the previous subsection. For the two remaining meshes, mesh alignment was considered. Mesh alignment is the orientation of element edges in the direction of opening cracks (see [7]). For mesh2, the element edges are aligned from the anchor head towards the support ring (such meshes are commonly used in anchor bolt analyses [2]). The element edges of mesh3 are adapted to the expected orientation of the circumferential crack, see Figure 11. The load-displacement curves obtained from the multi-surface model for a=d=4 are depicted in Figure 12. Remarkably, the in uence of the underlying FE mesh on the peak load is rather small. The obtained peak loads vary only by 4.4%. Moreover, almost the same load-displacement response is observed for the aligned FE meshes, i.e., for mesh2 and mesh3. The orientation of the circumferential crack obtained by means of the structured mesh, i.e., mesh1 (see Figure 12(a)), does not coincide with the element edges of this mesh. This resulted in an arti cial stress transfer in consequence of element locking (see [6] [5]) and, hence, in additional cracking in neighboring elements. An increase of the crack band width because
axis of symmetry
axis of symmetry
n=994
mesh2
n=2676
mesh3
Figure 11: Study II: FE meshes characterized by mesh alignment (n: number of elements) of cracking of more than one row of nite elements leads to an increase of the released energy and, hence, to an overestimation of the load-carrying behavior (see pre-peak response obtained from mesh1 in Figure 12). Figure 13 shows the crack pattern at the respective peak loads by means of the distribution of "pmax . The distribution of "pmax obtained on the basis of mesh1 (see Figure 13(a)) indicates representation of the crack by at least three rows of elements. Mesh alignment towards the support ring (mesh2, see Figure 13(b)) provides the desired representation of the crack in the context of the ctitious crack concept [4], i.e., the representation of the crack in one element row. However, crack propagation is strongly a ected by the orientation of the element edges. Alignment towards the support resulted in a straight crack reaching from the
P u
P [kN]
100
111 000 000 111 000 111
50
0
mesh1 mesh2 mesh3 0
0.5
1.0
u [mm] 1.5
2.0
Figure 12: Study II: load-displacement curves
anchor head to the support. This crack pattern does not coincide with the crack pattern obtained on the basis of mesh1. Mesh1 and mesh3 (see Figures 13(a) and (c)) gave the presumably correct crack pattern. In contrast to mesh1, however,
[ 10 3 ]
(a) mesh1
1.00
5.000e+00
0.78
0.000e+00
0.56
-5.000e+00
0.34
-1.000e+01
(b) mesh2
0.12
-1.500e+01
-0.10
-2.000e+01
(c) mesh3
Figure 13: Study II: distribution of maximum plastic strain in the axisymmetric plane, "pmax mesh3 provides the correct representation of the crack within one row of elements. The numerical results obtained from the second study are summarized in Table 2. 3.4 Numerical study III: variation of material model
The last part of the numerical investigations deals with the in uence of the employed material model on the numerical results for an a=d-ratio of 4. For the numerical simulations, mesh3 is employed (see Figure 11). From the mesh study performed in the previous subsection mesh3 was found to give best numerical results as regards the crack pattern and the representation of cracks by the FEM. For the analysis based on the Extended Leon Model, a non-associative ow rule is considered. Moreover the dependence of the strength on the Lode angle is accounted for by means of e=rt /rc 1. Figure 14 shows the load-displacement curves obtained from the Extended Leon Model and the multi-surface model. A strong in uence of the employed material
model on the peak load is observed. The peak load obtained from the Extended Leon Model is only 55% of the peak load predicted by the multi-surface model.
P
P [kN]
100
u
1111 0000 0000 1111
multi-surface model Extended Leon Model
50
0
u [mm] 0
0.5
1.0
1.5
Figure 14: Study III: load-displacement curves obtained from the multi-surface model and Extended Leon Model The reason for the large deviations between the two model answers might stem from di erent behavior on
the constitutive level and/or the structural level caused by di erent modes of cracking.
As regards the latter, similar crack pattern were obtained from both analyses. The dominating circumferential crack developed exactly in the row of nite elements which was prespeci ed for cracking by means of mesh alignment. Hence, the reason for the observed large deviations must be found at the constitutive level. Figure 15 shows the distribution of the internal variables of the multi-surface model, i.e., DP and RK for the Drucker-Prager and the Rankine criterion, respectively. A shear failure mode characterized by an active Drucker-Pager criterion and an active Rankine criterion is observed. In order to investigate the performance of the employed material models when applied to the simulation of such shear failure modes, a plane-stress benchmark problem is considered (see Figure 16(a)). The model depicted in Figure 16(a) is loaded by means of a vertical pressure p. Thereafter, a horizontal displacement u is prescribed at the top of the model. The respective stress path in the 1 -2 stress space is depicted in Figure 16(b) for di erent values of p. According to the shape of the initial and failure surfaces shown in Figure 17, this type of loading will result in the desired shear failure mode.
[ 10 3 ] (a)
2.5
5.000e+00
2.0
0.000e+00
1.5
-5.000e+00
1.0
-1.000e+01
0.5
-1.500e+01
(b)
0.0
-2.000e+01
Figure 15: Study III: distribution of internal variable of (a) the DruckerPrager criterion, DP , and (b) the Rankine criterion, RK (a)
p
(b)
u
application of con nement, p
2 1 increase of u
Figure 16: Study III { benchmark problem: (a) loading conditions of the considered plane-stress benchmark problem and (b) stress path in 1 -2 stress space Figure 18 shows the stress paths obtained from the analysis of the benchmark problem. As regards the multi-surface model (see Figure 18(a)), an increase of 1 for an increasing value of u is observed until the stress path reaches the Rankine loading surface. It is noteworthy, that the contribution of the Rankine criterion to the plastic strain rate tensor is controlled by means of an associative ow rule. Consequently, softening, which is characterized by the decrease of 1 , is accompanied by an increase of the compressive stress 2 . The stress path drifts towards the Drucker-Prager loading surface, nally reaching the intersection point of the Rankine surface with the Drucker-Prager loading surface. Consideration of hardening within the Drucker-Prager criterion results in a continuous increase of the compressive stress 2 .
2 f
(a)
cu
-1.0
1 f
cu
cu
-1.0
1 f
cu
initial surface
initial surface failure surface
2 f
(b)
-1.0
failure surface
-1.0
Figure 17: Study III { benchmark problem: initial and failure surface in 1 -2 stress space of (a) multi-surface model and (b) Extended Leon Model The shape of the loading surface of the Extended Leon Model and the employed plastic potential (see [9]) results in buy far lower values of the compressive stress 2 (see Figure 18(b)). For the analyses with p=0, 1, and 2 N/mm2 , the stress path turns towards the origin of the stress space. The maximum values of the compressive stress 2 are obtained as maxj2 j=6.7, 9.3, and 11.8 N/mm2 for p=0, 1, and 2 N/mm2 . For the multi-surface model, the compressive stress 2 increases until the uniaxial compressive strength is reached and, hence, softening of the Drucker-Prager criterion is initiated. The stress-strain curves corresponding to the considered benchmark problem are depicted in Figure 19. Whereas a reduction of the shear stress is obtained for the Extended Leon Model for p=0, 1, and 2 N/mm2 , the multi-surface model shows a continuous increase of the shear stress for con ned loading conditions, i.e., for p>0. The latter seems to be responsible for the resti ening observed in the load-displacement curve of the headed stud obtained from the multi-surface model (see Figure 14). Similar to the benchmark problem, resti ening is observed until the uniaxial compressive strength is reached. Softening in the context of the Drucker-Prager criterion, characterized by DP > DP;m (see Figure 15(a)), nally leads to failure of the headed stud in the form of the expected cone-shaped failure surface 1 . The same failure mode was detected by the Extended Leon Model, however, at a buy far lower load level (see Figure 14). The numerical results obtained from the material model study are summarized in Table 2. DP = DP;m , the compressive strength is equal to the uniaxial compressive strength fcu . In the context of the employed Drucker-Prager criterion, DP;m depends on the level of con nement [9]. For the case of no con nement, DP;m =0.0022. 1 At
(a)
4
2 [N/mm2 ]
(b)
4
2 [N/mm2 ]
1 [N/mm2 ] -2
2
-4 -8
1 [N/mm2 ]
4
-2
p=0 p=1 p=2 p=5
2
4
-4
p=0
-8
p=1
-12
-12
-16
-16
-20
-20
p=2 p=5
Figure 18: Study III { benchmark problem: stress paths in 1 -2 stress space obtained from (a) multi-surface model and (b) Extended Leon Model
[N/mm2 ]
[N/mm2 ] 12
12
9
p= 5
9
6
p= 2 p= 1
6
3 0 0
p= 0 N/mm2 [10 3] 0.4 0.8 1.2 1.6 2.0 (a)
3 0 0
p= 5 p= 2 p= 0 N/mm2
p= 1
[10 3 ]
0.4 0.8 1.2 1.6 2.0 (b)
Figure 19: Study III { benchmark problem: stress-strain curves obtained from (a) multi-surface model and (b) Extended Leon Model
study I: span/depth-ratio
a=d model 4 3 2
II: FE mesh III: material models
1
4 4 4 4 4
DP-R DP-R DP-R DP-R DP-R DP-R DP-R
DP-R ELM
mesh 1 1 1 1 1 2 3
3 3
P
[kN] 91.7 109.0 115.0 142.5 91.7 87.7 91.2 91.2 50.6
max
u (P =P
max
1.56 1.43 1.06 1.03 1.56 1.25 1.30 1.30 0.31
) [mm]
Table 2: Peak load Pmax and prescribed displacement u at peak load obtained from numerical studies (DP-R: multi-surface model consisting of Drucker-Prager and Rankine criterion, ELM: Extended Leon Model) 4. Conclusions
In this paper, the dependence of the failure behavior of headed studs with inclined shoulder on the a=d-ratio, the discretization, and the material model was investigated. For this purpose, two material models for plain concrete were used. Both models are formulated within the theory of plasticity. One of them is a multi-surface model, whereas the other one is a single-surface model. From the numerical simulations of a headed stud with inclined shoulder the following conclusions can be drawn:
As for the analyses based on di erent geometric properties, a strong in uence of the a=d-ratio on the peak load and the load-carrying behavior was observed. Whereas a compressive strut from the anchor head to the support ring was identi ed for a=d-ratios ranging between 1 to 3, a strut consisting of two separated parts was obtained from the analysis with a=d=4. As for the analyses based on di erent FE discretizations, almost the same value of the peak load was obtained for all considered FE meshes. In contrast to the employed aligned FE meshes, the structured mesh resulted in element locking and, hence, in an overestimation of the load-carrying behavior in the pre-peak regime of the analysis. As for the analyses based on di erent material models for concrete, a crucial in uence on the predicted peak load was observed. Both the shape of the loading surface and the plastic potential were identi ed as the main reasons for the obtained deviations.
References
[1] Comite Euro-International du Beton CEB. Fastenings to Concrete and Masonry Structures. Thomas Telford Publishing, London, England, 1991. [2] L. Elfgren. Fracture mechanics of concrete structures. Technical report, RILEM, Technical Committee 90, 1990. [3] G. Etse and K. Willam. Fracture energy formulation for inelastic behavior of plain concrete. Journal of Engineering Mechanics (ASCE), 120:1983{2011, 1994. [4] A. Hillerborg, M. Modeer, and P.E. Petersson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and nite elements. Cement and Concrete Research, 6:773{782, 1976. [5] Th. Huemer, R. Lackner, and H.A. Mang. Implementation and application of an algorithm for adaptive nite element analysis of concrete plates. In Z. Bittnar, G. Pijaudier-Cabot, and B. Gerard, editors, Mechanics of Quasi-Brittle Materials and Structures, Prague, Czech Republic, March 1999. Hermes Science Publications, Paris. [6] M. Jirasek and Th. Zimmermann. Analysis of rotating crack model. Journal of Engineering Mechanics (ASCE), 124(8):842{851, 1998. [7] R. Lackner and H.A. Mang. Adaptivity in computational mechanics of concrete structures. International Journal for Numerical and Analytical Methods in Geomechanics, 25(7):711{739, 2001. [8] H.A. Mang, R. Lackner, P. Pivonka, and Ch. Schranz. Selected topics in computational structural mechanics. In W.A. Wall, K.-U. Bletzinger, and K. Schweizerhof, editors, Trends in Computational Structural Mechanics, pages 1{25, Lake Constance, Austria/Germany, 2001. [9] P. Pivonka, R. Lackner, and H. Mang. Numerical analyses of concrete subjected to triaxial compressive loading. In CD-ROM Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, Spain, 2000.
[10] P. Pivonka, R. Lackner, and H. Mang. Numerical simulation of concrete failure in pull-out experiments. In CD-ROM Proceedings of the 10th International Congress of Fracture, 2001. [11] E. Pramono. Numerical simulation of distributed and localized failure in concrete. PhD thesis, University of Colorado, Boulder, USA, 1988. [12] K. Willam and E. Warnke. Constitutive models for the triaxial behavior of concrete. In International Association of Bridge and Structural Engineers Seminar on "Concrete Structures Subjected to Triaxial Stresses", volume 19, pages 1{30, Bergamo, Italy, 1975. Int. Assoc. Bridge Struct. Eng. (IABSE), Zurich.
SIMULATING A RESPONSE OF CONNECTIONS Radomír Pukl, Jan Červenka and Vladimír Červenka Červenka Consulting, Czech Republic
Abstract Nonlinear simulation using the finite element package ATENA is presented on several practical applications. The selected examples show the possibilities of the numerical simulation of connections between steel and concrete in both composite structures and anchorage technology. The presented examples show that advanced constitutive models implemented in a finite element code such as ATENA can serve as an efficient tool to explain behavior of connection between steel and concrete. This approach can be used to support and extend experimental investigations and to predict behavior of structures and structural details.
1. Introduction Computer simulation based on realistic nonlinear material model enables successful simulation of the real structural behavior. Selection of practical applications dealing with connections between steel and concrete is presented in this paper. The numerical simulations were performed using the finite element package ATENA developed by the authors. ATENA employs advanced material models reflecting all the essential features of concrete behavior in tension as well as in compression. Tensile cracking model is based on the smeared crack approach, which replaces the discrete cracks, occurring in real concrete structures, by strain localization in a continuous displacement field. Concrete fracture is covered by nonlinear fracture mechanics based on fracture energy with exponential softening law derived experimentally by Hordijk. Objectivity of the finite element solution is assured by crack band approach - the descending branch of the stress-strain relationship is adjusted according to the finite element size and mesh orientation. In compression, the plasticity model according to Menetrey-Willam is able to capture concrete crushing under multi-axial pressure (confinement). More details
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concerning the program ATENA and the implemented material models with further references can be found in [1] and [2]. As documented on following examples, various methods are available in ATENA for modeling of connection between steel and concrete: fixed bond or interface elements. In case of fixed connection the bond failure is covered by fracture mechanics of the concrete layer surrounding the steel inlay. Three examples of the numerical simulation of connections between steel and concrete in both composite (reinforced concrete) structures and anchorage technology are presented. The optimization of a prestressed precast hollow core slab and the analysis of prestressed cable anchor region document the possibilities of modeling connection between reinforcing steel bars and surrounding concrete. Further examples on this topics, namely simulation of cracking in a four-point bending reinforced concrete beam and tension stiffening effect on a steel reinforcing bar embedded into concrete block, can be found in [2] and [3]. The analysis of a containment liner anchor represents the anchorage in concrete by steel fasteners and liners. Other examples of anchor simulations were published in [4] (contribution to the RILEM Round Robin analysis of anchor bolts in concrete structures) and [5] (simulation of powder actuated anchors).
2. Precast hollow core slab Geometry of a new type of prestressed precast hollow core slab was optimized for the producer, DYWIDAG Prefa Lysá nad Labem, Czech Republic, in order to minimize concrete cracking due to prestressing in the anchoring region. Influence of hole shape, number of holes, type and number of prestressing cables, prestressing force, thickness of the concrete cover and age of the concrete by application of prestressing force were investigated in numerical study [6]. A slab with the height of 200 mm and prestressing cables with the diameter of 12.5 mm was analyzed (Fig.1).
Fig.1 Cross-section of hollow core slab with analyzed detail (dimensions in cm) As a basic model, the lower part of one rib with one prestressed cable (see detail in Fig.1) and length of 1 m was modeled by 4000 concrete 3D finite elements (Fig.2). The prestressing cable was modeled by volumetric elements with steel material properties. It was prestressed in the longitudinal direction using step-by-step loading procedure.
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V1 C1
Y X Z
Fig.2 Finite element model of the lower part of the rib with one prestressing cable V1 C1
0.0001
0.00009
0.00008
0.00007
0.00006
0.00005
0.00004
0.00003
0.00002 Y X
0.00001
Z Output Set: Load Step ID 20 Contour: C:COD CRACK_ATTRIBUTES
0.
Fig.3 Crack widths (in m) in the anchoring region at bond failure
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A bond failure and a longitudinal crack in the concrete cover were obtained. Based on the numerical results, optimal geometrical shape with sufficient concrete cover was recommended and optimal prestressing force was adjusted. Numerically obtained crack widths for one particular case are shown in Fig.3 for illustration. Figures 2 and 3 shows models for two different geometrical shapes of the rib for illustration. The next task was to determine the shear carrying capacity of the projected slab. Because of lack of shear reinforcement, avoiding the shear failure is the crucial point in design of the precast hollow core slabs. Therefore, shear-loading test was simulated on threedimensional model of the symmetrical half of the slab. Finite element mesh with over 8000 volumetric elements is shown in Fig.4. V1 L1
Fig.4 Finite element model of the symmetrical half of the hollow core slab In this case, the prestressing cables were modeled by one-dimensional bar elements. After prestressing the slab was subjected to the local shear load. Slab failed due to bond failure of prestressing cables in anchoring region with consequent opening of a shear crack near the support. The allowed shear loads for design tables were determined based on the numerical results. Simulated failure pattern of the projected slab (Fig.5) is compared with a typical shear test failure of a hollow core slab of recently produced type (Fig.6).
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V1 L1
0.000866 0.000812 0.000758 0.000704 0.00065 0.000596 0.000541 0.000487 0.000433 0.000379 0.000325 0.000271 0.000217 0.000162 0.000108 0.0000541
Output Set: Load Step ID 40 Contour: C:COD CRACK_ATTRIBUTES
-3.02E-12
Fig.5 Numerically obtained crack widths (in m) at slab shear failure
Fig.6 Typical failure of a hollow core slab in the shear loading test
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3. Pre-stressing cable anchor Three-dimensional simulation of prestressing cable anchors was performed using the fracture-plastic material model [7]. Prestressing force is transferred from prestressing cables to concrete through special cylindrical anchors, which are embedded into concrete during casting. Shape of the anchor is shown in Fig.7 along with the finite element model. The objective of the analysis was to simulate experiments, which are undertaken during the anchor validation process. In the experiment, the prestressing cable anchor was embedded into a concrete block. The anchor is surrounded by spiral reinforcement and loaded by compressive forces at the top to simulate the action of prestressing. Very good agreement between analytical and experimental peak loads can be seen in Fig.8. The load-displacement curve shown in the figure was obtained from the numerical analysis, while the experimental curve is not available to the authors. The final failure pattern with radial cracking and crushing shear failure around the anchor is shown in Fig.9.
Fig.7 Finite element model for the prestressing cable anchor analysis
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Pre-stressing force [kN]
9000 7000 Analysis
5000 3000
Experimental peak load
1000 -1000 0
2
4
6
8
10
12
Anchor insertion displacement [mm]
Fig.8 Load-displacement diagram for prestressing anchor analysis
Fig.9 Final failure mode for prestressing cable anchor analysis. Crushed concrete is shown in the left figure as contours of maximal plastic strain. Major radial/splitting cracks on the specimen surface are shown in the right figure.
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4. Containment liner anchor In nuclear containment vessels, a steel liner is attached to the concrete using T-shaped line anchors. Load-carrying capacity of these anchors is usually determined by experiments (Fig.10). Experiments are performed for a single anchor, while in reality there are many anchors in the containment vessel, and it can be expected that an anchor behavior may be affected by neighboring anchors. The experimental setup was designed using non-linear two-dimensional analyses, such that the behavior of the experimentally tested single anchor is similar to the behavior of the real anchor in the containment vessel. The fracture-plastic concrete model [7] was used in three-dimensional numerical study to verify some of the assumptions in the two-dimensional analyses: namely, the increase of compressive strength and ductility due to three-dimensional confinement in front of the anchor. The specimen was loaded by horizontal force at the right end of the liner up to the failure. The load-displacement diagrams are compared in Fig.11 and they show very good agreement of numerical and experimental results. Cracking and crushing patterns obtained in the 3D numerical simulation are shown in Fig.12.
Fig.10 Failure pattern in liner anchor experiments. (Photo: courtesy of Ishikawajima Harima Heavy Industries and Tokyo Electric Power Company, Japan)
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Horizontal anchor force [MN]
0.9 0.8
Experiment 1
0.7
Experiment 2
0.6
Experiment 3 Experiment 4
0.5
Experiment 5
0.4 0.3
Numerical Analysis 0.2 0.1 0.0 0.000
0.005
0.010
0.015
0.020
Horizontal anchor displacement [m]
Fig.11 Load-displacement diagrams for liner anchor three-dimensional analysis and comparison with experimental data. (Experimental data are courtesy of Ishikawajima Harima Heavy Industries and Tokyo Electric Power Company, Japan).
Fig.12 Failure mode for liner anchor analysis - concrete cracking and crushing at the and of the analysis
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5. Conclusions Three practical examples demonstrate the possibilities of numerical simulation in the field of connections between steel and concrete, namely optimization of the precast hollow core slab, investigation of the anchor region of prestressing cable and analysis of the containment liner anchor. Further practical applications can be found in reference [2] to [5]. As documented in the paper, the nonlinear finite element package ATENA, based on advanced constitutive models, is able to predict and explain behavior of steel reinforcement as well as steel anchors in concrete structures. It can be effectively used to support and extend experimental investigations by innovative solutions.
Acknowledgment The results presented in this paper are related to the research topics supported by grant of Grant Agency of Czech Republic (GAČR) No. 103/99/0755. The financial support is greatly appreciated.
References 1.
2. 3.
4.
5.
6. 7.
Červenka, V., Červenka, J. and Pukl, R., 'ATENA - an advanced tool for engineering analysis of connections', Proceedings of the RILEM Symposium on Connections between Steel and Concrete, Stuttgart, Germany, September 2001. Červenka, V., 'Simulating a Response', Concrete Engineering International, 4 (4) (2000) 45-49. Margoldová J., Červenka V., Pukl R. and Klein, D., 'Angewandte Sprödbruchberechnung', Bauingenieur 74 (3), (Springer VDI, München, Germany, 1999), A22A29 (in German). Pukl, R., Eligehausen, R. and Červenka, V., 'Computer simulation of pullout test of headed anchors in a state of plane-stress', In: Concrete design based on fracture mechanics (eds. W. Gerstle and Z.P. Bažant), ACI SP-134, Detroit, Michigan, USA, 1992, 79-100. Červenka, J., Červenka, V. and Eligehausen, R., 'Fracture-plastic material model for concrete, application to analysis of powder actuated anchors', Proceedings of the International Conference on Fracture Mechanics of Concrete Structures FraMCoS 3, Gifu, Japan, 1998 (Aedificatio Publishers, Freiburg, Germany, 1998) 1107-1116. Pukl, R., 'Optimization of hollow core slab geometry' (Červenka Consulting, Praha, Czech Republic, March 2001, in Czech). Červenka, J. and Červenka, V., 'Three Dimensional Combined Fracture-Plastic Material Model for Concrete', Proceedings of the 5th U.S. National Congress on Computational Mechanics, Boulder, Colorado, USA, August 1999.
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NON-SUPPORTED CRASH BARRIERS - PROOF OF THE CONCRETE RESISTANCES ACCORDING TO THE CONCRETE-CAPACITY-METHOD Jochen Buhler f i s c h e r w e r k e, Germany
Abstract Crash barriers (see fig. 1.) made of reinforced concrete shall protect the tunnel tube against exceptional effects caused by the traffic. These barriers are in generally fixed additional to the bearing precast concrete tunnel segments by bonded shear bolts. The proofs of the barrier`s concrete failure mostly result from the method of Rasmussen according to „Deutscher Ausschuß für Stahlbeton, Heft 346“. The proofs of the concrete segment`s failure results from the wellknown κ - method. The Concrete-Capacity-Method provides a more economic design method and will be applied on the shear bolts of the non-supported crash barriers in the recent Elbtunnel project in Hamburg, Germany. As best possible solution a shear bolt with a diameter of 35mm and an effective anchorage depth of 220mm was designed. The bolt is bonded with hybrid resin mortar and is made of stainless steel A4-70 (316Ti). This paper will present the proofs according to the ETAG of Metal Anchors for use in concrete, Annex C considering all edge and axial influences. The edge influence results from both the external dimension and the screw joint bay`s locations of the concrete lining elements. The results of pull-out tests for determining the characteristical resistance to proof the concrete pryout failure will be shown as well as the recommendations for additional reinforcement to transmit the shear force in the crash barriers. The summary compares the results of the CC-Method with those of the Method of Rasmussen and κ - method respectively.
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figure 1: build-up of tunnel tube
1. Introduction The interior of road tunnels with circular section are often additionally completed with side walls, which among other things are used as crash barriers to protect the supporting structure, as fire protection and as support for such as emergency lights. The continous concreted side wall will be connected by post-installed anchors to the structural lining segments. A tension anchor – an adhesive anchor M16 for cracked concrete in the structural lining segments in combination with a waved anchor in the side wall cast in situ – are installed in the top region. Taking up the shear loads which are mainly originated by dead loads adhesive shear bolts are designed at the bottom regions. This paper will work on the design of these adhesive shear bolts.
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figure 2: tunnel tube The first design recommendation based on DafStb book 346 according to Rasmussen results in eight shear bolts per precast lining segment. Rasmussen calculates the existing load capacity of the shear bolts by
Fu = c ⋅ d ⋅ β s ⋅ β c ⋅ 1 + (c ⋅ ε ) − c ⋅ ε 2
.
(1)
s β ε = 3⋅ k ⋅ c d βs This equation assumes that the force acts parallel to the surface of the concrete wall. Using the dimensionless safety factor for the working load c = 1,3, the effective buckling length sk = 102,5mm, the bolt diameter d = 30mm, the compressive strength of a cylindrical concrete test specimen βc = 25N/mm² and the yield strength of steel βs = 360N/mm² the ultimate load capacity results in Fu = 87,4kN and by considering of an additional safety factor the permissible load capacity in Fperm = 34,9kN. The dead load per lining segment width is G = 193,5kN, this means shear action of VSk = 24,20kN per shear bolt. The successful proof is obvious VSk = 24,20kN ≤ 34,9kN = Fperm.
2. Concrete Capacity Method Recently designing anchors, the so-called C(oncrete) C(apacity) method results in economic solutions and should be applied also for the crash barriers. The tension anchors in the top region are proofed according to CC-method. This design method proofs in the ultimate limit state for each load direction (tension and shear) all failure modes - the concrete and steel failure modes, the pull-out failure. This is done according the safety concept with partial safety factors. The existing application requires to consider and calculate the resistances due to shear load in case of steel failure, concrete edge failure and pryout failure. The proofs for the concrete failure modes have to be done for the crash barriers as well as for the lining segments.
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The following material data are given: a) concrete: a1) lining segments: a2) crash barriers:
βW,N = 45N/mm² h = 700mm βW,N = 25N/mm² h = 520mm fyk = 560N/mm² fuk = 700N/mm² hef = lf = 220mm d = dnom = 35mm
b) anchor:
stainless steel 316Ti
The acting design value of shear load is originated by the permanent weight of the side wall VS,d = 96,75 ⋅ 1,35 = 130,61kN/m. 2.1. Steel failure For calculation the resistance in case of steel failure
VRk, s =
α M ⋅ M Rk, s l
(2)
we use the following static assumption: full restraints on both sides but mutual displacement. The value αM = 2,0 is given for those full restraint supports. The lever arm l= 40mm considers that the location of the restraint for calculation have to be assumed half of the bolt diameter behind the concrete surface, because hammer drilling leads to slight spallings at the drill hole. The characteristic bending moment can be calculated by
M 0Rk,s = 1,2 ⋅ Wel ⋅ f uk = 3535,764kNmm
(3)
and as consequence we can derive the resistance in case of steel failure as VRk,s = 176,79kN. According to the European Technical Guideline ETAG 001, Annex C the partial safety factor in case of steel failure due to shear load is derived from
γ M,s =
1 = 1,25 . f yk f uk
(4)
This leads to the design value VRd,s = 141,43kN.
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2.2. Concrete edge and Pryout failure for the precast lining segments Four different arrangements of anchor position per lining segment width are necessary cause of the lining segment arrangements in the tube. As example this paper shows the worst case only. The resistance in case of concrete edge failure have to be calculated by 0 VRk,c = VRk, c⋅
A c,V ⋅ ψS,V ⋅ ψ h,V ⋅ ψ α,V ⋅ ψ ec,V ⋅ ψ ucr,V A c,0 V
(5)
The initial value of the characteristic resistance of an anchor placed in cracked concrete and loaded perpendicular to the free edge depends on the edge distance c1 0 VRk, ⋅ f ck,cube ⋅ c1.5 c = 0.45 ⋅ d nom ⋅ (l f /d nom ) 1 0.2
(6)
where the value (lf/dnom)0,2 consider the stiffness of the anchor. The factor ψh,V takes account of the fact that the shear resistance does not decrease proportionally to the 0
concrete member thickness as assumed by the ratio Ac,v / A c,V . The factor ψα,V consider the angle between shear action and the free edge. The factor ψs,V takes account of the disturbance of the distrubution of stresses in the concrete due to further edges of the concrete member on the shear resistance. 0
The area of concrete cone of an individual anchor A c, V at the lateral concrete surface not affected by edges parallel to the assumed loading direction, member thickness or adjacent anchors, assuming the shape of the fracture area as a half pyramid with a height equal to c1 and a base length of 1,5c1 and 3c1. The actual area Ac,V of concrete cone of the anchorage at the lateral concrete surface is limited by the overlapping concrete cones of adjacent anchors (s ≤ 3c1) as well as by edges parallel to the assumed loading direction (c2 ≤ 1,5c1) and by the concrete member thickness (h ≤ 1,5c1). The factor ψucr,V consider the condition of concrete and of the type of reinforcement. If anchor is placed in cracked concrete with straight edge reinforcement the increase of load capacity is considered by ψucr,V = 1,2. If there are additional closely spaced stirrups as in this case or if the anchor is placed in the compression zone of concrete ψucr,V = 1,4. Considering now two bolt anchors per precast lining segment with the equation (6) we can calculate for the worst case VRd,c = 342,61kN which includes a partial safety factor of γM,c = 1,8. The existing edge distances are c1 = 492mm (edge parallel to the load direction) and c2 = 295mm , the axial spacing s = 690mm. The resistance in case of concrete pryout failure is principally dependent on the concrete strength, the anchorage depth and in anchor groups the spacing of anchors. Tests showed that a relationship to concrete cone failure approach this failure mode sufficiently
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VRk,cp = k ⋅ N Rk,c
(7)
where the factor k was evaluated from test results. For this application the initual value for one anchor without any edge and axial spacing influence was determined as 300kN. By considering the influences we calculate VRd,cp = 482,92kN which includes a partial safety factor of γM,c = 1,8. 2.3. Concrete edge and Pryout failure for the side wall cast in situ The values for the respective resistances of the side wall are VRd,c = 352,54kN and VRd,cp = 359,95kN. The side wall is concreted continously without any additonal edges in the direction of the tunnel. There might be overlapping concrete edge cones, whose influence aren’t evaluate. Therefore the calculation assume concrete components from same width as the respective lining segment with imaginary edges. This assumption can be considered as calculation on the safety side. In addition for safe load transfer in the side wall we recommend hairpin reinforcement around the bonded bolt anchors and to limit the crack width some stirrups in the region of the pryout failure. 2.4. The proofs All proofs are shwon in the table below: Summary of the proofs [kN] anchor bolt
• steel failure
VSdh ≤ VRd,s
130,61 ≤ 141,43
precast lining segment
• concrete edge failure
VSdg ≤ VRd, c
261,22 ≤ 342,61
• concrete pryout failure
VSdg ≤ VRd,cp 261,22 ≤ 482,92
• concrete edge failure
VSdg ≤ VRd, c
261,22 ≤ 352,54
• concrete pryout failure
VSdg ≤ VRd,cp
261,22 ≤ 359,95
side wall cast in situ
h indicates the shear load acting on the most stressed anchor bolt, g the shear load acting on the sheared anchor of the group of two anchors.
3. Summary This example demonstrates impressive the opportunities of the CC method. The proofs according to CC method lead to two bolt anchors with d = 35mm per precast lining
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segment, the design according to Rasmussens equation to eight anchors with d = 30mm. The reduction of costs is obvious. The economy is result of both the material and the labour costs. The theoretical assumption were confirmed by site tests.
figure 3: post-installed adhesive shear bolts
4. References 1. 2.
EOTA: 'Guideline for European technical approval of metal anchors for use in concrete, Annex C: Design methods for anchorages', (February 1997). Kühn, Siegfried, 'Speziallösungen für Seitenwand-Verankerungen bei der 4. Röhre Elbtunnel', Beton- Und Stahlbetonbau, 95[2000] Heft 12, S.727-740.
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RECONSTRUCTION OF MULTI-LAYER-WALLS Edwin Dereser, Jochen Buhler f i s c h e r w e r k e, Germany
Abstract For reconstruction of multi-layer concrete panels special bonded anchors are used to secure the outer leaf. If those sandwich walls (see fig. 1.) are reconstructed without an additional insulation, thermal induced constraining stresses have to be considered. A static model will be suggested, which enables the calculation of the thermal constraining forces by considering the concrete stretch stiffening’s positive effect. Different fixings are used for taking compression caused by negative wind tension. The buckling model is based on the permissible pressure loads of the respective approvals. Both static models serve as base for the proofs of the ultimate limit states and are applied on a recent refurbishment of a office building. The figure below shows the build-up of the existing sandwich wall where the reason of the required refurbishment is obvious.
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Figure 1. 1. Introduction Multi layer concrete panels were frequently used for casing of public buildings during the seventies and early eighties. A lot of the buildings need to be reconstructed over the next years, as the supporting structure used for attaching the panels is seriously affected by corrosion and therefore the stability of the multi layer construction endangered. For the reconstruction of the front panelling several conditions and factors need to be considered. If there is no additional insulation applied to the front to panelling the stress caused by displacements due to temperature needs to be taken in account for the design of the
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fastener. As the fasteners for the panels can only take shear loads, the additional tension and compression loads caused by wind need to be supported by other means. In the following paper the Multi Layer Panel Reconstruction system is detailed using an example from field experience.
2. Basis of design for Multi Layer Panel Reconstruction System Conditions for the reconstruction: • • •
For the three layer panelling the fasteners are placed in the either reinforced or standard concrete of the supporting layer. The concrete rating of the supporting layer needs to be at least B15. The thickness of the supporting layer needs to be 120mm at minimum.
The follwing sketch outlines the basic design of the three layer panel system: insulation
concrete layer
concrete panel
≥ 120
25
35
80
2.1. Definition of the lever arm The geometric dimensions of the three layer panel system define the anchor that should be used. From the approval of the anchor, the lever arm can be derivated. For the purpose of this example calculation the lever arm is set to z = 128mm.
(1)
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2.2. Calculation of the constraining forces According to DIN 1045 paragraph 16.5, the impact of changing temperatures caused by different weather conditions needs to be taken in to account for constructions in concrete and reinforced concrete. For the statically defined basic system the following values are presumed: Temperature gradient ∆T = 70 K Coefficient of thermal expansion αk = 1*10-5 1/K Modulus of elasticity (B15) EB = 26.000 N/mm2 AB = 80.000 mm2 EI = 1,42*1010 Nmm2 a = 450 mm
∆l = α T ⋅ a ⋅ ∆T
Elongation caused by temperature can be computed to:
(2)
The statically indeterminate system for the anchors in the three layer panel system can be simlifiedaccording to the following sketch, where the constrained loads are shown.
FZ
EAAB
FZ
Z EI
EI a
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The bending for the statically defined system can be derived x
M 1 = − FZ ⋅ x
-
for the anchor
-
thenormal force for the outer panel (4)
(3)
N 1 = FZ
Using the theorems of Castigliano, the equation for the lenght change can be calculated . CASTIGLIANO`S THEOREM The first partial derivative of total strain energy in a structure with respect to an external load is equal to the displacement at the point of application of that load and in the same direction of the load.
δ=
z
∆l = 2 ⋅ ∫ 0
∂U ∂F
M 1 ∂M 1 N 1 ∂N 1 dx + ∫ dx ⋅ ⋅ EI ∂FZ E A F ∂ B B Z 0
2 z3 a = FZ ⋅ ⋅ + 3 EI E B AB
a
770
(5)
With the elongation from temperature ∆l (2), the constrained loads are defined to
FZ =
∆l 3
2 z a + 3 EI E B AB
= 3195 N
In the example used here, the constrained load computes to 3195 N for one anchor. Assuming a usage of 4 anchors per panel, by considering the weight of the panels (G), a resulting load of 8,45 kN per anchor derives:
FZ
FZ
G/4 R
G R = FZ2 + FZ + 4
(6)
The bending moment in the anchor equates with the lever arm (1) and the resulting load (6) to:
M =R⋅z
(7)
in this case 1080 Nm, wich is less then the allowed bending moment for the choosen anchor.
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3. Absorbtion of the compression loads due to wind The rotation in the front panel is prevented. An tensile- and compression load of 1 kN is assumed with a slip size of 1mm. The critical column load with no torsion allowed is according to the Euler Theorem:
P
PK =
4 ⋅ π ⋅ EI l2
(8)
with the distance between the panels l=70mm follows ⇒ EI=124,12 *103 Nmm2 Now it will be presumed, that rotation in the front panel is permissible, which leads to the following load case according to the Euler Theorem:
P
772
4,49 2 ⋅ EI PK = l2
(9)
Ö Pk=0,695 kN The result for the reduced maximum column load is, that the fastener with rotation permissible can withstand a recommended maximum load of 0,6 kN with a presumed maximum slip of 1mm.
4. Summary In this paper a way of calculating the loads due to temperature changes using the theorems of Castigliano was introduced. This allows to chose the anchors on basis of this additional design parameter more efficient. Furthermore a method of calculating the maximum column load for the fasterners due to wind was explained.
5. References 1. 2. 3. 4.
Prof. Dr.-Ing. Gerhard Adomeit, Mechanik für Ingenieure, Band 2, Festigkeitslehre (1988) Bauaufsichtliche Zulassung, Zul.-Nr. Z-21.2-973 Bauaufsichtliche Zulassung, Zul.-Nr. Z-21.8-1557 Gutachten FWS
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LOAD CARRYING CAPACITY OF FASTENERS IN CONCRETE RAILWAY SLEEPERS Håkan Thun*, Sofia Utsi*, Lennart Elfgren*, Paul Nilsson** and Björn Paulsson** *Division of Structural Engineering, Luleå University of Technology, Luleå, Sweden **Swedish Rail Administration, Borlänge, Sweden
Abstract The horizontal load-carrying capacity of fasteners in concrete railway sleepers is investigated. Tests are performed on un-cracked as well as cracked concrete sleepers. Small cracks do not seem to influence the load-carrying capacity and it is first when cracking is very severe that the load-carrying capacity is reduced significantly.
1. Introduction Concrete sleepers are very economic as a base for rails. The fastening of the rails is usually taken care of by fasteners imbedded in the concrete. Due to bad production methods, many sleepers in Sweden, produced during the 90ies, have obtained cracking of a more or less severe kind. The cracking is believed to be cause by delayed ettringite formation, see e g Tepponen & Eriksson (1987). In order to investigate the horizontal load-carrying capacity of the fasteners, a test program is being carried out at Luleå University of Technology in Sweden, Utsi & Elfgren (2000), Thun & Elfgren (2001). The test set-up and the fasteners are illustrated in Figures 1 and 2.
F
Figure 1. Concrete sleeper with fasteners. Illustration showing test set-up.
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Figure 2. Photos of a fastener. View in the direction of the rails (top left) and in the direction of the sleeper (top right and bottom).
2. Loads The horizontal forces that act on a sleeper are partly caused by the centripetal acceleration. It can be written as v2/R, for a train travelling with the speed v in a curve with the radius R. In order to reduce this force, the curve can be sloped, i.e. one of the rails is placed higher than the other one, see Figure 3.
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Figure 3. Forces acting on a mass in a vehicle moving in a curve. The influence of a slope ϕs is shown to the right. Using the level of the track as reference the horizontal force due to acceleration is:
v2 ay = ⋅ cosϕ s − g ⋅ sin ϕ s R
(1)
Horizontal forces ay from equation (1) are shown in Figure 4 for two cases, a freight train carrying iron ore and a high-speed train. The smallest radii R are used, which exist on the railway line they traffic. From the figure it can be seen that the maximum force from one axle is approximately 35 kN for the freight train at 70 km/h and 50 kN for the high speed train at 130-140 km/h. This load is distributed by the rail to two or three neighbouring sleepers. For one fastener the maximum horizontal load will thus be of the order of 12 to 25 kN.
Horizontal force [kN]
100
100
Curve radius: 335 m Train type: Iron ore Axle load: 30 tons
80 60
h=
40 20
m 0m
h=
0m 15
60
m
h
=
0 h
40
m
m
=
15
0
m
m
20
0
0
-20
-20
-40
-40
0
a)
Curve radius: 600 m Train type: X2000 (High speed) Axle load:18.75 tons
80
20
40 60 Train speed [km/h]
80
100
0
b)
40
80 120 Train speed [km/h]
160
200
Figure 4. Horizontal force, ay , as defined in Figure ,3 as function of train speed, v, and heightening, h, of one sleeper end. (a) Freight train with iron ore, R= 335 m. (b) High speed train, R= 600 m.
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3. Material properties The tested sleepers are divided into three categories depending on the cracking: Class 1 “Green” No cracking Class 2 “Yellow” Some cracking Class 3 “Red” Severe cracking The yellow sleepers are subdivided into three categories: Group 1 No cracking on the upper side Group 2 Some cracking on the upper side Group 3 Severe cracking on the upper side The material properties of the concrete have been determined from uniaxial tensile and compression tests on drilled out cores with a diameter of 68 mm, see Figure 5. The concrete was specified to have a cube strength of 60 MPa. The cement content was ordinarily 420 kg/m3. In order to increase the production speed, the cement amount was increased to 500 kg/m3 and heat was used during the hardening process in some of the production plants. The test results are summarised in Table 1.
i:3
i:2
i:1
i = sleeper no. I:1 = tensile I:2 = compression I:3 = reserve
Mid section sleeper
9:1p 9:1 12:1p
b)
a)
Figure 5. Test of material properties. (a) Location of cores. ( b) Crack planes for the test specimens 9:1p, 9:1 and 12:1p. The mean value for 16 compression tests was 100.7 MPa with a standard deviation of 5.9 MPa and a coefficient of variation of 0.06. The mean value for 13 tensile tests was 3.9 MPa with a standard deviation of 0.35 MPa and a coefficient of variation of 0.09. Three test specimens that had cracks according to Figure 5 (b) have not been included in the mean value. If these tests are also included in the mean value the results are 3.3 MPa with a standard deviation 1.29 MPa and a coefficient of variation of 0.39. The sleepers are reinforced with 10 prestressed strands of 6.5 mm in diameter.
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Table 1. Summary of the results from the compression and tensile tests. Index p means that the core comes from that half of the sleeper that has been exposed to the horizontal pull test. Sleeper no. Sleeper Compression Sleeper strength a) No. Class No σc [MPa] mean 8:2 96.5 8:1 8 green 8:2p 101.5 8:1p 9:2 102.6 9:1 9 green 9:2p 95.0 98.9 9:1p 10:2 105.7 10:1 10 yellow/group1 10:2p 98.0 10:1p 11:2 108.9 11:1 11 yellow/group1 11:2p 109.3 105.5 11:1p 12:2 104.5 12:1 12 yellow/group2 12:2p 99.3 12:1p 13:2 104.2 13:1 13 yellow/group2 13:2p 100.8 102.2 13:1p 14:2 86.6 14:1 14 yellow/group3 14:2p 93.3 14:1p 15:2 101.8 15:1 15 yellow/group3 15:2p 103.3 96.3 15:1p a)
Tensile strength σt [MPa] mean 4.25 4.10 (0.90) (0.99) 3.78 3.42 4.04 3.33 4.00 (0.38) 3.76 4.23 3.78 3.34 4.40 3.74
4.17
3.64
4.00
3.81
Test evaluation according to the Swedish Code BBK 94 (1996).
4. Test results The test arrangement is shown in Figure 1. The sleeper was placed on a steel girder and tightened to prevent movement. A hydraulic jack and a load cell were mounted on a bar. To measure the displacement a LVDT was placed horizontally against the fastening. Typical failures are shown in Figures 6 and 7 and typical test results are given in Figures 8 to 9. In Table 2 a summary of all horizontal shear tests is presented. The horizontal load carrying capacity, 100-130 kN, for the fasteners in the green and yellow sleepers are much beyond the load imposed by the trains, cf. section 2. Even the red sleeper with a maximum capacity of 18 kN for a deformation of 5 mm may function if it is surrounded by green and yellow sleepers.
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Figure 6. Failure of sleeper no. 10.
Figure 7. Failure of sleeper no. 11.
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140 Horizontal force [kN]
120 100 80 60 40 20 0 0
2 4 6 8 Displacement fasteners [mm]
10
Tested sleepers Nr 7 - red Nr 5 - green Nr 8- green Nr 9 - green Nr 10 - yellow, group1 Nr 11 - yellow, group1 Nr 12 - yellow, group2 Nr 13 - yellow, group2 Nr 14 - yellow, group3 Nr 15 - yellow, group3
Figure 8. Result from horizontal shear test of fasteners.
Horizontal force [kN]
140
Tested sleepers Nr 5 - green Nr 8- green Nr 9 - green Nr 10 - yellow, group1 Nr 11 - yellow, group1 Nr 12 - yellow, group2 Nr 13 - yellow, group2 Nr 14 - yellow, group3 Nr 15 - yellow, group3
120
100
80
60 0
0.4 0.8 1.2 1.6 Displacement fasteners [mm]
2
Figure 9. Result from horizontal shear test of fasteners. Enlarged detail of figure 8.
5. Failure mechanism The load-carrying capacity according to the Ψ-method, Eligehausen et.al. (1994), can be written as: 0.2
href 1.5 Vu = Ψ ⋅ d ⋅ f cc ⋅ ⋅ c1 d c2 75 á 100 where ψ c′ = = = 0.156 á 0.208, see Figure 10, 1.5c1 1.5 ⋅ 320 ' c
0.5
0.5
d = diameter, varies between 12 and 60 mm, fcc = concrete cube strength, 100 MPa, and href = effective depth, 110 mm.
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Table 2. Summary of all horizontal shear tests. Sleeper no. Class a)
Group b)
Max. horizontal force Fmax, [kN] red 18.0 7 green 117.1 5 green 133.5 8 green 111.0 9 yellow 1 108.1 10 yellow 1 103.8 11 yellow 2 110.9 12 yellow 2 114.1 13 yellow 3 133.5 14 yellow 3 122.9 15 a) Classification performed by the Swedish Rail Administration. b) Classification performed by Luleå University of Technology (LTU). V
c2
c2 c1
c1 = 320 [mm] c2 = 75 to 100
Figure 10.Failure mode of a single anchor loaded in shear when located in a narrow member, Eligehausen et.al. (1994). For c2 = 75 to 100 mm and d = 16 to 60 mm, the ultimate load Vu varies between 52 and 104 kN which can be compared to the test results of 103-133 kN for the sleepers in classes 1 and 2 (green and yellow). When the failure mechanism is compared for the three classes, the red sleeper shows a completely different failure process then the green and yellow ones. The failure process for the red sleeper is calm and steady, i.e. the fastening was slowly pulled out with no large concrete parts falling of. On the other hand, the failure process for the yellow and green sleepers was explosive. The failure started with a crack growing from the fastening and down towards the base where it was divided into two horizontal cracks, one going
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towards the end and the other towards the mid section. When enough energy was built up large sections of the concrete fell of. Possible failure mechanisms are illustrated in Figures 11-14. F e = 130 mm lb = 320 b = 200
Figure 11. Possible failure mechanism at shear test of fasteners. If a simplified stress distribution according to figure 12 is assumed, where the tensile stress decreases linearly along the length, lb, an equilibrium equation around A gives: F e = 130
A
σ
H
[mm] lb/3
σ t ⋅ lb ⋅ 2lb ⋅ b = 0 ⇒ 3 2
A : F ⋅e−
σt =
2lb/3 lb = 320
F ⋅e 3 ⋅ b ⋅ lb
2
200 ⋅ 320
2
≈ 1,98 MPa
→: F − τ ⋅ lb ⋅ b = 0 ⇒
F e = 130
3 ⋅ 103800 ⋅ 130
=
τ
τ =
A
σt
F b ⋅ lb
=
103800 200 ⋅ 320
≈ 1,62 MPa
[mm] 2lb/3
lb/3
lb = 320
Figure 12. Simplified stress distribution. The stress is distributed along the length lb. The lengths lb and e are measured on the tested sleepers. F=103.8 kN (sleeper no. 11). F e = 130 [mm]
A σ lb/9 lb/3
2lb/3 lb = 320
H
A : F ⋅e−
σt =
(
σ t ⋅ lb 8lb 2 ⋅3
27 ⋅ F ⋅ e 4 ⋅ b ⋅ lb
2
=
⋅
9
)
⋅ b = 0 ⇒ σt =
27 ⋅ 103800 ⋅ 130 4 ⋅ 200 ⋅ 320
2
27 ⋅ F ⋅ e 4 ⋅ b ⋅ lb
2
≈ 4, 45 MPa
Figure 13 Simplified stress distribution. The stress is distributed along the length lb/3. The lengths lb and e are measured on the tested sleepers. F=103.8 kN (sleeper no. 11).
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A more realistic assumption is that the tensile stress, σt, is distributed on a distance of lb/3, see figure 13. The propagation of the crack may be studied if the softening properties of the concrete are taken into consideration, cf. Figure 14 and Elfgren (1989, 1998).
F e = 130 [mm]
lb/3 σt
2lb/3 A
H
lb/3 11lb/18 lb/2 lb/6 lb = 320
Figure 14. Failure process if the softening properties of the concrete is taken into consideration.
6. Discussion and Conclusions Small cracks, corresponding to class 2 (yellow sleepers), do not seem to influence the horizontal load carrying capacity of the tested fasteners significantly. It is first when the cracking is very severe (red sleepers) that the load-carrying capacity is reduced so much that it is approaching the level of the applied load. The sleepers produced with inferior methods are now inspected annually in order to see at what rate the cracking is progressing.
7. References BBK 94 (1996): Swedish Handbook on Concrete Design, Vol. 1 and 2. (Boverkets Handbok om Betongkonstruktioner, In Swedish), Boverket, Karlskrona 1994, 1996, 185 pp and 116 pp, ISBN 91-7332-686-0, 91-7332-687-9. Elfgren, Lennart, Editor (1989): Fracture mechanics of concrete structures. From theory to applications. Chapman & Hall, London, London 1989, 407 pp. ISBN 0 412 30680 8. Elfgren, Lennart, Editor (1998): Round Robin Analysis and Tests of Anchor Bolts in Concrete Structures. RILEM Technical Committee 90-FMA Fracture Mechanics of
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Concrete - Applications. Research Report 1998:14, Division of Structural Engineering, Luleå University of Technology, 54 + 371 pp. Eligehausen, Rolf, Editor (1994): Fastenings to concrete and masonry structures. State of the art report. Comité Euro-International du Béton, CEB Bulletin 216. Thomas Telford, London 1994, 249 pp. ISBN 0 7277 1937 8. Tepponen, Pirjo and Eriksson, Bo-Erik (1987): Damages in concrete railway sleepers in Finland, Nordic Concrete Research, Oslo, V.6. 1987, pp. 199-200. Thun, Håkan and Elfgren, Lennart (2001): Testing of concrete sleepers (In Swedish). Project report 1047106:1, Preliminary version, February 2001. Division of Structural Engineering, Luleå University of Technology, 26 pp. Utsi, Sofia and Elfgren, Lennart (2000): Testing of concrete sleepers (In Swedish). Test Report. May 2000, Division of Structural Engineering, Luleå University of Technology, 20 pp.
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ANCHORAGE WITH HEADED BARS IN EXTERIOR BEAM-COLUMN JOINTS J. Hegger, W. Roeser Institut für Massivbau, RWTH Aachen, Germany
Abstract In exterior RC beam-column joints the anchorage of the beam reinforcement within the joint is of great importance for the load bearing capacity of the connection. The classical arrangement is to bend down the beam bars into the column. The high amount of reinforcement causes detailing problems in terms of placing the reinforcement bars and casting the concrete. Therefore the application of headed bars in beam-column joints was investigated in three test specimens. Employing headed bars the handling on site is much easier and the load-bearing capacity can be increased. In addition to the tests a numerical investigation was carried out.
1.
Introduction
Exterior beam-column joints are subjected to high normal and shear forces as well as to bending moments, which lead to high shear and bond stresses acting inside the joint. Thus particular importance is assigned to the detailing of the exterior beam-column joints because of the complex state of strains. The high amount of reinforcement requires a special detailing with respect to the placing of reinforcing bars and obstacles during casting the concrete. In order to achieve a short anchorage length with negligible slip the application of headed bars was investigated.
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2.
Test specimens with welded heads
The experimental study on exterior beam-column joints [1] consisted of three specimens with welded heads and five specimens with U-bended bars. The diameter of the beamflexural-reinforcement varied between 20 and 25 mm. The area of the welded head is 6.25 to 7.3 times as large as the bar area (Fig. 1a). The head of the bars was placed within the concrete cover behind the column reinforcement (Fig.1b). The ratio between the anchorage length and the bar diameter lb/∅ = 6.8 to 10 was very short.
2 ⋅ 3 ∅ 16 Anchor ∅ 20
2 ∅ 20 –25
Head
hbeam 30 cm
Head ∅ 50
Stirrups ∅ 10
hcol 20 –24 cm Fig. 1: a) Headed bar ∅ 20 mm
b) Detailing of the beam-column joint
The shear slenderness of the beam-column joint varied from hbeam/hcol = 1.25 to 1.5 and the concrete strength between fc,cyl = 55 and 85 MPa (table 1). The bending moment was created by a hydraulic jack at the end of the beam. A normal force was applied to the column independently with respect to the bending moment. The stress conditions of an exterior beam-column joint could be simulated with sufficient accuracy by the test arrangement. The crack pattern was characterised by bending cracks in the beam and by diagonal cracking in the joint. The diagonal cracks in the region of the joint developed parallely to the direction of the concrete compressive strut. At serviceability limit state all crack widths were less than w = 0.3 mm.
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In the tests two different modes of failure were observed: •
Ductile beam failure (Fig. 2a)
At ultimate limit state the main cracks in the beam opened more than w = 1.0 mm and the tensile reinforcement yielded. The load deflection curve revealed a very ductile behaviour (Fig. 3) with large plastic beam rotations. •
Semi ductile joint failure (Fig. 2b)
At ultimate limit state one main diagonal crack developed from the compression zone of the beam to the compression zone of the upper column. Finally a concrete crushing of the compression zone of the lower column was observed. The load deflection curve is characterised by a semi ductile behaviour (Fig. 3) with considerable shear distortions in the joint.
a) beam failure
b) joint failure
Fig. 2: Characteristic failure pattern: a) Beam failure; b) Joint failure
In none of the tests a local anchorage failure or lateral “blow out failure” of the concrete cover was observed. This is in accordance to pull-out tests of Bashandy [2], who observed a “blow out failure” only in cases with an anchor in front of the column reinforcement. In comparison to tests with hooked bar reinforcement the load bearing was increased considerably.
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160 RK 3: beam failure (ductile)
140 120 F [kN]
100 80 RK 5: joint failure (semi ductile)
60 40 20 0 0
20
40
60
80
100
w [mm]
Fig.3:
Load deflection curves of the test specimens RK 3 (beam failure) and RK 5 (joint failure)
Table 1: Test Parameters Test
hbeam/hcol
fc,cyl
∅
[MPa]
[mm]
[kN]
Ncolumn,ULS Mtest/Mcalc
Mode of failure
RK 3
1.25
57.2
20
-500
1.13
Beam
RK 5
1.50
54.9
25
-500
0.75
Joint
RK 6
1.50
86.5
25
-500
1.03
Joint
hbeam/hcol = shear slenderness; fc,cyl =concrete cylinder strength; ∅ = diameter anchored bar; Ncolumn = axial column load at ultimate load; Mtest/Mcalc = ratio maximum bending moment in the test and calculated bending moment of the beam
In figure 4 the measured stresses of the reinforcement in the beam-column intersection σbeam and at the anchor head σanchor are compared. As a result of the bond action in the joint area the stress of the reinforcement is decreased. The bond forces depend on the anchorage length, the bar diameter, the column load and the concrete strength. Within the anchorage length lb the following observations were done: If the column load
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decreases the bond action close to the beam decreases. If the beam moment decreases the bond action in the anchor region increases and decreases close to the beam. In the ultimate limit state 50 to 60 % of the yield load was carried by the anchor.
600
lb
T
σanchor [MPa]
500
σanchor σbeam
400 300
bond action
200 100
anchor action
0 0
100
200
300
400
500
fy 600
σbeam [MPa] Fig. 4: Stress of the beam reinforcement versus stress of the anchor for the specimen RK 5
3.
Semi Empirical Model
In [1] a semi empirical model on the basis of the formula of Vollum [3] was developed, which can predict the failure mode and the load bearing capacity in good accordance with a test databank including more than 180 tests on exterior beam-column joints. This model takes into account different detailing of the beam reinforcement (180° hook, 90° hook, anchor) and the shear reinforcement. The variation coefficient of Vx = 12% confirms the good agreement between predicted and experimental failure load (Fig. 5). On the basis of the half-empirical model simple design rules were developed for traditional detailing with bended bars (chapter 3.1) and headed bars (chapter 3.2). These design rules already includes the partial safety factors for material properties.
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600 Vj,exp / Vj,calc Mx = 1,0 Sx = 0,12 Vx = 0,12 Xk = 0,8 Mx
Vj,exp [kN]
500 400
Mx
Xk
300 200 100 0 0
100
200
300
400
500
600
Vj,calc [kN] Fig. 5: Comparison of experimental and predicted joint failure load by semi empirical model [1]: mean value Mx; standard deviation Sx, variation coefficient Vx, characteristic value Xk 3.1
Design in the case of anchorage with hooked bars
In the case of anchorage with hooked bars the design joint shear resistance can be calculated with the equations (1) to (3). •
Design shear resistance without stirrups: Vj,cd
Where: hbeam/hcol beff •
= 1.4 (1.2 – 0.3
hbeam ) beff hcol fcd1/4 hcol
(1)
= slenderness (1.0 ≤ hbeam/hcol ≤ 2.0) = (bcol+bbeam/2) ≥ bcol
Design shear resistance with stirrups: Vj,Rd = Vj,cd + 0,4 ⋅ Asj,eff ⋅ fyd
Where: Asj,eff γ
≤ 2 Vj,cd ≤ γ 0.25 ⋅ fcd ⋅ beff ⋅ hcol
(2)
= effective shear reinforcement (stirrups in the joint area above the beam compression zone) = Min {1; 1.5 (1-0.8 NSdcol/(Ac ⋅ fck)} ⋅ Min {1;1.9 –0.6 hbeam/hcol}
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•
Design shear force: Vjh,Sd = As ⋅ fyd – VSd,col
(3)
It has to be shown that the design shear force Vjh,Sd is less than the resistance Vj,Rd. 3.2
Design in the case of anchorage with headed bars
In the case of headed bars the improved anchorage behaviour is considered in equations (4) to (6): •
Design shear resistance without stirrups: Vj,cd = 1.55 (1.2 – 0.3
Where: hbeam/hcol beff •
hbeam ) beff hcol fcd1/4 hcol
(4)
= slenderness (1.0 ≤ hbeam/hcol ≤ 2.0) = (bcol+bbeam/2) ≥ bcol
Design shear resistance with stirrups: Vj,Rd = Vj,cd + 0.45 ⋅ Asj,eff ⋅ fyd
Where: Asj,eff γ •
≤ 2 Vj,cd ≤ γ 0.3 ⋅ fcd ⋅ beff ⋅ hcol (5) = effective shear reinforcement (stirrups in the joint area above the beam compression zone) N Sd ,col )} ⋅ Min {1;1.9 –0.6 hbeam/hcol} = Min {1; 1.5 (1- 0.8 Ac ⋅ f ck
Design shear force: Vjh,Sd = As ⋅ fyd – VSd,col
(6)
It has to be shown that the design shear force Vjh,Sd is less than the resistance Vj,Rd.
4.
Numerical Investigations
In addition to the tests extensive numerical simulations were carried out. Finite Elemente studies on exterior beam-column joints employing the program SBETA were already done by Hamil [4]. The successor program ATENA 2D [5] was applied for the own simulations. In difference to Hamil the arc-length-method was used instead of the Newton-Rhapson-solution method, so that a descending branch in the load deflection curve could be simulated and the load bearing capacity could be clearly identified. In the own calculation the compressive fracture energy Gc was modified in order to prevent a
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progressive concrete failure within the two axial compressive zone at the beam-column intersection. In ATENA rigid bond is assumed between concrete and reinforcement. Therefore the FE-mesh in the area of the joint was refined, in order to simulate the bond characteristics by the local deformations of the concrete elements. The anchors were simulated by elastic sheet elements. Figure 6 compares the load-deflection response of ATENA and test specimen RK 5. Before reaching the maximum load the simulation is very close to the test results. After joint failure at maximum load a descending branch could be observed. Figure 7 compares the measured with the calculated strains of the stirrup in the middle of the joint of test specimen RK 3. Due to the crack formation in the joint at a load level of F ≈ 60 kN the strains of the stirrups increase. Generally, the calculated values are in very good accordance with the measured values, confirming that ATENA can predict the anchorage behaviour quite well. Figure 8 presents the calculated deformations and crack formations, being in good accordance with the test specimens. 140 RK 5 120
Vbeam [kN]
100 F
80
ATENA
60 w 40 20 0 0
10
20
30
w [mm] Fig.6:
Load-deflection-diagram calculated by ATENA and from test RK 5
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40
160 140 ATENA
120 F [kN]
100
RK 3
80 60 40 20 0 0
0,0005
0,001
0,0015
0,002
0,0025
0,003
ε [-]
Fig.7:
Load-strain-diagram of joint-stirrup calculated by ATENA and from test RK 3
Fig. 8: Specimen RK 6 after test and numerical simulation (principal compression strains ε2, crack pattern and deformations)
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5.
Conclusions
From the test results and the numerical simulations the following conclusions can be drawn: • • • •
• •
In the tests of exterior beam-column joints two different failure modes were observed: a) beam failure with ductile behaviour and b) joint failure with semi ductile behaviour. Employing headed bars the load bearing capacity increased by 20 % in comparison to hooked bars. The anchor head was placed behind the exterior column reinforcement. At serviceability limit state the crack width in all specimens was less than w = 0.3 mm. From theoretical investigations a semi empirical model was developed. This model predicts the failure mode and the ultimate bearing load in good accordance with the own data-base of more than 180 tests on exterior beam-column joints. Simple design rules for the use of welded anchors were developed. Numerical simulations with the nonlinear FE-program ATENA demonstrate a very good correlation with the test program. The handling on site with headed bars is much easier compared to traditional detailing because only straight bars are used.
Further investigations are going on and will be published soon. 6.
References
[1]
Hegger, J., Roeser, W.: Bemessung und Konstruktion von Rahmenendknoten; Abschlußbericht zu AiF-Vorhaben 11834 N (DBV 213), Bericht des Institutes für Massivbau der RWTH Aachen, 2000
[2]
Bashandy, T.R.: Application of Headed Bars in Concrete Members; Dissertation; University of Texas, Austin, 1996
[3]
Vollum, R.L.: Design and Analysis of reinforced concrete beam-column joints; PhD-Thesis; Concrete Structures Section; Department of Civil Engineering; Imperial College; London; April 1998
[4]
Hamil, S.J.: Reinforced Concrete Beam-Column Connection Behaviour; PhD Thesis (Final Draft); University of Durham; 1999
[5]
Cervenka Consulting: ATENA Program Documentation (Revision 05/2000); Prag, 2000
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HALFEN HDB-S BARS AS SHEAR REINFORCEMENT IN SLABS AND BEAMS J. Hegger*, K. Fröhlich***, R. Beutel**, W. Roeser* * Institut für Massivbau, RWTH Aachen, Germany ** Hegger und Partner GbR, Aachen, Germany *** Halfen GmbH & Co KG, Wiernsheim, Germany
Abstract By obtaining the German approval Z-15.1-165 (DIBT) [1] the application of Halfen double headed studs has been extended generally to slabs and beams subjected to shearforces.
1.
Introduction
HDB bars are reinforcement devices made of high bond reinforcement S 500 with forged plate-shaped heads at both ends (triple stud diameter; the ribbed surfaces reach to the heads). In slabs with a low effective depth the heads ensure a very effective anchoring behaviour. Up to 1999 the double headed studs have been used successfully as punching shear reinforcement in slabs and foundations. In such situations, notable features are the high shear capacity and the easy installation on site. An effective shear reinforcement can also be required for line-supported slabs of highly loaded industrial constructions as well as in the areas of concentrated loads in ordinary buildings. The Institute for Structural Concrete (IMB) of the Aachen University of Technology (RWTH) carried out tests on shear reinforced line-supported slabs and beams in order to determine the ultimate shear capacities of HDB bars (figure 1) [2].
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Phase I Q
Q
Series P
h a
a
40
Series A and B
h 40
Phase II
Q
68
h h
a 30
Series C
Fig. 1: Tests on shear reinforced slab-strips and beams: left : HDB-stud ; right : test specimens-geometry and loading
2. 2.1
Tests on slabs Ultimate load bearing capacity of shear reinforced slabs (DIN 1045: τ < τ02)
For load levels which induce yielding of the shear reinforcement the structural behaviour of HDB studs was investigated in test-series P, with the dimensions l/b/d = 3.20/0.40/0.25. Intention of these tests was to evaluate the influence of the longitudinal and transverse spacing of the HDB bars, the influence of the transverse reinforcement and the combination of HDB bars and stirrups. For this purpose two slab-strps with stirrups were tested, four with a mixed reinforcement of HDB bars and stirrups as well and six slabs reinforced by HDB bars only. The concrete compressive cube strength βw200 (200mm side length) of the specimens reached 20.2 to 24.5 MPa. The flexural reinforcement ratio varied between µL = 1.52 % and 1.85 %. All tests failed in shear. After formation of the first shear cracks the strains of the HDB bars increased considerably and an early failure of the concrete compressive zone was avoided by the HDB anchors. By increasing the load the yield strength of the HDB anchors was reached. Due to the well anchored HDB bars the concrete contribution of the shear capacity increased in comparison to stirrups. Therefore, the amount of the HDB bars could be decreased in comparison to slabs with ordinary shear reinforcement. Figure 2 shows an example for the midspan deflection behaviour and the strain developement of the HDB bars in specimen P2. The verification of the measured strains by a strut and tie analogy results in a strut inclination between θ = 35 ° and 45 °. The
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evaluation of the failure loads according to DIN 1045 (88) [3] leads to the following results: ●
Each specimen of the series P required shear reinforcement.
●
All specimens with HDB bars reached a considerably higher shear capacity than the calculated shear capacity for members with stirrups according to DIN 1045 (88).
•
All specimens including stirrups and HDB bars and all tests with HDB bars only reached a higher shear capacity than the tests with stirrups. This also applies to shear stresses that are higher than the admissible shear stresses for shear assemblies (shear ladders) according to DIN 1045 (88). 200
2Q 160
160 70
Shear force V in [kN]
Shear force V in [kN]
200
70
120 80 40
120 80 40
0 0.0
0 0
2
4 6 8 Deflection in midspan in [mm]
10
0.5
12
1.0
1.5
2.0
2.5
3.0
3.5
strains HDB-anchor in [‰] Plastic strains of phase I
Fig. 2: Slab test P2: left: Load-deflection behaviour; right: anchor strains 2.2
Maximum shear capacity of shear reinforced slabs (DIN 1045: τ = τ02)
The specimens in test series A and B are very similar in dimensions and structural design. The specimens (h/b/l = 0.14-0.25/0.40/1.40-2.50) were tested with a shear slenderness a/d of 3 up to 4. An early bending failure was avoided by a T-beam cross section and flexural reinforcement of grade St885/1080. More over, an anchorage failure of this reinforcement was excluded by detailing. The variation of the test parameters are given in table 1. Table 1: Parameters in Test Series A and B ßw200 [MPa] sl st Series ∅HDB [mm] A 14-25 mm 25.4-43.5 0.75 d 0.6 d B 14-25 mm 28.8-40.0 0.75 –1.5 d 0.6 –1.5 d ∅HDB = diameter HDB studs; βw200 =concrete cube strength according to DIN 1045(88); sl =longitudinal HDB spacing; st =transverse HDB spacing
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The crack formation of the specimens during loading can be characterised by the following items: The first cracks occurred in the middle of the beam due to bending and continued up to the compression zone. Further bending cracks appeared near the supports. Out of these bending cracks first shear cracks developed by increasing the load. Finally, two main shear cracks with a large width of 1 to 2 mm were observed. The crack inclination at failure formed approximately a line between support and load bearing plate. In addition, horizontal cracks occurred suddenly before reaching the ultimate load. Their width increased at once to several millimetres and leads to a splitting of the concrete compression zone (figure 3). In the area of the load bearing plate the concrete split of above the studs. Usually, the shear reinforcement did not reach the yield strength in series A and B. Thus, in contrast to the test series P a concrete failure was always observed. This concrete failure is typical for slabs reaching the maximum shear capacity, being lower compared to beams with an large effective depth.
Load bearing
Tensile reinforcement
IMB
RWTH Aachen
Halfen HDB-Stud Ø16
A1-left Fig. 3: Test specimen A1 after failure The maximum shear capacity is determined by the failure of the concrete struts or by splitting of the bending compression zone. This behaviour is considered by the admissible design shear strength τ02 according to DIN 1045 (88) in dependence of the concrete strength. Figure 4 shows that a global safety factor γ > 2,1 was reached.
798
3.0
2.5
Mean value γ = 2,37
2.0
Required safety factor γ = 2,1
1.5
1.0 0.6
0.7
0.8
0.9
1.0
1.1
1.2
Ratio asw,prov. / asw,req. [-]
Fig. 4: Influence of shear reinforcement ratio on global safety factor γ in series A and B (Vu = Ultimate load at test; VDIN τ02 = Upper design shear strength for slabs according to DIN 1045 (88); asw = amount of shear reinforcement) Furthermore, the flexural reinforcement ratio determines the maximum shear load, as well. In order to determine the required amount of HDB bars as shear reinforcement in spot-supported and line-supported slabs the upper stress limit was formulated according to the regulations for HDB bars as punching shear reinforcement (equation 1). max τ = 0,7 ⋅ 1,4 ⋅ τ02 ⋅
µg .
(1)
with:
τ02 = upper shear limit for slabs according to DIN 1045 (88) µg = geometric ratio of longitudinal reinforcement according to DIN 1045(88)
3
Test on beams
Three beam specimens (h/b/l = 0.71/0.08/3.90) were tested in series C with a Icrosssection and Halfen HDB bars as shear reinforcement. The test parameters were the diameter and the longitudinal spacing of HDB bars (∅ 16, sl = 13 cm and ∅ 20, sl = 15 cm) as well as the concrete compressive strength (26,5 < βw200 < 35,8 MPa). The longitudinal reinforcement was designed to exclude a bending failure. The test set-up corresponded to a three-point bending test with a shear slenderness a/d of 3. All three tests failed by a concrete strut crushing in the thin web, when the HDB bars did not reach the yield strength (figure 5). In order to verify the results, the variable strut inclination method for shear design was employed. All measured strains could be verified considering a strut inclination between 37° and 39°.
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Fig.5:
Test specimen C2 after failure
The beams with HDB-studs reached the maximum shear capacity according to DIN 1045 and EC 2 [4]. The global safety factor γ between the failure shear stress of the tests and the ultimate limit shear strength τ03, according to DIN 1045, exceeded the value 2.1.
4
Anchorage behaviour
The tests indicated that the HDB stud-diameter of the shear reinforcement has to be limited in dependence on the total slab depth (figure 6). It has to be pointed out, that stirrups and bend-up bars also require a similar limitation. These limits are governed by the anchorage behaviour in the compression zone. For HDB studs the limitation was defined according to the test data by equation (2). ∅HDB max ≤ 4 ⋅ with:
(2)
d
∅HDB max d
bar diameter in [mm] height of slab or beam in [cm]
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 10
12
14
16 18 20 Anchor diameter in [mm]
22
24 25
Fig. 6: Influence of the anchor diameter ∅HDB on the global safety factor γ =VTest / VDIN 1045(88)
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The local bearing behaviour of HDB bars can be compared directly with headed dowels of fixing systems. Eligehausen et al. [5] defined three different types of failure for headed dowels in tension. The lateral “blow out” concrete failure (figure 7) has to be controlled in case of slabs and beams reinforced with HDB studs. In order to avoid this concrete failure the edge distances aQHDB according to tables 2 and 3 are required.
FHDB
Lateral blow out failure
Concrete wedge
0.2.FHDB
aQ,HDB Fig. 7: Blow Out failure The reduced edge distances aQHDB in table 4 may only be used if at least one longitudinal bar and a stirrup is placed between the free edge and the HDB stud (figure 8). Due to the large stud diameter of the HDB bars there will be a medium level of local compression under the head, thus, according to [5] a lateral force of 0,2 FHDB can be estimated (figure 7). The stirrups in the lateral blow out area have to be designed in minimum for this force. For structural reasons the stirrup cross section shall not be smaller than ∅ 8. Profiled cross sections generally have to be designed for shear between web and flanges. This required shear reinforcement is also able to carry the tension force Z according to figure 7 and to avoid a blow-out failure.
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Table 2: Minimum distances to free edges aQ,HDB [cm] of double headed studs depending on concrete strength βwN and stud diameter ∅HDB.
βwN [N/mm2]
25
10 12
12 15
∅HDB [mm] 14 16 17 20
20 25
25 31
35 45 55
11 9 8
13 11 10
15 13 12
21 19 17
26 23 21
17 15 13
Table 3: Reduced minimum distances to free edges aQ, HDB [cm], by providing a minimum stirrup diameter and longitudinal bar diameter according to fig. 8. Ø HDBanchor
Minimumstirrup-Ø
Minimum longitudinal-Ø
[mm] 10 12 14 16 20 25
[mm] 8 8 8 8 10 12
[mm] 10 10 10 10 12 16
stirrup
HDB stud
longitudinal reinforcement
aQ,HDB Fig. 8 : Clear distance to free edges aQ, HDB
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Clear distance aQ, HDB [cm] depending on concrete strength B25 B35 B45 B55 7 6 6 5 9 8 7 6 10 9 8 7 12 10 9 8 15 13 11 10 19 16 14 13
Fig. 9: Installation of HDB double headed studs after placing the main flexural reinforcement
Fig. 10: Installation clip bars can be fixed between any position of the clear stud space
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5.
Summary
By obtaining the new approval Z-15.1-165 of the Halfen HDB double head studs the application of punching reinforcement was extended to slabs and beams subjected to shear-stresses. The maximum shear stresses according to DIN 1045, τ02 for slabs and τ03 for beams, can also be employed for HDB anchors. In case of thin slabs the shear reinforcement quantity can be reduced by 20 % in comparison to stirrups. The substantial advantage of the HDB shear reinforcement is the quick and easy placing on site and thus the reduction of the labour costs. During a pilot project two days of the construction time could be saved by using the HDB assemblies. Moreover, the installation of the HDB studs allows any adjustments to the positioning after placing the flexural reinforcement. The disadvantages of high stirrup quantities can be reduced considerably by using HDB studs with larger diameters so that gravel damps in concrete can be easily avoided. Large bar diameters can also be used in beams with thin webs, because the plate-shaped heads of the stud require less space than the bends of the stirrups.
6.
References
[1]
Zulassung Nr. Z-15.1-165: Halfen –Schubbewehrung Typ HDB-S; Deutsches Institut für Bautechnik, 1999
[2]
Hegger, J.: Albartus, D.; Beutel, R.; Roeser, W.: Neue Anwendungen für HDB-Doppelkopfanker, Schubbewehrung in Platten und Balken; Beton- und Stahlbetonbau, Heft 12/1999; S. 537-545
[3]
DIN 1045: Beton und Stahlbeton: Bemessung und Ausführung. Juli 1988.
[4]
Eurocode 2: Design of Concrete Structures, Part 1: General Rules and Rules for Buildings; December 1989
[5]
Eligehausen, R.; Mallee, R.; Rehm, G.: Befestigungstechnik; Betonkalender 1997; Ernst und Sohn
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BEHAVIOUR OF FASTENERS IN CONCRETE WITH COARSE RECYCLED CONCRETE AND MASONRY AGGREGATES D.A. Hordijk*, R. van der Pluijm** *Adviesbureau ir. J.G. Hageman B.V., The Netherlands **TNO Building and Construction Research, The Netherlands
Abstract In the Netherlands for already about two decades, there is a strong interest in reuse of concrete and masonry aggregates in new concrete structures. According to the current Dutch Concrete Code it is allowed to replace 20% of coarse dense aggregates by mixed recycled aggregates (combination of concrete and masonry aggregates). Furthermore according to a CUR Recommendation [1] replacement of 100% of the coarse aggregates is allowed in concrete walls for structures in safety class 1 and 2 (no or small risk for human life). Before further extending the possibilities for the use of concrete and masonry aggregates in concrete, it was decided to first investigate the behaviour of mixed recycled aggregate with respect to several phenomena. As part of an extensive research programme TNO Building and Construction Research performed tensile tests on cast-in-place and postinstalled anchors. The anchors were loaded in tension till failure. For the base material gravel concrete (reference), mixed recycled aggregate concrete and masonry concrete (100% masonry aggregates for the coarse aggregates) was used. In the paper the experiments and the obtained results are presented.
1. Introduction The interest for our environment and the effect of all our human actions on it, is getting more and more interest nowadays. So, also in the construction industry building activities are increasingly being judged from a sustainability point of view. In that respect the use of recycled concrete and demolition waste, as aggregate in new concrete structures, can be regarded as one of the best ways to meet the challenges of sustainability in the concrete industry. Already for many years reuse of concrete and masonry is an issue in crowded countries with limited land space for dumping demolition debris. In the Netherlands, a first extensive investigation with respect to reuse of concrete and masonry aggregates was
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performed in the first half of the eighties. As an outcome of these investigations it is in the Netherlands allowed to replace coarse aggregates by a maximum of 20% by volume. As replacement concrete aggregates, masonry aggregates, lightweight aggregates, or a combination may be used with the restriction that the total amount of masonry and lightweight aggregates is not more than 10% by volume. For these replacements the Concrete Code can be used without any modification. According to a CUR Recommendation [1], dating from 1997, replacement of 100% of the coarse aggregates is allowed in concrete walls for structures in safety class 1 and 2 (no or small risk for human life). In order to extent the possibilities for reuse of concrete and masonry aggregates in concrete an extensive research programme was performed by the Delft University of Technology and TNO Building and Construction Research under the auspices of CUR Research Committee C107B [2]. As part of the investigations the behaviour of anchors in concrete with mixed recycled aggregates was investigated. The experiments and results are presented in this paper.
2. Aim Mixed recycled aggregate concrete also contains masonry aggregates with a relative low stiffness and strength. In that respect questions were raised about the possible consequences of these weak spots on mechanisms were concentrated loads play an important role, like for instance with short (expansion) anchors. The same, of course, holds true for lightweight aggregate concrete. It is known that the behaviour of lightweight aggregate concrete under concentrated loads is different from gravel aggregate concrete [3]. However, for the behaviour of short anchors in lightweight concrete only very little is known. Since fastenings made with short anchors are more and more being used in daily practice it was decided to study their behaviour in mixed recycled aggregate concrete in a pragmatic way by applying a number of tensile tests.
3. Effect of base material on the behaviour of anchors The behaviour of various types of anchors and anchor groups is studied extensively in recent years (see for instance [4]). However, for the effect of the base material on the anchor properties, not much information can be found in the literature. In the following, first some properties of recycled aggregate concrete will be discussed. From the investigations into the behaviour of concrete with mixed recycled aggregates it appeared that there is a great similarity with lightweight aggregate concrete. So, for most clauses in the Concrete Code adaptations in a way analogous to lightweight aggregate concrete are applicable. For instance, the Young’s modulus is lower than for normal weight concrete and a reduction factor based on the concrete density can be used to account for this. It appeared, however, that the time dependent properties, shrinkage and
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creep, are significantly larger for recycled aggregate concrete than for lightweight aggregate concrete [4]. Tensile experiments on anchors in concrete and/or masonry aggregate concrete as well as in lightweight concrete are not known to the authors. Therefore, in order to get an idea about the possible influence of the base material on the anchor behaviour, a theoretical model in [4] can be used. For the tensile strength Nu for concrete failure of headed and expansion anchors usually the following empirical equation is used: Nu = a ⋅ fc0.5 ⋅ hef1,5
(1)
In equation 1 a is a constant, hef is the effective depth and fc is the concrete compressive strength. In this relation the compressive strength is used for practical reasons. Since a concrete cone is breaking out using the concrete tensile strength would be more logical. Eligehausen and Sawade [4,6], however, presented a model based on nonlinear fracture mechanics and concluded that the cone failure load depends on the factor (E⋅GF)0.5 and not on the tensile strength. E is the Young’s modulus and GF is the fracture energy of the concrete. The term (E⋅GF)0.5 represents the term fc0.5 in equation 1 and accounts for the influence of the concrete mix on the failure load [4].
4. Experiments 4.1 General Tensile tests are performed on anchors in three different types of concrete. Besides the concrete with mixed recycled aggregates, concrete with ordinary river gravel was used as a reference. Furthermore, concrete with solely masonry aggregates as coarse aggregates. In fact, it was intended to investigate a possible effect of a masonry aggregate in the highly stressed anchorage area of an anchor. Since, in theory, with mixed recycled aggregates it is still possible that only concrete aggregates are located around the anchorage zone, the masonry aggregate concrete was introduced. 4.2 Concrete The mix compositions for the applied types of concrete are given in Table 1. There, also some properties of the fresh concrete are given. The goal was to obtain the same compressive strength for the three types of concrete. Because of the weaker masonry aggregates the cement content was increased and the water-cement ratio was decreased for the mixed recycled aggregate concrete and even more for the masonry aggregate concrete. It turned out that for the latter these measures caused a little too much increase in strength, as can be seen in Table 2, where the measured properties of the hardened concrete are listed.
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Table 1 Mix compositions and some fresh concrete properties for the three applied types of concrete.
Mix composition cement CEM III/B 42.5 LH HS (kg/m3) 3
water content
(kg/m )
water/cement-ratio dry sand 0-4
masonry aggregate concrete
280
300
320
180
181
170
0.64
0.60
0.53
822
896
857
3
1017
-
-
-
815
-
(kg/m )
mixed recycled aggregate1) 4-16 (kg/m3) 1)
mixed recycled aggregate concrete
3
(kg/m )
river gravel 4-16
gravel concrete
3
masonry aggregate 4-16
(kg/m )
-
-
839
fines < 250 µm
(l/m3)
133
143
146
(kg/m )
2328
2204
2207
(% V/V)
0.4
1.0
2.2
fresh density air content 1)
3
The coarse mixed recycled and masonry aggregates were pre-wetted.
From Table 2 it can be seen that the tensile splitting strength after 28 days was almost equal for the three applied concrete mixes. The Young’s modulus of the mixed recycled aggregate and the masonry aggregate is approximately 70% of the Young’s modulus of the gravel concrete. A reduction of Young’s modulus coincides with what is usually found for lightweight aggregate concrete. Although a decrease of 30% is relatively large for a concrete with a density of 2200 kg/m3. The fracture energy was not determined for the concrete mixes used for the tensile tests on anchors. However, in an accompanying test programme performed in the Stevin Laboratory of the Delft University of Technology, fracture energy was determined on concrete specimens made with a slightly different concrete composition. The obtained values for the fracture energy of mixed recycled aggregate and masonry aggregate concrete are in the range that is found for lightweight aggregate concrete [3]. For the fracture energy of gravel concrete in Table 2 a value is listed, that can usually be found in the literature.
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Table 2 28-day-properties of the hardened concrete; variation coefficient between brackets ( ). gravel concrete
Mix composition cube compressive strength (N/mm2) cube splitting strength Young’s modulus
Fracture energy 1)
1)
masonry aggregate concrete
31.1 (1.7)
31.8 (2.4)
37.8 (2.6)
2
2.72 (0.6)
2.71 (4.2)
2.80 (5.1)
2
30700 (9.3)
21700 (2.4)
21500 (2.5)
(kg/m )
2328 (0.2)
2204 (0.2)
2207 (0.5)
(N/m)
80 - 100
(N/mm ) (N/mm ) 3
density
mixed recycled aggregate concrete
62
60
Fracture energy as obtained in an accompanying test programme with slightly different mix compositions.
Based on the values obtained for respectively the Young’s modulus and the fracture energy and the theory that the tensile capacity of an anchor for concrete cone failure depends on a factor (E⋅GF)0.5 a reduction of the tensile capacity till a value between 65% and 75% of the capacity for normal gravel concrete can be expected. 4.3 Fasteners In the experiments two types of cast-in-place and two types of post-installed anchors were used (see Figure 1). For the post-installed anchors torque-controlled expansions anchors M8 and M16 with an effective depth of respectively 44 mm and 66 mm were used. For the cast-in-place anchors a M12 threaded inserts with an effective depth of approximately 55 mm and a headed anchors M16 with an effective depth of 127 mm were used.
Fig. 1: Photo of the anchors used in the experiments
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Per type of anchor four tensile tests were performed. The anchors were placed in concrete elements with the dimensions of 1.6m x 1.3m x 0.3m. For each type of concrete two elements were used. The cast-in-place anchors were placed in the bottom of the formwork. After the concrete was hardened, the elements were turned around and the expansion anchors were placed in the same cast site as the cast-in-place anchors. 4.4 Experiments For the tensile tests on the anchors the guidelines given in Annex A of the ETAG (European Technical Approval Guideline) for metal anchors for use in concrete [7] were followed. A photo of the applied tensile equipment is given in Figure 2. For the measurement of the deformation of the anchors two displacement transducers (LVDT’s) at a distance 1.5⋅hef from the anchor were used. For the M8 and M12 anchors the LVDT’s were mounted to the anchor at a distance of 65 mm above the concrete surface, while this was 100 mm for the M16 anchors.
Fig. 2: Photo of the test arrangement used for the tensile tests on the anchors. The load was applied by means of an actuator connected to a hand pump. By this way also a descending branch could be obtained.
5. Results In Table 3 the measured maximum load in the tensile tests is given. In Figures 3 to 6 hand-smoothed average load-deformation relations are presented for the four types of anchors respectively.
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Table 3: Measured maximum loads (kN) in the tensile test on the anchors. Headed anchors M16 Threaded insert M12 Gravel Mixed Masonry Gravel Mixed Masonry recycled recycled fck = 31.8 fck = fck = 37.8 fck = 31.1 fck = 31.8 fck = 37.8 31.12) 105.6 106.2 32,1 31,2 30,4 106.2 (3.0)3) (3.7) (2.7) (1,1) (3,1) (6,2) Torque-controlled expansion anchor M16 Torque-controlled expansion anchor M 8 Gravel Mixed Masonry Gravel Mixed Masonry recycled recycled fck = 31.1 fck = 31.8 fck = 37.8 fck = 31.1 fck = 31.8 fck = 37.8 43.4 33.4 33.1 17.1 15.2 16.0 (7.5) (9.4) (6.9) (0.5) (7.2) (6.9) 1) Type of aggregate used 2) fck is the mean concrete compressive strength in MPa; 3) Coefficient of variation in % between brackets. 1)
For the headed anchors the maximum load was more or less equal for the three concrete mixes. This can be explained by the fact that steel failure was governing instead of concrete cone failure. For the bolt steel grade 8.8 was used. The part with the inner thread, however, was of a lower strength preventing concrete cone failure to occur. Based on a relation in the literature [4] (eq. 1 with a=15.5) for the mean concrete cone failure load of headed anchors a value of 124 kN can be calculated for the cube compressive strength of 31.1 MPa and the effective depth of 127 mm. The (steel) failure load of 106 kN is about 86% of this value. Therefore, it can be assumed that the failure load of the investigated mixed recycled aggregate concrete and masonry aggregate concrete is at a maximum not more reduced than 14%. As far as the load-deformation relation is concerned (see Figure 3), no significant differences were found. Also in case of the threaded inserts the governing failure mode was steel failure (see Figure 7) causing a rather plastic behaviour (see Figure 4). Again, the load-deformation relations are almost similar for the three types of concrete. Assuming an effective depth determined by the horizontal pin (see Figure 1) and equal to 55 mm a mean concrete cone failure load of 35 kN can be calculated. Although the effect of the pin on the effective depth is not known, it can be assumed that for all the three types of concrete the maximum load in the experiments was not far from a concrete failure load. In case of the torque-controlled expansion anchors the failure mode was that significant radial cracking could be observed on the concrete surface, which was followed by the pulling-out of the anchor. For these anchors a reduction of the maximum load for the mixed recycled aggregate concrete and masonry concrete, as compared with the gravel
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tensile load (kN)
concrete, could be observed. For both types of recycled aggregate concrete the maximum load was almost equal and about 77% and 90% of the maximum load for gravel concrete for respectively the M16 and the M8 anchor. It should be noted, however, that the compressive strength of the masonry concrete was larger than that of the two other types of concrete. For the M16 anchor (see Figure 5) a little less stiff behaviour for the recycled aggregate concrete compared to the gravel concrete can be seen, which can be explained by the lower Young’s modulus. This was not observed for the M8 anchor, for which no explanation is found. Furthermore, the load-deformation relations did not differ significantly, especially when the scatter (not shown) is taken into account.
120 100 80 60
headed anchors M16 gravel aggregates mixed recycled aggregates masonry aggregates
40 20 0 0
1
2
3
4
5
6
deformation (mm)
tensile load (kN)
Fig. 3: Average load-deformation relations for the headed anchors M16.
40 32 24
threaded inserts M12 gravel aggregates mixed recycled aggregates masonry aggregates
16 8 0 0
1
2
3
4
5
6
deformation (mm) Fig. 4: Average load-deformation relations for the threaded inserts M12.
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tensile load (kN)
50 40 30
torque-controlled expansion anchor M16 gravel aggregates mixed recycled aggregates masonry aggregates
20 10 0 0
1
2
3
4
5
6
deformation (mm)
tensile load (kN)
Fig. 5: Average load-deformation relations for the torque-controlled expansion anchors M 16. 20 16 12
torque-controlled expansion anchor M8 gravel aggregates mixed recycled aggregates masonry aggregates
8 4 0 0
1
2
3
4
5
6
deformation (mm) Fig. 6: Average load-deformation relations for the torque-controlled expansion anchors M 8.
6. Concluding remarks The effect of the use of concrete with recycled aggregates for the coarse aggregates on the behaviour of short anchors was investigated. For the applied cast-in-place headed anchors and threaded inserts the effect of the different base material on the concrete failure load could not be studied, because steel failure was governing. Nevertheless, it is expected that, if there is a reduction in failure load, it will be less than what would be expected on basis of a fracture mechanics model presented in literature [4,6].
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Fig.7.: Failure mode governed by steel failure in case of cast-in-place threaded inserts (figure at left and left-hand side of figure at right) and headed anchors (right-hand side of figure at right). For the torque-controlled expansion anchors used in this investigation the maximum load was reduced by using the mixed recycled and masonry aggregates instead of gravel for the coarse aggregates. However, the reduction as observed, was less than what is predicted by the nonlinear fracture mechanics model. For all applied types of anchors the types of concrete did not significantly influence the load-deformation relations.
7. References 1. 2.
3. 4. 5.
6.
7.
CUR-Recommendation 58, ‘Mixed aggregates in concrete walls for structures in safety class 1 and 2, 1997, (in Dutch). Hordijk, D.A., ‘Mixed recycled aggregate concrete; Results of experimental investigation and background report to CUR-recommendation’ TNO report 00CON-BM-R1270, October 2000 (in Dutch). Walraven, J.C., Den Uijl, J., Stroband, J., Al-Zubi, N., Gijsbers, J. and Naaktgeboren, M., ‘Structural lightweight concrete’, Heron 40(1), 1995. CEB, ‘Fastenings to concrete and masonry structures – State-of-the-art’, CEBBulletin no. 216, Thomas Telford, July 1994. Hordijk, D.A. and Den Uijl, J., ‘Creep and shrinkage behaviour of concrete with mixed recycled aggregates’, in ‘Construction materials - Theory and application – For the 60th birthday of Hans-Wolf Reinhardt’ (Ed. R. Eligehausen), pp. 341-350. Eligehausen, R. and Sawade, G., ‘A fracture mechanics based description of the pull-out behaviour of headed studs embedded in concrete’ in ‘Fracture mechanics of concrete structures from theory to application’, Report of RILEM Committee TC90FMA. London: Chapman and Hall, pp. 281-299. Guideline for European Technical Approval of Anchors (metal anchors) for use in concrete. Part 1, 2 and 3 and Annexes A, B and C, EOTA, Brussels.
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REGARDING STRENGTH OF ANCHOR BOLTS USED FOR PCa CURTAIN WALL FASTENERS Hiroyuki Kawamura*, Taizo Otobe**, Seiichi Oka*** *Kyushu Sangyo University, Japan **PRE-CON System Association, Japan *** PRE-CON System Association, Japan
Abstract PCa concrete curtain wall panels are attached to the structural frames by the jointing methods that enable the walls to rock or to sway, so as to be able to follow the horizontal displacement of the frames without sharing shear force. But, it was discovered from the results of the damage investigation caused by the Hanshin-Awaji earthquake, 1995 in Japan that some cracks occurred around the anchor bolts in concrete curtain walls. The anchor bolts receive not only tensile force caused by negative wind pressure, but also shear force shared by the dead weight and seismic inertia force. While they are apt to be located near the corner of the thin walls, that is, the end distances or edge distances are short because of design details. In this paper, the authors present the results of the experiments on the tensile and the shear strength of the anchor bolts with several kinds of anchor bolts shapes, that were embedded at short end distances or short edge distances in the full size walls. And propose the estimating method of the strength of these anchor bolts, then introduce the cautions and the measures on the occasion of the installing fasteners.
1. Introduction During the past 10 years, demand for PCa curtain walls in Japan has soared to 200,000 to 250,000 walls, with a total surface area of 1.8 to 2.0 million m2. However, due to the absence of official design specifications and strength design equations for the fasteners used to attach curtain walls to buildings, manufacturers set their own specifications. Therefore about 8 years ago, the Precast Concrete System Association of manufacturers surveyed the existing fastener and anchoring methods of anchor bolt developed by various manufacturers, and performed loading tests on popular anchoring methods
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using full-size specimens to establish fastener design specifications. This report introduces typical methods of installing PCa curtain walls, proposes an appropriate fastener design method based on the test results, and reports on outstanding problems.
2. Installing PCa curtain walls on building bodies The method of installing a PCa curtain wall on a building body must of course guarantee safety against its dead load, but must also be safe from negative and positive wind force during a typhoon and from in-plane and out-of-plane inertial forces during an earthquake. In Japan, PCa curtain walls are treated structurally as non-bearing walls because many exterior walls have windows and other openings and the shear resistance of the panels is low compared with its stiffness [1]. Installation methods that satisfy the sway method or the rocking method as shown in Figure 1 (a) (b) are recommended to prevent the panels from carrying in-plane shear force caused by deformation of building stories in particular, and large- to medium-size PCa panels (10 to 20 m2) almost all conform to the latter method. Figure 2 shows an example of this representative PCa panel installation [2]. As shown in Figure 3, shows the anchor bolt and anchoring methods used to install fasteners, and anchors are of installed-in-site type in almost all cases. The plate type is used most often followed by the stick type, and then the hook type. In some cases, under spread type post-installed metallic anchors are used.
3. Relationship between strengths and bolt anchoring method a) Force applied to anchor bolts
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As shown in Figure 2, with a rocking method fastener, the vertical portion of the dead load is supported by a height adjustment bolt installed on a load bearing fastener. To guarantee safety even under out-of-plane forces produced by wind load or in-plane and out-of-plane inertia during an earthquake of P = KH*W (KH = 1.0, W is the dead load), the out-of-plane force must offset the fastener on the positive side and the tensile force of anchor bolt on the negative side, and the horizontal shear force by the inertia of the earthquake of the in-plane force must offset the shear force of the anchor bolt. b) Anchor bolt loading test Many experiments have been performed to test the strength of anchor bolts, but there have been few experiments on anchor bolts embedded in thin panels such as curtain walls. To verify existing empirical equations, loading tests of typical plate type and stick type anchor bolts were conducted. The test
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Table.1 Resurts of anchor bolt tension and shear test Specimen number
Projected Calculated Compressive Corrected Anchor End Edge Anchor Ratio strength value strength depth distance distance area bar P1/P2 Mean Fc(kg/cm2) P1(kg) h e1(cm) e2(cm) Ac(cm2) P2(kgt)
Maximum load (kgf) No.1
No.2
No.3
TS24E 2.82 3.30 3.27 3.13 TS24E 3.06 3.20 3.09 3.12 TS24C 2.90 2.58 2.41 2.63 TS24C 2.55 2.88 2.75 2.73 TS24C 2.87 2.68 3.08 2.88 TP24E 5.53 4.92 5.08 5.18 TP24E 5.01 4.89 5.47 5.12 TP24E 5.72 5.79 5.62 5.71 TP24E 6.37 6.82 5.83 6.34 TP24E 4.49 4.51 4.75 4.58 TP24C 5.64 5.60 6.40 5.88 TP24C 10.37 9.66 9.69 9.90 TP24C 16.93 15.49 15.29 15.90 TP24C 7.11 7.17 7.67 7.31 TP24C 7.39 7.95 7.42 7.59 TP24C 6.19 6.41 6.55 6.38 TP24C 6.00 6.58 6.66 6.41 SoS24EA 3.93 4.10 3.73 3.92 SoS24CA 5.45 5.33 4.51 5.10 SoS24CA 10.58 9.67 8.95 9.73 SoS24EA 3.87 3.70 3.50 3.69 SoP24E 5.07 5.18 4.62 4.96 SoP24C 6.82 5.78 4.96 5.85 SoP24C 9.30 9.32 9.30 9.31 SoP24C 3.86 3.35 3.19 3.47 SoP24C 4.10 2.86 3.08 3.34 P1=P* (300/Fc) P2=0.9* Fc*Ac
358.0 386.0 307.0 369.0 380.0 468.0 394.0 340.6 325.3 344.0 348.0 321.2 304.9 404.8 379.3 344.0 386.0 358.0 297.8 344.7 386.0 394.0 305.9 335.5 281.4 337.5
F6 F6 F6 F6 F6 F1 F1 F1 F1 F1 F1 F2 F3 F4 F5 F1 F1 F6 F6 F6 F6 F1 F1 F1 F2 F3
2.87 2.75 2.60 2.46 2.56 4.14 4.47 5.36 6.09 4.28 5.46 9.57 15.77 6.30 6.75 5.96 5.65 3.59 5.11 9.08 3.25 4.33 5.80 8.80 3.58 3.15
8 8 8 8 8 8 8 8 8 8 8 11 14 8 8 8 8 8 8 8 8 8 11 14
15 15 25 15 15 15 25 8 8
15 15 50 50 50 15 15 15 25 15 50 50 50 50 50 50 50 8 ∽ ∽ 8 8 ∽ ∽ ∽ ∽
145.3 145.3 145.3 145.3 145.3 329.0 329.0 364.4 364.4 329.0 364.4 604.8 901.6 389.6 427.3 364.4 364.4 297.0 362.4 550.2 297.0 297.0 362.3 549.6 219.3 219.3
2.27 2.27 2.27 2.27 2.27 5.13 5.13 5.68 5.68 5.13 5.68 9.43 14.05 6.07 6.66 5.68 5.68 4.63 5.65 8.58 4.63 4.63 5.65 8.57 3.42 3.42
1.27 1.21 1.15 1.09 1.13 0.81 0.87 0.94 1.07 0.83 0.96 1.02 1.12 1.04 1.01 1.05 1.00 0.78 0.90 1.06 0.70 0.94 1.03 1.03 1.05 0.92
Legend ：Loading direction(T:tension,So:shear outside) Loading direction┐ ┌Bolt size ┌Anchor bar Anchor type(P:plate,S:stick) Anchor bar location(C:center,E:end) T P 24 C A orientation Anchor bar orientation(A:90゜,B:180゜,C:0゜) └Anchor type└Anchor location
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results are presented in Table 1. As shown in Figure 4, the tensile tests were done by loading experiments as shown in Figure 4 and the shear tests were done under loaded conditions as shown in Figure 5. c) Results of tensile loading test of anchor bolts and estimation of the tensile strength Pu Regarding the tensile tests, the suitability of the equation shown below was examined for anchor bolt strength, which is proportional to the laterally projected effective area of the failure cone when the vertical angle/2 = 0.785 radians. This equation is now used by the Composite Construction Guideline [3] and the Seismic Retrofitting Design Guideline [4]. Pu(Qu) = 0.9 * Fc * Ac (kg) Fc: concrete strength (kg/cm2) Ac: laterally projected effective area of the failure cone (cm2)
(1)
The Pu – Ac relationship is for the anchor plate type shown in Figure 6, and when Ac was found as shown in Figure 7(a), it conformed closely to the case where the edge distance e2 was adequate for the anchor depth. But when specimens with a small edge distance were tested, the test value was about 20% smaller then the calculated value even accounting for the loss of the laterally projected effective area. Possible causes were that the failure cone’s vertical angle is about 90° near the anchor hardware, but the further away the larger the angle, and also that the stress distribution is not point symmetrical. It is assumed that if an edge distance of about 3 times the anchor depth h
Tensile strength Pu(t)
20.00 Specimen of changing anchor depth Specimen of changing plate size Plate type Specimen of changing edge distance Stick type
15.00 10.00 5.00 0.00 0.0
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Laterally projected effective area (cm2)
Figuer 6. Pu-Ac relation of tensile test
820
1000.0
is ensured, the edge distance will be adequate. Therefore, equation (1) should be used in such a case, and a value 0.8 times that obtained by equation (1) should be used to ensure safety when the edge distance is smaller. When a stick type anchor bolt is subjected to tensile force, a well-shaped failure cone is not observed because failure occurs so the panel peels off from the anchor bar location, but for convenience, as shown in Figure 7(b), if Ac is found assuming that the anchor depth is the surface of the anchor bar and assuming spindle-shaped failure, and the tensile strength Pu is estimated by equation (1), then good fit is obtained as shown in Figure 6. When the anchor depth and edge distance are sufficiently large, the strength is determined based on the tensile yield of the bolt and: Pu = sσy *sae sσy: yield point of the bolt sae: effective section area of the bolt
(2)
d) Results of shear loading tests of anchor bolts and estimation of shear strength Qu Because the shear loading tests were conducted by applying shear force to the concrete surface, if the end distance e1 was small and the bearing strength was determined based
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on spindle-shaped failure of the concrete, there was little difference between the shear strengths of the plate type and the stick type, and the difference according to the anchor depth h is also negligeable. The size of the end distance e1 has the greatest effect on the shear strength, but if the thickness of the base concrete for embedded anchors is adequate compared with the end distance, spindle-shaped failure occurs. In the case of a thin material such as a wall panel, failure occurs outwardly as shown in Figure 8. But because the shape of failure was spindle-shaped near the loading point, as in the case when subjected to tension, the laterally projected effective area of the failure cone is accounted for. Hence, assuming that the failure cone’s vertical angle/2 = α is equal to the experimentally obtained vertical angle/2,α= 0.925 radians when the end distance e1 = 8 cm,α= 0.750 radians when e1 = 15 cm, andα= 0.611 radians when e1 = 25 cm. The relationship of effective projected surface area Ac and experimental value Qu is as shown in Figure 9. If in the plate type case Pu in equation (1) is substituted by Qu, the experimental values and calculated values almost concur. But if the edge distance e2 is smaller than the end distance e1, as in the tension case, the calculated value indicates a high risk. Therefore, e2 ≧ 2e1 is recommended. There is a danger of the stick type losing some strength as well. If the edge distance and end distance are both sufficiently large, Qu is determined by the bolt’s shear strength equation (3) or by the concrete bearing strength equation (4), whichever is smaller.
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Shear strength Pu(t)
20 Specimen of changing end distance Specimen of changing edge distance
15 10 5 0 0
200
400
600
800
1000
Laterally projected effective area(cm2)
Figuer 9. Pu-Ac relation of shear test
Qu = 0.7 sσy * sae Qu > 0.3 Ec･σ B
(3) (4)
*sae
4. Anchor bolt design strength and design precautions a) Tensile strength Ac is calculated based on Figure 7(a) (b), Pu is obtained with equations (1) and (2), and the smaller is considered to be the design strength. But the anchor should be set so that the edge distance e2 ≧ 3h. b) Shear strength Ac is calculated based on Figure 8, Qu is obtained with equations (1), (3), and (4), and the smallest is considered to be the strength. But the anchor should be set so that the end distance e1 ≧ 15 cm, and the edge distance e2 ≧ 2e1.
5. Outstanding issues In a case where shear force is applied to an anchor bolt that is embedded in a thin PCa concrete panel, in this experiment, PL 50 x 100 x 100 was applied to the side surface as load reaction force on the concrete surface, but because the location of the actual external force is considered to be the center of the panel thickness, in reality slightly larger out-of-plane bending force is applied locally. Therefore, because the tension generated by this bending force is added to the concrete tension near the bolt’s bearing pressure point, the bearing strength could be slightly lower. Further experiments should be conducted to confirm this.
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References 1.
‘Exterior finishing construction seismic resistance manual – medium rise buildings’, Building Center of Japan, June 1998 2. ‘Seismic design for non-structural building parts: guidelines and commentaries, and seismic design and execution guidelines’, Architectural Institute of Japan, November 1985 3. ‘Composite structure design guidelines and commentaries’, Architectural Institute of Japan, August, 1988 4. ‘Reinforced concrete structure seismic retrofitting design guidelines and commentaries’, The Japan Building Disaster Prevention Association, July, 1995
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NEW METHOD OF RECONSTRUCTIONSTRENGTHENING OF OLD BUILDINGS M. Marjanishvili *,T.Zuzadze**, D. Ramishvili**, A.Lebanidze* *Tbilisi, Georgia **Company “Kvali”, Tbilisi, Georgia
Abstract During the recent decade the reconstruction and strengthening of buildings of the significance of architectural heritage, which are located in the historical parts alongside with constructions of modern buildings has become rather urgent in Georgia. The resources of carrying capacity have been noticeably decreased during 100-150 years exploitation of such buildings. It was abetted by the performed planned changes (new openings, dismantling of walls and etc.) and damages of conduits during exploitation in different periods, which followed urbanization process (water supply, sewerage, heating, ventilation, power supply).Building-designed company “Kvaly” was set up in 1995, it has elaborated original methods for reconstruction and strengthening of old buildings. Strengthening of foundations is made by means of the reinforced concrete edge supported monolith plates, which greatly reduces the loading on the ground and is easy to be realized technologically. Strengthening of damaged carrying walls is performed by the application of rigidly reinforced air-placed concrete; replacement of the old wood floors is made by edge supported reinforced concrete plates on the counters, which are fixed in a carrying wall by means of the edges and anchor dowels existing on the counter.The above given measures of constructional work offered by us enable one to increase the carrying capacity and exploitation term of buildings. Furthermore arrangement of additional storeys is also available.
1. Introduction In order to take successful measures for strengthening of buildings it is necessary to determine the causes of their damages. The major cause often represents to the nonuniformly laid foundation, as well as decreased capacity of currying vertical elements and roofs.
Marjanishvili. “Reconstruction of Buildings”, 1 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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D.1. Reinforced Concrete Space Foundation 3
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1-Plate; 2-Rigid edge; 3-Anchor dowels; 4-Artificial base; 5-Tamping ground 6-Ground.
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There is a scheme of the reinforced concrete space foundation on the draft No 1, which enables us to strengthen various kinds of foundations. The space foundation is a box resembling construction that consists of monolith reinforced concrete plate (1) and rigid edges (2). It is connected to the foundation and walls of the building by means of anchor dowels (3). Space foundation is formed in the cells of closed counters of the building after pressing down the ground (5) and arranging the artificial base (4).Space foundation may be arranged on the different levels- according to a building constructional scheme, deepening and type of a foundation, geological conditions.Space foundation gets into work after a building has additionally settled down. In accordance with our practice its arrangement reduces a settle process minimally and stabilization is guaranteed after a certain period of time.
2. Different cases of use of space foundation For the most part strip foundations are deformed as a result of settling processes. We have elaborated a new method of strengthening of strip foundations. It provides for a combination of a new space foundation with the inner space of an existing strip foundation (D.2). The reinforced concrete plate (1) and reinforced concrete rigid beam (7) situated on its perimeter are its principal elements. Space foundation is connected to a building by means of previously arranged plummets of reinforcement of a strip foundation. These plummets from their part provide moving up of the vertical loading of the building into the space foundation. Combination of the space foundation with the strip foundation and walls of the basement provides an increase of a building’s supporting area and strengthening of walls of the basement that from its part excludes development of settling processes and increases the seismology of a building. In most cases because of its insufficient rigidity ground floor is damaged by non-uniform laying of the foundation. For this matter it is necessary to enlarge the length of a rigid beam up to the level of the ground floor’s covering.
Marjanishvili. “Reconstruction of Buildings”, 2 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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D.2 Strengthening of Strip Foundation. a) Plan b) Cut 1-Plate; 2-Rigid beam; 3-Rigid edge; 4-Anchor dowels; 5-Wall of an existing building; 6-Strip foundation of an existing building; 7-Rigid beam. During strengthening of basement buildings that are damaged by non-uniform settling processes it often occurs that virgin bases are very weak and principal rocks are of noticeable deepening. In this case application of only strip foundation doesn’t produce a desired effect. Many problems are causes while strengthening such kinds of buildings. Load on space foundation may be moved up to principal virgin by means of piles of little diameters (3). For this reason, latitudinal and longitudinal rigid beams (4) must be arranged in the plate of foundation, which are combined with reinforced concrete pile (5) fixed on the principal virgin lands.
Marjanishvili. “Reconstruction of Buildings”, 3 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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D.3 Strengthening of a Building By Means of Space Foundation and Piles. a) Plan b) Cut 1- Plate; 2- Rigid edge 3- Anchor dowels 4- Rigid beams; 5- Piles of a little diameter; 6- Weak ground; 7- Principal rock.
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D.4 Strengthening of Building in Case of Ground Water Existing in a Basement. 1- Plate; 2- Rigid edge 3- Anchor dowels; 4- Artificial foundation; 5-Level of the ground water.
Marjanishvili. “Reconstruction of Buildings”, 4 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
In this case, in order to be able to strengthen the building by means of space foundation, we must throw crushed stone into the building (4) in such way when the surface of its level covers the water level. Than space foundation must be laid on an artificial foundation of crushed stone according to the mentioned method. Non-inform laying of foundation are noticed in such buildings that are of little deepening and have no basement (5). Strengthening of such kind of damaged buildings by means of space foundation is typical for its certain specifications.
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D.5. Strengthening of a Building without a Basement 1-Plate; 2- Rigid edge 3- Anchor dowels 4- Artificial foundation 5-Wall of a Building 6- Foundation of a building In contrast to other cases here rigid edges situated on the plate counter must be arranged not above the plate but under it. For this reason ground level must be raised below floor mark on the entire perimeter of the currying walls, rigid edges must be combined with previously arranged anchor dowels of the walls, reinforced concrete monolith plate of space foundation must be placed on the floor mark. In case of large vertebra damaged building it will be better to use modified variant of the present construction. In this case we can use either negative or positive hulls of curve instead of flat plate.(D.6). In the first case it will work as a hull of jam and in the second case as a membrane of tension. In case of positive hull of curve if a large bracer is formed, counters of the hull may be connected by means of binding plate, which will perform a function of a floor.
Marjanishvili. “Reconstruction of Buildings”, 5 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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D.6 Space Foundation for Strengthening of a Large Vertebra Building 1 – Plate –“hull” 2 – Plate - “membrane” In contrast to other existing methods of damaged foundations’ strengthening, after a certain modification the space foundation offered by us may be used for strengthening of damaged buildings having different kinds of constructions. One of these kinds of cases is given in the D.7. The present building has a reinforced concrete monolith foundation plate (1). It is settles non-uniformly as a result of the ground washing off. The ground must be excavated and rigid edge must be arranged (2). This will provide for increasing of the entire building’s steadiness and stopping of washing process of the ground.
Marjanishvili. “Reconstruction of Buildings”, 6 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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D.7 Strengthening of a R/C Monolith Foundation 1- Monolith foundation plate of a building; 2- Rigid edge; 3- Anchor dowels. A computational model (8) of the space foundation represents to the combination of existing foundations (C1) situated on the flexible base and new foundations (C 11). It is formed by means of flexible connections of shearing action (t). Rigidity of connections is equal to rigidity of reinforcement bar. Flexible base is modified according two coefficients of lining, shear and compression. Vertical load is applied onto the basement wall of the existing building and is moved up to the foundation. Space foundation is put to work proportionally to the intensification of settling processes caused by decreasing of virgin land properties. N t
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D.8 Computational Scheme of Space Foundation We have elaborated various variants of computation, which provide for imitation of nununiform lying of foundation. These changes in the computation model are expressed by means of changes of lining coefficient in certain zones of the foundation.
3. Strengthening of floors and currying walls Setting of building-construction foundations often causes a decrease of currying capacity of the currying walls and floors. It becomes necessary to elaborate measures for their
Marjanishvili. “Reconstruction of Buildings”, 7 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
constructional strengthening. Using of reinforced air-placed concrete for strengthening of walls built by bricks or small blocks is effective (D.9). For this reason existing damaged walls must be cleaned off grinding material and anchor dowels (5) must be assembled in them. Reinforcement bars are arranged on these dowels horizontally and vertically as well. These form a metal lath. Reinforcement vertical bars through the floors are extended for the full height of the wall without a break. Walls felt into reinforcing fabric are covered with air-placed concrete (2), which has a thickness of 5-8 sm. Air-placed concrete increases the damaged wall’s currying capacity of vertical load. a)
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D.9 Strengthening of Currying Walls and Floors a) Plan b) Cut I-I 1-Currying walls of a building; 2-Reinforced air-placed concrete 3-R/C plate without a girder; 4-Rigid edge; 5- Anchor dowels 6-Foam plastic insets.
Marjanishvili. “Reconstruction of Buildings”, 8 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
In case of damages of floors (mainly old, wood currying elements) old covering may be used as a gauge. The monolith reinforced concrete plate without a girder (3), which is lightened by means of foam plastic insets (6) in certain cells, must be arranged above it. The reinforced concrete monolith plate arranged on the perimeter by means of rigid edge (4) is fixed into currying walls with the aid of anchor dowels (5). The new reinforced concrete floors and air-placed concrete on the walls provide the building with additional vertical and horizontal rigidity.
4. Arrangement of additional storeys of a building City planing development and urbanization processes are often accompanied by arrangement of additional storeys of the existing building. It increases vertical loads on a building that is why it becomes necessary to enlarge a supporting area of the foundation and distribute vertical loads. In this case application of the space foundation will produce an effect (1). It increases a supporting area of the building. Metallic columns (2) combined with the existing walls must be arranged on the rigid edges of a new foundation. It will provide for moving up of an additional loads, which are caused by additional storeys, to space foundation.
Marjanishvili. “Reconstruction of Buildings”, 9 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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D.10 Increasing of a number of storeys of the building 1- Space foundation; 2- Metallic columns; 3- Currying elements of an additional storey; 4- Currying walls of a building 5- Old floor 6- New floor
Marjanishvili. “Reconstruction of Buildings”, 10 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
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5. Implementation examples of the given strengthening methods In 1995 the letters patent No 185 –“Strengthening of Foundations of BuildingConstructions” was issued in the name of the Studio “Kvali”. During the past period according to the mentioned method many important objects have been reconstructed and strengthened: - “Georgian Bank”, Tbilisi - Georgian Central Television, Tbilisi - No3 Experimental Secondary School, Tbilisi - Secondary School , Signagi - Secondary school, Gurdjaani - A building of 9 storeys, No 25 Gamsakhurdia St., Tbilisi - A building of 5 storeys, No 26 Chavchavadze St., Tbilisi
6. Conclusion Special tools for fixing deformations have been assembled on the buildings, which were strengthened according to above-mentioned method. In accordance with the monitoring results it has been determined that no deformation took place in any of these buildings. The stabilization proves the affectivity of this given method. Building- reconstructing works are easy to be curried out from the point of view of technology and is not of need of much investigation. Implementations of this given method enable us to increase exploitation term of buildings and their seismology.
Marjanishvili. “Reconstruction of Buildings”, 11 of 11 Fax +(995-32) 22 79 01 E-mail
[email protected]
FASTENING IN MASONRY Andrea Meyer, Thilo Pregartner Institute of Construction Materials, University of Stuttgart, Germany
Abstract In this paper the behaviour of plastic and injection anchors in masonry will be discussed. The results of tests with different anchors in different types of brick and the main parameters influencing the behaviour are presented.
1. Introduction Masonry is a very diverse material. It is composed of masonry units (i.e. bricks) and mortar. The bricks used in masonry structures are made of a variety of materials including clay, lime stone and concrete. They differ in geometry (e.g. dimensions, holes). For fastenings in masonry several plastic and injection anchors are typically used. Their behaviour is influenced by many parameters such as design of the fastener, type of brick, the drilling system and hole configuration. Admissible loads are defined in Technical Approvals for the different fastening systems. The main parameters influencing the behaviour of plastic and injection anchors in different materials were investigated extensively in tensile tests with different fastening systems [2, 5, 6, 9, 10]. In this paper the key results of these tests are presented. An overview on bricks used in Germany will also be given.
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2. Masonry in Germany In Germany, mainly four types of masonry units are typically used (Figure 1): (a) solid or hollow clay bricks, (b) solid or hollow bricks made out of limestone, (c) solid units produced from aerated concrete and (d) hollow units made from lightweight or normal weight concrete. According to Figure 1 the most popular brick material is clay (42% market share) followed by limestone units (33%) and aerated concrete (15%). The use of bricks made from lightweight or normal weight concrete has been constantly decreasing over the past few years. There market share is only about 10%. 100% 11,9 27,8
Normalbetonsteine Normal weight concrete
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Leichtbetonsteine lightweight concrete
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Porenbetonsteine aerated concrete
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Percent [%] Anteil [%]
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Kalksandsteine limestone
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0% 1950
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Jahr
Year
Figure 1: Market shares of different brick types The requirements for dimensions, density and strength of masonry units are given in DIN Standards. Additionally units are produced according to Technical Approvals of the “Deutsche Institut für Bautechnik” (DIBt). These products are developed for better heat insulation or improved economy. In general large size masonry units are increasingly used to speed up construction. The standards or Technical Approvals only regulate the ratio of hole area to total area. Therefore the shape and size of holes, as well as the thickness of the walls, may vary significantly. Figure 2 shows two examples of bricks that satisfy DIN standards. To improve heat insulation properties, the ratio of the area of holes to the total area of the brick has increased and the thickness of the walls has decreased during the last two decades. This is problematic in respect to the transmission of loads by fastening systems
837
because less and less material is engaged. Therefore, it become important to investigate the behaviour of typical fastening systems in a variety of types of masonry used in Germany.
38
6 38
14 38 6
38 235
13 11 8 16 8 16 8
ca. 17
15-17
ca. 17
78
70
78
60
60
240
14 16 6
6
Maße [mm]
300
40 490
(b)
(a) Figure 2:
Examples for bricks as defined by a DIN Standard (a) HLz 12-0,9-16DF; (b) KSL 12-1,2-10DF
3. Anchors with a Technical Approval for use in masonry There are basically two anchorage systems used in Germany for fastening in masonry. These are plastic anchors and injection anchors. They are described in detail in [11]. Plastic anchors (Figure 3) can be used in concrete and in masonry. They consist of a plastic sleeve made of polyamid PA6 and a screw or nail. These two parts work together to provide anchorage. The embedment depth is clearly marked on the sleeve and a collar on the top inhibits the sleeve from slipping into the borehole. The load transmission results from friction between the sleeve and the base material. In perforated blocks supplemental tensile resistance is provided by keying action. The loaddisplacement behaviour of the anchorage is mainly influenced by the thickness and the number of webs along the embedment depth. Plastic anchors usually fail by pullout without destroying the base material. The use of injection anchors (Figure 4) is allowed in solid block and hollow masonry. An injection system consists of a mesh sleeve, an adhesive mortar and a threaded rod. There are many different systems on the market. They differ in the type of filling material, the design of the sleeve and in the method of injection. The mortar is injected into the sleeve and allowed to cure before loading.
838
Figure 3 :
Examples for plastic anchors with a Technical Approval of the DIBt
Mesh sleeves and threaded rod
Figure 4 :
Injection cartridge, mixing nozzle and pressure tool
Examples for injection systems with a DIBt Technical Approval
4. Behaviour of plastic anchors The behaviour of plastic anchors is influenced by several parameters. Moisture and temperature in particular change the properties of the plastic sleeve. The moisture content of plastic anchors made of polyamide under standard conditions is about 2.5%. If the moisture content increases, the material becomes softer and the maximum load decreases. On the other hand the failure load increases for lower moisture contents. A similar effect can be observed for temperature. With increasing temperature the stiffness and strength of the plastic decreases, therefore the failure load decreases. The opposite is true for decreasing temperatures. A significant influencing factor for plastic anchor behaviour in hollow masonry units are the thickness and strength of the walls. In the following, results of tests using perforated bricks made out of clay and limestone are presented. In all tests, anchors with a Technical Approval were used. The numbering of the anchor types used in the following figures does not correspond with the ordering of the anchors in Figure 3. The moisture content and temperature of the sleeves was maintained at about 2,5% and 20°C, respectively. More test results in other materials are given in [12].
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4.1 Plastic anchors in vertically perforated clay bricks In the Technical Approvals for plastic anchors, it is required that the drillhole in hollow brick masonry be made by rotary drilling (without percussion). Percussion drilling is allowed only under special circumstances. In Figure 6 the pullout loads for different anchor types of plastic anchors in Hlz 12-0,916DF (sleeve diameter d= 10mm) are shown. The drillholes were made by rotary drilling. The anchors were set with the nominal embedment depth. In this brick two positions for setting are possible because of the hole configuration (Figure 5). 5,0
Position B
anchor type22 Dübel Typ
anchor type11 Dübel Typ
Position A
Dübel Typ anchor type 33
Dübel Typ anchor type 44
hef,soll= 70mm
4,0
failure load[kN] [kN] Höchstlast
anchor type55 Dübel Typ
anchor Dübel type Typ 66
anchor type 77 Dübel Typ
DIN 105 HLz12-16DF, Drehbohren
4,5
hef,soll= 90mm
3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0
Zulässige Last Admissible
A
B
load
A
B
A
B
A
B
A
B
A
B
A
B
Setzposition Setting position
Figure 5: Setting Figure 6: Pullout loads for plastic anchors d= 10mm in Hlz12-0,9positions in Hlz12- 16DF as defined in DIN Standard 105 in dependence of anchor 0,9-16DF type and setting position The embedment depth effectivly amounts to 70mm or 90mm depending on the anchor type. For these two possibilities, the anchor can reach one large cell or one small and one large cell. As it is shown in Figure 6, the measured failure loads scatter significantly and depend on the anchor type. Anchor type 1 and 5 show comparatively high failure loads. The lowest failure load measured for anchor type 4. It is important to note that a larger embedment depth does not necessarily result in higher failure loads. The influence of setting position is not predictable. The ultimate loads decreases significantly if the drillhole is made by a percussion drill, as it is often done in practice [11]. In figure 7 pullout loads for plastic anchors recorded during the last 20 years are shown. This diagram is base on more than 2000 tests, which have been carried out on- site and in the laboratory 1982. The mean failure loads and the standard deviation are plotted. The letter “H” means percussion drilling, the letter “D” means rotary drilling. One can observe that the pullout loads have decreased over the years.
840
This is due to changes in the hole configuration and the reduced thickness of the webs in masonry. 7,0
1994- 96
1990
1982 Baustelle on site
1982
6,0
Mean value of failure load [kN] [kN] Mittelwerte Bruchlast
1990
Baustelle on site
Labor laboratory
Labor laboratory
Dübel Typ 2 (10 mm)
5,0
4,0
3,0
2,0
1,0 D 0,0
Figure 7:
HLz
H
D
HLz20-1,2-2DF
H
HLz12-0,9-16DF
D LHLz
H
LHLz4-0,9-2DF
Development of failure load of plastic anchors (d= 10mm) in vertically perforated bricks since 1982, data taken from [1,2,5,6,9,10]
4.2 Plastic anchors in perforated limestone bricks According to DIBt Technical Approvals the admissible load for plastic anchors with diameter of d= 10mm embeded in perforated limestone bricks, which conform to DIN standard 106 (strength ≥ KSL 6), is admF= 0,4kN. This value assumes that holes are made using drill. If the conditions are not complied within an application (maybe none conform brick or percussion drill), then tensile tests on construction site are obligatory. 4,5
hef,soll= 90 mm
hef,soll= 70 mm
4,0 3,5
failure load [kN] Höchstlast [kN]
3,0 2,5 2,0 1,5 1,0 0,5
Zulässige Last
0,0
Dübel Typ 1
Dübel Typ 2
Dübel Typ 5
Dübel Typ 3
841
Dübel Typ 4
Dübel Typ 7
Figure 8 :
Pullout loads for plastic anchors d= 10mm in KSL12-1,2-16DF (DIN 106 )
Bricks such as those shown in Figure 2 are not optimal for fastening due to the large holes and the thin webs. In Figure 8 pullout loads are plotted for different anchor types (d=10mm) in KSL12-1,210DF with dimensions as given in Figure 2. The web thickness in the middle of the brick was 19mm. Rotary drilling was used. It is obvious that the ultimate load depends on the anchor type. The lowest failure loads were measured for anchor type 3 and 7. 4.3 Tensile tests performed on a construction site According to the Technical Approvals of the DIBt, tests on- site are required if plastic anchors are to be fastened in bricks whose strength or density does not reach the minimum value that is given in the approvals or if the drillhole is drilled by percussion drilling. For the determination the admissible load,at least 15 pullout tests are required. Thereby, the load N1 (load plateau at increasing displacement) and the failure load NU have to be measured. N [kN] NU
N1
NN1:: load plateau erstes Lastmaximum NNU1:: failure load Höchstlast
s [mm]
U
Figure 9
Typical load- diplacement curve for plastic anchors with load plateau N1 and failure load NU.
The admissible load is calculated by 0,23 ⋅ N1m zulF = Min 0,14 ⋅ NUm
Mit N1m= mean value of the 5 lowest values N1 NUm= mean value of the 5 lowest values NU
(4.1)
During the test, the load must be applied slowly and continuesly. The failure load should not be reached in under 1 minute. The calculated admissible load must not exceed the maximum allowable load, which amounts to 0,6kN for vertically perforated bricks and perforated calcium silicate bricks and 0,5kN for precast concrete blocks. Both values are valid for plastic anchors with diameter d= 10mm or d= 14mm.
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5. Behaviour of injection systems Injection systems transmit load by mechanical interlock. The mortar passes through the openings of the mesh sleeve and forms a grafting. Injection installed anchors are typically very stiff, so that failure is caused by a type of cone failure and the failure load depends on the brick strength. A typical load- displacement curve first increases steeply untill reaching the maximum load and drops sharply after brick failure. One injection system is approved for use in hollow bricks and solid bricks. The functioning in solid units differs from the behaviour in hollow bricks, because the failure load in solid bricks is influenced by the bond between mortar and base material. The behaviour is strongly influenced by the cleaning of the borehole. For these anchors the installation instructions provided by the manufacturer have to be observed. 5.1 Injection systems in vertically perforated bricks The admissible load in vertically perforated bricks as defined in DIN Standard 105 with a strength equal to or greater than 12N/mm² amounts to 0,8kN (hammer drilling). The load can be increased to 1,0kN if rotary drilling is used. The admissible load decreases with decreasing strength of the bricks. Parameters affecting the performance are the brick strength, hole configuration, anchor type, drilling system and setting direction. An injection anchor can be set in the vertical or in the horizontal direction. In the laboratory, vertical setting usually is choosen. In practice however the anchors are often set in the horizontal direction. In Figure 10 the ultimate loads of different anchor types are plotted. Parameters are the anchor type, the setting position (see Fig. 5) and the setting direction. 10,0
Dübel TypAA anchor type
Dübel TypBB anchor type
Dübeltype TypD D anchor
9,0 8,0
Höchstlast [kN] Failure load [kN]
7,0 6,0 5,0 4,0 3,0 2,0 1,0
Zulässige Last load Admissible
vertikal 0,0
Figure 10 :
A
B
horizontal
A
B
vertikal
horizontal
A
B A Setzposition setting position
B
vertikal
A
B
horizontal
A
B
Pullout loads for injection systems in Hlz12-0,9-16DF as defined in DIN standard 105 depending on anchor type, setting position and setting direction
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The failure load are not significantly influenced by setting position and setting direction but are slightly influenced by anchor type. Figure 10 shows the development of pullout loads since 1984. In the diagram the mean failure load and the standard deviation are given. Similar to plastic anchors the pullout loads of injection anchors decreased over the past years because of the reasons given in section 4. 9,0
1984
1994
1994
1999
1)
1986
1999 HLz12-0,8-12/ 16DF Drehbohren
8,0
Mean value of failure load [kN] Mittelwerte Bruchlast [kN]
7,0 6,0 5,0 4,0 3,0 2,0 1,0 0,0 1):
Hersteller B
Hersteller A Typ C
Typ B
Typ D
Typ G
Versuche mit Hammerbohren
Figure 11: Development of failure loads of injection anchors in vertically perforated bricks since 1984 5.2 Injection systems in perforated limestone bricks According to the Technical Approvals of the DIBt the admissible load for injection anchors in perforated limestone bricks as defined in DIN 106 with a strength ≥ 12N/mm² amounts to 0,8kN (percussion drilling). The load can be increased to 1,4kN if rotary drilling is used and the thickness of the exterior web is ≥30mm. The admissible load decreases with decreasing strength of the bricks. In figure 11 the failure loads of different anchor types in KSL 12 for both setting directions are shown. Bricks with one hole configuration were used for these tests (see Figure 1), however the thickness of the exterior web changed in some of the sperimens from 20mm to 15 (17)mm. The failure loads for anchor type E, F and G are noticeably lower.
844
10,0
DIN 106 KSL12-1,2-10DF 9,0 8,0
Failure load [kN]
Höchstlast [kN]
7,0 6,0 5,0 4,0 3,0 2,0 Admissible Lastload 1,0 Zulässige vertikal
0,0
horizontal
horizontal
B
C
vertikal
horizontal
vertikal
horizontal
E
D
horizontal
F
vertikal
G
vertikal
H
Dübeltype Typ Anchor
Figure 12 :
Pullout loads of injection anchors in KSL12-1,2-16DF (DIN 106 ), rotary drilling
6. Summary Masonry is a challenging base material for fastenings because of the multitude of types, geometries, density classes, hole configurations and strengths. The form and size of the holes and the thickness of the webs vary between the manufacturers. There are two possibilities for fastening systems in masonry: plastic anchors and injection systems. Plastic anchors are cheap and mounting is very fast. Anchors with technical approvals are qualified for fastening in concrete and in solid bricks. In hollow bricks, it is recomended to make tests on- site in the material in which the anchor will have to work. Injection systems are suitable for hollow bricks because load transmission results from mechanical interlock. Here the strength of the brick is the decisive factor. The installation procedures given by the manufacturer have to be observed.
7. Acknowledgement Special thanks are accorded to Matthew Hoehler who spent many hours in reviewing the paper.
845
8. References 1. Rehm, G., 'Gutachterliche Stellungnahme zur Frage der Beanspruchbarkeit von Kunststoffdübeln, not published (1982) 2. Sippel, T., 'Einfluss des Bohrverfahrens auf das Tragverhalten von Kunststoff- und Injektionsdübeln in Mauerwerk', Universität Stuttgart, Institut für Werkstoffe im Bauwesen, Bericht Nr. 8/8-90/1, not published, (1990). 3. Mitteilungen DIBt, 'Aus der Arbeit der Sachverständigenausschüsse- SVA Verankerungen und Befestigungen', (1995). 4. Bundesverband der Kalksandsteinindustrie e.V., 'Jahresberichte', (1996) 5. Weber S., Lehr, B., Sippel T., Eligehausen R., 'Tragverhalten von Kunststoffdübeln in Hohlmauerwerk', Universität Stuttgart, Institut für Werkstoffe im Bauwesen, Bericht Nr. AF 97/1-1/1, not published, (1997). 6. Weber S., Eligehausen R., 'Tragfähigkeit von Injektionsdübeln in Mauerwerk', Universität Stuttgart, Institut für Werkstoffe im Bauwesen, Bericht Nr. AF 97/596407/1, not published, (1997). 7. Eligehausen R., Mallée R., Rehm G., 'Befestigungstechnik', in 'Betonkalender 1997', (Verlag Ernst & Sohn, Berlin, 1997). 8. Mitteilungen DIBt, 'Aus der Arbeit der Sachverständigenausschüsse- SVA Verankerungen und Befestigungen', (1997). 9. Pregartner T., Eligehausen R., Fuchs W., 'Zugversuche in Hochlochziegeln, Leichtbeton-Hohlblöcken und Kalksandlochsteinen mit Kunststoffdübeln verschiedener Hersteller', Universität Stuttgart, Institut für Werkstoffe im Bauwesen, Bericht Nr. AF 98/4-402/4, not published, (1998). 10. Pregartner T., Eligehausen R., Fuchs W., 'Zugversuche in Hochlochziegeln, Leichtbeton-Hohlblöcken und Kalksandlochsteinen mit Injektionsankern', Universität Stutt-gart, Institut für Werkstoffe im Bauwesen, Bericht Nr. AF 98/4-402/4, not published, (1998). 11. Laternser K., 'Dübelverankerungen in Mauerwerk', in 'Mauerwerkkalender 1999', (Verlag Ernst & Sohn, Berlin, 1999). 12. Eligehausen R., Pregartner T., Weber S., 'Befestigungen in Mauerwerk', in 'Mauerwerkkalender 2000', (Verlag Ernst & Sohn, Berlin, 2000). 13. Bundesverband der deutschen Ziegelindustrie e.V., 'Statistische Angaben', not published. 14. Bundesverband Kalksandsteinindustrie e.V., 'Die Kalksandsteinindustrie in der Bundesrepublik Deutschland', Kalksandstein-Kurzinformation.
846
STUDY ON DESIGN METHOD OF JOINT PANELS FOR HYBRID RAILWAY RIGID-FRAME BRIDGES Hisao Nishida , Kiyomitsu Murata , Tomohiro Takayama Railway Technical Research Institute,Japan
Abstract Railway elevated bridges in urban areas are often constructed under spatial restrictions in a limited span of time. So, an improved work efficiency and rapid work progress are essential requirements. Moreover, railway structures are required to show a high seismic resistance. The hybrid railway elevated bridge is a type of structure which meets such requirements. The authors have already proposed a method of evaluating the performance of the column of concrete filled steel tube (CFT) and beam of steel/reinforced concrete beam, which compose the hybrid railway rigid frame elevated bridge. However, there has been almost no study on the joint with concrete filled steel tube column. This paper discusses a design method of a newly developed beam-to-column insert joint, with cruciform steel and reinforcing bars inserted into CFT, on the basis of experimental study on its load bearing capability.
1. Introduction These days an ever increasing number of railway elevated bridges are built in urban areas as part of projects for augmenting the transport capacity or for constructing continuous overhead crossings. This type of projects must be carried out at a very restricted space surrounded by existing structures and within a short period of time at night when there is no train service. This results in high demands for a technique enabling more efficient and more rapid work. In addition, structures have been required to be more seismically resistant since Hyogoken Nanbu Earthquake caused serious damages. Under the circumstances, the concrete filled steel tube (CFT) has come to the fore. Its essential merit is higher seismic performance providing a great load bearing capability and an excellent ductility. Furthermore, it enables a shorter work period because the steel tube can be used as a form for concrete placing. So it is frequently used for
847
constructing columns and piles. As a technique of joining different materials of hybrid rigid frame elevated bridges, the insert joint has been devised, which offers ease of construction, labor-saving effect, and offsetting construction errors1). By the inset joint practice, inserts of cruciform steel and reinforcing bars (rebars) are made to penetrate into a specified depth in the CFT column, which transmit loads between beams and columns. The design principle of avoiding failure of joint considers the possibility that fracture of the joint, being a weak point, would induce falling down of the whole structure. However, this principle may require an excessively large strength than other members, resulting in difficult arrangement of steel members in the joint in some cases. It is necessary, therefore, to accurately assess the load bearing capability of the joint and reflect its results upon the design method. In the study reported here, for cases where bending fracture of the joint takes place before the column fails from bending, the fracture mode of the joint was investigated through alternating loading test, to review the load bearing capability of the insert joint already proposed.
2. Alternating loading test of insert joint
Shear span
750
Insertion length
1600
Horizontal load 2.1 Overview of the experiment Axial force The test specimen is an about 1/2-scale model of the beam-column joint of an ordinary railway rigid frame elevated Steel tube 406.4 diam bridge. The standard column tube is 406.4 CFT column mm in diameter, 6.4 mm thick (STK490). Cruciform steel Rebar The filling concrete f’ck was 24 N/mm2. The strength of the joint was determined, according to Design standard for railway structures and commentary, Steel-concrete hybrid structures 2) (hereinafter referred to as “Hybrid Structure Design Standard”). The strength of the insert was assumed to be not more than the bending strength of the CFT member, so as to induce bending failure of the insert before the CFT member Footing 1400 fracture. The shape and characteristics of the test specimens are shown in Table 1 and Figure 1: Geometry of the specimen Figure 1. Alternating horizontal loads were applied in the quasi-static manner to the loading point of column head. Specimens JTSC-7 and 8 were subjected to constant compressive axial forces equal to the fully plastic compressive strength multiplied by a factor of 0.1 and 0.25, then to horizontal loads. Every specimen underwent the same loading pattern. The horizontal displacement of the loading point on the column head when the insert cruciform steel or rebars yielded,
848
was deemed as experimental yield displacement δy. The displacement was gradually increased, with the amplitude of integral multiples of δy in each direction, and three cycles per step. Table 1: Specifications of the specimens Specimen No. JTSC-1 JTSC-2 JTSC-3 JTSC-4 JTSC-5 JTSC-6 JTSC-7 JTSC-8 JTSC-9 JTSC-10
Tube diam (mm) 406.4 406.4 406.4 400.0 406.4 406.4 406.4 406.4 406.4 406.4
Thickness
(mm) 4.0 6.4 9.0 9.0 6.4 6.4 6.4 6.4 6.4 6.4
Steel tube
Inserts
Type
D/t
Steel grade
Insertion length (mm)
Ordinary Ordinary Ordinary w/protrusions Ordinary Ordinary Ordinary Ordinary Ordinary Ordinary
102 64 45 44 64 64 64 64 64 64
SM490 STK490 SM490 SKK490NR STK490 STK490 STK490 STK490 STK490 STK490
530 520 510 510 520 520 520 520 520 520
Inserts No.
1 2 3 4 5 6 7 8 9 10
Parameters
Cruciform steel
Rebar
H260×130×6×12 (SM490) H260×130×6×19 (SM490) H260×130×12×25 (SM490) H260×130×12×25 (SM490) H280×150×12×22 (SM490)
D13-16 (SD345） D16-16 (SD345） D19-16 (SD345） D19-16 (SD345） D10-16 (SD345） D22-24 (SD345） D16-16 (SD345） D16-16 (SD345） D16-16 (SD345） D16-16 (SD295）
-----------------H260×130×9×19 (SM490) H260×130×9×19 (SM490) H260×130×6×12 (SM570) H260×140×12×25 (LYP253)
Steel ratio
Cruciform steel / rebar ratio
Axial force ratio
0.051
2.24
0
Steel ratio
0.078
2.18
0
Standard
0.105
1.97
0
Steel ratio
0.108
1.97
0
0.082
8.26
0
0.072
0.00
0
0.078
2.18
0.10
Axial force ratio
0.078
2.18
0.25
Axial force ratio
0.059
1.43
0
Steel grade
0.098
3.00
0
Steel grade
Parameters
Tube w/protrusions Cruciform steel/rebar ratio Cruciform steel/rebar ratio
2.2 Test results a) Fracture mode All the specimens for this test were designed in such a manner that they would fail from bending fracture of inserts. Nevertheless, both bending fracture of CFT column and that
849
of inserts occurred in the test. The fracture mode was assessed by strain of the inserts, local buckling of the steel tube and cracking in the footing. Photos 1 and 2 are the views of the fractured specimens. In the case of CFT tube bending fracture, the steel tube locally buckled near the insert tip, at around the maximum load. Due to cracking induced by development of the local buckling and low cycle fatigue at the top of locally buckled portion, the specimen reached the ultimate state. On the other hand, the cracking in the footing surface, which was observed from yield point to maximum load, ceased growing as the local buckling developed. In the case of bending fracture of inserts, no local buckling was found in the steel tube; the axial strain of the insert cruciform steel and rebars developed as the loading cycle increased, resulting in floating up of the steel tube from the footing surface, and separation of concrete in the vicinity of the boundary between steel tube and footing. There were cases where exposed rebars were broken. Figure 2 illustrates the cracking status in the upper surface of footing concrete of JTSC-9 broken at the joint, at the time of initial cracking observed (5δy), maximum load (7δy) and near the ultimate strain (11δy). The circle at the center represents the steel tube section. Bending fracture of inserts Bending fracture of CFT column Damaged concrete
Local buckling of tube and cracking
Photo 1: View after loading (JTSC-9)
Photo 2: View after loading (JTSC-2)
Loading direction
(5δy) (7δy) (11δy) Figure 2: Crack propagation in upper surface of concrete footing (JTSC-9) b) Load-displacement relationship
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Table 2 shows the experimental maximum load of each specimen with calculated bending strength of CFT member and insert. The bending strength of the CFT member was calculated according to Design standard for railway structures and commentary, Seismic design 3) (hereinafter referred to as “Seismic Design Standard”). In this calculation, the distance from loading point to insert tip was taken as the shear span, and the maximum bending moment Mm was obtained; the magnitude of Mm was divided by the shear span to determine the magnitude of load at the loading point. The bending strength of the insert was calculated conforming to the Hybrid Structure Design Standard, assuming a circular SRC section in the boundary between footing and steel tube. The figures in the shaded cells represent the calculated strength corresponding to the fracture mode. In the case of CFT column bending fracture, there is a good agreement between the calculated bending strength of the CFT column and experimental maximum load. In contrast, in the case of insert bending fracture, the experimental maximum load significantly exceeds the calculated bending strength. Considering such a large difference, we can conclude that predicted fracture (bending fracture of the insert) did not take place. Table 2: Maximum load and fracture mode Experimental max.load (kN)
313.4 455.3 580.0 563.0 448.0 341.0 467.2 468.9 456.1 433.9
Calculated bending strength (kN)
Fracture mode
600
600
400
400
200
0
-200
Insert 188.0 282.3 348.9 351.8 276.4 283.5 299.3 300.1 247.1 262.6
200
0
-200
-400
-400
-600 -200
CFT column 317.7 429.7 551.8 551.1 430.9 432.4 461.5 487.4 427.8 452.8
CFT column bending fracture CFT column bending fracture Insert bending fracture Insert bending fracture CFT column bending fracture Insert bending fracture CFT column bending fracture CFT column bending fracture Insert bending fracture Insert bending fracture
H o rizo n tal lo ad (k N )
Horizontal load (kN)
Specimen No. JTSC-1 JTSC-2 JTSC-3 JTSC-4 JTSC-5 JTSC-6 JTSC-7 JTSC-8 JTSC-9 JTSC-10
-600 -150
-100
-50
0
50
100
150
200
-150
-100
-50
0
50
100
Horizontal displacement (mm)
Horizontal displacement (mm)
Relationship between horizontal load and column head displacement Figure 3: JTSC-9 Figure 4: JTSC-2 Figures 3 and 4 show the load
851
150
500
Horizontal load (kN)
hysteresis curves of JTSC-2 (CFT column bending fracture) and JTSC-9 400 (insert bending fracture) respectively, and Figure 5 provides comparison of 300 envelopes of both cases. It has been 200 said that the insert is prone to brittle fracture. However, as known from JTSC-2 ( Bending fracture of CFT column ) 100 these graphs, with the case of bending JTSC-9 ( Fracture of insert joint ) fracture of inserts, the displacement at 0 0 25 50 75 100 125 150 175 the maximum load and displacement Horizontal displacement (mm) up to ultimate state are larger than the case of CFT column bending fracture, Figure 5: Comparison of envelopes of loaddisplacement relationships offering qualitatively higher ductility. This can be explained by the fact that, with CFT column bending fracture, the structural performance continues to degrade because of local buckling of the steel tube, and finally, the ductility is limited by cracking from low cycle fatigue. On the other hand, with insert bending fracture, the deterioration depends upon relatively slow progress of concrete damage in the footing surface at the steel tube base, resulting in a greater ductility. Furthermore, the shape of the hysteresis curve demonstrates that high energy absorbing capability of the CFT structure is sufficiently maintained even at the bending fracture of inserts.
3. Evaluation of the load-carrying capacity of the inserts The Hybrid Structure Design Standard considers these three fracture modes of the joint with cruciform steel/rebar inserts. - Yielding failure of steel tube at the joint - Bending fracture of inserts - Shear fracture of inserts In the study on yielding failure of steel tube at the joint, and bending fracture of inserts, whichever smaller the bending strength of CFT column (ultimate strength Mu calculated by the Hybrid Structure Design Standard) multiplied by 1.4 or the bending strength of RC or SRC beam multiplied by 1.3, is taken as the design moment, that is, validation reference for the bending strength of each member. This prescription considers the largest difference between past experimental results and calculated strengths, and is based on the principle that the joint will not fail before the fracture of column or beam. As for the bending strength of CFT member, a study1) published after the edition of the Hybrid Structure Design Standard proposes Mm which is obtained by multiplying Mu, involving the equivalent plastic hinge given as a function of the axial force ratio. In the design of the specimens, the bending strength of the inserts were set to a value equal to or less than that of the CFT column, in order to focus upon the study of bending failure of the inserts. However, as mentioned earlier, no specimen showed the predicted fracture mode, with significant disagreement between test results and calculation. Considering such disagreement, we will study below corrections of the current
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calculation method of the bending strength of inserts. The following are possible causes for the significant difference between design bending strength and test results of the inserts. (1) According to the conventional design practice, the weak axis member of the cruciform steel (i.e., member whose web is normal to the loading direction) is ignored in calculation of the bending strength. (2) By the effect of steel column restraining the concrete, the strength of concrete in the axial direction increases. The calculation does not take into account this phenomenon. Involving these points, we corrected the calculation method as follows. The weak axis member of the cruciform steel is also included in the bending strength calculation (corrected calculation 1). In stead of the strain at the concrete compressive fiber, 0.0035, specified for calculation of bending strength of SRC member, the compressive strain at the outermost fiber of concrete for calculation of bending strength of CFT member is used3) , to involve the concrete restraining effect by the steel tube, as with CFT member. (corrected calculation 2) The yield stress of the steel tube is supposed to work as concrete restraining force in the circumferential direction, since in the test the strain in the circumferential direction was around the yield point in any specimen. Under this supposition, on the basis of the references by Park, R. et al.4) and Mander, J.B. et al.5), the compressive strength corrected as follows is used. (corrected calculation 3) The restraining stress f l is given by f l = 2t ⋅ fy / D Equation (3.a) where f y = yield stress of steel tube D = steel tube diameter t = steel tube wall thickness
The compressive strength of concrete f ' cc in this case is given by 7.94 ⋅ fl f − 2 l − 1.254 f 'cc = f 'c 2.254 1 + f 'c f 'c
Equation (3.b)
where f ' c = unconfined compressive strength of concrete As demonstrated by the values in Table 3, the experimental magnitudes of bending strength of the inserts can be predicted with a much improved accuracy, by the calculation with fully plastic moment, and taking into account the weak axis member and concrete restraining effect. Figure 6 shows the ratio of bending strength of the inserts (corrected calculation value 3) to that of CFT column (converted from the load at the loading point). Since this ratio of the specimens of the present test lies in a narrow range from 0.9 to 1.1, it is difficult to predict which fracture mode would occur for each specimen. However, as shown in the figure, different fracture modes are distinctively distributed around the ratio of 1.0.
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Table 3: Comparison between maximum load and calculated strength Experimental max.load (kN)
313.4 455.3 580.0 563.0 448.0 341.0 467.2 468.9 456.1 433.9
Fracture mode CFT column CFT column Insert Insert CFT column Insert CFT column CFT column Insert Insert
The ratio of JTSC-3 is 1.01, so either fracture mode would take place with approximately the same probability. In conclusion, it is possible to predict the fracture mode by the bending strength ratio. The insert joint section is designed by the current assessment method so as to present a ratio of about 1.9 or more, if expressed by the evaluation technique of Figure 6. We know that the evaluation has been (excessively) conservative for inducing insert bending fracture, under the principle of avoiding joint fracture preceding mode.
Calculated strength of CFT column (kN) calculation 1 calculation 2 calculation 3 229.4 243.6 318.8 321.6 344.5 466.9 383.4 411.0 557.3 390.1 416.9 518.8 329.5 351.6 475.3 283.5 294.4 343.2 318.0 344.1 479.8 321.0 349.8 509.4 275.7 303.9 414.9 306.8 322.1 427.0 1.50 Bending strength of inserts / CFT bending strength
Specimen No. JTSC-1 JTSC-2 JTSC-3 JTSC-4 JTSC-5 JTSC-6 JTSC-7 JTSC-8 JTSC-9 JTSC-10
1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0
2
4
6
8
10
12
Specimen No.
Figure 6: Bending stress ratio of CFT column and inserts
4. Design method of the insert joint The alternating loading test revealed that, even in the case of insert bending fracture, there is little risk of brittle fracture, and the subject configurations offer an excellent energy absorbing capability. However; - There remain unknown points about the behavior with further decreased ratio of the strength of the inserts to that of CFT member. - It is easier to repair the damaged tube than replacing the damaged inserts. - Through review of the evaluation method of the bending strength of inserts, it will be possible to design more compact inserts. For these reasons, the joint fracture preceding mode is not allowed when designing the insert, following the design principle. It is therefore necessary in designing to provide inserts with a bending strength (moment) higher than that of CFT column, when
854
compared at the same section. It should be noted that, considering possible variance of calculation accuracy of each bending strength, the strength should be conservatively determined. As for the bending strength of the CFT column, calculation may underestimate it by up to 10 % in terms of the experimental value, as revealed by the results of the previous loading test with a simple CFT column 1) and those of the present test with 22 specimens in total. In contrast, as for the bending strength of inserts, even the maximum calculated value is about the same as the experimental value, that is, calculated values are in general equal to or less than experimental results. Hence, we can achieve conservative assessment by designing a strength of inserts 1.1 times as large as the bending strength of CFT column. It is reasonable to apply Equation (4.a) when assessing the safety for bending fracture of inserts.
γ i⋅
Md l j ⋅ ≦ 1.0 M ud l c
Equation (4.a)
where Md = design bending moment, whichever smaller that of CFT column or beam. In the case of CFT collumn, 1.1 times the maximum bending strength calculated by the Seismic Design Standard. In the case of RC or SRC beam, 1.3 times the bending strength calculated by the RC standard6) or Hybrid Structure Design Standard. Mud = bending strength of inserts (fully plastic moments of steel and concrete are used in calculation) l j = span from loading point (bending moment = zero) to the steel tube base l c = span from loading point (bending moment = zero) to the tip of insert When the bending moment of beam is used as Md, 1j = 1c. In almost all cases of assessment of the bending strength of inserts by this method, the bending moment of CFT column is used for determining the design bending moment Md. This method provides a section with a bending strength decreased by about 55% (from 1.9 to 1.1) in terms of the strength by the current evaluation method.
5. Conclusions Alternating loading tests were conducted with specimens simulating the specifications of cruciform steel/rebar joints. These joints are proposed for hybrid rigid frame elevated bridges with CFT column and RC or SRC beams. Based on the experimental results, the load carrying capability and ductility of CFT columns with such a type of joint were evaluated. The results of the study are summarized as follows. (1) It has been said that inserts are prone to brittle failure. However, if the CFT/insert strength ratio is similar to that of the present test, even in the case of bending fracture of the inserts, brittle failure does not occur, and a satisfactory ductility is provided.
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(2) The bending strength of the inserts can be accurately evaluated, through calculation of the fully plastic moment of the section, involving the contribution of weak axis member of the cruciform steel and concrete restraining effect by steel tube. (3) For assessing the safety of the inserts, the bending strength of CFT member multiplied by a factor of 1.1 is taken as design bending moment, and is multiplied by the ratio of spans to each failure point. This technique ensures a suitable safety margin. References 1) K.Murata, M.Yamada, M.Ikeda, M.Takiguchi,T.Watanabe,M.Kinoshita: Review of the ductility of concrete filled circular steel columns, Proceedings of the Japan Society of Civil Engineers, No.640/I-50, pp.149 to 163, January 2000 2) Railway Technical Research Institute, under the editorship of Railway Bureau of Ministry of Transport : Design standard for railway structures and commentary, Steelconcrete hybrid structures, July 1998, Maruzen 3) Railway Technical Research Institute, under the editorship of Railway Bureau of Ministry of Transport : Design standard for railway structures and commentary, Seismic design, October 1999, Maruzen 4) Park,R., and T.Paulay : Reinforced Concrete Structure, Wiley, New York, p.769, 1992 5) Mander,J.B., M.J.N.Priestly, and R.Park : Theoretical Stress-Strain Model for Confined Concrete : Journal of the Structural Division, ASCE, Vol.114, No.8, pp.18041826, 1998.8 6) Railway Technical Research Institute, under the editorship of Railway Bureau of Ministry of Transport : Design standard for railway structures and commentary, Version in SI unit system (Concrete structures), October 1999, Maruzen
856
TENSION STIFFENING MODEL BASED ON BOND Maria Anna Polak* and Kevin Blackwell** *Department of Civil Engineering, University of Waterloo, Waterloo, Ontario,Canada **Morrison Hershfield Ltd, Burnaby, British Columbia, Canada
Abstract The paper presents a new formulation for modelling tension in cracked reinforced concrete where the main parameter influencing the response of a member is bond between concrete and reinforcement. The proposed formulation consists of a model for concrete before and after cracking, bond model and a method of predicting crack spacing. The formulation was developed for members subjected to bending and axial loads. It was implemented into a cross-sectional analysis program and was used to analyze specimens which were designed to study the influence of bond on the amount of tension carried by cracked concrete. The comparison between the experiments and the analyses is presented and it shows the same characteristics for both the experimental results and the analyses.
1. Introduction Bond between concrete and reinforcement is necessary for a composite reinforced concrete material behaviour. After cracking of a reinforced concrete member it allows to transfer tensile stresses between reinforcement and the uncracked pieces of the concrete. The phenomenon is called tension stiffening and its proper modeling is important in many design and analysis situations. In flexure, the influence of tension stiffening is most important up to service loads and should therefore be included in the deflection calculations. The ability of concrete to carry tension between cracks is also important in the analyses where cracking is a primary concern (e.g. thermal analysis) and where significant shear stresses exist. Tension stiffening has been studied and modelled in the past and it is included in several structural analysis material models (e.g. Gupta and Maestrini 1990, Marti et. al 1998, , Izumo et. al 1992, Clark and Spiers 1978). This paper presents a new formulation for modeling tension in cracked reinforced concrete where the main parameter influencing the response of a member is bond
857
between concrete and reinforcement. The formulation was developed for members subjected to bending and in-plane loading only, however, the presented concepts can be extended to more complex loading conditions. The development of the model (Polak and Blackwell 1998 1, Blackwell 1996) was done after the analysis of recently conducted tests (Polak and Killen 1998, Polak and Blackwell 1998 2, Polak and Vecchio 1994) on the behavior of members subjected to bending and in-plane loading. In the specimens, the flexural reinforcement was provided using different sizes of reinforcing bars. Since reinforcement sizes varied, the bond characteristics of these bars varied, leading to different load-displacement responses. The model was developed from the analysis of the mechanics of the behaviour, implemented into a numerical routine and used to analyze the tested specimens.
2. The Proposed Formulation Let us consider a reinforced concrete member subjected to bending and in-plane load. In the presented description, the moment causes tension in the bottom part and compression in the top part of the member. Member cross-section is divided into concrete and steel layers (Fig. 1, 2). Uncracked concrete subjected to tension is treated as a linear elastic material. It is assumed that cracking occurs first when the centroid of the first concrete layer from the bottom reaches the tensile strength, f’t. and it is also assumed that the layer is subjected to uniform stress equal to f’t, . The total force in the bottom layer is thus equal to: / (1) F 1 = f t A c1 = ε cr E c A c1 where ε cr is the cracking strain of concrete, Ec is the Young's modulus of uncracked concrete, and Ac1 is the cross-sectional area of the bottom layer. With further load increase, the stress at the centroid of the second layer from the bottom approaches the tensile strength. At this instant it is assumed that the stress in the second layer is equal to the tensile strength (Fig.1.), the first bottom layer has completely cracked, the strain in the first layer away from the crack is equal to the cracking strain, and the first layer does not transfer any axial stress directly across the crack. Therefore, the total force in the layer second from the bottom is now equal to (Fig.1): / (2) F 2 = f t A c2 + F V1 where Ac2 is the cross sectional area of the layer second from the bottom and FV 1 = F 1 = f t / A c1 is the force transferred between bottom two layers. With the increase of the applied load, the concrete layers systematically reach the cracking strain. The total force transferred between cracked and uncracked layers can be expressed as:
F Vt = ε cr E c ∑ i A ci t
(3)
858
where: Aci is the cross-sectional area of the "i" cracked layer and t is a number of cracked layers. The process of force transfer described above continues until the crack tip reaches the reinforcing steel. At this instant the steel layer reaches the cracking strain of concrete. From this moment, it is assumed that all forces from all cracked layers (below and above reinforcement layer) are transferred to the reinforcement layer (Fig.2). This transfer is now dependent also on bond between concrete and reinforcement.
3. Bond Between Concrete and Reinforcement Bond between concrete and reinforcement depends on chemical bonding between steel and concrete, friction developing between steel and concrete, and mechanical interlock, i.e. bearing of the concrete on the reinforcement lugs. In the proposed model the adhesion and friction bond are ignored and it is assumed that the bearing of concrete on the reinforcing bar lugs is the primary source of force transfer. At every reinforcing bar lug, the force transferred to the reinforcement from the surrounding concrete equals the bearing stress times the contact area (Fig.3a and b). This contact area is located between the outer perimeter of the lug and the inner perimeter of the concrete (Fig.3b). As the reinforcing bar undergoes tensile strain, the contact decreases due to the Poisson effect and due to slip between concrete and reinforcement (Fig.4a and b). Slip between concrete and reinforcement occurs when the strain in reinforcement becomes greater than the cracking strain of concrete (crack tip is above the reinforcement layer). It is assumed that the slip is the largest at the crack, it is equal to zero at the midpoint between cracks and there is a linear change in slip between these two locations. Slip is is expressed by the following relationship: (4) s(D) = ( ε s - ε cr ) D for ε s ≥ ε cr where s is the slip, D is equal to the distance between the given location where slip is calculated and the midpoint between the cracks and ε s is strain in reinforcement. Several reinforcing bars were examined and the ratio of "rise to run" (Fig.3a) for the lug was found to be equal to approximately three. Therefore, the increase in radius of concrete inner perimeter is defined as: ∆r = 3 s (5) and the expression for the calculating the contact area between the concrete and one lug (lug "i") is given by:
Ai =
[(φ − ε µ φ ) 4
π
s
2
− (φ − 2 d h + 6 s i )
859
2
]
(6)
where φ is the bar diameter at the lug location, µ is the Poisson ratio for steel, dh is the height of the lug, and si is the slip between the steel and concrete at lug “i”. The bearing stress on lugs is based on the assumption that it is zero at the midpoint between the cracks and increases linearly to f'c at the crack. The stress produced by the concrete bearing on a lug "i" is calculated from the following expression: Di (7) σ bi = f 'c cl where σ bi is the bearing stress on lug “i”, Di is the distance of lug "i" from the from the centerpoint between two cracks, cl is equal to half crack spacing. The total bond force that can be transferred between concrete and reinforcement can now be calculated as: n F B= N ∑ j Ajσ
(8)
j
where FB is the total bond force, N is the number of tension reinforcing bars contributing to bond, n is the number of lugs between the crack and midpoint between the cracks (n = cl/dl ,where dl is the lug spacing).
4. Crack Spacing Crack spacing influences bond forces (Eq. 4 to 7) and it depends on the type, size, amount and distribution of reinforcement. In the presented formulation, the CEB-FIP model was adopted (CEB 1978) to estimate crack spacing:
cs
= 2 (c c +
φ lb ) + k1k2 b 10 ρ ef
(9)
where: cc is the clear cover, lb the maximum spacing between the longitudinal bars, φ b is the bar diameter, k1 is a coefficient which characterizes the bond properties (equals 0.4 for deformed bars), k2 is a coefficient to account for strain gradient: ε 1 + ε 2 , ε and ε are the largest and the smallest tensile strains in k 2 = 0.25 1 2 2 ε1 the effective embedment zone, ρ ef is equal to As/Aecf, where As is the area of reinforcement and Aecf is the area of the effective embedment zone. The effective embedment zone is the area of concrete around the reinforcing bar at the distance of 7.5 bar diameter. In the proposed formulation, the crack spacing is evaluated using Equation (9) for strain distribution corresponding to yield of the tensile reinforcement. Based on test observations it is assumed that right after first cracking the crack spacing is approximately two times larger than the crack spacing at yield of the tensile reinforcement. Therefore, crack spacings for different strain distributions are calculated using the following approximate expression:
860
2
c (10) c s = c s y 1 + H where csy is the crack spacing at yield (evaluated using Equation 9) , c is the distance of the neutral axis to the compression face of a member and H is the height of a member.
5. Experimental Verification The presented formulation for tension was implemented into a cross-sectional analysis program BARC. For concrete in compression, the model proposed by Thorenfeldt, Tomaszewicz and Jenssen (1987) and calibrated by Collins and Porasz (1990) was used. The constitutive model for reinforcement is linear elastic until yielding and then perfectly plastic. An iterative solution is used which allows to find the strain distribution corresponding to the specified load: axial force and bending moment. The presented experimental verification includes analyses of specimens (slab-strips) which were tested in bending and in-plane loading (specimens KB1-KB8) (Polak and Blackwell 1998, Blackwell 1996). The goal of the experimental program was to study the influence of the ratio of in-plane loading to bending, bar diameter, reinforcement ratio and concrete cover on the behavior of members. The specimens were cast in pairs where one specimen was reinforced with large diameter bars while the other was reinforced with small diameter bars. Both specimens had identical overall dimensions, were cast from the same concrete batch, contained the same cross-sectional area and centroid location of the longitudinal reinforcement and were subjected to the the same moment to axial load ratio. The specimens were symmetrically reinforced at both faces, in tension and compression zones. Both the analytical predictions and experimentally obtained moment-curvatures for 3 pairs of specimens (KB1 and KB2, KB5 and KB6, KB7 and KB8) are shown in Figures 5, 6 and 7. The first specimen in each pair had smaller diameter bars. Each pair was tested at different axial force to moment ratio (N/M). Good agreement between the predicted and observed responses is clearly visible from these Figures. A good match was achieved at the load levels close to cracking and up to the service load. These are the load levels for which the influence of tension stiffening is most important.
861
crack plane location c
c o m p re s s io n
l c o m p re s s io n in s te el te n s ion in s te e l 0
0
0
5
10 -0 ,0002
State of Concrete Layers Just After Cracking
cra ckin g stra in S train D is trib u tio n Aw ay F ro m C ra c k P la n e
F o rc e F v1 tra n s fe0re d fro m c ra c k e d 5 c o-6n c re te la ye r
te n s io n S tre ss e s an d F o rc e s T ran s fe red Ac ro s s C ra c k P la n e
Figure 1. Stress and strain distributions just after first cracking
c l
crack plane location
steel in compression
compression
0 0
l5 c
10
steel in 0 -50tension -39 -28 -17 -6
0 -0.003
cracking strain
Concrete La ye rs After Significant Cracking
Strain Distribution Away From Crack Plane
tension 5
16 27 38 49
Plus additional force at steel layer from bond
Stresses and Forces Transferred Across Crack Plane
Figure 2. Stress and strain distribition after significant cracking
862
A 29
1 (run)
bearing component 27
concrete
3 (rise)
25
reinforcing bar
23 tensile 21 force 19 in bar 17
A
15
inner perimeter of concrete outer perimeter of the bar lug
5
(a)
Cross Section A-A
surface contact area between concrete and bar lug
inner perimeter of concrete
outer perimeter of the bar lug
(b) Figure 3. a) Reinforcing bar and concrete geometry before cracking, b) contact area between concrete and reinforcement before cracking 6.
Conclusions
The paper presents a constitutive formulation for modeling tension stiffening in the cracked reinforced concrete. The approach taken in the development of the model was to assume that bond between concrete and reinforcement was the main factor influencing the tensile response of cracked members. The formulation considers different factors incluencing mechanics of the behaviour. It is formulated for the analysis of members subjected to monotonic bending and axial load. However, the same concepts can be extended in future for the analysis of members subjected to other combination of forces
863
and it can be implemented into nonlinear structural analysis of reinforced concrete.
B
inner perimeter 29 of concrete
outer perimeter of the bar lug
27 perimeter of inner the bar 25
space
P
23
reinforcing bar
inward 21 movement from Poisson
space
19
outward movement 17 = 3x slip
concrete
slip
15 5
B (a)
Cross Section B-B
reduced surface contact area between concrete and bar lug
inner perimeter of concrete
outer perimeter of the bar lug
(b) Figure 4 a) Reinforcing bar and concrete geometry after cracking b) Contact area between concrete and reinforcement after cracking
8. References Blackwell, K.G., (1996), "Modeling the Behavior of Reinforced Concrete Members Subjected to Bending and Axial Loads", M.A.Sc. thesis, University of Waterloo, 281 pp. CEB-FIP Model Code for Concrete Structures, Third Edition, CEB, Paris. 1978, 348 pp. Clark, L.A., Spiers, D.M., (1978), " Tension Stiffening in Reinforced Concrete Beams and Slabs Under Short term Load", Cement and Concrete Association, Report 42.521 19.
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MOMENT (kNm)
Collins, M.P., Porasz, A. (1989), "Shear Strength for High Strength Concrete", Bulletin D'Information, No. 193, "Design Aspects of High Strength Concrete", CEB, pp.75-83. Gupta, A.K., Maestrini, S.R. (1990), "Tension Stiffness Model for Reinforced Concrete Bars", ASCE Journal of Structural Engineering, 116(3), pp.769-790. Polak, M.A., Blackwell, K.G., (1998), "Modeling Tension in Reinforced Concrete Members Subjected to Bending and Axial Load", ASCE Journal of Structural Engineering, 124(9), 1018-1024. Polak, M.A., Blackwell, K.G., (1998), " Reinforced Concrete Members Subjected to Bending and In-Plane Loading ", ACI Structural Journal, 95(6), 740-748. Polak, M.A., Killen, D.T.( 1998), "The Influence of the Reinforcing Bar Diameter on the Behavior of Members", ACI Structural Journal, in print. Polak, M.A., Vecchio F.J., (1994) " Reinforced Concrete Shell Elements Subjected to Bending and Membrane Loads", ACI Structural Journal, Vol.91, No.3, pp.261-268. Thorenfeldt, E., Tomaszewicz, A. and Jensen, J.J., (1987), "Mechanical Properties of High-Strength Concrete and Application in Design", Proceedings of the Symposium "Utilization of High-Strength Concrete", Stavanger, Norway, June, Tapir Trondheim. Marti, P., Alvarez, M., Kaufmann, W., Sigrist, V., (1998), "Tension Chord Model for Structural Concrete", Structural Engineering International 4, pp. 287-298.
90 80 70 60 50 40 30 20 10 0
KB1 (10M) KB2 (25M) N/M = 4 [1/m]
KB1 Test KB2 Test KB1 Analysis KB2 Analysis
0
2
4
6
8
10 12 14 16 18 20
CURVATURE (RAD/1000)
Figure 5. Moment -curvature response for specimens KB1 and KB2
865
MOMENT (kNm)
90 80 70 60 50 40 30 20 10 0
KB5 (10M) KB6 (20M) N/M = 4 [1/m]
0
2
4
KB5 Test KB6 Test KB5 Analysis KB6 Analysis
6
8
10 12 14 16 18 20
CURVATURE (RAD/1000)
MOMENT (kNm)
Figure 6. Moment -curvature response for specimens KB5 and KB6 90 80 70 60 50
KB7 (10M) KB8 (20M) N/M = -3 [1/m]
40 30 20 10 0
KB7 Test KB8 Test KB7 Analysis KB8 Analysis 0
2
4
6
8
10
12
14
16
CURVATURE (RAD/1000)
Figure 7. Moment -curvature response for specimens KB7 and KB8
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18
20
OVER-CLADDING OF EXISTING CONCRETE BUILDINGS USING COLD FORMED LIGHT STEEL SECTIONS AND COMPOSITE CLADDING PANELS S.O. Popo-Ola+*, R.M. Lawson*, P.J. Sullivan$ Department of Civil Engineering, Imperial College of Science,Technology & Medicine * The Steel Construction Institute, Ascot, United Kingdom $ City University London, United Kingdom +
Abstract The results of research into the effective use of steel sub-frames as part of re-cladding and over-cladding systems for high- and low-rise buildings are presented. An objective of the research was to study the interaction between new cladding systems and their attachment to existing buildings, and to develop appropriate guidance on the use of steel in this application. Existing over/re-cladding systems using aluminium extrusions require many fixings to attach the support rails to the underlying concrete structure. Cold-formed steel (CFS) sub-frames exist whose greater stiffness helps to reduce the number of fixings. Such a sub-frame, with fewer but stronger fixings yet with the redundancy to provide alternative load paths once one fixing fails, has been the subject of an experimental study, with the results correlated with individual fixing tests. The sub-frame systems were also modelled numerically and a design model was developed. The numerical work has been used to interpret the sub-frame tests and to establish the criteria for the overall factor of safety for such systems. The analysis evaluates the effects of the sub-frame flexibility and anchor stiffness on the behaviour of the cladding support system.
867
1. Introduction 'System' buildings were constructed prior to the energy crisis of the mid-1970's by public authorities to offer low-cost post-war housing and even now, many continue to be built in the former Eastern block countries of Europe. It is estimated that over 4000 tower blocks will need major renovation in the UK(1), of which currently less than 2% have been overclad. This indicates a large potential market for cladding renovations. Cold-formed steel sheeting and purlins have been used as cladding and sub-frame materials in industrial buildings for many years yet, despite an established technology for the manufacture and construction of these components, they are little used in the over-cladding or re-cladding of non-industrial, housing or office buildings. This project concerns the effective use of cold-formed steelwork in a re-cladding and over-cladding system for high- and low-rise buildings. Of particular interest was to explore the structural performance of the cladding support frame and its attachment to the building, and to develop appropriate design guidance.
2.
Experimental work
2.1 Fixing tests A study was carried out of the variability of response of a wide range of undercut (U), expansion (E) and resin (R) anchors. The effects of the proximity of a concrete edge, of variations in concrete strength, and also of concrete type (normal (NWC) and light weight (LWC) concrete) were explored(2). Key performance parameters identified were the fixing's stiffness, strength and ductility. 2.2 Sub-frame tests Sixteen tests were carried out, based on a cold-formed steel lipped channel, attached either directly through the flange or through cleats to the web, using fixings selected from the small scale tests. Two point loads were applied to the frames, to allow study of the redistribution of loading between fixings as the highly loaded fixings began to fail (Figure 1). To represent the worst case from the point of view of distribution of fixing loads the subframe was loaded in line with fixing Nos. 2 and 4. The load was however, distributed over a 200mm length of steel plate attached to the web of the sub-frame. The extent to which first fixing failure did not mean system failure was demonstrated(3).
868
Figure 1: Sub-frame tests set-up. TABLE 1: Summary of sub-frame tests results Tes Fixing Thickness Type Applied t type of subof failure No. and Dia. frame Concrete load d (mm) t (mm) P (kN) 1 E4 (8) 2.0D NWC 81.2 2 E4 (8) 2.0 D NWC(R) 93.4 3 E4 (8) 2.0 C LWC 83 4 E4 (8) 2.0 C+ NWC(R) 73.4 5 E4 (10) 2.0 D NWC 115 6 E4 (10) 2.4 D NWC 120 7 E4 (10) 2.4 D LWC(R) 120 8 E4 (10) 2.4 D NWC(R) 134 9 E4 (10) 2.4 C NWC(R) 111 C+ 10 E4 (10) 2.4 NWC(R) 94.1 11 E1 (8) 2.0 D NWC 86.8 12 E1 (8) 2.0 D NWC(R) 96.2 13 E1 (8) 2.4 C NWC(R) 90 14 E1 (10) 2.4 D NWC 95.5 15 E1 (10) 2.4 D NWC(R) 117 C 16 R1 (10) 2.4 NWC(R) 58 D
Attachment directly to slab, CAttachment using stell cleat, Attached to edge beam with 75mm edge distance. NWC(R) = Reinforced concrete grade 15.
+
869
Sum of fixing forces F (kN) 193 147 171 159 195 321 318 271 317 167 195 242 269 233 287 105
Ratio F/P
Mode of Failure
2.38 1.57 2.06 2.17 1.70 2.68 2.65 2.02 2.86 1.77 2.25 2.52 2.99 2.44 2.45 1.81
C+P C+P+S C+P S+P+C T Cs+P C+P C+P C+P C+P C+P P P+S T+P T+P+C S+P
Figure 2 shows a typical graph of load against vertical displacement of fixing and Table 1 shows the results of a series of tests with the following parameters being investigated: • • • • •
Fixings characteristics i.e. expansion anchors with stiffer or more 'ductile' load slip relationships, and resin anchors. Fixing diameter (8mm or 10mm diameter) Channel stiffness (thickness of 2.0 or 2.4mm) Fixing of channel to the slab (directly or via cleats) Concrete type (normal and lightweight concretes of various grades, with or without reinforcement, and with or without the proximity of an edge)
Applied Load, P (kN)
140 120 100 80 60 40 20 0 0
5
10
15
20
25
Vertical deflection, v (mm)
Figure 2:
Load against vertical displacement of a typical fixing (Test 5).
2.3 Failure modes The following failure modes were identified : -
Tearing of the flange of the section through the head of the fixing (T) see Figure 3a. Anchor bolt pull-out from the concrete base (P) see Figure 3b. Cracking/Splitting of the concrete base (Cs). Concrete cone break-out (C) see Figure 3c.
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-
Stud failure in tension (S) see Figure 3d
Figure 3a
Figure 3b
Figure 3c
2.4 Basic structural action Fixing 'E4' was considered to have a 'ductile' load-displacement relationship and therefore would potentially give a significant sharing of load among the fixings in the event of one or two fixings reaching their maximum load. At system failure, attention is focused on the pattern of the individual fixing forces F and on the ratio of the sum of all the forces ΣF to the applied load P (where F includes fixing pre-load), as follows:
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•
More uniform patterns of fixing forces result from a combination of a flexurally rigid channel section and flexible fixings.
•
Once preload is overcome, values of the ratio ΣF/P much greater than unity indicate significant contributions of prying to the fixing forces.
3.
Discussion of test results
The results of 16 sub-frame tests are summarised in Table 1. The effect of various test parameters is discussed in the following paragraphs. 3.1 Effect of fixing types and characteristics In general the results showed a less uniform distribution of fixing forces for stiffer, lessductile fixings, although, distortion of the channel cross-section at the fixing point often muted the influence of fixing stiffness. 3.2 Thickness of Cold-formed channel section Only one test, Test 5, used 10mm fixings in 2mm thick channel as this combination resulted in tearing of the channel. Test 6 which uses 2.4mm thick channel, but is otherwise similar, failed by splitting of the concrete along the line of the fixings, coupled with fixing pull-out at 4% higher maximum load (see Table 1). 3.3 Effect of concrete type Expansion fixings in lightweight concrete (LWC) develop less interlock between the expansion sleeve and the drilled hole. This results in reduced embedment of the failing cone of concrete and a reduction in load capacity (compare Tests 7 and 8 of Table 1). Also a fixing in LWC will tend to have greater secondary expansion and hence a greater overall ductility, which may explain the more uniform force distribution in LWC than in NWC. 3.4 Method of attachment Comparing Tests 8 (direct system) with 9 (cleat system), or Tests 12 with 13, shows that prying in the fixings increased with the use of cleats with a consequent reduction in maximum applied load. Comparing Tests 9 and 10 it can also be seen that the effect of a partially developed cone due to the proximity of an edge has reduced the maximum load by 15%.
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3.5 Distribution of load to the fixings Generally, the tests showed that on overcoming preload, fixings 2 and 4 carried most load as expected, but are frequently almost matched by fixing 3, due to the flexibility of the sub-frame and of its attachment to the concrete. Once fixings 2 and 4 begin to fail more load distributes to the other fixings, especially to fixing 3 (see Figure 4). The maximum applied load is up to 20% greater than the load causing first fixing failure, after which the fixing loads become more uniform. This behaviour demonstrstes the load re-distribution capability of the system as failure is approached.
'E4' M10 Fixings and 2.0mm thick channel on direct connection
60 50 40 30 20 10 0 0
20
40
60
80
100
120
140
Applie d Load, P (kN)
Figure 4:
Load distribution among fixings (Test 5).
3.6 Prying action Eight control tests (in pairs) isolated the effect of prying on the fixings. These tests consisted of two separate lengths of channel beneath the two load points described in section 2.2. These tests eliminate any redistribution of load among the fixings as the fixings are subject only to the applied load and any prying action. Prying forces are determined by comparing fixing forces with applied load. Figure 5 shows typical graphs of fixing forces against applied load from which the non-linear calibration of prying was found, enabling the elimination of prying forces from the sub-frame test results. The resulting reactions were then compared with reactions found from the finite element
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Fixing force f (kN)
analysis. Prying forces varied from 70% to 200% of nominal bolt force, being greater for thinner sections, or where cleats were used.
60 50
Exp1
40 Preload
30
Exp4
20 10 0 0
10
20
30
40
50
60
Applied load, P (kN)
Figure 5: Measured fixing forces against applied load (Control Tests).
4.
Analysis
The experimental results were modelled numerically using the finite element program LUSAS. The analysis was also used to demonstrate the influence of various parameters, for example evaluating the effects of sub-frame flexibility and anchor stiffness on structural performance.
Figure 6: Finite element modelling using LUSAS. 3D 4-noded shell elements were used to represent the cold-formed channel section as shown in Figure 6. The fixing/channel connection to the concrete base was modelled
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using a non-linear spring element with the spring stiffness determined from control tests described in section 3.6. Table 2 compares the results of the LUSAS analysis with Test 1 at maximum load. TABLE 2: Fixing No. B1 B2 B3 B4 B5
Comparison of theoretical reactions with experimental values. Experimental Estimated Exp. Theoretical beam reaction at reactions Ratio fixing forces at failure (LUSAS) Fr.exp / Fc failure, Fr.exp (kN) Fc (kN) Fexp (kN) 26.2 13.6 14.0 0.97 36.4 17.7 17.3 1.02 32.8 16.3 18.2 0.90 32.1 16.2 16.8 0.96 30.6 15.2 13.9 1.09 Average = 0.986
Fixing forces (Fexp) in Table 2 were adjusted to (Fr.exp) to eliminate prying effects and to better estimate the experimental beam reactions. The ratio of these estimated reactions to the finite element values was very close to unity. Comparisons with 12 of the sub-frame tests gave an average ratio (at maximum load) of 0.962 with a standard deviation of 0.31. Having thus validated the numerical model, LUSAS was used to undertake a parametric study on the effect of the following parameters: spacing between anchors, anchor type and diameter, anchor strength and ductility, section properties of the sub-frame and load type(4).
5.
General conclusions
(i)
The behaviour of concrete fixings is more variable than that of the supported steelwork giving rise to a commonly used factor of safety of 3 to 5 in fixing design, much greater than would be used in the design of concrete or steelwork. It is thus important to identify the degree to which a fixing failure does not mean system failure. Tests described herein have achieved their objective of demonstrating reserve of strength after first fixing failure.
(ii)
In these tests a cleated connection increased bolt prying and reduced maximum load by 14% but remains preferable to direct connection as it is easier to install and provides some tolerance for attachment to uneven surfaces. Furthermore, overcladding through existing facades will necessitate some form of cleat or bracket.
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(iii)
Basic tension tests on the fixings are recommended prior to commencement of any overcladding project and such tests should take the edge-distance into account.
(iv)
Transverse bending of the channel flange and consequent prying action was found to increase the fixing forces by 70% to 200%. This can be reduced by minimising eccentricity between the line of applied load and the point of fixing (i.e. reduction of the prying lever arm). Prying variability along with that noted in (i) may require higher factors of safety for fixings in this application.
(v)
The sub-frame system studied was able to carry an additional 20% of load after first fixing failure, with consequent re-distribution of fixing force, before reaching maximum load capacity.
6.
Acknowledgement
The Imperial College research was funded by SERC under the LINK CMR programme, with industrial input from Consulting Engineers, Architects, Fixing Manufacturers, Kingspan Ltd, Hi-Span Ltd and British Steel plc. Industrial contribution was coordinated by the Steel Construction Institute. The authors are grateful to all for their generous contributions.
References 1.
Pedreschi R.F. (1992). "The use of Cold-formed Steel in re-cladding and Overcladding." Dept. of Architecture, University of Edinburgh, Scotland.
2.
Popo-Ola O.S., Lawson, R. M., Sullivan, P. J. (1991) "Small Scale Tests on Fixings." Dept. of Civil Eng. Imperial College, London, Phase I report (RT-04).
3.
Popo-Ola O.S., Lawson, R. M., Sullivan, P. J., Davidson, P. C., England, G. L. (1992). "Re-distribution of Load in Over/Re-Cladding Sub-frame fixed to Concrete base with five anchor bolts." Dept. of Civil Eng. Imperial College, London, Phase II report (RT-07).
4.
Popo-Ola O.S. (1996) "Cold Formed Steel Support Systems in the Over/ReCladding of Concrete Buildings." PhD Thesis. Dept. of Civil Eng. Imperial College, University of London.
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REDUNDANT STRUCTURES FIXED WITH CONCRETE FASTENERS Michael Rößle and Rolf Eligehausen Institute of Construction Materials, University of Stuttgart, Germany
Abstract Concrete fasteners providing redundant fixture for structures will be covered in the future by ETAG, Part 6. The requirements for anchors for these applications should be less strict than for anchors used to fasten statically determinant attachments. The logic behind this is that failure of a single anchorage in a redundantly supported structure will normally not cause complete structural failure, as long as load transfer to neighboring anchors is possible. The probability of failure of redundant structures fixed with fasteners according to ETAG, Part 6 should be in the same range as statically determinant structures fixed with fasteners according to ETAG, Part 1. The failure of anchors is significantly influenced by the presence of cracks in concrete and in particular their widths. Anchors designed according to ETAG, Part 6 may fail if they are located in a wide crack. Therefore, to ensure that a structural system behaves in a redundant way, the degree of utilization of the admissible bending stress and deflection of the attachment must be relatively small in the intact state (i.e. the state where no anchor failure has occured). Finally, requirements for the behavior of anchors in redundant use are shown in Chapter 4.
1. Introduction Fastenings to concrete of various types are used for a wide variety of applications in the building industry. They are often used to fasten statically indeterminant structures such as suspended ceilings, pipes, railings and facades. For these applications, it should be allowed in the future not only to use fasteners that fulfill the stringent requirements of ETAG, Part 1 [1], which may be used to fasten statically determinant attachments, but also fasteners optimized for redundant systems. Requirements for fasteners in redundant structures will be covered in ETAG, Part 6 'Metal anchors for redundant use in concrete for lightweight systems'. The test conditions and the requirements for these anchors should be less strict than those for anchors
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according to ETAG, Part 1. Accordingly, anchors for redundant use should be tested in concrete members with reduced crack widths, e.g. w = 0.2mm and 0.4mm. Anchors tested only in relatively small cracks, however, might fail if located in a relatively wide crack, e.g. w = 0.5mm. In this case the structural system must transfer the load taken by this fastener to neighboring anchors. Redundancy is the intentional overspecification of anchorages to maintain structural integrity when such a failure occurs. The probability of failure of redundant systems fixed with fasteners suitable for such applications should be in the same range as systems providing statically determinant anchorage. Failure of a statically determinant system occurs when one anchors fails, because no state of equilibrium can be found after failure of a single support (see Figure 1a). Failure of a redundant system, however, does not necessarily occur after the failure of one anchor, but rather when the bending strength (design resistance) of the structure is exceeded (see Figure 1b). anchor failure (≠ system failure)
anchor failure (= system failure)
EI q N1
N2
N3
N4
N5 l
l
l
l
N2 falls down a) single use (SU)
b) multiple (redundant) use (MU)
Figure 1: Relation between anchor failure and system failure; a) single use, b) multiple use To ensure that structural systems behave in a redundant way and still fulfill the requirements in the serviceability limit state, they must fulfill following requirements: • The structural system must have sufficient resistance to transfer the load from one fastener to neighboring fasteners if one anchor should fail. The admissible stresses of the structural system should be observed after failure of only one anchor. • The deformations caused by the load transfer should not significantly exceed the requirements in the serviceability limit state of the structure. • The neighboring fasteners should not fail, even they are stressed beyond their admissible load.
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If the above mentioned requirements are observed, failure of the complete structural system will be avoided in case of failure of one anchor. Furthermore, the structural system can still be used without any restrictions. Load transfer within redundant systems is governed by the geometry and stiffness of the attachment (i.e. the structural system) and the performance of the fasteners characterized by their load-displacement-behavior.
2. Behavior of anchors in cracked concrete Under service conditions cracks are to be expected in reinforced concrete structures. There is a variety of reasons for the formation of cracks in concrete. A survey of possible reasons is given in reference [2]. Cracks may form before or after hardening of the concrete. More interesting for fastenings are cracks that develop after hardening of the concrete. These cracks may be caused by load effects (design loads, accidental overload, creep), imposed deformations (due to shrinkage, early thermal contraction, external seasonal temperature variations, freeze/thaw cycles and/or support settlements) and by chemical or physical actions. Fasteners tend to initialize crack formation. Torqueing and loading of anchors creates splitting forces in the surrounding concrete (see Figure 2a). Furthermore, drill holes have the effect of notches in concrete (see Figure 2b). If the tension strength of the surrounding concrete is exceeded the concrete will crack near the anchor [3].
σ
F
σmax
σm = F/Ab b) Drill holes have the effect of notches in concrete
a) Splitting forces caused by torqueing and loading of anchors
Figure 2: Crack initiation by anchors Therefore, anchors must be tested in cracked concrete. The crack widths may significantly influence the behavior of anchors.
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Figure 3 to Figure 5 show load-displacement curves of various anchors obtained from centric tension tests in non-cracked and cracked concrete. Figure 3 shows load-displacement curves of torque-controlled expansion anchors M12, which were developed for use in non-cracked concrete. In non-cracked concrete the load-displacement curves show a continuous increase of load with displacements. In contrast, the behavior of the anchors in cracked concrete is quite poor. The ultimate load and the load-displacement curves vary greatly and cannot be predicted.
hef = 60 mm
Figure 3: Load-displacement curves of torque-controlled expansion anchors M12; which were developed for use in non-cracked concrete, after [5] Figure 4 shows load-displacement curves of torque-controlled expansion anchors that are often used for fixing suspended ceilings. This anchor does not have a Technical Approval. In non-cracked concrete these anchors perform excellently. In cracked concrete, however, the test results show poor performance for crack widths as small as 0.2mm. Anchors fail by pull-out in cracked concrete. The ultimate load can be less than 10% of the value in non-cracked concrete. This anchor is not suitable for use in cracked concrete. Figure 5 shows load-displacement curves of torque-controlled expansion anchors that are also often used for fixing suspended ceilings. This anchor has a Technical Approval for this application. The admissible load is 0.8 kN. This anchor fails in non-cracked and in cracked concrete (w=0.2mm) by steel failure. The displacements are increased in cracked concrete. If this anchor is tested in wide cracks (w=0.5mm) the failure mode changes. Three of the five tested anchors failed by pull-out. The minimal measured ultimate load is about 0.3 kN. That is less than 40% of the admissible load of the anchor.
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14 non-cracked concrete cracked concrete; w=0.2mm
12
cracked concrete; w=0.4mm 10
Load [kN]
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
Displacement [mm]
Figure 4: Load-displacement curves of torque-controlled expansion anchors M6 (hef=46mm), anchor without a Technical Approval, behavior in non-cracked and cracked concrete, after [6]
10 non-cracked concrete 9
cracked concrete; w=0.2mm
8
cracked concrete; w=0.5mm
7
Load [kN]
6 5 4 3 2 1 0
0
2
4
6
8 10 12 14 Displacement [mm]
16
18
20
Figure 5: Load-displacement curves of torque-controlled expansion anchors M6 (hef=40mm), anchors with a Technical Approval (adm. load = 0.8 kN), behavior in non-cracked and cracked concrete, after [6]
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3.
Load redistribution after support failure
After failure of a support (e.g. anchor) the length of the assumed continuous span doubles. This influences the behavior of the overall structural system. 25 Deflection Bending moment Support reaction
F2/F1, M2/M1, f2,f1
20 16
15 10
54 2
0 0
0.5
1 1.5 lspan2/lspan1
2
2.5
Figure 6: Influence of span on support reaction, bending moment and deflection
The results of statical analysis of continuous beams with an infinite number of spans depend on the span length, the applied load and bending stiffness of the beam. The support reaction increases linearly, the bending moments quadraticaly and the deflections to the 4th power with reference to the span length. Doubling the span length (lspan2/lspan1 = 2) causes an increase of support reaction by a factor of 2, bending moments by a factor of 4 and deflections of the beam by a factor of 16 compared to the base value (lspan1). Figure 6 shows these relationships.
If only one fastening element fails in a continuous beam (infinite number of spans) these values are not exactly correct, because the span length doubles only once and the neighboring spans are constant. This very simple investigation, however, gives an approximation of the expected values for the increase of internal forces, moments and deflections if one anchor fails in a redundant structure. To illustrate these results, the values for an intact 4-span beam and the values valid after failure of one support are given in Table 1. To ensure that a 4-span beam is not overloaded after failure of one support (i.e. it continues to fulfill the requirements in the serviceability limit state), the utilization of the bending stress for the intact system should not be more than 21% and the utilization of the deflection not more than about 3% of the allowable values (see Table 2, failure of external support). Beams with more than 4 spans and frame systems behave in general more favorably and therefore the allowable degree of utilization can be higher. Furthermore, one can get a higher allowable degree of utilization after optimization of the length of each span.
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4-span-beam
intact system failure external support failure first internal support failure internal support
support reaction Nmax . ql 1.142 2.033 2.021 1.781
span moment Msp,max . q l² 0.077 0.089 0.332 0.219
support moment Msu,max . q l² -0.107 -0.500 -0.369 -0.281
deflection of beam fmax . q l4/EI 0.0065 0.2442 0.1172 0.0677
Table 1: Results of statical analysis valid for 4-span beams: intact structural system - failure of one support
4-span-beam
failure external support failure first internal support failure internal support
Msp,max,int Msp,max [-] 0.870 0.233 0.353
Nmax,int Nmax [-] 0.562 0.565 0.641
Msu,max,int Msu,max [-] 0.214 0.290 0.380
fmax,int fmax [-] 0.027 0.055 0.095
Table 2: Ratio of support reactions, moments and deflections for the intact system to values valid after failure of one support, 4-span beam
4. Probability of failure: anchors for single use - anchors for multiple use The probability of failure Pf of redundant systems fixed with fasteners according to ETAG, Part 6, should be in the same range (Pf ≈ 1.0 10-6) as statically determinant structures fixed with high performance anchors for single use (i.e. anchors according to ETAG, Part 1). . In this section the probability of failure for a statically determinant and indeterminant structure is calculated. For the statically indeterminant structure it is assumed that the fastened structure is stiff enough to transfer the load to neighboring anchors after failure of one anchor. Failure of a statically determinate structure is defined as failure of only one anchor. In contrast, failure of a statically indeterminant structure that has sufficient resistance (strength and stiffness) for the load transfer to the neighboring anchors after failure of one anchor (see Chapter 3) is defined in this investigation as failure of two neighboring anchors. In the following the probabilities of failure of both systems (see Figure 1) were calculated with the program SYSREL (SORM-method). The anchor loads for the single
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use system (SU) are assumed to be the support reactions of the intact 4-span beam (MU). This allows for comparison of the results for both systems. In the stochastical model the ultimate anchor load, as well as the applied load, are taken into account. It is assumed that 50% of the anchors (e.g. M6/M8) are influenced by cracks in concrete. The ultimate anchor load depends on the measured crack width W under quasi permanent load and the increase of the crack width under maximum load of the structure (see [8], [9]). The reduction of the ultimate anchor load Nu,o dependent on the crack width w is described by Equation (2). The factor (fb.b) is responsible for the degree of load reduction dependent on the crack width w (Figure 8). The load for each anchor is calculated by the FE-Program NELIN with consideration of any cases of anchor failure dependent on the applied load (g, p) and the span l. The span l is assumed to be deterministic. The limit state function for every anchor is given in Equation (4). The distribution functions, mean values and standard deviations of all variables are summarized in Table 3 and Table 4. − 0.7 -w Nu,i(w) = f N ⋅ N u , 0 , i ⋅1− f b ⋅ bi ⋅ w i ⋅ e i
wi
+ PStruc G = Wi ⋅ 1.6 ⋅ Struc 2
0.64
(Eq. 2)
Si
= fL,i . l . (0.33 . g + 0.667 . p)
(Eq. 3)
Gi
= Ri - Si = Nu,i(w) - Si
(Eq. 4)
Basic Variable Nu,0,1 … Nu,0,5 Ultimate load (w=0) Crack width (under W1 … W5 quasi permanent load) Factor for load b1 … b5 reduction Dead load (line load) g Live load (line load) p Dead load GStruc (concrete structure) Live load PStruc (concrete structure) 1)
(Eq. 1)
[kN] [mm] [-]
Distrib. function Lognormal
Mean 8
Standard deviation 0.8
Gamma1)
0.11)
0.11)
Lognormal
1
0.1 - 0.3
Normal Gumbel
1 1
0.1 0.1
Normal
1.3
0.1
Gumbel
1.3
0.2
[kN/m] [kN/m] [-] [-]
values taken from [8]
Table 3: Basic variables for probabilistic analyses
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Basic Variable fb Scale factor for b fL,i Load factor for anchor i l Span
[-] [-]
Value 1-3 Statical analyses
[m]
1.0
Table 4: Deterministic parameters for probabilistic analyses The results of this probabilistic investigation are shown in Figure 7 and Figure 8. To observe a probability of failure of about Pf = 1.10-6 in the single use system (SU), the mean of factor b should be less than bm = 1.15 with a coefficient of variation of 20% (Figure 7). If the complete system does not fail by the failure of only one anchor (multiple use, MU) the requirements for the anchor are less strict. In this case the appropriate value is about bm = 1.95, with a coefficient of variation of 20%. 1.0E-9 SU (bv=10%) SU (bv=20%) SU (bv=30%) MU (bv=10%) MU (bv=20%) MU (bv=30%)
Probability of failure P
f
[-]
1.0E-8 1.0E-7 1.0E-6 1.0E-5 1.0E-4 8,5
1.0E-3 1.0E-2 1.0E-1 1.0E+0
1.15
0.5
1
1.95
1.5
2 2.5 Factor bmean [-]
3
3.5
4
Figure 7: Probability of failure dependent on the factor bmean (V=10, 20 and 30%), Single Use (SU) - Multiple Use (MU) Figure 8 shows the different requirements for anchor behavior in cracked concrete dependent on their use in a single or multiple (redundant) system. To observe the same probability of failure (Pf = 10-6) the ratio Nu,w/Nu,0 for anchors in single use must be about 0.7, for anchors in multiple use only 0.5, with a crack width w = 0.4mm. The
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difference is even more clear, if one considers the 5%-fractiles. The value valid for single use anchors is about 0.6, for multiple use anchors about 0.3. The results for anchors for single use agree approximately with the requirements in [1]. 1,2
Nu,w/Nu,0 [-]
1,0
SU: SU: MU: MU:
95%-fractile
0,8
bm = 1.15 bV = 20% bm = 1.95 bV = 20%
0,6 0,4 5%-fractile
0,2 0,0 0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
crack width w [mm]
Figure 8: Requirements for behavior of anchor in cracked concrete: single use (SU) - multiple use (MU) In further calculations the influence of • the different distribution functions and standard deviations of the applied load, • the distance between the mean of applied load and ultimate anchor load and • the behavior of anchors after exceeding the ultimate load must be investigated.
5. Conclusions For redundant structures it should be allowed in the future not only to use fasteners that fulfill the stringent requirements of ETAG, Part 1, which covers anchors for fastening of statically determinant structures. The test conditions and requirements for fasteners for these applications will be covered in ETAG, Part 6 'Metal anchors for redundant use in concrete for lightweight systems'. These anchors should be tested in smaller cracks than anchors according to ETAG, Part 1. Therefore, it may be possible that anchors according ETAG, Part 6 will fail in a relatively wide crack, e.g. 0.5mm. To ensure load transfer to
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neighboring anchors after failure of one anchor, the degree of utilization of allowable bending stress and allowable deflection in the intact state should be limited. Probabilistic investigations show that the requirements for anchors in redundant use can be significantly lower than for anchor in single use, if the structural system is able to transfer the load taken by the failed anchor.
6. Acknowledgement The primary funding for this research was provided by the firms fischerwerke, Hilti and Würth. The support of these manufacturers is very much appreciated. Special thanks are also accorded to Matthew Hoehler who helped review this paper.
7. References [1] European Organisation for Technical Approvals (EOTA): ETAG 001, Guideline for European Technical Approvals of Metal Anchors for Use in Concrete. Part One: Anchors in General, 1997 [2] Beeby, A.W.: Causes of cracking. Proceedings, CEB/RILEM Workshop on 'Durability of concrete structures', Copenhagen 1983, also in CEB Bulletin No. 158 'Cracking and deformation', Paris 1983 [3] Lotze, D.: Untersuchung zur Frage der Wahrscheinlichkeit, mit der Dübel in Rissen liegen - Einfluß der Querbewehrung (Investigation of the probability that anchors are located in cracks - influence of transverse reinforcement), Report No. 1/24-87/6, Institute of Construction Materials, University of Stuttgart, 1987, not published [4] Eligehausen, R.; Bozenhardt, A.: Crack widths as measured in actual structures and conclusions for the testing of fastening elements, Report No. 1/42-89/9, Institute of Construction Materials, University of Stuttgart, 1989, not published [5] Dieterle, H.; Bozenhardt, A.; Hirth, W.; Opitz, V.: Tragverhalten von Dübeln in Parallelrissen unter Schrägzugbeanspruchung (Load bearing capacity of anchors located in parallel cracks under combined tension and shear loading), Report No. 1/45-89/19, Institute of Construction Materials, University of Stuttgart, 1990, not published [6] Rößle, M.: Redundante Befestigungen - Verifizierung des Prüfprogrammes Zusammenstellung aller bisherigen Versuche in statischen Linienrissen (Redundant Fastenings - verification of test conditions - review of all previous tests in static line cracks), Report No. 00/33-3/11, Institute of Construction Materials, University of Stuttgart, 2000, not published
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[7] Rößle, M.; Eligehausen, R.: Metal Anchors for Redundant Use in Concrete, Behavior of Anchors in cracked concrete and statically effects after failure of one anchor, Report No. 1/03-3/13, Institute of Construction Materials, University of Stuttgart, 2001, not published [8] Bergmeister, K.: Stochastik in der Befestigungstechnik mit realistischen Einflußgrößen (Stochastics in fastening technology with realistic parameters), Dissertation, Universität Innsbruck, 1988 [9] Bergmeister, K.: Neue Bemessung von Dübelverbindungen im Stahlbetonbau (New design of connections using anchors in reinforced concrete), Report No. 7/5-89/20, Institute of Construction Materials, University of Stuttgart, 1989, not published
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NUMERICAL AND EXPERIMENTAL ANALYSIS OF POSTINSTALLED REBARS SPLICED WITH CAST-IN-PLACE REBARS Hannes A. Spieth, Joško Ožbolt, R. Eligehausen, Jörg Appl Institute of Construction Materials, University of Stuttgart, Germany
Abstract Post-installed rebar connections are increasingly used in practice. Several different systems are on the market. To investigate the bond behavior of these systems pullout tests with single rebars and tests with splices were performed. Cast-in-place and post-installed rebars using different systems were tested side-by-side. To investigate the influence of different bond stiffness on transverse cracking three dimensional finite element simulations of splices with different splice length were done. The Investigations show that the bond stiffness and bond strength influences the splice strength and the crack formation along the lap length. When the used systems to postinstall rebars provide comparable bond stiffness and no lower bond strength than cast-inplace rebars, design can be done according to the codes for reinforced concrete. Exceptions have to e made at minimum concrete cover, minimum embedment length and at elevated temperature.
1. Introduction In practice more and more connections between reinforced concrete elements are carried out by bonding deformed reinforcing bars with an adhesive mortar in holes drilled into the existing concrete. Examples are casting secondary floor slabs, closing temporary openings, connecting new walls and columns to the existing foundation, connecting cantilevering elements such as balconies with the existing structure, etc. In these cases the reinforcing bars have to be anchored in existing reinforced elements or have to be spliced with existing reinforcing bars. Normally holes are drilled in the existing concrete with hammer or diamond drilling machines. After cleaning the hole the adhesive mortar is injected; subsequently the reinforcing bar is pressed into the filled hole.
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2. Types of systems and installation There are different systems on the market. They vary in the type of used mortar and the installation procedure. Two systems have been officially approved for this application [3,4]. All systems have in common that a hole has to be drilled and cleaned. The cleaning procedure vary with each product. In most cases the hole has to be cleaned by brushing and pumping. The officially approved systems require cleaning of the hole with compressed air and machine driven wire brush. Most common are the so called injection systems. Here the hole is filled with mortar using an injection tool. The two components of the mortar are mixed automatically during injection. Used are mortars based on organic compounds (epoxy, polyester, vinylester), inorganic compounds (cementious) and combinations of organic and inorganic compounds. After filling the hole the bar is pressed in with a twisting motion. The officially approved systems are as well injection systems with a combination of organic and inorganic compounds. Furthermore glass capsule systems are used. The capsules contain the mortar which is based on the above mentioned resins. They are put into the hole. Then the bar is driven into the hole by hammer blows. There by the capsule is destroyed and resin and hardener are mixed.
3. Transmission of load Bonded reinforcing bars can be separated into two kinds of applications: • Bonded bars in concrete without connection reinforcement (Figure 1 a)). These bonded rebars transfer the load into the concrete in the same way as bonded anchors. • Bonded bars in concrete with connection reinforcement (Figure 1 b)). These bonded rebars act in the same way as spliced reinforcement.
F
F
F
F
F
F
a) With connection reinforcement
b) Without connection reinforcement
Figure 1: Bonded reinforcement
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In these two cases the transmission of load is totally different. In case of bars without connection reinforcement the load must be taken up by the surrounding concrete, utilizing the concrete tensile strength in a rather large volume. Failure may be caused by bar pullout or by concrete breakout. With rebars spliced with existing reinforcement the load is transferred by compression struts to the cast-in-place reinforcing bar. The tensile strength of concrete is utilized only locally.
4. Experimental studies To investigate the influencing parameters on general bond behavior of post-installed rebar connections pullout tests with single post-installed rebars were performed. Further tests of post-installed rebars spliced with cast-in-place rebars were done to investigate the bond distribution of the rebars and load transfer between the spliced rebars. 4.1.
Bond behaviour of single post-installed rebars without connection reinforcement The bond behavior of single post-installed rebars may be influenced significantly by several material, installation, environmental and geometrical parameters. The influencing parameters of the installation can be e.g. drilling system, hole cleaning and injection tools used. As environmental parameters e.g. temperature of base material and mortar as well as the moisture content of concrete can influence the bond behavior. Further material and geometrical parameter as concrete strength and cracks in the concrete influence the performance of post-installed rebars. The influence of these parameters is discussed in more detail in [1]. It has been shown by pullout tests where concrete cone failure was restricted, that post-installed rebars can behave as cast-in-place rebars, provided that a suitable product is used and the installation is done properly. Different behavior is observed at elevated temperatures and in cracked concrete. 250 Epoxy System
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Even if the installation is done properly and the hole cleaning is done perfectly there are large differences between the bond behavior of different products. In Figure 2 the load
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displacement curves measured in confined pullout tests of post-installed rebars installed with different products are shown. All bars were installed with large concrete cover to prevent splitting of the concrete. The formation of a concrete cone was prevented by placing a steel plate with a hole on the concrete surface, where the bars were pulled through. The curves show that rebars embedded with different products show a different behavior in respect to stiffness and bond strength. The Hybrid-System (combination of Vinylester and cementitious compounds) has a behavior closest to a cast-in-place rebar, which is included in the graph for comparison. While the Epoxy-System showed a much higher stiffness and a larger bond strength than the cast-in-place rebar, the PolyesterSystem had a softer behavior and a significantly smaller bond strength. The stiffness of the Cement-System was comparable to the Epoxy-System but the bond strength was smaller than for cast-in-place rebars. While the stiffness is influenced by the composition of the mortar (mainly amount of aggregates) and the diameter of the drilled hole in relation to the bar diameter, the bond strength is mainly influenced by the shear strength of the mortar and the gluing capacity of the resin with the wall of the concrete hole. 4.2. Bond behaviour of post-installed rebars spliced with cast-in-place rebars In most applications the post-installed rebars are spliced with existing reinforcement. Often the concrete cover is rather small. These connections must be treated as an overlap splice. In general the failure mode is splitting of the concrete cover or of the concrete member. To investigate the influence of bond strength and bond stiffness on the behavior of postinstalled rebar connections, splice tests with all product shown in Section 4.1 and Figure 2 were performed. A drawing of the tension test specimens is shown in Figure 3. Splice length and clear spacing were kept constant. To get a more ductile failure transverse reinforcement was placed along the splice length. To simulate two sections of the splice separated by a transverse crack, crack formers were placed in the middle of the test specimen. The rebars were loaded displacement controlled until the specimens failed by splitting. The failure was very brittle. The splitting failure plane is shown in Figure 3. The outer bars were cast-in-place. 28 days after casting holes were drilled into the elements and the inner bars were post-installed. For comparison elements with cast-in-place spliced rebars only were tested. The displacements at the unloaded and loaded ends of the rebars in reference to the concrete surface as well as the opening of the splitting cracks were measured. All together 12 tests with post-installed rebars and 3 tests with spliced cast-in-place rebars only were performed. Failure of the specimens was caused by splitting cracks along the crack plane indicated in Figure 3. Figure 4 (a) shows the steel stress at peak load of the performed tests. The rebars post-installed with the Hybrid-System show failure loads comparable to cast-inplace rebars, which was expected taking into account the results shown in Figure 2. The low failure loads of the bars post-installed with the Polyester-System were expected as well, because of the low stiffness and the low bond strength of single bars (compare Figure 2). The tests using a cementious mortar showed a similar splice strength compared to cast-in-place spliced bars, even though the bond strength of single rebars is
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significant lower than the bond strength of cast-in-place rebars (compare Figure 2). This is due to the fact, that splitting failure occurred before the pullout bond strength was utilized. The splices with the Epoxy-System show a larger scatter of the peak loads than the tests with cast-in-place rebars. Test S1 showed a much lower steel stress at peak load compared to cast-in-place spliced rebars, even though the bond strength of single rebars is significantly higher than the bond strength of cast-in-place rebars. The reasons of the lower strength of the splices with rebars installed using a Epoxy-System is discussed below using the measured distribution of the steel strains along the bond length. 600
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In Figure 4 (b) the average steel stresses – splitting crack opening curves of the tested specimens are shown. It can be seen that at all tests, not relevant if the bars were cast-inplace or post-installed using anyone of the systems, the splitting cracks started forming at the same load level. Due to this it can be assumed that the splitting force development is only dependent on the bond stress. At further elevated loads differences can be seen. The specimen with the cast-in-place splices showed the smallest crack openings. It can be assumed that differences in the bond distribution and different behavior of the bars in cracked concrete caused the larger crack openings. 500
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To investigate the bond distribution along the lap length of spliced rebars, strain gauges were applied at the cast-in-place and post-installed rebars. A slot was milled into the reinforcing bar and the strain gauges were applied at the center of the rebar. The spacing of the strain gauges was 75 mm. Figure 5 shows the distribution of steel stresses (calculated from the measured strains) of two cast-in-place rebars spliced with each other and of a cast-in-place rebar spliced with a post-installed rebar for stress levels 150 N/mm², 300 N/mm² and at failure load. At the element with cast-in-place spliced rebars the measured steel stresses are almost symmetrical to the middle of the element, where a transverse crack formed. At failure the bond stresses are almost constant along the bond length. At the element using the HybridSystem the steel stresses are slightly unsymmetrical. The loaded ends of the postinstalled rebar transfers a higher tension force than the cast-in-place rebar at the loaded end. Due to the high stiffness of the Epoxy-System (specimen S1) high bond stresses were generated which caused an extensive transverse cracking of the specimen in this area. Due to this the far end of the bond length was only slightly activated and the bond stress distribution was highly non-linear. Therefore the steel stress at failure was lower than for the other tests. At the test using the Polyester-System bond was activated already at a lower load level than at the other tests due to the low bond stiffness of the Polyester-System. Failure occurred also due to splitting but at an lower level. As seen in Figure 4 b) splitting cracks formed at the same load level at all tests. As seen in Figure 5 the bond capacity of the specimen using the Polyester-System at the time of splitting crack formation was utilized higher and bond was activated over a larger area than at the other specimen. Therefore the splitting cracks enlarged faster at this specimen at increasing load and failure occurred at a lower load level. cast-in-place
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5. Numerical Analysis 5.1. Finite element program MASA and calibration of the bond element The used finite element code Masa is based on the microplane model. It can be used for the two and the three-dimensional analysis of quasi-brittle materials. The model allows a realistic prediction of the material behavior in case of three-dimensional stress - strain states. The smeared crack approach is employed. To ensure mesh independent results the crack band approach is used. More detail related to the used model can be found in [2]. The calibration of the different bond elements was performed based on pullout tests with cast-in-place and post-installed rebars using different types of systems. The bond elements were calibrated at tests with embedment depth of 10 and 15 times of the bar diameter. At some of the pullout tests strain gauges were applied at the bars to measure the bond distribution along the embedment length. These data were taken to calibrate the bond stiffness of the different types of systems for the numerical simulation. A bond element for each of the systems shown in chapter 4 was calibrated. 5.2. Numerical Simulation of splices To investigate the influence of bond properties on splice behavior numerical simulations of splices were performed. A post-installed bar spliced with a cast-in-place bar in a tension element were simulated. In the numerical simulations the failure mode splitting was excluded to get an more stable behavior and to study the transverse crack formation at higher loads. Two different splice length were analysed – ls = 30ds as in the experimentals (Figure 3) and ls = 70ds which is according to the codes for reinforced concrete approximately the maximum splice length that is required. simulation cast-in-place
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Figure 6 shows the distribution of calculated steel stresses for two cast-in-place rebars spliced with each other and of a cast-in-place rebar spliced with a post-installed rebar. The results are shown for the stress levels of 150 N/mm², 300 N/mm² and 500 N/mm² (lv = 30 ds). In all simulations the splitting was excluded. The calculated failure loads are higher than measured in the experimental studies. Therefore the curves are shown only up to the yield strength of the steel. It can be seen that the distribution of the steel stresses is comparable with the distribution obtained in the experiments (Figure 5). The splice with cast-in-place rebars has symmetrical distribution of stresses. At the postinstalled splice using the Hybrid System the steel stress distribution is slightly unsymmetrical and shifted towards the post-installed side. The Epoxy System shows as well a stiffer bond characteristic than the cast-in-place rebar. At the Polyester System it can be seen that at steel stress of 300 N/mm² bond at the whole splice length is already activated. This is in good agreement with the experiments. The numerical simulations compared to the experimental studies show that the different calibrated bond elements can simulate the post-installed rebars using the here presented three systems and the cast-in-place rebar realistically. Using the same bond elements splices with length lv = 70 ds were investigated. Again splitting failure of the element was excluded. To investigate the influence of the bond stiffness on steel stress distribution and transverse crack formation, simulations with the stiffest (Epoxy) and softest (Polyester) system were carried out and compared with the spliced cast-in-place rebars. Figure 7 shows the steel stress distribution and the concrete strain distribution along the lap length of the performed simulations. It can be seen that the bond stiffness influences significantly the shape of the steel stress distribution and crack formation. At the graphs of the steel stress distributions it can be seen, that the bond stiffness effects the gradient of the curve. At the loaded end the reduction of the steel stresses at the simulation with Epoxy System is rather fast. In the case of the Polyester System the force is introduced much slower into the concrete member. At the specimen with cast-in-place spliced rebars the cracks are symmetrical to the middle axis (see Figure 7). The crack distances measured from both sides are comparable. The specimen with the Epoxy System the crack pattern is slightly unsymmetrical. The crack distances on the side of the postinstalled rebar are smaller than on the side of the cast-in-place rebar. At the specimen with the simulated soft Polyester System the first crack occurs at a much larger distance measured from the end of the specimen and just one crack occurs at the side of the postinstalled rebar. Comparing all three graphs it can be seen that the crack pattern at the side of the simulated cast-in-place rebar is comparable for all simulations. The numerical simulations show that the bond stiffness influences the crack spacing and the number of cracks formed. Further numerical investigations are in progress to investigate the influence of bond stiffness and bond strength to the crack formation and to the displacement at the loaded ends of spliced rebars.
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Figure 7: Stress distribution along the lap length of spliced rebars(a) and concrete strain distribution along lap length (b); numerical simulation; lv =70ds
Figure 8: Finite element mesh; max. principal strains in concrete; splice with post-installed rebar using simulated Epoxy System; numerical simulation; lv =70ds
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6. Conclusions The systems to post-install rebars can provide different bond strength and bond stiffness than comparable cast-in-place rebars. The experimental investigations show that if bond stiffness and bond strength of the systems used are comparable to the behavior of castin-place rebars, splices with post-installed and cast-in-place rebars show the same behavior, even at failure mode splitting of the concrete element. The numerical studies show that the bond stiffness and the bond strength influence the splice strength and the crack formation along the lap length. The crack distances are directly dependent to the bond stiffness of the used system. With increasing bond stiffness the crack distances at the loaded ends become smaller. The effect of the bond stiffness can be seen as well at the gradient of the steel stress distribution of the spliced rebars (bond stress). Further numerical simulations are currently in progress to investigate the influence of bond characteristic to splice strength, crack formation and displacements at the loaded ends of the splices. The investigations show that when the used systems of post-install rebars provide comparable bond stiffness and not lower bond strength than the cast-in-place rebars, design can be done according to the codes for reinforced concrete. Exceptions have to be made for the minimum concrete cover and minimum embedment length as well at elevated temperature. These exceptions are discussed in [1].
7. Acknowledgements This work was supported by the following companies: Fischerwerke and Hilti. The support is very much appreciated. 8. References [1] Eligehausen R., Spieth H. A., Sippel Th. M.: Eingemörtelte Bewehrungsstäbe. Beton- und Stahlbetonbau, 12/1999, pp. 512 – 523 [2] Ožbolt, J., Li, Y.-J., Kožar, I.: ‘Microplane model for concrete with relaxed kinematic constraint’, International Journal of Solids and Structures, 38, 2001, 2683-2711 [3] Deutsches Institut für Bautechnik (DIBT): Allgemeine bauaufsichtliche Zulassung (Z-21.8-1648). Bewehrungsanschluss mit Hilti-Injektionsmörtel HIT – HY 150; 2000 [4] Deutsches Institut für Bautechnik (DIBT): Allgemeine bauaufsichtliche Zulassung (Z-21.8-1647). Bewehrungsanschluss mit Upat-Injektionsmörtel UPM 44; 2000
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DOWEL ACTION OF TITANIUM BARS CONNECTING MARBLE ELEMENTS Elizabeth Vintzileou, Konstantinos Papadopoulos National Technical University of Athens, Greece
Abstract This paper presents the results of 48 tests that were performed to gain evidence concerning the dowel action of titanium bars connecting marble elements. The parameters investigated within the program were: the diameter of titanium bars (6, 8, 10 and 12 mm), their cover (2, 4 or 6 bar diameters), as well as the loading direction (against the strong or the weak direction of marble’s anisotropy). The main aim of the testing program was to determine the minimum cover required to ensure that failure will occur in the titanium bar and not in the marble. It was proved that a cover equal to 6 times the dowel diameter is sufficient to ensure dowel failure, whereas for loading against the marble’s strong direction, even a cover of 4 times the bar diameter is sufficient. Adequate formulae, calibrated on the basis of the experimental results, are proposed for the calculation of the dowel resistance.
1. Introduction Titanium is quite extensively used in the conservation works of the monuments at the Athens Acropolis. The commercially pure titanium was selected both for its resistance to all types of corrosion and for its physicochemical compatibility with the marble. Threaded titanium bars, installed in drilled holes and connected with the marble by means of a white cement mortar, have been used up to now, to connect pieces of fractured architectural members. In those applications, in which titanium bars are subjected to tension, the connections are designed in a way to exclude failure of the connected marble pieces. The relevant design method1,2 is supported by experimental evidence.
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There are, however, numerous applications, in which the marble to titanium connection is expected to be subjected to shear. For this type of loading, neither experimental evidence nor a design method is available. In order to provide relevant experimental evidence, an experimental program was carried out at the Laboratory of Reinforced Concrete, NTUA. Threaded titanium bars were installed in drilled holes in Dionysos marble and they were subjected to shear up to failure. Various parameters were investigated, namely the diameter of the titanium bars, their cover and the direction of loading (against the strong or the weak direction of marble’s anisotropy). In this paper, the main experimental findings of the program are presented and commented. In addition, formulae are proposed for the calculation of the maximum shear force carried by the titanium to marble connection.
2. The materials 2.1. Dionysos marble Pentelic marble is the basic material of the Acropolis monuments. However, since the quarries of Penteli were closed for environmental reasons, marble from Dionysos mountain, near Penteli, is used in restoration works, to produce both patches and copies of lost members. Dionysos marble was selected because its physical and mechanical properties are similar to those of the remarkably durable Pentelic marble.1 According to tests carried out at the National Technical University of Athens3,4, the compressive strength of Dionysos marble is equal to 83 N/mm2 and 70 N/mm2 in its strong and weak direction respectively. Its strength in direct tension is equal to 8.7 N/mm2 in the strong direction of the marble. The available data regarding the tensile strength of the marble in its weak direction are not considered to be reliable. The Poisson’s ratio is equal to 0.33 in both directions. 2.2. Titanium Titanium bars, threaded along their whole length, are used to provide continuity between the fractured pieces of the architectural members. Commercially pure titanium (Grade 2, in accordance with ASTM B348) was selected because of its high resistance to all types of corrosion, as well as for its physical and mechanical properties that render it suitable for joining together pieces of the original marble. In fact, the Poisson’s ratio of titanium (=0.32) is practically equal to that of the marble. In addition, titanium exhibits a low coefficient of thermal expansion (=9x10-6 grad-1), sufficient (but not excessively high) mechanical strength and high elongation at failure (20%÷22%). The yield strength of titanium is equal to 300 N/mm2, whereas its tensile strength is equal to 420 N/mm2.
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2.3. Cement mortar As mentioned previously, titanium bars are inserted into drilled holes and connected to the marble by means of white cement mortar. To this purpose, white Portland cement is used. The mechanical properties of the mortar were measured on conventional 40x40x160 [mm] specimens. Its mean compressive strength at 28 days was equal to 12.1 N/mm2, whereas its tensile strength (in flexure) was equal to 0.96 N/mm2.
3. The specimen Two pieces of Dionysos marble, 0.24x0.24x2.64 [m], were used for testing, one for each loading direction. Both were cut from the same major piece of marble and they were free of discontinuities and imperfections. Holes were drilled to the marble, perpendicular to the marble face, to accommodate titanium dowels. 0.22
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in case of cone failure. The depth of holes was equal to 10 times the dowel diameter. The holes were cleaned from dust before the insertion of titanium dowels. Four titanium bars, 2 meters long, with a diameter of 6mm, 8mm, 10mm and 12mm respectively were used to form the dowels. The bars were first threaded and they were subsequently cut into pieces. Each piece was of a length equal to 10 times the bar diameter (equal to their embedment length) plus 50mm (equal to their protruding length). Cement mortar was poured into each hole and the respective dowel was pushedin by hand. All tests were carried out 28 days after the application of dowels, to allow for sufficient hardening and strength gaining of the mortar.
4. Experimental set up Fig. 2 shows the set up used for testing the dowels: The specimen was placed horizontally on the strong floor of the Laboratory. A steel ring (A) was screwed to the dowel under testing. Subsequently, a steel plate (B), having a hole of diameter by 2mm larger than the external diameter of the ring was placed on the specimen. Gradually increasing displacements were applied by an MTS hydraulic actuator (C), with maximum capacity of 500 KN, to the steel plate. The longitudinal axis of the actuator coincided with the surface of the marble element, to avoid eccentric loading of the dowels. The reaction was transmitted to one of the strong steel frames of the Laboratory
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testing. Three LVDTs (E) were used to record displacements of the steel plate and of the marble element during testing.
5. Experimental results 5.1. Failure mode Two failure modes were observed, depending on the cover of the dowels, as well as on the direction of loading. Both failure modes are schematically shown in Fig. 3: Failure mode I consists in fracture of the dowel at the surface of the marble element, accompanied by limited in depth spalling of the marble. Failure mode II consists in the separation of a cone of marble. The angle of separation was approximately equal to 23°, whereas the depth of the cone was almost equal to 2c (c being the cover of the dowel). It was observed (see also Table 1) that failure mode I occurred to all dowels to which a cover equal to 6 times the bar diameter was provided. The same failure mode was observed also for a cover equal to 4 times the bar diameter, when the dowels were loaded against the strong direction of the marble. On the contrary, a cover equal to twice the dowel diameter led to a cone failure. The same holds true for dowels with a cover of 4 times the bar diameter, loaded against the weak direction of the marble. Failure mode I
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Fig. 3 Modes of failure (schematic) 5.2. Shear force-shear displacement curves In Fig. 4, some shear force vs. shear displacement curves are presented. It may be observed that, independently of the failure mode that occurred, there is a practically linear relationship between shear force and shear displacement up to approximately 80% of the maximum mobilized shear force. A less steep curve follows up to failure. Since for both failure modes failure is brittle, the falling branch was practically vertical. In several cases, an initial part of the curve was recorded, for which shear displacement was increasing without substantial increase of the mobilized shear resistance. This feature is attributed to the fact that this initial part of loading is governed by the characteristics of the cement mortar that lies between the dowel and the marble. Expectedly, this layer of (much softer and less strong than the marble) mortar affects more the behaviour of the smaller diameter dowels, as explained in section 6.1.
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It may also be observed (see also Table 1) that the values of shear displacement at failure are very scattered. In some cases, the failure was very sudden and, thus, the displacement at failure was not reliably recorded. 6,6,w 6,6,s 6,4,w 6,4,s 6,2,w 6,2,s 8,6,w 8,6,s 8,4,w 8,4,s 10,6,w 10,6,s 10,4,w 10,2,w 10,2,s 12,6,s 12,4,w 12,4,s 28000 12,2,w 12,2,s 26000 24000 22000
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6. Discussion of test results Concerning the failure mode of the dowel mechanism, it seems that the results obtained within this program are in accordance with the available experimental data that regard the dowel mechanism of steel bars embedded in concrete. In fact, numerous tests (summarized by Vintzileou5) have shown that a concrete cover equal to 4 to 6 times the bar diameter is sufficient for a concrete cone failure to be avoided. Nevertheless, in case of steel bars embedded in concrete, failure mode I implies simultaneous yielding of the bar and failure of the concrete due to local crushing under the bar, thus ensuring a very ductile behaviour. On the contrary, the combination of a relatively low strength dowel (made of titanium) and a very strong substrate (marble) leads to fracture of the dowel, hence, to a brittle failure of the connection.
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Table 1. Summary of test results Dowe db c/db Load. Du (N) du (mm) l No. (mm) Dir. 1-6 6 6 W 3,780-6,230-6,9102.34-(*)-1.705S 2,370-4,710-5,125 5.52-6.525-2.33 7-12 8 6 W 10,780-10,945-11,095- (*)-0.16-4.66S 9,940-9,940-12,210 4.77-8.59-3.73 13-18 10 6 W 18,440-18,690-18,145- 7.49-0.865-(*)S 18,430-16,290-18,340 9.12-6.75-10.49 19-24 12 6 W 22,520-24,365-23,430- 0.41-(*)-(*)S 22,890-23,390-22,925 8.91-8.24-5.75 25 6 4 W 5,015 2.51 26 6 4 S 5,525 3.71 27-28 8 4 W 11,020-11,360 6.4-5.52 29-30 8 4 S 7,980-10,365 3.66-7.24 31 10 4 W 18,375 9.315 32 10 4 S 15,605 (*) 33-34 12 4 W 21,045-20,270 1.945-3.4 35-36 12 4 S 23,210-27,235 20.0-8.23 37-38 6 2 W 2,210-2,285 1.11-0.405 39-40 6 2 S 3,210-2,630 3.48-3.148 41 8 2 W 6,370 (*) 42 8 2 S 6,700 2.466 43-44 10 2 W 5,760-4,735 4.94-1.66 45-46 10 2 S 4,220-5,235 0.77-1.04 47 12 2 W 7,745 3.154 48 12 2 S 11,265 7.91 Notation Nominal bar diameter db: c: Cover of the dowel Maximum mobilized shear resistance Du: Shear displacement corresponding to Du du: W,S: Loading against weak or strong direction of marble
Failure mode I I I I I I I I II I II I II II II II II II II II
6.1. Prediction of ultimate shear force-Failure mode I In an attempt to predict the maximum shear force transferred by the titanium dowels, the following two well known formulae were applied: (1) (a) Fracture of dowel in shear: Du=0.6Asft (b) Simultaneous fracture of the dowel in shear and crushing of the marble:
Du =1.3d b2 ft fm
(2)
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where, As denotes the area of the dowel, db denotes the diameter of the bar, ft denotes the tensile strength of the dowel, and fm denotes the compressive strength of the marble (=83 or 70 N/mm2 depending on the loading direction) Equations (1) and (2) were applied for the dowels that exhibited failure mode I. In Table 2, the predicted Du values are compared with the experimental ones. One may observe that Equ. (2) clearly overestimates the maximum dowel resistance, whereas the predictions of Equ. (1) are more accurate. The fact that Equ. (2) fails to accurately predict Du insinuates that dowel and marble resistances cannot be simultaneously mobilized due to the substantially diferring mechanical properties of the two materials. In addition, as shown in Tables 1 and 3, in case of 6mm dowels, less accurate prediction of the maximum shear force is observed even in case of Equ. (1), due to the large scatter of the experimental results. This large scatter is attributed to the more pronounced effect of the cement mortar when it surrounds small diameter dowels. In fact, the inspection of specimens after the completion of tests has proved that some 6mm dowels have failed due to a combination of shear and bending. Those dowels failed under lower shear force than expected for pure dowel action. It seems, therefore, that in order to take into account this feature, adequate partial safety factor values should be adopted, when the design shear resistance of a connection is calculated. 6.2. Prediction of ultimate shear force-Failure mode II Although this failure mode is to be avoided by an appropriate arrangement of dowels, the following empirical formula was derived for calculating the maximum shear resistance of dowel to marble connection, in case of cone failure: Du=1.625c2fmt (3) where fmt denotes the tensile strength of the marble in the relevant loading direction.
Equ. (3) was applied to calculate the ultimate dowel resistance of the 15 bars that exhibited a cone failure. A quite satisfactory agreement was observed between calculated and experimental Du values. In fact, the mean value of the ratio between calculated and experimental values of the shear resistance was equal to 0.97, whereas its standard deviation is equal to 0.25.
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Table 2. Failure mode I: Comparison between experimental and predicted ultimate shear force values Dowel db calc.Du(N) calc.Du(N) Loading exp. Du (N) No. equ. (1) equ. (2) (mm) direction 1-3 6 W 3,780-6,230-6,910 6,173 6,953 4-6 6 S 2,370-4,710-5,125 6,173 7,571 7-9 8 W 10,780-10,945-11,095 10,794 12,157 10-12 8 S 9,940-9,940-12,210 10,794 13,238 13-15 10 W 18,440-18,690-18,145 16,570 18,662 16-18 10 S 18,430-16,290-18,340 16,570 20,321 19-21 12 W 22,520-24,365-23,430 23,883 26,898 22-24 12 S 22,890-23,390-22,925 23,883 29,289 25 6 W 5,015 6,173 6,953 26 6 S 5,525 6,173 7,571 27-28 8 W 11,020-11,360 10,794 12,157 29-30 8 S 7,980-10,365 10,794 13,238 32 10 S 15,605 16,570 20,321 35-36 12 S 23,210-27,235 23,883 29,289 Table 3. Application of Equs (1) and (2): Statistical data Equation (1) Equation (2) pred.Du/exp.Du pred.Du/exp.Du Diameter mean standard COV mean standard (mm) value deviation value deviation 6 1.37 0.54 0.40 1.62 0.69 8 1.03 0.13 0.12 1.22 0.19 10 0.94 0.07 0.08 1.11 0.12 12 1.01 0.06 0.06 1.20 0.08 All 1.09 0.31 0.29 1.29 0.39
COV 0.42 0.15 0.11 0.07 0.31
7. Conclusions Regarding the dowel action of titanium bars connecting marble elements, the following conclusions can be drawn: 1. A cover equal to 4 or 6 times the dowel diameter is required to avoid a cone failure of the marble, depending on whether the dowel is loaded against the strong or the weak direction of the marble. 2. When sufficient cover is provided to the bars, failure of the dowels occurs, whereas the substrate remains practically unaffected.
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3. In case of very small dowel diameters, the maximum mobilized shear resistance is substantially affected by the cement mortar used to connect the dowels to the marble. 4. The maximum dowel resistance can be quite accurately predicted by means of simple formulae, for both failure mechanisms.
8. References 1. Zambas C., “Principles for the structural restoration of the Acropolis monuments”, The Engineering Geology of Ancient Works, Monuments and Historical Sites, (Edited by P.Marinos and G.C.Koukis), Balkema, Rotterdam, 1988, pp. 1813-1818. 2. Zambas C., “Structural repairs to the monuments of the Acropolis-The Parthenon”, Proceedings of the Institution of Civil Engineers, 1992, pp. 166-176. 3. Vardoulakis, I. And Kourkoulis, S.K., “Mechanical properties of Dionysos marble”, Final Report of the Environment Project EV5V-CT93-0300 “Monuments under seismic action”, Nat. Tech. Univ. of Athens, Athens, 1997. 4. Vardoulakis, I., Stavropoulou, M., and Papadopoulos, Ch., “Direct tension tests on Dionysos marble”, EU DG XII SMT Programme No SMT4-CT96-2130, Final Report, 2000 5. Vintzileou, E., “Shear transfer by dowel action and friction as related to size effects”, CEB Bulletin No 237, “Concrete tension and size effects”, 1999, pp. 53-77.
9. Acknowledgments The materials needed for testing (Dionysos marble and titanium bars) were offered by the Committee for Conservation of the Acropolis Monuments.
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CASE STUDY -APPLICATION OF HIGH STRENGTH POSTTENSIONED RODS FOR ANCHORING AERIAL TRAM STRUCTURES TO ROCK George Patrick Wheatley Heery International, Inc.
Abstract Forces generated by large aerial trams with rigid track cable end anchorage can be significant at locations where the cables anchor to the concrete. These forces are typically accounted for by providing mass concrete foundations or reinforced concrete mats and rock anchors. This paper presents a case study of an 80 person aerial tram located at Stone Mountain, Georgia, USA. This tram’s reinforced concrete bollards used high strength posttensioned rock anchors to anchor the bollards. This system minimized the amount of concrete transported to the top of the mountain and the impact to the environmentally sensitive mountaintop area Addressed is a description of the post-tensioned rock anchor/concrete bollard design philosophy and system behavior. Focus is made on strength of rock, high strength rod and rock anchor grout characteristics, reinforcement details for localized concrete posttensioning stresses, the post-tensioning operation, and an overview of admixtures used in the long distance concrete pump mix design.
1. Introduction The Stone Mountain Aerial Tram was designed and constructed in 1996 as a replacement of the existing tram which was constructed in 1962. Located adjacent to the existing tram, it consists of an upper station at elevation 692m, one intermediate tower with two 1.8m diameter pipe columns, and a lower station at elevation 474m. There are two tracks that have two, 49mm diameter track cables each. The project was on an accelerated schedule and required close attention to construction materials and procedures in order to meet the aggressive schedule in time for the Atlanta
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1996 Olympic Games. The new tram was scheduled to carry the Olympic Flame to the mountain top for it‘s journey to Atlanta‘s Olympic Stadium. Feasibility studies for the tram replacement were conducted previously to determine options of everyday visitor transportation to the mountaintop and the most economically viable means to do so. Options included a funicular tram, aerial tram with counterweight/hydraulic track cables, and an aerial tram with rigid track cables. The most viable choice for the configuration at Stone Mountain was to use an aerial tram with rigid track cables (haul ropes have counterweights). The tram manufacturer selected was VonRoll out of Seilbahnen, Switzerland who contracted with North+Perret SA, out of Neuchatel, Switzerland for the cable and intermediate tower analysis.
2. Engineering 2.1 Configuration/Criteria Because of the rigid attachment of the track cables, forces generated by the tram when between supports became significant at the bollards (upper and lower station anchor points). The forces from the analysis to be used in design were 1690 KN per track which generated approximately 1290 KN at each anchor location at the base of the bollards. Adding to the complexity of the forces was configuring the bollard structure at the mountaintop around existing operational facilities. These facilities included a public television transmitter station, public radio transmitter station, emergency medical transmitter relay station, cellular telephone broadcast grids, and existing tram. All of which had to remain in service and effected the design and procedures used to construct the bollard structure. To accommodate these facilities, the new upper bollard structure was placed behind the existing mountain top facilities and cantilevered over those one and two story structures. This cantilever turned out to be approximately 12m where the track cables attached and created large overturning forces. Because of concern to minimize the scarring impact of new construction on the mountain, reducing the footprint of the bollard structure was a priority. This necessitated using high strength rock anchors to resist the overturning forces. Rigid track cable attachment also created large sliding forces on the bollard structures that would have to be resisted by either blasting and socketting the foundation into rock or, use of post-tensioned rock anchors to essentially clamp the bollards to the rock utilizing Sliding Resistance (R) = µN, where µ is the coefficient of friction between concrete and rock of 0.4 and N is the post-tensioning force. To minimize impact to the mountaintop, the post-tensioning option was used.
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2.2 The Rock Geologically, the project site is in the Piedmont Physiographic Area of the North American Continent which is underlain by igneous and metamorphic rock formations whose age is around 600 million years. Within this region, the Stone Mountain formation is predominantly an intrusive dome mass igneous structure. Five rock cores of this igneous mass were taken in accordance with ASTM D 21131 at depths varying from 2m to approximately 5.5m at the proposed location of the lower station. All samples extracted from depths shallower than 2m were observed to be moderately soft to moderately hard gray fractured granite. All samples extracted from depths deeper than 2m were observed to be moderately hard gray continuous granite. Rock samples were then sent to the laboratory to determine the ultimate unconfined compressive strength, unit weight, REC (recovery) and RQD (rock quality designation). Rock lab results are as follows: Approximate Depth (m)
Unit Compressive Weight (KN/m3) Strength (MPa) REC
RQD
Above 2m Below 2m
24. 25.
12.5% 100%
26. 53.
100% 100%
RQD ratings below 25% are generally considered to be poor quality fragmented material and somewhat undesirable. A RDQ rating of 100% is considered to be rock of excellent quality. The 25% RDQ rock at the lower station was removed down to the 100% RDQ rock and at the upper station, the 100% RDQ rock was already at the surface. 2.3 The Rods To resist overturning from the forces generated by the track cables, mass rock had to be engaged. To accomplish this, rock anchor rods were embedded deep into the rock mass and attached to the rock at the base of their embedment. This entailed a portion of the rod that is bonded at the base of the embedment and remainder of the rod unbonded (free stressing length). By doing this, a wedge of rock is engaged starting at the top of the bonded area and extending to the surface. Two rock failure modes were investigated: one of an individual anchor failing under a rock wedge within an included angle of 90° projecting from the top of the bonded area and, one of a group effect that used the same 90° included angle failure plane which essentially became a truncated pyramid of the group of anchors. This failure plane was determined by the geotechnical engineer based on subsurface investigations and
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laboratory testing. Calculations using the established rock unit weight indicated the truncated pyramid condition controlled the design embedment length. To determine grout-to-rock bond length of the rock anchor and diameter of hole, on-site testing was conducted to determine the bond strength between the rock and grout. This testing consisted of drilling and grouting with a non-shrink hydraulic cement grout three, 63mm diameter test holes around a 25mm ASTM A7222 Grade 1034MPa allthread bar. Test cubes were taken at the time of grouting and when the test cube compressive strength reached 28MPa the reinforcing bar was pulled with a calibrated hydraulic jack until failure of the bond between the grout and rock occurred. The allowable working bond strength was then determined to be 1.4 MPa and incorporated a factor of safety of two. Under North+Perret‘s worst load condition (there were 65 loading combinations), it was found that under the group effect that a 130mm diameter hole with 3m of bond length and 8m free stressing length would be required. Calculations indicated the upper bollard required a mat foundation with 10 rock anchors at 2.5m on center each way, the intermediate tower required two mat foundations with 4 anchors each, and the lower bollard a mat foundation with 8 anchors. The rods used for the rock anchors were 64mm diameter 1034 MPa all-thread rod that conformed to ASTM A6153 and ASTM 722. Threads for these rods were cold cut and were specified to be throughout the entire length; including the free stressing area. While continuous threading increased the initial cost of the rods, adjustments of length in the field because of increasing bond lengths due to the type of rock material encountered, varying surface contours, and construction tolerances more than offset the additional initial cost. Anchor holes were drilled with a self propelled mechanical air drill and the anchors included a plastic grout tube affixed from the bottom of the bar and extended to the anchor bearing plate. To provide free stressing length, anchors had mastic filled PVC sleeves along the entire free stressing length. 2.4 The Rock Anchor Grout Under normal grouting procedures in mass rock, the hole in the rock is flushed with water to remove laintent dust from drilling. For this project, it was not allowed to flush holes due to potential contamination of adjacent wet weather pools by rock dust/drill hydraulics. These pools were classified as environmentally sensitive spawning areas for seasonal small freshwater shrimp. Because of this condition, the grout mix design had to be formulated with additional water content to account for the residual dust in the holes. Shrinkage of the grout was of great concern and, the grout properties of the on-site field testing had to be replicated for the test data to remain valid. Also, during the original on-site testing, holes were
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flushed with water. Another concern because of schedule, was that a high early compressive strength would be required which would increase the potential for shrinkage and was not used in the original test configuration. To address these concerns, a grout mix was designed using an ASTM C 1504 type III portland cement (high early strength), fly ash (pozzolan), masonry sand conforming to ASTM C335 (a readily available sand to reduce shrinkage), and a high water/cement ratio of 0.55 (to provide additional moisture to compensate for residual drill dust in the holes). Potential shrinkage of the mix was further reduced by adding a shrinkage compensating admixture that was specified to conform to ASTM C 9376. A trial mix of the grout was made and test cubes taken of the grout mix design. During curing of the test cubes in the prism molds, it was observed that the exposed top of the test specimens domed during hydration indicating a slight expansion of the grout during curing and no shrinkage. Laboratory compression tests indicated 6 day break compressive strengths of 36 MPa, well above the 28 MPa strength of the grout used for determining rock bond strength. Based on the test results, approval was given to the contractor to proceed with installation of the anchors. 2.5 The Concrete Reinforcement The reinforced concrete bollard structures were designed to resist track cable forces by shear wall behavior with pure tension elements (as defined in ACI 3187, Section 12.15) on the boundaries. These tension elements extended from track anchor attachment to the mat foundations at the base and are 35M reinforcing bars conforming to ASTM A615 . All tension elements used threaded mechanical couplers at bar splice locations and were staggered in accordance with ACI 318, Section 12.15. The tension forces applied to the mat foundations are resisted through bending and shear to the post-tensioned rock anchors. For the localized post-tensioning forces on the mats at the rock anchor attachments, additional reinforcement had to added to account for bursting forces. Instead of using a tight wound, continuous spiral wound sets of reinforcing ties around each rock anchor in the mat, pipe sleeves were used with steel studs attached around the outside perimeter of the pipes. These sleeves were sized as freestanding columns supporting the posttensioning load and stud size and quantity determined by allowable stud shear in concrete of 70 KN/stud. Length of stud was determined by assuming a shear failure plane at stud length/2 and concrete capacity of φ2(f‘c)(perimeter length)(depth). 2.6 The Post-tensioning Operation Two post-tensioning operations occurred: one in which the anchors were installed and post-tensioned and proof-tested prior to constructing the reinforced concrete bollards and, one in which the anchors were post-tensioned and locked-off after the bollards were constructed.
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Proof-testing of the anchors prior to constructing the bollards was an additional step but in the event of anchor failure, it facilitated reinstallation/replacement of anchors while drilling and grouting equipment was still on-site and anchor locations were readily accessible. The proof-test configuration consisted of calibrated, 227 tonne (t) hydraulic, center pull rams (jacks) reacting against a grouted 76mm thick steel bearing plate. All anchors were loaded in accordance with ANSI B77.18 in increments equal to 25% of the design load up to the proof-test load of 133% of the design load (1721KN). Movement of the anchor bar was monitored by an independently mounted micrometer dial gauge which measured movement of the top of the anchor and readings were taken at the time of load application and after 5 minutes. To determine reserve strength of the anchors, four anchors were stressed above the 133% to maximum capacity of the rams of 2224KN which was still below the ACI maximum jacking force of 0.8fpu = 3457KN. Using load vs. displacement data, curves were plotted and that indicated direct linear behavior through the loading cycle including the four anchors jacked above 0.6fpu. Measurements indicated no positive creep (pullout) occurred and rebound was to 0. All anchors were found to be acceptable and approval was given to proceed with construction of the reinforced concrete bollards. Upon completion and acceptance of the bollard and tower construction, the anchors were post-tensioned using a calibrated system of two, 91t hydraulic jacks connected in parallel. Each anchor was stressed to a load of 1512KN (= 0.44f pu) and the anchor nuts were tightened (locked-off) while the load was held.
3. Construction Construction of the bollard and tower at the top of the mountain required evaluating options to get concrete to the top. One option was to batch (mix) concrete on top of the mountain which was quickly ruled out because of the environmental issues. Another option was to airlift concrete from the base of the mountain to the top which was also quickly ruled out because of expense. The last option considered was to pump the concrete up the mountain and turned out to be the most viable option it terms of meeting budget and schedule. To accomplish pumping concrete 600m horizontally and 140m vertically, it required a pump mix that had the characteristics of low set time (to avoid setting in the line), high early compressive strength (to meet schedule), flowable (to minimize friction forces in the pump line), and minimal setting shrinkage (to minimize cracking in the exposed concrete structure). This pump mix had two primary admixtures and adjustments were made to the aggregates. As with most pump mixes, adjustments to the aggregates consisted of a smaller large aggregate and natural sand in greater proportion for the fine aggregate. For the sand, natural sand has smooth edges together with greater proportion increased the
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pumpablity of the mix. To further increase pumpability and obtain the desired set characteristics, a high-range water reducing admixture (superplasticizer) conforming to ASTM A4949 type F was added. This admixture has the characteristics of placing the concrete in an almost fluid state for pumping and accelerates set time but, could cause segregation of cement and aggregate that could clog the pump line. To offset this segregation characteristic, a water reducing and retarder adimix conforming to ASTM 494 type A and D was used. This admix increases the gel content of the concrete which adds to internal cohesiveness and retards the set time allowing longer time to pump and place. Performance of this mix was better than expected. It pumped well and would remain plastic for an extended period of time and obtain a high early strength. During construction, it was noted that the pour of the bollard mat concrete remained plastic 24 hours after placement and then hydrated to a 3 day strength of 24MPa with no significant shrinkage cracking. 28-day strength test results for this mix averaged 34MPa, well above the required 28MPa for the bollard and tower structures.
4. Conclusion This moderately sized project provided some interesting challenges to the design and construction aspects of completing a project successfully. As with many projects, testing was a very important factor in evaluating materials and verifying design assumptions. The Stone Mountain Aerial Tram project met it’s budget and completed on schedule in time to transport the Olympic Flame to the mountain top.
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5. References 1. 2. 3. 4. 5. 6. 7. 8.
9.
ASTM D 2133, Standard Specification for Practice for Diamond Core Drilling for Site Investigation. ASTM A 722, Standard Specification for Uncoated High-Strength Bars for Prestressing Concrete. ASTM A 615, Standard Specification for Deformed and Plain Billet-Steel Bars for Concrete Reinforcement. ASTM C 150, Standard Specification for Portland Cement. ASTM C 33, Standard Specification for Concrete Aggregate. ASTM C 937, Standard Specification for Grout Fluidifier for PreplacedAggregate Concrete. ACI 318, Building Code Requirements for Structural Concrete, American Concrete Institute, Farmington Hills, Mich. ANSI B77.1, Aerial Tramways, Aerial Lifts, Surface Lifts, Tows and Conveyors - Safety Requirements, American National Standards Institute, Washington, DC. ASTM A 494, Standard Specification for Chemical Admixtures for Concrete.
Note: ASTM is the American Society for Testing and Materials, West Conshohocken, Pennsylvania.
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BEHAVIOUR AND DESIGN OF FASTENINGS WITH CONCRETE SCREWS Jürgen H.R. Küenzlen* and Thomas M. Sippel** Institute of Construction Materials, University of Stuttgart, Germany ** Engineering Office Eligehausen and Sippel, Stuttgart, Germany *
Abstract Concrete screws are a new fastening system easy to install. Concrete screws are screwed into predrilled cylindrical holes. During installation, concrete screws cut a thread into the wall of the drilled hole. Therefore, tensile loads are transferred into the base material by mechanical interlock. The load transfer mechanism is similar to that of deformed reinforcing bars cast into concrete. In the present paper the results of installation and tension tests in non-cracked and cracked concrete are presented. Furthermore, the test results are compared with the prediction of the CC-method for the concrete cone failure load. It is shown that the CCmethod cannot be used for the design of fastenings with concrete screws without some modification.
1. Introduction Concrete screws should be easy to install and the torque moment at failure should be sufficiently high to prevent failure of the fastening during installation. Therefore the behaviour of concrete screws during installation was investigated in numerous tests. Varied were the types of screws, type of electrical-screw-gun, drill hole diameter, strength and composition of concrete. The torque moments at correct installation and at failure were measured. Furthermore, a large number of tension tests were performed in non-cracked and cracked concrete. Varied parameters were the type of screw, their diameter and embedment depth, installation torque moment and crack width. In this paper the results of these tests are presented.
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2.
Tests
2.1 Setting tests At the Institute of Construction Materials at the University of Stuttgart several setting tests in concrete with a cube strength fcc ~ 30 N/mm² and 60 N/mm² with different grading curves were carried out. The concrete screws portrayed in Figure 1 (drill hole diameter d0=10mm) were installed into concrete slabs which were produced from concrete with a grading curve BC8 (aggregates with maximum size 8mm) to AB32 (aggregates with maximum size 32mm) according to DIN 1045. Natural round aggregates from the Rhine valley were used. Moreover, the drill hole diameter was varied. Measured were the torque moment for correct installation and the failure moment of the concrete screw. Digital torque wrenches were used for this. Figure 2 shows a concrete screw which cut a thread into a large aggregate. Figure 3 shows the thread cut into the concrete by the used concrete screws. The maximum aggregate size in these tests was 16mm. In order to cut a thread into the concrete, a certain torque moment is necessary. Depending on type of screw, composition and strength of concrete and the drill hole diameter the torque moment for correct installation can vary in wide range (Figure 4).
Figure 1:
Concrete screws used in the setting tests [1]
Figure 2:
Concrete screw in a big piece of concrete aggregate [1]
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Figure 3:
Threads cut into the wall of the drilled hole using different concrete screws [1]
2.1.1
Influence of concrete composition and drill hole diameter on installation and failure torque If during installation the torque is increased beyond the value which is valid for correct installation, failure may occur by shearing off the thread cut into the concrete or by steel failure. The torque moment for shearing off the thread cut into the concrete depends significantly on the design of the concrete screw. Further influencing factors are the hole diameter (d0), concrete strength and maximum aggregate size (BC 8, fcc = 20,2N/mm² and AB 32, fcc = 70N/mm²). The failure mode “shearing off the thread” should be prevented because in this case the tension resistance is reduced almost to zero. This can be achieved by increasing the embedment depth. 80
Typ 1
Typ 2
70
60
TE [Nm]
50
40
30
20
10
0
BC 8 dcut = 10,40mm fcc = 20N/mm²
Figure 4:
BC 8 dcut = 10,06mm fcc = 20N/mm²
AB 32 dcut = 10,42mm fcc = 70N/mm²
AB 32 dcut = 10,08mm fcc = 70N/mm²
Influences on the installation torque moment TE (do = 10mm; hef = 45mm) [2]
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250 steel failure, Typ 1 steel failure, Typ 2 shearing of thread, Typ 2
TU [Nm]
200
150
100
50 BC 8 dcut = 10,40mm fcc = 20N/mm²
BC 8 dcut = 10,06mm fcc = 20N/mm²
AB 32 dcut = 10,42mm fcc = 70N/mm²
AB 32 dcut = 10,08mm fcc = 70N/mm²
0
Figure 5:
Influences on the failure torque moment TU (d0=10mm, hef = 45mm) [2]
2.1.2 Influence of electrical-screw-gun on installation and failure In [3] tests with 2 different electrical-screw-guns were carried out. The setting tests were carried out in low-strength concrete (fcc ~ 20N/mm²) with natural round aggregates in the range of the grading curve BC8. A torque moment was put onto the screws with the electrical-screw-gun until the concrete screws started to shear off the thread. In Figure 6 the time until failure of both concrete screws with the used electrical-screw-guns is portrayed. It can be seen that the time tK until failure depends significantly on the type of screw and is also influenced by the used screw gun. 60 Typ 1 Typ 2 50
tK [sec]
40
30
20
10 electrical-screw-gun 1
electrical-screw-gun 2
0
Figure 6:
Influence of electrical-screw-gun on the time until failure tK (d0=10mm, hef = 45mm) [2]
In practice it may happen that after installation the screw is partly unscrewed (e.g. to ease the installation of all fasteners of a group). Additional tests with screws which were slightly unscrewed and then torqued again show that the time to shear off the thread is
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significantly reduced compared to the results shown in Figure 6. If the installation of the screw is relatively easy then it is difficult to switch off the screw-gun exactly when the correct installation is achieved. Therefore, a certain minimum time should be required to shear off the thread in the concrete in order to prevent this failure mode in practice. This requirement can be achieved by a proper embedment depth. 2.2 Pull-out-test under static tension load Static tension load tests were carried out in cracked and non-cracked concrete. The test equipment shown in Figure 7 was used. The load and the displacements were continuously measured electronically and recorded. Moreover, the crack width was recorded for the tests in cracked concrete. The embedment depth, the type of concrete screw, the installation torque moment and the crack width were varied. The diameter of the screw and the drill hole diameter (d0=10mm) were kept constant. Figure 8 shows typical load-displacement curves of tests with concrete screws with an embedment depth at hef = 45mm. 30 1 2
25 3 4
load [kN]
20 5
15
10
5
0 0
Figure 7:
Test equipment which was used [4]
Figure 8:
0.5
1
1.5 2 2.5 displacement [mm]
3
3.5
4
Typical load-displacement curves (hef = 45mm) [1]
2.2.1 Influence of type of concrete screw on failure load According to Figure 9, the failure load is significantly influenced by the embedment depth. A further major influencing factor is the type of screw. This may be due to the dimensions of the screws (external and core diameter) and how precisely the threads are cut into the concrete. However, further research is needed to clarify the reasons for the different behaviour of different concrete screws. This will be carried out within the near future. FEM modelling will be done as well.
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60
50 hef = 85mm
Nu [kN]
40
hef = 65mm 30
hef = 45mm
20
hef = 35mm
10 Typ 1
Typ 2
0
Figure 9:
Influence of the embedment depth (hef) and the concrete screw type on the failure load (Nu) in non-cracked concrete (d0 = 10mm, fcc = 30N/mm²) [1]
2.2.2 Influence of embedment depth on failure load Figure 10 shows that the failure load in non-cracked concrete increases continually with increasing embedment depth. Steel failure was achieved for part of the tests. The deeper a concrete screw is screwed into the concrete, the more threads are cut into the concrete. Therefore, the mechanical interlock improves and the failure load increases. 60
50
Nu [kN]
40
30
20
10
0 20
30
40
50
60
70
80
90
h ef [mm]
Figure 10: Influence of embedment depth (hef) on the failure load (screw type 2, fcc = 30N/mm²; d0 = 10mm) [1] 2.2.3. Influence of installation torque moment on failure load To clarify the influence of the installation torque moment on pullout load, tests in [3] were carried out in low-strength concrete. Concrete screws (type 1) were installed at different embedment depths and torqued with installation torques Tinst = 30Nm to 105Nm. Figure 11 shows the results of these tests. It demonstrates that the ultimate
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failure load is not much influenced by the installation torque moment, provided the threads have not been damaged significantly during installation. 50 Tinst = 30Nm Tinst = 80Nm Tinst = 105Nm
40
Fu [kN]
30
20
10
0 30
35
40
45
50
55
60
65
70
75
hef [mm]
Figure 11: Influence of installation torque moment (Tinst) and embedment depth (hef) on failure load (Fu) (fcc = 30N/mm², d0=10mm, screw type 1) [2] 2.2.4. Influence of the kind of installation In order to check the influence of the kind of installation on the failure load, tests were carried out in [3] with concrete screws in low-strength concrete. The screws (type 1, d0=10mm) were installed at two embedment depths using an electrical-screw-gun or a torque wrench. When using the screw gun the installation was intentionally prolonged to 11 seconds after reaching the correct installation. With the torque wrench the installation torque was varied. According to Figure 12 the failure load is not much influenced by the type of installation. Precondition is of course that the threads in the concrete are not significantly damaged during installation. 30 screw-gun, tK = 11s torque wrench, Tinst = 30Nm
25
torque wrench, Tinst = 105Nm
Fu [kN]
20
15
10
5
0 35
40
45
50
55
hef [mm]
Figure 12:
Influence of kind of installation moment on the failure load [2]
2.2.5 Influence of crack width Tests in cracked concrete with a crack width of 0,3mm and 0,5mm were carried out in low-strength concrete [6]. Figure 13 shows typical load displacement curves in non-
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cracked and cracked concrete. In Figure 14 the measured failure loads are plotted as a function of the crack width. Figure 13 and 14 demonstrate that cracks in the concrete influence the behaviour of concrete screws almost in the same way as with undercut anchors: the anchor stiffness is slightly reduced and the failure load is decreased compared to non-cracked concrete. This could be expected because of the load transfer mechanism “mechanical interlock”. 30
hef = 65 mm = 10,25 mm dcut fcc200 = 30 N/mm² Aggregate Size AB 16 uncracked concrete cracked concrete ∆w = 0,3mm
25
Last [kN]
20
15
10
5
0 0.5
0
1
1.5
2
2.5
3
Verschiebung [mm]
Figure 13:
Typical load-displacement curves in cracked and non-cracked concrete [5]
50
Failure Load Nu [kN]
40
30
20
10
0 0
0,1
0,2
0,3
0,4
crack width ∆w [mm]
Figure 14:
Influence of crack width on failure load [6]
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0,5
0,6
2.2.6 Failure mechanism of concrete screws In the tests in non-cracked concrete the concrete screws failed at low embedment depth due to a complete concrete cone failure (Figure 15). With increasing embedment depth the concrete cone failure depth became smaller (Figure 16).
Figure 15: Concrete failure cone at hef = 45mm [1]
Figure 16: Concrete failure cone at hef = 85mm [1]
3. CC-method used for concrete screws For the design of fastenings with metal anchors the CC-method which is described in detail in [7, 8] is used. To check whether the equation for concrete cone failure given in [7, 8] can also be used for concrete screws all results of tests in non-cracked concrete were plotted in Figure 17 as a function of the embedment depth. In Figure 17 the influence of type of concrete screw on the failure load is neglected. The figure shows that the measured failure loads are smaller than the concrete cone failure load of metal anchors predicted by the CC-method. This can be explained by the failure mechanism (compare chapter 2.2.6). The test results show that the CC-method cannot be used for concrete screws without some modifications. Corresponding investigations are under way.
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120
100
Nu,cc = 13,5 * β w * h1,5 ef
Nu [kN]
80
60
40
20
0 20
30
40
50
60
70
80
90
100
110
120
hef [mm]
Figure 17:
Results of tests [1] with different concrete screws in uncracked lowstrength concrete and comparison with prediction by the CC-method for concrete cone failure.
4. Summary Concrete screws are a new fastening system easy to install. Concrete screws are screwed into predrilled cylindrical holes. During installation, concrete screws cut a thread into the wall of the drilled hole. Therefore, tensile loads are transferred into the base material by mechanical interlock. The load transfer mechanism is similar to that of deformed reinforcing bars cast into concrete. In the present paper the results of installation and tension tests in non-cracked and cracked concrete are presented. Furthermore, the test results are compared with the prediction of the CC-method for the concrete cone failure load. It is shown that the CCmethod cannot be used for the design of fastenings with concrete screws without some modification. Much more research is needed to clarify the behaviour of concrete screws in non cracked and cracked concrete.
5. Acknowledgement The primary funding for this research was provided by the Ludwig Hettich GmbH & Co., Toge-Dübel A. Gerhard KG and the Adolf Würth GmbH & Co. KG. The support of these manufacturers is very much appreciated. Special thanks are also accorded to Beate Vladika who spent many hours in improving the English.
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6. References [1]
Küenzlen, J.H.R.; Eligehausen, R. 2001 Tragverhalten von Schraubdübeln in niederfestem Beton, Bericht über Ausziehversuche mit Schraubdübeln; W8/1-01/1 (in preparation)
[2]
Küenzlen, J.H.R; Eligehausen, R. 2001 Tragverhalten von Schraubdübeln in ungerissenem Beton; Einflüsse auf das Setzverhalten von Schraubdübeln in Beton und die Auswirkungen auf die Ausziehlasten; W8/2-01/2 (in preparation)
[3]
Küenzlen, J.H.R; Eligehausen, R. 2001 Bericht über Setz- und Ausziehversuche in ungerissenem Beton mit Schraubdübeln; AF01/01-E00202/1 (not published)
[4]
Müßig, M.G. 2001 Tragverhalten von Schraubdübeln in ungerissenem Beton; Untersuchung verschiedener Einflüsse auf das Eindrehverhalten und Entwicklung eines Sicherheitskonzeptes im Versagensfall Durchdrehen. Diplomarbeit, Institut für Werkstoffe im Bauwesen, Universität Stuttgart (in preparation)
[5]
Eligehausen, R.; Hofacker, I.N.; Spieth, H.A.; Küenzlen, J.H.R. 2000 Neue Entwicklungen in der Befestigungstechnik Tagungsband, IBK-Bau-Fachtagung 263; Dübel und Befestigungstechnik 2000
[6]
Küenzlen, J.H.R.; Eligehausen, R. 2000 Forschungsdatenbank Schraubdübel Version 1.5 (not published)
[7]
Fuchs, W.; Eligehausen, R.; Breen, J.E. 1995 Concrete Capacity Design (CCD) Approach for Fastening to Concrete. ACI Structural Journal, Vol. 92 (1995), No. 1, S 73-94
[8]
Eligehausen, R.; Mallée, R. 2000 Befestigungstechnik im Beton- und Mauerwerkbau Ernst & Sohn 2000
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BEHAVIOUR AND DESIGN OF ANCHORS FOR LIFTING AND HANDLING IN PRECAST CONCRETE ELEMENTS Dieter Lotze Halfen GmbH & Co. KG, Wiernsheim, Germany
Abstract Lifting anchors are widely used in the precast concrete industry. If anchors are failing, lives are endangered and considerable material damage can occur. Therefore anchors for lifting and handling should be chosen carefully and the anchor design should be done by engineers. Technically, three major questions have to be answered: a) How to determine the type and magnitude of loads and how to distribute it on the anchors? The most important loads like self weight, adhesion, form friction and dynamic actions will be described and discussed b) What are the possible failure mechanisms and which one is governing? The most important failure mechanisms depending on the shape, size and reinforcement of the precast element, on the lifting situation and equipment, and on the type and size of the anchor will be described and discussed. Failure can occur by fracture of the anchor, fracture of the reinforcement, breakout of a concrete cone, pullout of the anchor, pullout of the reinforcement, splitting of the concrete or local lateral breakout of the concrete. c) How to get characteristic resistance values for the different failure modes? Design models which allow design by calculation are only available for very few situations and failure modes. In all other cases values are taken from tests performed by anchor manufacturers or by precast concrete manufacturers. A common basis how to perform tests and how to evaluate the results is not established up to now. Different test methods will be shown. Their significance on real applications and the effect of the test method on the results will be discussed.
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1. Introduction Precast elements are taking an increasing part in concrete construction. These elements have to be moved, in the precast plant as well as on the construction site using cranes or similar devices. In most cases cast in lifting anchors are used to connect the elements to the lifting equipment. The design of anchors for lifting and handling of precast concrete elements is not regulated in European design standards because the anchors are used temporarily and not loaded permanently. National regulations show major differences between European countries. Nevertheless in case of an anchor failure, lives can be endangered and considerable economic damage can be done.
2. Origin, Magnitude and Distribution of Loads Lifting anchors are loaded by the self weight of the concrete element, by forces due to adhesion and form friction and by dynamic actions due to acceleration. The self weight of the precast concrete element can be calculated using a specific gravity of 23 to 25 kN/m³ for normal weight concrete, depending on the percentage of reinforcement. Mostly this value is already known from the static calculation. Inertia forces act when the element is accelerated or decelerated by the lifting equipment. These forces must also be transferred by the lifting anchors. The size of the inertia forces scatters between 5 and 50 % of the elements weight depending on the type of crane and the ratio between the weight of the element and the capacity of the crane. Under normal conditions it should be conservative to calculate inertia forces with 30 % of the self weight . Additional considerations have to be made for special situations like transport of elements through rough terrain, for example with an excavator. Inertia forces up to 300 % of the self weight can be expected in such cases. When the concrete element is lifted out of the mould, forces between the concrete and the formwork surface, due to adhesion and form friction must be added to the self weight. As long as the formwork is fixed to the floor or heavy enough to stay in place (it normally is), dynamic actions must not be considered together with adhesion and form friction. Only in cases where the form is not fixed and not heavy enough to stay in place, inertia forces have to be taken into account on the mass of the element and on the mass of the formwork as well. Later, when the element is moved in the precast plant or on site, self weight and inertia forces both have to be considered. After the estimation of the forces acting on the element, forces on each anchor have to be calculated, taking into account the position of anchors, number and length of ropes or chains and the static system. In most cases, the aim is to have a statically determinate system, because then the forces on each anchor and on each rope or chain can be clearly calculated. In statically indeterminate systems, load distribution depends on length and stiffness of the ropes, which are mostly unknown. If statically indeterminate systems are
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used for special reasons, only the statically determinate part should be used in calculating the load distribution, and additional ropes or chains should only be used for stabilisation. Figure 1a: statically indeterminate system
Figure 1b: Statically determinate systems Vges
Vges
Vges F δ
β F
β
β
F F
G
F
F
F
δ
F
G
F
G F
4 anchors loaded
Only 2 anchors loaded
4 anchors loaded
3. Failure Mechanisms of Lifting Anchors Analogous to other fastening elements, many different failure modes are possible depending on the anchor itself, the concrete, edge distances, anchor spacing, loading direction and, of course, reinforcement. Within the limits of this paper, the failure modes described in the following will only refer to common lifting situations with anchors in slabs, beams and walls loaded in tension, shear, or combined tension and shear. The following drawings and photos will illustrate the various failure modes obtained in anchor testing. 3.1 Failure in pure tension: Figure 2: Anchor failure and steel failure of special hanger reinforcement /2/, /3/
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Figure 3: Concrete cone failure for anchors in top surface (lifting of slabs) /3/
Figure 4: Concrete cone in tension for anchors in edge surface (lifting of walls) /2/
Figure 5: Splitting failure in tension for anchors in edge surface /2/
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Figure 6: Lateral Blow Out failure of the concrete /4/
3.2 Failure in pure shear Pure shear can occur, when wall elements have to be erected from the mould, when anchors in beams and columns are placed on the side surface and when walls are mounted with the tilt up method (almost pure shear). Figure 7: Erection of wall element, Small cone starting at anchor position, big cone starting at the anchorage depth of the reinforcement /5/
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Figure 8: Steel failure in shear /3/ (anchor far from edges)
Figure 9: Anchor far from edges, Splitting and local failure of concrete /3/
Figure 10: Pure shear in a wall Splitting Failure /4/
3.3 Failure under combined tension and shear Combined tension and shear mostly occurs due to inclined ropes or chains, but also in tilt up mounting or when precast elements must be turned while they are lifted. The failure mechanisms in the following pictures are representing examples observed in tests done by the author. Figure 11: Steel failure (fracture of the insert), angle of loading 45° /2/
Figure 12: Concrete cone failure angle of loading 45° /2/
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Figure 13: Splitting cracks to both sides under oblique loading /2/
Figure 14: Local failure of the concrete in front of the ring clutch /4/
4. Effect of reinforcement Only two of the above described failure modes, concrete cone failure and splitting failure may be significantly influenced by placing reinforcement in the area of the anchor. Forming of a concrete cone does not lead to failure, when stirrups are placed closely around the anchor. The stirrups have to be designed with sufficient anchorage length in the cone itself and in the concrete outside of the cone and they have to be placed parallel to the loading direction. A mash reinforcement perpendicular to the loading direction (parallel to the surface in slabs) does not significantly increase the failure load (see Figure 3). In case of splitting of the concrete, reinforcement can keep the cracks small and take up the splitting forces. The best example for effective reinforcement are stirrups on both sides of the anchor in thin wall elements. These stirrups can act as a hanger reinforcement for concrete cone failure and also as a splitting reinforcement. In addition, horizontal U-shaped stirrups (shear stirrups) are usually placed around the anchor as a hanger and splitting reinforcement for the shear components of the load. Figure 15 demonstrates this kind of reinforcement for a wall element.
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Figure 15: Wall element with lifting anchor, shear stirrup and hanger / splitting stirrups
Very special types of hanger reinforcement can be seen when wall elements are cast horizontally and shall be erected for transport and assembly. The anchors then are positioned in the middle of an edge surface and a hanger reinforcement is normally placed around the anchor to transfer the load a far as possible towards the unloaded side of the wall (Figure 16). Figure 16: Shear reinforcement for walls to be erected a) Lifting socket
b) Frimeda erection-anchor
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5. Test Procedures for Lifting Anchors The optimal way of testing cast in lifting anchors is to perform pullout tests in unreinforced concrete with minimum embedment, minimum edge distances, and minimum member thickness, and always keep a distance of at least 2 times the anchors length between the anchor and the support of the load on the specimen. This procedure has only one negative: it is not possible to do it this way! Therefore, test procedures have to be chosen in such a way that yields results relevant to the practical applications and therefore should be standardised to a point which ensures comparable results for different test series. In the following, test procedures for the most common situations will be presented and discussed. 5.1 Test procedures for tension 5.1.1 Steel failure of the anchor Steel failure of the anchor under tension can usually be tested in a universal testing machine on anchors which are not cast in concrete. The test setup has to be chosen according to the anchors construction and dimensions. 5.1.2 Tension tests on cast in anchors in concrete slabs For tests on anchors far from edges frequently used test configurations can be divided in two fundamentally different systems. The system illustrated in Figure 17 is based on a simple beam and results in bending cracks in the area of the anchor, leading to an anchor position in a concrete crack. On the other hand a system based on a cantilever beam can be used, resulting in cracks underneath the support (Figure 18). The load level of crack initiation depends on the spacing of support and on the member thickness. The advantage of the simple beam setup is, that cracks which can also occur during a real situation are included in the testing procedure. On the other side bending reinforcement is needed in the area of the anchor to prevent a bending failure of the concrete specimen. In addition this setup is not possible in corner situations with small edge distances. Figure 17: beam setup Reinforcement Support
Support Anchor Force
>=4 * anchor length
Bending cracks
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Figure 18: Cantilever setup Support Anchor Force >=2 * anchor length
Reinforcement
Bending cracks
5.1.3 Tension tests on cast in anchors in concrete beams and walls In beams and walls longer anchors are used than in slabs to compensate for smaller edge distances. Therefore in the plane of the wall the necessary edge distances for full concrete capacity and the necessary spacing of supports are high. In addition splitting failure and lateral blow out failure become more likely. Therefore anchorage principles with distributed load transfer along the anchor i.e. with reinforcement bars are used in many cases. For very long anchors the minimum distance between the anchor and the end of the wall or beam is usually smaller than 1.5 times the anchors length. Therefore no support should be placed between the anchor and the end of the wall or beam. This is only possible using the cantilever setup very similar to the setup for oblique loading shown in Figure 19 . For anchors anchored by bond of reinforcement it is very difficult to keep a distance between the anchor and the support of 2 times the anchors length which is needed to allow a complete concrete cone breakout. Because for anchorage by bond this failure mode is not likely, a smaller clearance can be used but not smaller than 1.5 times the anchors length for reinforcement bars with hooks or similar anchorage devices and 1.0 times the anchors length for straight bars. It should never be smaller than twice the thickness of the wall or beam. 5.2 Test procedures for combined tension and shear 5.2.1 Steel failure of the anchor For anchors loaded in combined tension and shear, the supporting action of the concrete is needed for the performance of the anchor and therefore in many cases tests have to be performed on cast in anchors. The test configurations can be chosen like described for concrete failure below. Simplifications are possible because no large spacing is needed between supports.
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5.2.2 Tests on cast in anchors under angled tension in concrete slabs, beams and walls Oblique testing of cast in anchors can be performed using a strong floor. Other testing procedures such as tests on two anchors together (so that the equilibrium between the horizontal forces on both anchors is satisfied) is not dealt with in this paper. An example for a configuration in a testing frame with a stiff baseplate acting like a strong floor is shown in Figure 19. This setup provides sufficient spacing of supports for vertical and horizontal load components as well. It is therefore usable for tests with horizontal load components towards the free edge like shown in Figure 19, but it can also be used for tests with the horizontal load component towards the centre of the wall. Figure 19: Cantilever setup for oblique loading with a test frame on a stiff baseplate /2/
5.3 Test procedures for shear Pure shear is not a very common load situation in lifting and handling, but it can occur, when wall elements are cast horizontally and have to be erected from the mould. Anchors designed for this situation are positioned in the middle of an edge surface and a hanger reinforcement is normally placed around the anchor to transfer the load towards the unloaded side (Figure 16). Testing is possible using the beam system or cantilever system. Using the beam system requires large bending reinforcement over the anchor which may increase the failure load, while cracks in the area of the anchor lead to lower failure loads. It is not known which effect governs depending on other parameters like the dimensions of the anchor, the shape and dimensions of the hanger reinforcement, and the elements thickness. Therefore the cantilever system appears to be the better solution. Figure 20 shows an example for a setup which was already used successfully.
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Figure 20: Test setup for shear tests (erection of walls) /5/
6. Summary and conclusions Anchorage points for lifting and handling of precast concrete elements must be designed for the self weight of the element and forces due to adhesion, form friction and dynamic actions (inertia forces due to acceleration). These forces must be distributed to the anchors in accordance with the static system. Depending on the steel and concrete strength, on the principle and length of the anchorage to the concrete, on the loading angle, on the amount and position of reinforcement, and on the edge distances of the anchor many different failure modes are likely to govern the behaviour of the anchor. In many cases the relevant failure mode and the capacity of the anchorage can only be identified by testing. Test conditions have to be chosen very carefully in order to get representative results with minimised influence of the reinforcement and the dimensions of the specimen. Test procedures should be harmonised to a point which allows comparable results in different test series in order to increase basic knowledge and maintain certain safety levels. 7. References /1/ /2/ /3/
/4/
/5/
Halfen GmbH & Co. KG, Catalogues and technical handbooks Lotze, D.; Sippel, T. M.: Bericht über Versuche mit einbetonierten Demu – Transportankern, Wiernsheim / Stuttgart 1993 Versuchsanstalt für Stahl, Holz und Steine (Amtliche Materialprüfanstalt), Universität Karlsruhe, Prüfzeugnis Nr. 90 0102 vom 10.08.1990: Untersuchung von Frimeda Transportankern in einbetonierten Beton-Versuchskörpern Versuchsanstalt für Stahl, Holz und Steine (Amtliche Materialprüfanstalt), Universität Karlsruhe, Prüfzeugnis Nr. 90 0480 vom 18.02.1991: Untersuchung von Frimeda Transportankern in einbetonierten Beton-Versuchskörpern Halfen GmbH & Co. KG, Internal test reports
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BEHAVIOUR OF PLASTIC ANCHORS IN CRACKED AND UNCRACKED CONCRETE Thilo Pregartner, Rolf Eligehausen Institute of Materials, University of Stuttgart, Germany
Abstract Plastic anchors consist of a plastic sleeve and a special screw or nail. In Germany the sleeve is made of polyamide PA6 or PA6.6. The behaviour of plastic anchors in concrete is influenced by different parameters changing the properties of the plastic (e.g. temperature, water content) [1]. Furthermore, the behaviour of plastic anchors in concrete is determined by the visco- elastic properties of the plastic (relaxation and creep). Therefore the pullout loads are dependent on time and load history. Other parameters affecting the pullout loads in concrete are the anchor type, the widths of cracks in the concrete, the drill bit diameter and the orientation of the sleeve in the cracks. The performance of plastic anchors in cracked and uncracked concrete has been investigated in pullout tests. In addition to tensile tests, creep tests and tests in opening and closing cracks have been performed. In tests in which the splitting force of plastic anchors has been measured the basic behaviour of plastic anchors in concrete has been investigated.
1. General behaviour of plastic anchors Plastic anchors are fastening systems consisting of a plastic sleeve and a special screw or nail. The sleeve is divided into an expansion area and a collar. The collar prevents the anchor from slipping into the hole during expansion (Figure 1). The screw or nail fits exactly to the geometry of the plastic sleeve, so an optimal expansion force is developed during the expansion of the anchor. The plastic sleeves used in Germany are made of polyamide PA6 or PA 6.6. In other European countries sleeves made of polyethylene or polypropylene are used as well. The test results shown in this paper are valid for plastic sleeves made of polyamide 6 or 6.6.
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Figure 2 shows the splitting force developed along the anchor axis of a typical German plastic anchor. The expansion area of the plastic sleeve and the special screw is shown as a location reference. The maximum splitting force is reached in an area where the screw is thickest. The splitting force has a nearly constant distribution along the anchor axis. During the first 10 minutes after expansion of the anchor, the splitting force is strongly reduced because of relaxation of the plastic (Figure 3). The distribution of the splitting force along the axis is dependent on the anchor construction.
Figure 1
Typical plastic anchors (screw-in anchors) for use in concrete. 1,2
Anchor Type 4 (d= 10 mm)
t = 0 min t = 0,5 min
Splitting force [kN]
1,0
t = 1,0 min t = 10,0 min
0,8 0,6 0,4 0,2 0,0 0
Figure 2
10
20
30 40 Anchor axis [mm]
50
60
70
Distribution of splitting force along anchor axis; anchor type 4 (d= 10 mm).
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Total Splitting force [kN]
11,0
Anchor Type 4 (d= 10 mm) Loss 34 %
9,0
7,0
5,0
3,0 0
2
4
6
8
10
Time [min]
Figure 3
Splitting force as a function of time; anchor type 4 (d= 10 mm); hef= 70 mm.
2. Influence of time on anchor behaviour For plastic anchors two major time dependent effects influence the pullout loads. The two effects are relaxation and creep. Due to relaxation, the expansion force decreases after expansion of the anchor (Figure 3). The behaviour is counteracted however, by an increase of the coefficient of friction over time because of the toothing of plastic with micropores of the concrete [3]. In summary the pull out loads increase slightly with time (Figure 4). The creeping of plastic results in increasing displacements for loaded anchors. For typical design loads however, plastic anchors do not reach critical displacements [1]. Figure 5 shows the total splitting force of a plastic anchor. The anchor is expanded in uncracked concrete. After 10 minutes (600 sec) a crack (w= 0,2 mm) has been opened in the concrete. The splitting force is reduced from 4,6 kN to 0,1 kN. Forty minutes later the splitting force has increased to a value of 1,3 kN. Figure 6 shows pullout loads of the same anchor in cracked concrete (w= 0,4 mm). It is obvious that the failure loads increase with increasing time difference between crack opening and testing. The mechanism behind the increase of the expansion force in cracked concrete is explained in Figure 7 by a rheological model. On driving the screw into the sleeve the plastic is strained. This is represented in the model by a compression of the “free” spring (Maxwell I). With increasing time the spring of the “Maxwell I”- system relaxes due to expansion of the damper in system “Maxwell II”, however the spring- dashpot- system “Kelvin- Voigt” is loaded too. When a crack is opened in the concrete the expansion force of the anchor drops. The elastic deformation in the “Maxwell”- system is immediately recovered, but the deformation in the “Kelvin- Voigt”- system increases over time. This time- dependent expansion accounts for the increasing expansion force after crack- opening observed in Figure 5 and Figure 6.
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Uncracked concrete
18
Anchor type 5 (d= 10 mm) hef= 70 mm
16
Maximum load NU [kN]
14 12 10 8 6 4 2 0 0,1
1
10
100
1000
Time [h]
Figure 4
Influence of time difference between loading and installation on pullout loads in uncracked concrete; anchor type 5 (d= 10 mm); hef= 70 mm [2]. Anchor Type 5 (10 mm)
10
Expansion of anchor
Splitting force [kN]
7.5
5
crack opening w= 0,2 mm
2.5
0 0
Figure 5
500
1000
1500 Time [sec]
2000
2500
3000
Total splitting force in cracked and uncracked concrete; anchor type 5 (d= 10 mm); hef= 70 mm.
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Maximum load NU [kN]
14,0
Cracked concrete w= 0,4 mm
12,0
Anchor type 5 (d= 10 mm) hef= 70 mm
10,0
8,0
6,0
4,0
2,0
0,0 0,1
1,0
10,0
100,0
Time [h]
Figure 6
Influence of time difference between crack opening and pullout test in cracked concrete (w= 0,2 mm); anchor type 5 (d= 10 mm); hef= 70 mm. "Maxwell II"
"Maxwell I"
"Kelvin- Voigt"
Initial state ε0
Sleeve Expansion εpl+εv-el
Relaxation w
Crack opening εv-el
Memory- effect
Figure 7
4- Parameter model explaining visco-elastic behaviour of plastic sleeve in uncracked and cracked concrete.
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3. Influence of crack width Figure 8 shows related pullout loads of anchor type 4 in cracked and uncracked concrete. The reference value is the median pullout load (NU,m) in uncracked concrete. The pullout loads decrease with increasing crack width. By opening the crack up to 0,2 mm, the pullout loads are reduced by 60%. With further crack opening the values are reduced nearly linearly. In very wide cracks of 0,5 mm, the pullout loads are still 20% of the median value in uncracked concrete (NU,m,uncracked= 19,9 kN). The behaviour of plastic anchors in cracked concrete depends on the anchor design. For other types of anchors a relation of about 50% of the average failure load valid for uncracked concrete for a crack width of w= 0,3 mm has been observed. 1,2
Anchor type 4 (d= 10 mm), hef= 70 mm Expansion direction perpendicular
NU/ NU,m,uncracked [-]
1,0
Expansion direction parallel NU,m,uncracked = 19,9 kN
0,8
0,6
0,4
0,2
0,0 0,0
0,1
0,2
0,3
0,4
0,5
Crack width [mm]
Figure 8
Influence of crack width in cracked concrete; anchor type 4 (d= 10 mm); hef= 70 mm.
4. Influence of temperature Temperature has an influence on the mechanical behaviour of plastic. With increasing temperature the stiffness and the strength of plastic decreases. Therefore, the pullout loads are lower in uncracked concrete at increased temperature [2]. Figure 9 shows the influence of temperature on pullout loads of tests in cracked concrete. The values are normalised by the median value of the reference tests (T= 20°C). Additionally, the reduction of pullout loads for anchors made of Ultramid B3L (PA6) as a function of temperature obtained from tests in uncracked concrete [3, 4] is shown. The figure shows, that the pullout loads in cracked concrete can increase or decrease with temperature depending on the type of anchor. This is partially in contradiction to the experience in
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uncracked concrete, because in uncracked concrete the pullout loads decrease with increasing temperature [3, 4].
5. Influence of water content of plastic sleeve Polyamide is a hygroscopic material. This means that the plastic sleeve absorbs water (up to a content of f= 9%). Under standard conditions the moisture content of the sleeve is 2,5%. Figure 10 shows the pullout loads of plastic anchors (diameter 14 mm) as a function of the water content of the sleeve. The values are normalised by the median value of the reference tests (f≈ 2,5%). Additionally, the reduction of pullout loads for anchors made of Ultramid B3L (PA6) obtained from tests in uncracked concrete [3, 4] is shown. According to these results in cracked concrete the pullout loads can increase with increasing water content, in contrast to the behaviour in uncracked concrete. In uncracked concrete the expansion force decreases because of the lower stiffness of the material with increasing water content. The pullout loads also get smaller. In cracked concrete the expansion force is reduced because of the crack opening, however, the loss of expansion force must be dependent on the water content of the sleeve. This behaviour is also time dependent (see Section 2). 1,6
Cracked concrete w= 0,2 mm
NU(T)/NU,m (T= 20°C) [-]
1,4 1,2 1,0 0,8 0,6 0,4 Anchor type 1 (d= 14 mm) Anchor type 5 (d= 14 mm) Ultramid B3L, uncracked concrete
0,2 0,0 0
10
20
30
40
50
60
70
80
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100
Temperature T [°]
Figure 9
Influence of temperature of plastic sleeve on pullout loads in cracked and uncracked concrete; d= 14 mm; hef= 70 mm.
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2,2
Cracked concrete w= 0,2 mm
2,0
NU(f)/NU,m(f= 2,5%) [-]
1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4
Anchor type 1 (d= 14 mm) Anchor type 5 (d= 14 mm) Ultramid B3L, uncracked concrete
0,2 0,0 0
1
2
3
4
5
6
7
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9
10
Moisture content of sleeve f [%]
Figure 10 Influence of moisture content of plastic sleeve on pullout loads in cracked and uncracked concrete; d= 14 mm; hef= 70 mm.
6. Behaviour in opening and closing cracks Figure 11 shows the behaviour of a nailed- in anchors in tests with opening and closing cracks. The crack width varied between 0,1 mm and 0,2 mm. The anchors were loaded by a constant tension load NP which was 30% larger than the design load (NP=1,3 zulN). The anchor displacements increase with an increasing number of crack openings. All anchors, however, endure the test without failure. The displacement behaviour fulfils the criteria of the ETAG [5].
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0,80
Crack opening tests (w= 0,1 mm- 0,2 mm) Nailed-in anchor (d= 8mm) NP= 1,3* zulN
Displacement s [mm]
0,60
0,40
0,20
0,00 1
10
100
1.000
Number of crack openings n [-]
Figure 11 Anchor displacements as a function of crack opening of a nailed- in anchor; anchor type 16 (d= 8 mm); hef= 55 mm.
7. Conclusions Plastic anchors are fastening systems consisting of a plastic sleeve and a special screw or nail. The sleeve is divided into an expansion area and a collar. The collar prevents the anchor from slipping into the hole during expansion (Figure 1). The screw or nail fits exactly to the geometry of the plastic sleeve, so an optimal expansion force is developed during the expansion of the anchor. The plastic sleeves used in Germany are made of polyamide PA6 or PA 66. In other European countries anchors of polyethylene or polypropylene are used as well. The test results are valid for sleeves made out of polyamide PA 6 or PA 6.6. The distribution of the expansion force along the anchor axis is dependent on the design of the anchor. Relaxation of the plastic reduces the expansion force mainly during the first 10 minutes after expansion. In spite of this, in uncracked concrete the pullout loads increase with time because of an increase of the friction coefficient. In cracked concrete the splitting force is sharply reduced by the crack opening, however, it increases very rapidly after crack opening. This increase is dependent on the stiffness of the plastic. The pullout loads increase in cracked concrete with increasing time, however much faster than in uncracked concrete. An increase of the temperature and the water content of the sleeve results in decreasing pullout loads in uncracked concrete. In cracked concrete this tendency could be reversed depending on the anchor type. Opening and closing cracks within a range of 0,1 mm to 0,2 mm are no problem for usual plastic anchors.
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8. Acknowledgement The primary funding for this research was provided by the manufacturers of plastic anchors fischerwerke, Hilti and Würth. The support of these manufacturers is very much appreciated. Special thanks are also accorded to Matthew Hoehler who spent many hours in reviewing the paper.
9. References [1] [2]
[3] [4] [5]
Eligehausen , R., Mallée, R.: “Befestigungstechnik im Beton- und Mauerwerksbau”, Verlag Ernst & Sohn, 2000. Eligehausen, R., Sippel, T., Pregartner, T., Mallée, R..: „Kunststoffe in der Befestigungstechnik“, Bauen mit Kunststoffen- Jahrbuch 2001, Verlag Ernst & Sohn, 2001. Ehrenstein, G. W.: Bauwerksdübel aus Thermoplasten, auch zugelassen als tragende Bauelemente; Verbindungstechnik 1976, Heft 4, S. 25- 28. Ehrenstein, G. W.: Aus Reihenuntersuchungen mit Bauwerksdübeln aus Polyamid; Verbindungstechnik 1976, Heft 12, S. 13- 14. European Organisation for technical Approvals (EOTA): Guideline for European Technial Approvals of Plastic Anchors for redundant Use in Concrete and Masonry for lightweight systems. DIBt April 2000, Draft ETAG, Part 1 and 2.
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TESTING OF A DOWEL CONNECTION FOR A BRIDGE WITH A CONCRETE DECK AND A SANDWICH PANEL TRUSS STRUCTURE Hendrik Blontrock*, Luc Taerwe*, Antonio Nurchi**, John Vantomme***, Cédric De Roover***, Jan Wastiels****, Kim Croes**** *Dept. of Structural Engineering, Ghent University, Belgium **Dept. of Structural Engineering, University of Cagliari, Italy ***Dept. of Civil Engineering, Royal Military Academy, Belgium ****Dept. of Mechanics of Materials and Construction, Vrije Universiteit Brussel, Belgium
Abstract Fastenings to concrete can be subjected to complex loading situations. The resistance of the connection under the combined action of shear, bending moment and normal force depends strongly on the failure mode of the connection. In order to investigate the resistance of dowel connections under combined actions, a special test set-up has been developed which allows to submit a dowel connection to complex loading conditions. A case study was made for a connection element of a light-weight pedestrian bridge, composed of a concrete deck with a truss substructure. The truss is composed of sandwich panels, consisting of glass fibre reinforced IPC skins (Inorganic Phosphate Cement, a non-alkaline inorganic resin developed at the Vrije Universiteit Brussel) separated by a polystyrene core. The dowel connection is needed for the connection between the concrete deck and the sandwich diagonal members of the truss. Connection elements with different dowel diameters and different spacings between the dowels are tested.
1. Introduction A design code for cast-in-place headed anchors is proposed in CEB bulletin N°226, part 3 'Characteristic Resistance of Fastenings with cast-in-place headed anchors'. The design procedure considers different failure modes of the connection in pure shear or in pure tension. For cases with combined shear and tension, an interaction formula is given. For this latter case however, experimental evidence is very limited [CEB Bulletin N°206]. In order to investigate the behaviour of cast-in-place headed anchors under the combined action of shear force, bending moment and normal force, an experimental programme was set up in which a specific connection element for the pedestrian bridge (described in section 2), was tested to failure.
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2. Concept of the pedestrian bridge IPC (Inorganic Phosphate Cement) is a non-alkaline inorganic resin developed at the Vrije Universiteit Brussel. Due to the non-alkaline conditions of the IPC (pH = 1 in fresh state and pH = 7 after hardening), it can be reinforced with glass fibre mats or with unidirectional glass fibres. The skins of the sandwich panels will be made of glass fibre reinforced IPC, while the core of the sandwich is expanded polystyrene foam. The result is a sandwich panel with a relatively high bending stiffness/weight and strength/weight ratio. [Wastiels 1999] The pedestrian bridge will be composed of three parallel truss girders (fig. 1). The sandwich panel for the bottom chord is composed of a polystyrene foam core with a thickness of 50mm with IPC skins reinforced with unidirectional glass fibres, in order to increase the bending stiffness of the total structure. The skins have a thickness of 10mm. The sandwich panels for the diagonals are composed of a polystyrene foam core with a thickness of 50mm (thickness required in order to avoid buckling of the sandwich panels) with IPC skins reinforced by random glass fibre mats. The top chord of the truss is a concrete deck with a thickness of 120mm. A concrete deck is needed to take up the compressive forces and to increase sufficiently the lowest natural frequency of the bridge .[De Roover 2000]
Figure 1 : Elevation and cross-section of the pedestrian bridge A design calculation was made in accordance with the requirements for pedestrian bridges in the Belgian Standard NBN B 03-101. The design load for the structure is a distributed load of 5 kN/m² and a concentrated load of 10 kN. The deflection at midspan, which is limited to span/500 in the design, is the most determining criterion. The hinges at the nodes of the structure are made of steel. A U-shaped profile with the same thickness as the sandwich-core, is inserted in the sandwich panels and the skins of the sandwich panels are bolted on the flanges of this U-shaped profile. The assembly of the panels is made by means of connection plates and pins. In order to transfer shear forces between the diagonals and the concrete deck, dowels welded on the upper flange of the T-shaped connection plates are provided (fig. 2).
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Figure 2 : Connection element between the diagonals and the concrete deck
3. Test programme and test set-up In order to test the mechanical behaviour of the connection between the diagonals and the concrete deck, a test set-up is proposed to subject the connection to a specific load combination (fig.3). A steel profile is fixed to two reaction walls. A compression jack and a tension jack are fixed to wedges attached to this profile, in order to obtain the same angle as in the truss system (the angle between the diagonal and the vertical is 27°). The ratio between the tensile and the compressive force applied in the tests, was determined from the design calculation. The magnitude of the compressive and tensile force and their ratio differs for the different nodes of the bridge. The forces in the test were applied according to the node in the bridge with the highest values for the compressive and tensile force. Although the ratio between the maximum compressive and maximum tensile force of this node is lower than for all other nodes of the bridge, it was assumed to be the most critical connection. Tension Jack Diagonal 2
Steel Profile Compression Jack Diagonal 1
LVDT's
Reaction wall
Slab specimen
500 mm
Figure 3 : test set-up
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Reaction wall
Small connection elements consisting of a T-shaped profile with two dowels welded on the flange were embedded in a concrete plate (dimensions : length 1000mm, width 300mm, height : 120mm) with the same thickness of the bridge deck. The internal reinforcement of the plate consisted of two bars of φ 10mm as upper reinforcement and two bars of φ 10mm as lower reinforcement. The plate is supported by two hinge supports with a free span of 500mm. Two types of connection elements were tested : type A with the centre lines of the diagonals crossing at the centre of the concrete deck and type B with the centre lines of the diagonals crossing at the bottom of the concrete deck (fig. 4). For type A, no local moment is introduced in the slab, whereas this is the case for type B. However, for type A the connection is submitted to bending whereas for type B this is not the case. The tests also had to clarify the possible influence of the bending moment on the resistance of the connection. The compressive force is measured with a pressure transducer, the tensile force is measured with a load cell. The horizontal displacement of the connection is measured with a LVDT, as well as the vertical displacements of the connection at the centre lines of the holes for the connection with the pins. Different hydraulic units are used for the compressive and tensile forces. The forces are applied in 8 steps to the SLS design load which equals 25.1 kN for the compressive force and 21.2 kN for the tensile force, ratio of 1.18. Next, the specimens is unloaded and finally reloaded up to failure, continuing with the same step size for both forces. The parameters of the test-specimens can be found in table 1.
Figure 4 : dimensions of connection type A and connection type B
4. Test results 4.1 Test results of connections with two dowels φ 16 mm The measured horizontal displacement in function of the compressive force can be found in figure 5 for connection type A and in figure 6 for connection type B. Since the maximum capacity of the compression jack was reached prior to failure, it was
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impossible to test these connections to failure. There is little difference in deformation behaviour between connection system type A and connection system type B.
Test Specimen 16-A1 16-A2 16-B1 16-B2 13-A1 13-A2 13-B1 13-B2 10-A1 10-A2 10-B1 10-B2
Table 1 : properties of the tested elements d2 d3 l2 k fcm fctm d1 [mm] [mm] [mm] [mm] [mm] [N/mm²] [N/mm²] 15.87 31.70 21.0 75.0 8.0 64.4 5.4 15.87 31.70 21.0 75.0 8.0 64.4 5.4 15.87 31.70 21.0 75.0 8.0 66.1 4.4 15.87 31.70 21.0 75.0 8.0 66.1 4.4 12.70 25.40 17.0 75.0 8.0 56.0 4.6 12.70 25.40 17.0 75.0 8.0 56.0 4.6 12.70 25.40 17.0 75.0 8.0 57.6 5.0 12.70 25.40 17.0 75.0 8.0 57.6 5.0 9.52 19.05 12.5 75.0 7.1 57.9 5.8 9.52 19.05 12.5 75.0 7.1 57.9 5.8 9.52 19.05 12.5 75.0 7.1 59.0 4.9 9.52 19.05 12.5 75.0 7.1 59.0 4.9
Type A A B B A A B B A A B B 0.80
Horizontal displacement [mm]
0.70 0.60 0.50 16-A1
0.40
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Figure 6 : test results for connections type 16-A 4.2 Test results on connections with two dowels φ 13 mm The measured horizontal displacement in function of the compressive force can be found in figure 7 for connection type A and in figure 8 for connection type B. Shear failure occurred in the shaft of the dowel just above the weld fillet. Damage to the concrete is limited to concrete crushing just in front of the dowels. Failure loads for connection types A and B are nearly identical, but the deformation capacity of connection type A is nearly twice as large as connection type B.
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1.00 0.90
Horizontal displacement [mm]
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Figure 6 : Test results for connections type 16-B 12.00
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Figure 7 : Test results for connections type 13-A 6.00
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Figure 8 : Test results for connections type 13-B 4.3 Test results on connections with two dowels φ 10 mm The measured horizontal displacement in function of the compressive force can be found in figure 9 for connection type A and in figure 10 for connection type B. The same
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failure mode for these connections is observed as for the dowels φ 13mm. The shafts of the dowels shear off immediately above the weld fillet, with little concrete crushing in front of the dowels. 6.00
Horizontal displacement [mm]
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Figure 9 : Test results for connections type 10-A 6.00
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Figure 10 : Test results for connections type 10-B 4.4 Summary of test results The failure load and the horizontal displacement at failure for the connections with dowels diameter 13 and 10 mm can be found in table 2.
5. Conclusions The connection systems tested failed in a quite ductile way (shear failure of the dowels with little concrete crushing). The location of the crossing point of the centrelines of the diagonals (Type A or Type B) has no significant influence on the magnitude of the failure load, but has a stronger influence on the deformation capacity (horizontal displacement). Connection type A with the centrelines of the diagonals crossing at the centre of the deck results in a greater deformation capacity at failure than connection type B with the centrelines of the diagonals crossing at the bottom of the concrete deck.
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The ratio between the failure loads of the connection elements diameter 10mm and the connection elements diameter 13mm (ratio of 0.61), corresponds well with the ratio of the cross sectional area of the dowels (ratio of 0.56). These two ratios should be equal for pure shear failure in the dowels. Table 2 : Summary of test results Compr. force Hor. displ. at failure at failure [kN] [mm] 13-A1 13-A2 13-B1 13-B2 10-A1 10-A2 10-B1 10-B2
180.0 173.0 175.6 169.6 96.0 110.8 110.6 110.8
9.1 10.3 5.3 5.1 4.6 4.6 2.6 3.5
Further testing will be performed on dowel connections with a shorter shaft to investigate changes in failure load and failure mode. Failure is then expected to occur in the concrete deck.
6. Acknowledgment Funding by the Flemish Fund for Scientific Research (FWO) under the contract of G.0191.98 is greatly acknowledged, as well as the Confibrecrete TMR network "Development of guidelines for the design of concrete structures, reinforced, prestressed of strengthened with advanced composites".
7. References Wastiels J., "Sandwich panels in construction with HPFRCC-faces : new possibilities and adequate modelling" in "High Performance Fibre Reinforced Cement Composites", ed. H. W. Reinhardt, A. E. Naamen, RILEM Publications, 1999, pp 143-151. De Roover C., Vantomme J., Wastiels J., Croes K., Taerwe L., Blontrock H., 'A new non-alkaline cement material reinforced by glass fibres (IPC) for the construction of bridges', Proceedings of the 3rd conference on Advanced Composite Materials in Bridges and Structures,Eds. J. Humar and A. Razaqpur, The Canadian Society for Civil Engineering, Ottawa, 2000, pp. 429-436
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De Roover C., Vantomme J., Wastiels J., Croes K., Cuypers H., Taerwe L., Blontrock H., "Modeling of a pedestrian Bridge composed of a Concrete Deck and a Truss Girder with IPC Sandwich Panels", Proceedings of the Fifth International Conference on Computational Structures Technology, Leuven, Belgium, September 6-8 2000 CEB Bulletin N°206, "Fastenings to reinforced concrete and masonry structures, Stateof-art report, Part I", 1991 CEB Bulletin N°226, "Design of Fastening in Concrete, Draft CEB guide - Part 1 to 3", 1995
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A NEW STEP FORWARD FOR COMPOSITE BRIDGES THE BRAS DE LA PLAINE BRIDGE Eric Barlet*, Gilles Causse** and Jean-Pierre Viallon** *JMI, France **BOUYGUES TP, France
Abstract This article presents the Bras de la Plaine Bridge on the island of Réunion in the Indian Ocean (France). The bridge structure is a single 280-m long span embedded in counterweight abutments. The deck is a composite truss structure comprising two concrete slabs linked by two planes of steel diagonals. Only the upper slab is continuous at the key. This bridge constitutes a step forward for composite structures.
1. Introduction The Bras de la Plaine Bridge, situated in the south of Réunion, was designed initially to provide a link between the towns of Le Tampon and L’Entre-Deux and will later become part of the planned link to improve access to the area known as the « Hauts du Sud-Ouest » link. The bridge structure is a single 280-m long span embedded in counterweight abutments. The deck is a composite truss structure comprising two concrete slabs linked by two planes of steel diagonals. Further to a restricted European tender during the first half of 1999, the Bras de la Plaine Bridge was awarded to the consortium BOUYGUES TP / DTP Terrassements. In its bid, the consortium eliminated the articulation at the key included in the basic design and made the upper slab continuous after horizontal jacking. The connection of the steel diagonals to the upper and lower slabs was completely modified. In addition, the abutments were reduced due to the effect of the horizontal jacking at the key before stitching the two halves together. Construction began in December 1999 and will last 24 months.
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2. Description of the chosen Structure 2.1. Functional Characteristics and Geometry Functional cross-section The bridge’s functional cross-section has a useful width (between the safety devices) of 10.90m which comprises: • a 6-m-wide bi-directional carriageway, • two pedestrian pavements each 1.35m wide, • two cycle-paths each 1.10m wide, • standard BN4-type lateral safety barriers. • the deck cross-section is roof-shaped: each side slopes down with a 2.5% gradient. Vertical alignment The vertical alignment is a convex parabola with a radius of 1,500 m. It slopes down to the right bank abutment with a 1.013% gradient and to the left bank abutment with a 5.017% gradient.
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Plane alignment The Bras de la Plaine Bridge is situated on a straight alignment over the ravine and slightly overlaps on either bank. 2.2. Structural Characteristics Background Information The structure designed to cross the Bras de la Plaine ravine comprises a single 280-mlong span embedded at both ends in huge abutments. At the key, only the upper slab is continuous.
The deck has a constant width of 11.90m and a depth varying between 17.60m on the abutment and 4m at the key. It is a composite prestressed concrete and steel truss structure comprising: • an upper slab with a constant section in high-performance prestressed concrete, • a lower slab with a variable section in high-performance concrete, • 2 planes of steel tubes arranged in V-shaped triangulation inclined at about 6° off vertical. The truss mesh is a constant 12.70 m along the whole structure. The deck intrados is a parabola with a radius of 661m.
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Abutments The abutments consist of a reinforced concrete box-shaped structure about 45m long, 11.90 m wide and between 18 m and 21 m in height. This structure has 2 compartments: • a back compartment 11m long, filled with ballast • a hollow front compartment. The invert (bottom slab) has a constant thickness of 1m. The side walls of the front compartment are 0.70m thick. The side walls of the back compartment are 1m thick. The upper slab has an average thickness of 0.60m.
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Deck: the upper slab The slab is built in B60 high-performance concrete (60 MPa characteristic strength at 28 days). Its total width is 11.90m. The slab is of varying thickness as follows: • 0.270m for the cantilevers which are 1.7m long • a constant 0.250m for the central part, 3.8m long • 0.810m at the ribs which are 0.850m wide edged by 2 gussets 0.735m and 0.775m wide. The slab formwork is constant for the whole structure except around the key where a transverse beam enables the structure to be jacked apart (6000 t horizontally at the key) before stitching the two cantilevers. The slabs for either side will be cast successively in 12.70-m-long segments. The upper slabs of each half are prestressed using 12 or 19T15 super tendons with an elastic strength of 1860 MPa. This cantilever prestressing can be divided into internal and external prestressing. On the deck side, the tendons are anchored in groups of four at the end of each segment and then at the back of the abutment. The tendons are tensioned at both ends. They are disposed in a plane alignment like fish bones and there is no vertical undulation in the slab except locally, near the deck anchoring points.
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Deck: lower slab Like the upper slab, the lower slab is in B60 high-performance concrete. The intrados is a parabola with a 661-m radius. The lower slab has variable width and thickness so as to both: • adapt to the transverse interval between the ends of the diagonals which is variable, and • accompany the increase in compression effort of the key towards the abutment. The section on the abutment is rectangular: 4,120m wide and 1,700m high. As it nears the key, the lower slab has the shape of an inverted cradle). The section near the key is 0,200m thick with ribbing 0,650m high. The lower slab is cast in place in 12.70-m-long sections (pours). Deck: Diagonals The diagonals are comprised of S355 steel tubes. A single range of tubes with an external diameter of 610mm is used. Their thickness varies between 28mm and 36mm for the compressed diagonals and is a constant 14.2mm for the tensioned diagonals. The diagonals are welded onto rectangular plates between 55mm and 65mm thick. Around the upper nodes, the meeting point of the diagonals is situated at the neutral axis. The plates are fixed onto the concrete by means of screws whose number varies depending on whether the diagonals are tensioned or compressed. The tensioned diagonals are prestressed by a pair of tendons comprising between 10 and 17 strands. The prestressing anchors are situated in the upper and lower slabs.
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3. Structural Behaviour 3.1. General Behaviour Apart from the aesthetic aspect which is visible in the original architectural design, the new bridge over the Bras de la Plaine river is an exceptional bridge structurally speaking. The structure functions like a variable depth Warren beam whose upper and lower slabs are the heart of an arch effect after horizontal jacking and stitching at the key. As the arch, or lower slab, is not continuous at the key, the positive flexion moment in mid-span generates compression efforts in the lower slab of the beam and in the upper slab at the key. Where the beam is embedded in the abutments, traction efforts are generated in the upper slab.
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3.2. General Stability The structure’s stability is achieved at each abutment by using ballast weighing 7500 t. The deadweight of the abutment is 7250 t whereas the deck weighs 4400 t on each bank (deadweight 3000 t, equipment 800 t, extra loads 600 t). The safety coefficient against overturning is 2.1 in Service Limit States and 1.6 in Ultimate Limit States. 3.3. Efforts in the Deck Efforts in the Diagonals Due to the curve of the lower slab, the normal efforts in the diagonals are similar in both the compressed diagonals and in the prestressed tensioned diagonals. The compressed diagonals bear an average effort of 600 t whereas the tensioned diagonals always remain compressed in Static Limit States due to their prestressing and the residual compression is 150 t on average. The prestressing using diagonals varies between 500 and 600 t. Efforts in the deck Under the effect of live loads (3.5 t/m), the arch effect of the stitched deck develops the following efforts: • compression at the key: 570 t, • traction of the upper slab where embedded at the abutment: 760 t, • compression of the lower slab where embedded at the abutment: 1300 t. Deflection at the key is 83mm. Under the effect of the deck dilating 20°, the structure moves vertically 214mm at the key resulting in compression of 2850 t in the upper slab and tension of up to 300 t in the lower slab near the abutments.
4. Building the Bridge 4.1. General Site Organisation As access from the right bank is difficult, the site was set up mainly on the left bank with a batching plant to produce the B35 concrete for the 2 abutments and the B60 concrete for the deck. For material supplies and concrete for the right band, an elevated cableway crane was set up between the two banks. Its span between the two pylons is 415m. The 2 pylons are 40m high and can be inclined ±10° which corresponds to a horizontal movement at the top of ±7m. The elevated cableway crane loading capacity is 8t.
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4.2. Building the Abutments The walls were built in sections 6m high and 10m long. The upper slab was built using sacrificial slabs resting on a temporary support half way along the transverse span. 4.3. Deck Construction To build the deck, 2 sets of travelling forms were designed, 1 for each side, each weighing 150 t. Each set of forms casts 12,70m of upper deck, then 12,70m of lower deck as shown in the diagrams below.
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The travelling forms are moved as follows: • upper part: drawer-like system with the formwork and the steel structure successively resting on the concrete upper slab already built; • lower part: the steel structure and the lower framework are moved as indicated on the diagram below.
In addition, the standard phasing for building a segment (upper slab and lower slab) is as follows: STANDARD SEGMENT PHASING Phase Description I Placing compressed diagonals in segment Vn II Reinforcing and concreting segment Vn top slab III Connecting the compressed diagonals of segment Vn with concrete slabs IV Tensioning the first pair of cantilever tendons in segment Vn V Removing the top slab formwork of segment Vn VI Tensioning the second pair of cantilever tendons in segment Vn VII Moving the travelling form to prepare for casting the bottom slab of segment Vn VIII Placing tensioned diagonals of segment Vn IX Reinforcing and concreting the bottom slab of Vn segment X Connecting the tensioned diagonals of segment Vn with concrete slabs XI Removing the bottom slab formwork of segment Vn XII Moving the travelling form to prepare casting of top slab of segment Vn+1 XIII Prestressing the tensioned diagonals of segment Vn XIV Placing compressed diagonals of segment Vn+1
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5. Main Quantities ABUTMENTS B35 CONCRETE B60 CONCRETE REINFORCEMENT RATIO
5437 M3 318 M3 910 T 158 KG/ M3
DECK B60 CONCRETE AVERAGE THICKNESS REINFORCEMENT RATIO INTERNAL LONGITUDINAL PRESTRESSING EXTERNAL LONGITUDINAL PRESTRESSING PRESTRESSING FOR DIAGONALS STEEL FOR DIAGONALS STEEL PLATES
2595 M3 0.72 M 530 T 221 KG/ M3 158 T 49 T 15 T 201 T 45 T
6. Participants Owner : Project Manager : (design and construction supervision) Owner’s Engineering Consultancy : Architect : Contractors : Final Designs : Principal sub-contractors :
Réunion (France) JMI & SCETAUROUTE JMI A. AMEDEO, PADLEWSKI & Associates Bouygues Travaux Publics / DTP Terrassements Bouygues Travaux Publics Design Office VSL (Prestressing)
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ANCHORAGE OF THE STEEL ELEMENTS TO THE CONCRETE PIERS AT THE SPECIFIC PIPE BRIDGES OVER A DANUBE-BAY IN BUDAPEST Béla Csíki Peristyl Engineering Consulting Ltd., Budapest, Hungary
Abstract The paper presents the details of anchoring the structural steel elements to the high volume reinforced concrete piers at two specific civil engineering structures recently have been built in Budapest, Hungary. Besides satisfying the load bearing requirements, the aspects of the special building technology and the demand for geometrical regulation of the structures during the construction had to be also taken into account at the design stage of the connections. To satisfy the latter two aspects creating special joins allowing free axial movement and rotation of the steel elements during the execution was necessary. The whole structures are also outlined shortly in relation to the local behaviour of the anchorages.
1. Foreword It is great honour to participate in this Symposium being held at the University of Stuttgart well-known for its famous structural engineers having been working in research and practice, respectively. Hopefully, the details will be presented herein are worth reviewing for both the design engineering public and the specialists. Two pipe bridges carrying waste water over a Danube-bay in Budapest were built in 1997 and put in operation in 1998. The bridges were designed in 1996 by the author working for Mélyépterv Komplex Engineering Co. Ltd. (Budapest) at the time. This paper gives a description of the special steel to concrete connections of the pipe bridges satisfying a combination of several requirements in relation to loading, construction technology and a special demand for geometrical regulation of the structural elements. Although the presentation focuses on the local behaviour of the joins, the general
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layout of the bridges will also be outlined, because certain knowledge on the global behaviour is necessary to have a better understanding of the requirements to be satisfied by the connections.
2. General layout of the pipe bridges The two new pipe bridges with parallel horizontal axes and the same axial heights and length surround symmetrically an existing combined foot- and pipe bridge which had been built a few decades earlier. This unusual arrangement of the three bridges is a result of consideration of several factors presented in Ref. 1. which are beyond the scope of this paper. An elevation of one of the two new pipe bridges is given in Fig. 1.
Fig. 1. View of the southern pipe bridge The new pipe bridges are of the same length of 87.40 m and of the same specific structural arrangement. Both of them fundamentally consists of three parts: the two joined, supporting (or bank) units on the banks of the Danube-bay and the pipe 1000 mm in diameter spanning the bank units. The two supporting units are arranged symmetrically to the middle of the whole structure on the banks. The longitudinal vertical section of a bank unit with the supported pipe is presented in Fig. 2.
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Fig. 2. Vertical section of a bank unit with the pipe The bank units are assembled from three main structural elements: the eccentric, high volume, 9.60 m high, reinforced concrete pier on pile foundation, the horizontal steel main beam of 28.00 m length - with a 17.20 m cantilever toward the middle of the whole structure - supported on the top of the pier, and anchored at the end to the bottom of the pier by the third element, an inclined steel bar. The main beam and the anchoring bar are joined structures themselves made of welded steel elements. They consist of doubled girders with axial distance of 2.80 m, connected by transverse beams and stiffening bars. The structural heights of the I-shaped cross-section doubled girders of the horizontal main beam and of the inclined anchoring bar are 2.00 m and 0.40 m, respectively. The steel pipe spanning freely the bank units is hidden in the horizontal main beams at the banks. Statically the pipe is a continuous beam of 81.80 m length on four elastic supports. Each bank unit contains two supports located on the transverse beams at the two ends of the main beam. (The pipe on the supporting units is independent statically from the connecting parts of the network arriving to or leading away the bridge.) The required camber of the pipe was produced by setting a specified difference between the absolute heights of the two pipe-supports on each bank unit before placing the pipe. The difference determined by considerations based on stress and strain calculations could be created by adjusting a prescribed inclination of the “quasi” horizontal main
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beam containing the pipe supports. The conceptual scheme of this geometrical adjustment of the bank units harmonising with the aspects of the assemble of the elements is shown in Fig. 3.
Fig. 3. Geometrical regulation of the bank units during construction The possibility of the denoted axial movements and rotations of the connecting steel elements at the top and at the bottom of the concrete pier was assured by using specific anchoring devices. These joins will be presented in the next paragraph. The third connection of the structural triangle between the steel main beam and the inclined anchoring bar is a usual bolted headplate join also involved in the adjustment. It should be mentioned that during the regulation the weight of the main beam was balanced by the crane hoisted it in place. Hence, the inclined bar was unloaded and the horizontal force at the support on the top of the pier could also be avoided to make easier the adjustment.
3. The connections between steel and concrete It was shown in the previous chapter that there are two steel and concrete connections at each bank unit: the support of the main beam at the top and the anchoring point of the inclined bar at the bottom of the pier. In harmony with the shaping of the whole structure and the structural elements the structural joins are traditionally formed, as well. In the final stage the connection at the top of the pier is a usual fix hinged support
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and the anchorage at the bottom seems to be a usual bolted bedplate join. But, because of the geometrical regulation during the construction, design of a first stage of the joins was necessary in order to make possible the required movements of the connecting structural elements. There was one common principle of forming the two different joins. Each had to be easily and quickly transformed into the final (service) stage after the regulation had been finished. 3.1. Anchoring at the bottom of the pier According to the functions of the anchoring the lower part of the reinforced concrete pier was built in two stages. In the first stage two “bites” were left at the transverse edges of the bottom of the pier in order to hide one-one regulation element of the anchorage in the axes of the doubled girders of the inclined bar (Fig. 4.).
Fig. 4. Anchorage of the inclined steel bar consisting of doubled girders (Ref. 1.) The lower ends of the regulation elements are tied to a common cylindrical compact steel dowel deeply embedded into the reinforced concrete rib shaping the final border of the pier between the “bites”. The upper headplate of the regulation elements is joined to the bedplate of the doubled girders of the inclined bar through a certain gap by screw shafts with fixing and adjusting nuts. The required movements of the inclined bar during the construction could be produced by a free rotation around the dowel and an axial displacement adjusted by the nuts of the screw shafts. The final (service) stage of
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the connection was reached simply by filling the “bites” with concrete in order to hide the elements of adjusting after the geometrical regulation had been done. Regarding the load-bearing behaviour the connection provides the anchorage of the axial tensile force of the inclined bar consisting of doubled parallel girders. Due to the forming of the join presented above the connection has the same load-bearing capacity during the regulation process as in its final stage. The tension of the anchoring elements is taken by shear and bending of the cylindrical dowel anchored with steel ties along the rib to the inside of the high volume pier. 3.2. Support on the top of the pier The main beam is supported under the doubled “quasi” horizontal girders on two hinged supports allowing free rotation around the common axis of the two cylindrical hinges in the final (service) stage (Fig. 5.).
Fig. 5. Hinged support on the top of the pier During the assemble and the geometrical regulation of the bank units allowing axial displacement of the main beam was also needed. Therefore in the first stage the lower parts of the two joints (the bedplates) were not fixed to the receiving steel boxes placed in advance into the concrete on the top of the pier. All the elements of the joints were fixed onto the corresponding girder of the main beam. Hence, the two hinges on the
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doubled girders were able to move together with the main beam. The possible displacements were limited to the extent of the gaps between the rigid lower part of the bedplates hanging down into the receiving boxes and the elements (walls and plates) of them. After the regulation had been finished the support was fixed on the one hand by welding the bedplate of the joints to the upper plate of the receiving steel boxes, on the other hand by injecting high strength epoxi resin into the boxes through the holes on the top. In the final (service) stage the connection supports vertically the main beam and transmits the horizontal projection of the tensile reaction force of the inclined anchoring bar to the pier balancing it by shear and bending. The transmitting of the horizontal force is solved by local pressures at the front walls of the receiving boxes anchored with vertical ties into the inside of the pier.
4. Summary The connections between the steel and the reinforced concrete structural elements of two specific pipe bridges were presented. Besides the load-bearing requirements the considerations of the construction technology in harmony with a special need of geometrical regulation of the structures had to be also taken into account during the design of the joins. Satisfying the latter two aspects by the shaping of the connections allowing free movements during the assemble of the main elements of the bridges were focused in the paper.
5. References 1.
Csíki, B., ‘Design of pipe bridges at People’s Island’, (11-12) (1997) 321-324. (in Hungarian)
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Magyar Építõipar,
BEHAVIOR AND DESIGN OF STEEL GIRDER-TO-CONCRETE COLUMN CONNECTION FOR A CANTILEVER-CONSTRUCTION HIGHWAY BRIDGE Ling Huang*, Hiroshi Hikosaka*, Masafumi Shimozono* and Katsuyoshi Akehashi** * Dept. Civil Engineering, Kyushu University, Japan ** Research Institute, Yokogawa Bridge Corp., Japan
Abstract Designing rigid and durable steel girder-to-concrete column connection is important for a new type of highway bridge constructed using a cantilever-erection method. To develop a full strength of the hybrid connection, the perforated steel plate is applied as a bonding means for the steel-concrete interface. A nonlinear finite element program has been developed to investigate the inelastic response of the steel-concrete hybrid structure. The model considers the essential nonlinearities arising in the materials: 1) nonlinear behavior of concrete under multiaxial stress states; 2) tensile cracking of concrete; and 3) elasto-plastic behavior of steel plates and reinforcing steel bars. Special attention has been paid to the two-dimensional nonlinear effect of perforated steel plates at the steel-concrete interface. Effectiveness of the analysis method is demonstrated through comparison of measured and numerical results on a highway bridge which has been constructed recently in Japan. It is followed by the analytical confirmation of the ultimate strength and deformation characteristics for a prototype connection region.
1. Introduction A new cantilever-erection method has recently been developed in Japan for the construction of two parallel steel plate girders spaced widely apart between axes and rigidly connected to reinforced concrete (RC) piers. By rigidly connecting the steel girders to concrete piers, high maintenance cost items such as bearings and deck joints are eliminated. The moment-resisting capacity of the connection creates the potential for additional redundancy in the seismic force resisting path. Wider spacing of girders means less steel fabrication cost although at the expense of deeper sections. Either a precast or cast-in-place prestressed concrete slab can be used for the deck, which may be designed as composite or non-composite. Use of the transverse prestressing increases the span length of the concrete slab with greatly reduced cracking. The large stiffness of
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the deck in the horizontal plane can also minimize the lateral bracing of plate girders. The new cantilever-erection method for steel plate girders would be a better choice, especially in the mountainous regions where the use of other conventional erection method is difficult and the construction yard is limited to a rather small space around the pier. However, particular attention has to be paid to the stability of laterally unstiffened plate girders under cantilever-erection. Designing the rigid and durable steel plate girder-to-RC column connection is significantly important for the bridge constructed using the cantilever-erection method. The perforated bonding plate, that is a steel plate with large holes at close intervals, is applied for the hybrid steel-concrete connection.
2. Description of the bridge and its cantilever erection 2.1 Bridge type and dimensions Fig. 1 shows an elevation of the prototype bridge1), for which the behavior and design of the steel girder-to-concrete column connection are discussed in detail. It has three continuous spans, 48.2+81.5+57.2 m, for a total length of 188 m, with two RC piers, P1 and P2, which are rectangular columns 2.5x6.7 m. The main girders are divided into 23 steel framework segments, each of which is made up of two parallel welded I-girders 5.6 m apart between axes. The girders are 2.9 m deep except for three segments of varying depth (4.5 m maximum) adjacent to each pier. The transverse beams are rolled steel profiles spaced every 4.8 m.
Fig. 1
Elevation view of the prototype bridge
2.2 Cyclic cantilever- erection of main steel girders The cantilever-erection method of the main steel girders as well as the construction sequence is illustrated in Fig. 2. The first step for steel girder erection after pier construction is rigidly connecting the steel framework No.1 to pier P2 using a truck
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Fig. 2
Cantilever-erection sequence of the main steel girders
crane. The steel segment is set on four stay-in-place supporting devices and positioned 800 mm above the pier top. After providing local reinforcement underneath the bottom flanges of the girders and setting up casting forms, concrete is placed in the 2.5x5.6x3.8 m pier head. The truck crane is also used to erect the steel segments 2 and 3 on alternate sides of the pier, and then to erect the traveling erection gantry (TEG) crane on the main girders. The TEG crane traveling on rails over the top flanges of girders is used for the cyclic cantilever-erection of main girders and later for the laying of precast concrete deck slabs. The TEG crane weighs about 600 kN including two main beams, a traveling device, a hoisting device running on the main beams, and a supporting floor used as the work platform during erection.
Photo 1
Cantilever-erection using TEG crane
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Each steel framework is assembled by bolting on the supporting floor at ground level, before it is hoisted and transported to the previously erected girders. The maximum segment weight is 250 kN. The main beams of TEG, hanging the supporting floor with an assembled steel segment as shown in Photo 1, travel first to the cantilever tip. The hoisting device alone then moves to the correct position to connect the joints between two steel segments. Combined welding and high-strength bolting is adopted for the field splice of main girders. The webs and bottom flanges are bolted together, whereas the welding of top flanges is required as the precast concrete deck slabs have to be laid on a smooth surface of the flanges.
3. Design evaluation of steel girder-to-concrete column connection 3.1 Design of girder-to-column connection The girder-to-column connection (Fig.3) has two main I-girders made of 570 MPa steel (yield strength 450 MPa). The top and bottom flanges have a constant width of 800 mm and 950 mm to limit their thickness to 59 mm and 50 mm, respectively, and the web thickness is 32 mm. Two cross beams have a web of 3,000x28 mm and are expected to transfer various forces between main girders and RC piers by means of four perforated vertical stiffeners and two perforated diaphragms of 22 mm thick steel plate with 70 mm diameter holes. The perforated stiffeners and diaphragms become embedded in the pier when concrete is placed up to the upper flange height of the cross beams. Stud connectors are also provided on the webs and underneath the bottom flanges of main girders to improve the bonding at the steel-concrete interface.
Fig. 3
Steel girder-to-column connection
The perforated steel plate was originally proposed and named “perfobond strip” by Leonhardt et al.2) as an efficient bonding means for steel-concrete composite structures. In their push-out type experiments on the perforated steel plate embedded in concrete, it was observed that shear-slip relations depend on factors including: 1) concrete
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compressive strength, 2) hole diameter, 3) lateral confining pressure, and 4) amount of lateral reinforcement provided through the hole. 3.2 Problem description The perforated steel plates have not been practically used in Japan as bonding means for the steel-concrete interface. Designing the rigid and durable steel girder-to-RC column connection is significantly important for the bridge constructed using the cantilever-erection. Because a single TEG crane is used for the cantilever-erection of the main girders, a large unbalanced pier moment will take place during the erection, producing a potential for damage in the connection region. One main design goal is to ensure that ultimate failure is associated with a flexural mechanism developing in either the main girder or column, rather than a failure in the connection region. Concerns regarding design details in the connection region prompted the testing programs3,4) and associated analyses5), as well as the monitoring of connection behavior during the cantilever-erection, as described hereafter. 3.3 Modeling of material nonlinearity and perforated bonding plate A finite element program suited to nonlinear analyses of the girder-to-column connection was developed in this study. The program solution algorithm and material models were verified through comparisons with various test results for RC structures6). Webs of the main I-girders are modeled by plane stress quadrilaterals, whose material model is based on a plasticity theory under von-Mises yield criterion. Flanges and cross beams are represented by 1-D truss elements, whose material model is idealized as bilinear elastic strain-hardening plastic. Concrete continuum is represented by plane stress elements. A plasticity-based constitutive Qy model is used to simulate the nonlinear behavior of concrete in compression. A smeared crack k sy model is used to represent the concrete fracture. k sx Qx Reinforcing bars are modeled in a discrete manner by the 1-D truss element described above. Fig.
4
Bond
link
element The 2-D link-type elements (Fig.4) are used to Q model the bonding actions between concrete and perforated steel plate. A series of pull-out tests on perforated steel plates with a single hole was performed by Japan Highway Public Corporation4). Qu /3 unloading reloading The test specimens had the same parameters as ｋ those in the prototype girder-to-column connection, unloading reloading such as the concrete strength (30 MPa), the plate se thickness (22 mm) and the hole diameter (70 mm). Fig. 5 Shear-slip relation for perfobond
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No lateral reinforcement was provided in both the specimen and the prototype structure. Based on the pull-out test results, nonlinear shear-slip relation for the perforated steel plate is assumed to take the form shown by a curve in Fig.5, in which Qu is the shear strength per hole of a perforated plate embedded in solid concrete. The orthogonal link shear stiffness, ksx = ksy in Fig.4, is defined as the secant modulus from the origin to Qu /3 and is adjusted by means of the nonlinear shear-slip relation given in Fig.5. 3.4 Two-dimensional model construction The steel girder-to-RC column connection is modeled using the steel framework segment connected to pier P2. The 2-D finite element idealization of the connection region and its boundary conditions is shown in Fig.6. The nodal loads are specified based on both the bending moments, Ml and Mr, and the vertical shears, Ql and Qr, acting on the field spliced cross-sections. In the analysis the load factor λ, multiplied to each load, is increased incrementally.
Fig. 6
FE idealization of the connection region
3.5 Monitoring of the connection region under cantilever-erection Because a single TEG crane was used for the cantilever-erection of main girders, a large unbalanced pier moment took place during the construction of the prototype bridge1). Several parameters were monitored in the steel-concrete connection region at each pier head, including strains in the main steel girders and RC piers, as well as the construction camber of each girder segment. Fig. 7 shows the variation of measured and calculated stresses in the longitudinal reinforcing bars at the positions 650 mm below top of pier P2, as the main girders were cantilevered on alternate sides of the pier. The largest unbalanced pier moment occurs when the girder segment G20 is being erected in the A2 side span before the segment G12
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Stress in rebar (N/mm2)
Variation of rebar stresses in pier P2 during cantilever- erection
Fig. 8
Variation of normal stresses in main girders during cantilever- erection
Stress in main girder (N/mm2)
Fig. 7
in the center span is completed. The measured stresses in three different rebars spaced 2.1 m transversely have almost the same values, validating the use of 2-D finite element idealization of the connection region. Fig. 8 illustrates the variation of normal stresses in the flanges and webs of the two parallel main girders, G1 and G2, measured at the cross-sections just out of the girder-to-pier connection. The differences between the measured and calculated values are relatively small, which indicates that the FE analysis model used for the calculation is satisfactory.
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4. Behavior and ultimate strength of girder-to-column connection Structural behavior and ultimate strength of the steel girder-to-RC column connection in the prototype bridge are numerically predicted using again the 2-D model of connection region already shown in Fig.6. The bending moments, Ml and Mr, and the vertical shears, Ql and Qr, are given the ratios Mr /Ml = 0.81 and Qr /Ql = 0.95, which were calculated from the completed prototype structure given in Fig. 1 for the design load including the dead and live load. The load factor λ is multiplied to the design load, with λ=1 corresponding to the design load, and λ=1.7 to the ultimate limit state until which the failure condition should not be exceeded.
Fig. 9
Fig. 10
Load vs. deflection curve
Normal stress distribution across vertical cross sections in the main girder
The vertical displacement versus load factor, at the left cantilever-tip of the steel girder segment, is plotted in Fig.9. The analysis predicts the linear relationship up to the first yield of the bottom flanges in main girders at λ=2.2. Fig.10 shows the normal stress distribution across vertical cross sections in the main girder, just to the left and right sides of cross beam and at the center of pier width, respectively, for several load levels. Since the concrete is placed up to 3 m from the bottom flange within the 4.5 m-deep
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connection, the change of normal stress distribution due to the sudden transition from non-composite to composite section is apparent. The distribution of horizontal and vertical shears, Qx and Qy, per hole on the perforated vertical stiffeners welded to the cross beam webs at λ = 1 is plotted in Fig.11. The distribution of Qx corresponds to the horizontal bearing pressure from the cross beam webs to concrete, although the severe horizontal pulling-out forces occur on the web A-A of cross beam above the neutral axis of the main girder. Fig.12 shows the distribution of shears Qx and Qy per hole along four edges on the perforated diaphragm at λ = 1.
Fig. 11
Distribution of shears on the perforated vertical stiffeners
Fig. 12
Distribution of shears on the perforated diaphragm (kN)
5. Concluding remarks Nonlinear behavior and design of the newly developed steel girder-to-concrete column connection, including its serviceability and ultimate strength, were discussed in the present paper. This type of connection was adopted in Japan for a cantilever-construction highway bridge, in which steel girders were rigidly connected to RC piers. Use of the perforated steel plates in place of conventional stud connectors led to simplification and rationalization in the construction of steel-concrete hybrid structure. A nonlinear finite element program was developed to investigate the inelastic response of the proposed hybrid connection, in which special attention was paid to the 2-D nonlinear effect of the perforated steel plates at the steel-concrete interface. The
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program solution algorithm and material models were verified through comparisons with some measured parameters, including stresses in the main girders and RC piers monitored during the girder erection. The FE analyses can provide simple, nonlinear descriptions of the connection behavior, particularly a clear concept of the stress flows in the connection region. Such information would be useful in the initial stage of design process and for making appropriate member changes prior to the final design. However, the 2-D approach to modeling the connection region is unable to account for 3-D phenomena, and its performance needs to be validated against additional experimental and theoretical results. References 1.
2.
3.
4. 5.
6.
Nakamura, K., Imaizumi, Y., Kaneshige, H., Nakahigashi, T., Sasaki, Y. and Ogawa, T., ‘Design and Construction of Imabeppu River Bridge’, Bridge and Foundation Engineering, 34 (12) (2000) 2-9. Leonhardt, F., Andrä, W., Andrä, H-P. and Harre, W., ‘Neues, vorteilhaftes Verbundmittel für Stahlverbund-Tragwerke mit hoher Dauerfestigkeit’, Beton- und Stahlbetonbau, (12) (1987) 325-331. Sasaki, Y., Hirai, T. and Akehashi, K., ‘Experimental study on rigid connection for hybrid frame bridge consisting of steel girder and reinforced concrete pier,’ Journal of Structural Engineering, JSCE, 44A (1998) 1347-1357. Kano, Y., ‘Studies on steel plate girder-to-RC column connection for highway bridges’, EXTEC, 13 (4) (2000) 41-43. Liu, Y., Hikosaka, H., and Huang, L., ‘Finite element analysis of steel girder-to-column connection considering nonlinear behavior of studs,” Journal of Applied Mechanics, JSCE, 1 (1998) 481-488. Han, S., Hikosaka, H., Huang, L., Bolander, J.E. and Satake, M., ‘Simulating distributed discrete cracking in reinforced concrete structures using smeared crack FE model’, Proc. 1st International Conference on Engineering Computation and Computer Simulation, Changsha, China, (1995) 284-293.
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RECENT DEVELOPMENTS AND CHANCES OF COMPOSITE STRUCTURES Ulrike Kuhlmann Institute of Structural Design, University of Stuttgart
Abstract Composite structures combine the advantages of both materials concrete and steel. Developments in the recent years show a tendency to optimise design and construction of composite constructions by an increasing flexible use of structural forms and techniques. An overview over some innovative trends is given. As a consequence of that tendency the borderline between buildings and bridges as well as the difference between girders, slabs and other structural elements start to diminish which demands of the structural engineers a broad knowledge and a holistic conceptual view.
1
Introduction
Composite constructions combine the high-strength performance of structural steel with the stiffness and compressive strength of concrete. As each material can be used to its best advantage, composite structures show economy in overall cost and are fast to construct. For these reasons they have become increasingly popular. As composite structures also show an increasing variety, it is nearly impossible to give a complete overview. In the following some specific topics showing especially innovative developments will be addressed such as - composite columns, - partially encased composite beams, - composite slabs and slim-floor structures, - connection devices and composite joints, - high strength structural steel and - composite bridges. On the basis of these examples the attempt will be made to highlight also some general tendencies and chances of composite structures in the future.
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2
Composite Columns
Columns have been one of the first elements built as composite. Nevertheless, two interesting new developments can be noticed.
moment due to imperfection
Eurocode 4: M Sd (Fd ) ≤ 0,9 ⋅ µ ⋅ M pl,Rd
DIN 18 800-5: M Sd (Fd , w 0 ) ≤ 0,9 ⋅ µ d ⋅ M pl,Rd
Figure 1: Verification of composite columns according to Eurocode 4 [1] and DIN 18800-5 [2], see also [3] The rules for composite columns according to Eurocode 4 [1] are restricted to non-sway systems. As shown in Figure 1 a simplified design method is applied. The global analysis has to be performed considering the second order effects whereas the local influences of second order theory and imperfections are taken into account indirectly by the design procedure based on the buckling length and the European buckling curves. For the column no equivalent imperfections are given. The moment due to imperfection is taken proportional to the moment belonging to the reduction value κ of the allowable compression force according to the European buckling curves. Therefore, for the moment induced by imposed loads only an amount of µ ⋅ M pl,Rd is available. The reduction of 90 % considers - the influence of the realistic stress-strain laws and - the approximation according to the effective stiffness values. This procedure is only valid for single columns in non-sway frames. For the verification of sway framed systems explicit values for the equivalent initial imperfection have to be known. Investigations by Dr. Bergmann in Bochum and Prof. Lindner in Berlin [3], [6] have determined representative values which have meanwhile been included in the recent version of the German standard DIN 18800-5 [2], see Table 1:
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Table 1:
Member imperfections and buckling curves for composite columns according to DIN 18800-5 [2]
cross-section concrete filled sections
axis of buckling
buckling curve
member imperfection
a
L/300 (C20 - C60)
b
L/250 (C20 - C35) L/210 (C40 - C60)
c
L/200 (C20 - C35) L/170 (C40 - C60)
y-y z-z
completely or partially encased I-sections
y-y
z-z
These imperfections are included in an ordinary verification according to second order theory. Figure 1 shows the procedure in comparison to the simplified method of Eurocode 4. The internal moments within the columns are now also determined under consideration of imperfections and local effects of second order theory. As a consequence the full plastic moment - only reduced to 90 %, see reasons above - is regarded as resistance. However, in contrast to pure steel structures an effective flexural stiffness has to be taken into account for the composite column to consider the effects of cracking and long term duration, see details in [2] and [3]. As often during erection the same column is first used as pure steel column and only later integrated in a composite frame, this change of stiffness plays an important role. By enlarging the scope to sway frame systems deformations become of eminent importance, therefore the temporal development of stiffness has to be followed consequently. The effects of creep and shrinkage or the temporal development of stiffness also have to be closely observed for a special kind of columns which are sometimes called “Mega columns” [7] or else “Super-columns” [8], see Figure 2. In fact, it is questionable whether these elements should be called columns or not. The framed steel structure is erected first and transfers gravity loads as well as horizontal loads. This allows the erection of the upper stories to proceed ahead of the concreting of the columns at the lower level. The procedure essentially speeds up the overall erection time and is regarded as a major advantage for tall buildings. However, because of the high percentage of concrete section and the high vertical loads loading history as well as creep and shrinkage are important.
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Cross-section StE 460 / St 52 studs 22 x1 00
B 65 BSt 500 S, ∅ 28
Figure 2: Mega column, Commerzbank Headquarters, Frankfurt/Main [7] Both developments of composite columns, the second order design of sway frames as well as the trend of giant columns show a tendency to enlarge the scope and enable a more flexible usage. However, this necessitates a more sophisticated calculation.
3
Partially encased composite beams
The second element which has traditionally been built as composite are beams. Nowadays they are often integrated into frame systems, as explained before. But also the shape has changed: Composite beams are today frequently partially encased into concrete.
Figure 3: Material distribution of the main girders of the body unit of Porsche and the paint unit of Opel according to Hanswille [9]. Originally the purpose of encasement was to improve the resistance to fire as e.g. for the main girder of the body unit of Porsche in Stuttgart (1985), see Fig. 3. For the normal temperature design following Eurocode 4 [1] only the improved buckling behaviour of the web could be taken into account. The development may be recognised considering the second girder in Fig. 3. For the main girder of the paint unit of Opel in Eisenach (1992) the concrete encasement and the reinforcement were also taken into account in calculating the bending resistance and the flexural stiffness for the normal temperature design. Instead of altering the lower steel flanges, additional reinforcement in the con-
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crete encasement was provided. The example given by Hanswille in [9] showed for a 20 m span a reduction of the steel weight from 7.85 tons to 6 tons and an advantage concerning the overall costs of nearly 6 %.
Figure 4: Partially encased composite beams, according to [10] Rules given explicitly in the new German standard DIN 18800-5 [2] restrict the consideration of the concrete encasement for the bending resistance to the compressed part, thus neglecting the concrete acting in tension. The regulations require a full shear connection to be provided between steel web and concrete encasement. It is also pointed out that for reasons of ductility the plastic zone in compression should be limited to 0.15 of the overall height and that reinforcement in the lower third of the concrete height should fulfil ductility requirements. A full moment redistribution according to plastic hinge theory should not take into account the concrete encasement, as the transfer of shear forces in a widely cracked area is uncertain, see also [3]. If adequately connected the reinforced concrete encasement is also able to carry part of the vertical shear load which originally is thought to be transmitted only by the steel web. The vertical shear force in the concrete encasement may be assumed proportional to the internal moment distribution between the moment of concrete encasement, the steel girder moment and the moment resistance based on the pair of internal normal forces of the composite section, for further explanation see [3].
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Neglecting the encased concrete in zones of tension may lead to unrealistic high deformations. So for this purpose it is proposed to consider an effective stiffness derived from the mean value of the cracked and uncracked section, see [10].
4
Composite slabs
Stiffness starts to be of importance also for another composite element: for composite slabs. As composite slabs consisting of thin, cold-formed metal sheeting and in-situ cast reinforced concrete, the steel-concrete interaction can be achieved by pure adhesion, frictional and mechanical interlock and end anchorage. In practice a combination of these effects exists. The efficiency of frictional and mechanical interlock mainly depends on the shape of the metal decking and its indentations. Therefore strong efforts have been undertaken to improve the shape e.g. by embossments or by end anchorage, see [11]. These improvements aim at a higher load capacity as well as at a more ductile behaviour. But however the full interaction leading to a full plastic moment resistance is nearly never attained. Therefore, for composite slabs the model how to consider the partial interaction between steel and concrete in design is of vital importance. In Eurocode 4 [1] two methods are given to verify the longitudinal shear resistance - the m + k method, a purely empirical shear bond method and - the partial connection method which is based on a mechanical model using tests only to obtain shear strength values. Especially the latter has recently been focused on by several researchers [11], [12], [13]. MRd (with end anchorage) MRd (without end anchorage) q
Mpl,Rd MSd
Nc Lx
Ved
L MSd
Lx
Lx
Mpla Lsf
L
Ved b ⋅ τ u ,Rd
Figure 5: Partial connection method [3] As explained in Figure 5, the moment resistance results from the pair of forces Nt of the steel sheeting and Nc of the concrete plus a small contribution of the plastic moment resistance of the pure metal decking Mpla. The concrete force Nc is equal to the longitudinal shear force τ u ,Rd ⋅ b ⋅ L x introduced from the sheeting into the concrete over a length
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Lx. With increasing length Lx starting e.g. from the support of a simple girder the moment resistance increases up to the full plastic moment Mpl,Rd. The verification is done if the moment distribution due to loading case MSd, see Figure 5, stays under the curve of resistance. The values τu,Rd are assumed to be constant over the length though in reality have proved to be locally influenced e.g. by friction. Thus it is recommended to shift proportionally to the friction force the graph of resistance into the negative length area, similar to the procedure for the end anchorage force Ved. However, the design of composite slabs is not restricted to single spans. In some cases it is useful to take advantage of the benefits of continuous slabs which are in comparison to single spans: reduced deflections, higher architectural slenderness and larger load capacity. To make use of the full redistribution of bending moments according to plastic analysis it is obvious that sufficient rotational capacity at the regions of negative bending moments is necessary. As also presented in [11] I. Sauerborn developed a modified plastic hinge method and defined some rules for the limits of application [14]. As a consequence and in contrast to the regulations of Eurocode 4 [1] the new German code DIN 18800-5 [2] restricts together with the corresponding new German concrete code DIN 1045-1 [5] the application of plastic hinge theory to composite slabs with - re-entrant profile shape with mechanical interlock, - highly ductile reinforcement, - spans L less than 6 m, - concrete compression zone at support with a height x less than 0,25 ⋅ d and - a relation Mpl,support to Mpl,span between 0.5 and 2. This close interference with the concrete code reminds of the fact that at least at the support the composite slab is a reinforced concrete slab which is of course largely improved by the ductility and bending resistance of the steel decking. It seems to be typical for the development of recent years that as well as the differences between concrete elements and composite elements diminish, also a clear distinction between composite slab and composite girder becomes more and more difficult. Examples of this are given in Figure 6.
5
Slim-floor structures
A light weight composite floor like the Hoesch additiv floor [15], see Fig. 6a), behaves very similar to a pure steel or a pure reinforced concrete beam, whereas slim-floor girders like the ASB section [16] or the UPE hat section.[17] in Figure 6b) and c) resemble composite slabs. Slim-floor structures are characterised by the supporting beam being within the depth of the floor deck. It has a number of advantages including reduced depth of construction and improved fire resistance. Currently most forms of slim-floor girders are designed as
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non-composite, but for an increasing number composite action is tried to be activated by means of mechanical shear connectors or by consideration of frictional interlock or clamping effects. However, a full shear interaction is seldom achieved, so that the rigidity in the interface between steel and concrete has to be considered especially when calculating deformations.
a)
b)
c)
Figure 6: Slim-floor systems: a) Hoesch additive floor [15], b) Slimdek construction with ASB section [16], c) UPE hat section [17] In Eurocode 4 [1], 5.2.2 (6) a factor is given to increase the deformation of full interaction in order to take care of the slip between steel and concrete. This factor is proportional to the relation between the deformations of the pure steel girder and the composite girder with full interaction. This relation increases to a value of 10 to 15, if slim-floor girders are concerned, see Figure 7. δa/δv 1
type of girder pure steel girder
1÷3
normal composite girder
4÷9
composite girder with reduced height
10 ÷ 15
slim-floor girder
Figure 7: Relation of deformations of pure steel girders δa and composite girders with full interaction δv [18] The diagrams in Figure 8 show – as has also meanwhile been proved by experimental and numerical investigations [17] – that the factor given in Eurocode 4 overestimates more realistic values as e.g. by Dabaon [19] by up to 5 to 2.
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δ/δv
δ/δv
8
8
7
7
6
6
5
5
4
4
3
0,4
2
3
0
2
0,6
1
0,6
1 0,8
0 19
16
δa/δv
13
10
7
1 4
0,8
0
η
19
δa/δv
1
a)
16
13
η
10
7
1 4
1
b)
Figure 8: Relation of deformations of composite girder with partial interaction δ and composite girders with full interaction δv in dependence of the degree of connection η a) by Eurocode 4 [1] and b) by Dabaon [19]
6
Connection devices
Composite action strongly depends on the connection devices which transfer the longitudinal shear from the steel interface into the reinforced concrete. Two main developments can be observed concerning these devices: - a more refined usage of headed studs, the most common connectors in composite construction and - the development of alternative devices. The usage of headed studs has recently been extended to unusual positioning like horizontally lying studs in thin concrete slabs, see [20]. It is shown that the reduction of the resistance due to splitting failure may be minimised by an optimum reinforcement. For studs in composite bridges the fatigue verification as given in Eurocode 4 Part 2 [4] has been reviewed, see [21]. It is discussed whether inconsistencies or scatter of results are not partly due to the various fatigue test evaluation methods, [22]. Stud connectors in troughs of profiled sheetings have been covered by many research projects. A thorough investigation of existing results [22] showed that in Eurocode 4 [1] not all relevant parameters are taken into account. Concrete dowels as alternative connection devices had been subject to an intensive research in Stuttgart already nearly 25 years ago [23]. But only now concrete dowels arouse a wider interest and are investigated by a number of groups in diverse countries. Thus, a thorough investigation of the fatigue behaviour has recently been undertaken
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[24], see Figure 9. In Japan concrete dowels are even applied in combination with corrugated webs for bridges [25].
Figure 9: Composite beam with concrete dowel [24] As an alternative to headed studs shear rib connectors of folded angles, of which one leg is embedded in the concrete, whereas the other is fastened to the beam by powder actuated fasteners, allow for a shear connection without welding [26]. Similar adapted to the special usage for composite columns with concrete filled tubes are nails which are shotfired from outside through the steel shell [27]. Besides the development of connectors and other devices the integration of these means in connections and the assembly of connections to joints have seen a rapid progress.
7
Composite Joints
In conventional steel structures the concrete slabs do not belong to the structural system. To avoid interaction the slabs are even separated by gaps from the column. With the spreading use of composite beams there is at least a longitudinal shear connection between slab and steel girder. But only if the gap around the column is closed and special reinforcement takes care for a systematic introduction of a normal force ∆N into the column, one speaks of a composite joint. Figure 10 gives an example of the Millenium Tower Vienna where these details have been realised even for composite slim-floor girders [28]. European recommendations [29], [30] have been developed to consider the influence of the slab reinforcement for the stiffness and resistance of such composite joints. The recommendations are based on the component method which has first been developed only for steel joints. A joint is considered as a set of individual basic components which are modelled as translational springs. The structural properties of the joints like stiffness and resistance are determined by assembly of the components characteristics. Thus most of the necessary tests can be made as component tests. Besides saving costs this procedure allows for a very flexible composition of various types of joints out of different components.
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tubular steel section Stahlrohr Träger steel girder
25
headed studs
Kopfbolzen
30
contact pieces Paßbleche bracket Knagge Stahlrohr
steel girder Träger headed studs Kopfbolzen
contact pieces Knagge Paßbleche bracket
Figure 10: Composite slim-floor joints of exterior columns in Millennium Tower Vienna [28] As a further step of the development these composite joints are integrated as semicontinuous joints in structural systems taking advantage also from plastic hinge theory. As the moment resistance of composite joints is in general lower than the beam bending resistance, the first plastic hinge is likely to form at the support within the joints. To exploit the real advantage of plastic hinge theory - which is especially interesting for composite structures because of the difference between the plastic moments of span and support - plastic rotation capacity is demanded also of the composite joints. This question is dealt at the moment in a number of research projects [29], [31].
8
High-strength materials
The use of high-strength materials allows a remarkable increase of the load-bearing capacities without increasing the dead load of the structure. For a composite beam, changing from a normal-strength steel S235 and a normal-strength concrete C30/37 to a highstrength steel S460 and a high strength concrete C70/85 means an increase of the plastic moment resistance of about 90 % for the sagging moment and of 70 % for the hogging moment region [32]. But some special considerations are needed to take advantage of this increase. The design regulations for beams and columns, especially those for practical application, are all based on the assumption of full plastic behaviour resulting in the model of a stress block diagram for the section. In reality the true stress-strain curves of steel and concrete lead to a different stress distribution. In general, this difference is neglected for normalstrength composite sections, whereas for high-strength materials it may lead to a reduction of the resistance which cannot be ignored anymore. For composite columns the steel strength and the buckling curve are based on Annex H of Eurocode 3 [33] dealing with the usage of steel grade S420 and S460. Due to the
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combination with concrete and taking account of the real stress-strain distribution Annex H of Eurocode 4 [1] gives reduction factors αN for the buckling factor κ and factors αM replacing the moment factor 0.9, see Table 2 according to [34]. As the material influence is of importance only for the low and medium slenderness range, the reduction factors depend on the reduced slenderness value λ . Examples as the Commerzbank Headquarters in Frankfurt/Main [7] show that the use of high-strength steel for the lower stories enables the designer to keep the same slender diameter for the composite columns over the whole building height. Table 2:
Reduction factors for composite columns for the use of high-strength steel, [34]
Cross-section
completely encased with concrete
partially encased with concrete
bending about strong axis bending about weak axis bending about strong axis bending about weak axis
concrete filled sections
Reducing factor of χ for pure compression α N ≤ 0,9
Replacement of 0.9 for compression and bending α M ≤ 0,9
0,1 ⋅ λ + 0,9
0,1 ⋅ λ + 0,8
0,2 ⋅ λ + 0,8
0,2 ⋅ λ + 0,7
0,1 ⋅ λ + 0,9
0,1 ⋅ λ + 0,8
0,2 ⋅ λ + 0,8
0,2 ⋅ λ + 0,7
0,1 ⋅ λ + 0,9
0,2 ⋅ λ + 0,7
Similar to composite columns, in Annex H of Eurocode 4 a moment reduction factor β has also been defined for the use of high-strength steel in composite beams. This factor has been reviewed within a comprehensive European research project and modified in order to take care also of the influence of high-strength concrete [32]. As an interesting observation it came out that the application of partial shear connection may lead to a higher bending resistance than the full shear connection if the strain restrictions of the concrete determine the resistance. This is due to the fact that the partial longitudinal shear connection has a balancing effect on the slip distribution, so that all studs can reach their ultimate resistance.
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9
Composite Bridges
Composite bridges used to be a field for experts, not only because bridges are submitted to special requirements of serviceability and durability, but also because designers had to be closely familiar with both materials steel and concrete, as for bridges the composite action of steel and concrete in general has to be calculated by elastic theory considering in detail all effects of creep and shrinkage. Meanwhile the singular position of composite bridges has changed: - As pointed out before, the increasing importance of serviceability criteria and the growing complexity of building structures as “ Mega columns” or composite frames with composite joints etc. nowadays also require a certain amount of sophistication for the structural design of buildings. - On the other hand the increasing use of composite bridges has driven forward the development of “simple systems” even for bridges which promise to see a vivid spread in future. So the borderline between buildings and bridges has started to vanish. Nevertheless bridge design still forms the origin of many interesting new trends, which may become a module for composite constructions in general. Therefore 3 examples for new tendencies are given in the following. Example 1: BW 1 near Ravensburg The first example concerns the development of so called “simple systems”. Supported by the Federal Ministry of Transport, a composite bridge system for small and medium spans of 25 to 45 m span lengths has been developed [35], which systematically makes use of precast concrete elements not only as lost falsework but also as part of the carrying concrete slab. A well defined reinforcement transfers the shear forces between precast and cast-in-situ concrete.
Figure 11: Steel girders and precast elements of a bridge structure near Ravensburg, Baden-Württemberg [36]
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The two small bridges shown in Figure 11 with a span length of only 28 meters are situated in the north of Ravensburg. The designer [36] has adapted the original design [35] by cutting the web of this simply supported girder system according to the shape of the bending moments. By such simple means the aesthetical outlook is improved. To allow the precast concrete deck to cantilever the headed studs on the external girders are welded in groups which are filled by the concrete cast in situ. As a special feature, these new composite girder systems are only stiffened by cross girders at the bearings. These cross girders made of concrete form a unity with the castin-situ part of the slab. End plates with horizontal studs transfer the shear forces from the steel girders into the concrete transverse girder. The transverse girders are only supported at two bearing points. The high amount of reinforcement is necessary because of the severe load introduction of shear forces and torsional moments, see Figure 11. These bridges form an example that by an optimum use of modern techniques of both materials, concrete and steel, very effective alternatives to standard bridge systems can be developed. The economy is mainly due to the advantages concerning the erection: So no scaffolding is needed and all elements which have a function during erection also assist in the final system. Example 2: Amperbrücke The following example should demonstrate that the consequent application of new design developments may also lead to new structural forms.
Figure 12: Amperbrücke [37]
Figure 13 shows the structural system and cross section of two composite tied-arch bridges with a span of 70.2 meters for the motorway A 96 across the Amper near Munich [37]. In standard composite tied-arch bridges [38] two main steel girder in the plane of the steel arches form the tension tie and equilibrate the compression force of the arch. At the same time they carry the transverse girders which form together with the concrete slab
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composite plate girders in transverse direction. The concrete slab acts in three structural subsystems - as deck for the direct wheel loading - as flange of the composite transverse girders - and as part of the tension tie of the arch system. Former tied-arch bridges had been designed to avoid or to reduce the contribution of the concrete slab as tension tie. For example the top steel flange of the transverse girder was tapered from the beginning of the slab towards the main girder. Thus, the horizontal connection between concrete slab and steel girder was weakened. Nevertheless, the participation of the concrete slab to the tension tie function could not be neglected. According to former design philosophy, the tension stresses in the concrete slab had to be surcharged by high prestressing by cables. Meanwhile concerning the prestressing of concrete slabs in composite constructions several developments have induced a general change of concept. Instead of longitudinal prestressing by cables the amount of simple reinforcement steel in the slab has been increased. As a consequence a controlled cracking of the concrete has been allowed. Besides economical advantages an increasing sensitivity for the importance of durability has led to a preference of simple reinforced slabs compared to slabs prestressed by cables. However, there are few examples of new tied-arch bridges which also try to adapt the cross section to the special needs of the new concept of simple reinforced slabs. So whereas the former design philosophy aimed at weakening the connection between main steel girder and concrete slab, the new concept requires a strong load transmission.
Figure 13: Structural system and cross section of Amperbrücke [37]
This idea is consequently realised by the system of the Amperbrücke [37]. There is no reason anymore to separate longitudinal steel girders and concrete slab: Instead of the two main girders aside of the concrete slab, three longitudinal steel girders underneath the slab act as composite plate girders in longitudinal direction. The deck is not spanned any longer between the transverse girders, but between the three longitudinal girders. The economical concept of a composite deck bridge has been combined with the system of a tied-arch bridge. By integrating steel and concrete into one single composite girder, a very close connection between concrete and steel member is attained. Rather than numerous transverse girders and hangers, there are only four strong girders and hangers transferring the loads
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from the deck system to the two arches. A considerable economical advantage is achieved by the obvious reduction of the number of structural members. The few points of crossing of transverse and main girders and the small number of joints of hangers to arches and girders contribute to this cost reduction. At the two bridge ends a strong bracing system connects the compressed arches to the tensioned deck. For the longitudinal girders as well as for the bracings, shear forces are transferred to the concrete slab by studs. The slab is not prestressed by cables, but only simply reinforced resulting in a considerable high amount of simple reinforcement. However, according to the new design philosophy the contribution of the concrete slab and its reinforcement to the tension tie function is no longer prevented but considered right on schedule. This example shows the mutual relationship between design and calculation philosophy and design concept. Considering criteria like safety, function, durability and economy may lead to new and even unconventional ideas. Example 3: Viaduct of Wilde Gera As an example of such new ideas some main features of the viaduct of Wilde Gera are explained in the following. As an alternative to a continuous deck bridge of 6 spans an arch bridge design was selected for the crossing of the deep valley of the Wilde Gera when constructing the new motorway A71 southwest of Ilmenau in Thüringen. Figure 14 shows the structural system and cross section according to [39], [40]. Besides of economical reasons the concept of a large arch bridge was chosen because of environmental and aesthetical advantages as it did nor require any foundations in the valley. The same reason has led to the choice of only one superstructure instead of two, which are normally constructed for motorways to be able to close one bridge for rehabilitation while the traffic is diverted to the second bridge. To allow also with one superstructure for a partial renewal of the concrete slab, the loading case of an opening of half of the deck for a length of 12 to 15 m, while the traffic is still running on the other half of the bridge section, had to be considered for the design of Wilde Gera and decisively determined the dimensions. The section consists of a composite hollow section with a trapezoidal steel trough and a simply reinforced concrete slab of multiple functions: - longitudinal compression and tension forces as part of the composite section - local bending stresses as a concrete deck spanned in transverse direction - transverse tension and bending stresses as part of the transverse girder and tension tie integrated in the transverse frame system. As can be seen in Figure 14 the transverse tension ties are formed by a reinforced concrete beam with a steel plate as external reinforcement. This may be considered as a kind of “slim-floor” section. The slab is supported by the two steel webs, two longitudinal composite girders at the cantilevers and a reinforced concrete beam in the middle. It is obvious that this unusual combination of concrete, steel and composite structural elements needed some special considerations, see [39].
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View
Cross section
Section B-B
Detail A
Figure 14: Structural system and cross section of Wilde Gera [39], [40]
This mixed section integrated into a mixed structural system of a concrete arch and a steel concrete composite bridge girder clearly demonstrates the need of strong collaboration of the concrete and the steel side. It is an example that the future requires engineers who do not only see themselves as “steel or concrete people”, but as structural engineers who dominantly try to find the best solution for a given problem. The University of
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Stuttgart has started a new educational program that tries to direct the new engineers to such a holistic view of conceptual design. It will hopefully enable them to develop new concepts of really mixed structures like the viaduct of Wilde Gera.
10 Summary and outlook For the fields of composite buildings and bridges a number of innovative developments have been pointed out. On this basis the attempt was made to highlight also some general tendencies and chances of composite structures in the future. Composite structures are especially qualified to satisfy basic modern requirements like - economy, - functional ability, - environmental and aesthetical needs and - durability. Fulfilling these requirements leads to new concepts of mixed structures and a new thinking of engineers as fair responsible partners regardless whether from concrete or steel side.
11 References [1]
[2] [3] [4] [5] [6] [7] [8]
[9]
[10]
ENV 1994-1-1, Eurocode 4: Design of composite steel and concrete structures Part 1.1: General rules and rules for buildings, 1992 DIN 18800-5, Stahlbauten Teil 5, Verbundtragwerke aus Stahl und Beton, Bemessung und Konstruktion, Draft, January 1999 G. Hanswille, R. Bergmann: Neue Verbundnorm E DIN 18800-5 mit Kommentar und Beispielen, Stahlbaukalender 2000, p. 288 - 461 ENV 1994-2, Eurocode 4: Design of composite steel and concrete structures – Part 2: Composite bridges, 1997 EDIN 1045 – 1, Tragwerke aus Beton, Stahlbeton und Spannbeton, Teil 1 Bemessung und Konstruktion, Draft, February 1997 J. Lindner, R. Bergmann: Zur Bemessung von Verbundstützen nach DIN 18800 Teil 5, Stahlbau 67, July 1998 W. Ladberg: Commerzbank - Hochhaus Frankfurt/Main, Planung, Fertigung und Montage der Stahlkonstruktion, Der Stahlbau 65, October 1996 R.T. Leon: Measurements on a large composite column during construction, Theorie und Praxis im Konstruktiven Ingenieurbau, Festschrift Bode, edited by W. Ramm, T. Däuwel, H.-J. Kronenberger, ibidem - Verlag, Stuttgart 2000, pp 237 – 259 G. Hanswille: Outstanding composite structures for buildings, Conference report, Composite Construction – Conventional and Innovative, IABSE – Conference, Innsbruck, September 1997, pp. 41 - 52 G. Hanswille: Bemessung von Verbundträgern nach EC 4, Proceedings of Verbundbau, Fachseminar und Workshop, FH München and Bauen mit Stahl e.V., Munich, November 1997
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[11]
[12]
[13]
[14] [15]
[16]
[17]
[18]
[19] [20]
[21]
[22]
[23]
[24]
H. Bode, T. Däuwel: Steel-concrete composite slabs - Design based on partial connection, Proceedings of Steel and composite structures, International conference, Delft, February 1999 R.G. Schuurman, J.W.B. Stark: Longitudinal shear resistance of composite slabs - A new model, Proceedings of Composite Construction IV, Engineering Foundation Conference, Banff, Alberta, Canada, May/June 2000 M. Patrick, R.Q. Bridge: Composite floors in Australian building practice, Theorie und Praxis im Konstruktiven Ingenieurbau, Festschrift Bode, edited by W. Ramm, T. Däuwel, H.-J. Kronenberger, ibidem - Verlag, Stuttgart 2000, pp. 261 - 272 H. Bode, I. Sauerborn: Zur Berechnung durchlaufender Verbunddecken, Stahlbau 66, July 1997 T. Winterstetter, H. Schmidt, A. Ross: Numerische Untersuchungen zum nichtlinearen Tragverhalten von Hoesch-Additivdecken, Theorie und Praxis im Konstruktiven Ingenieurbau, Festschrift Bode, edited by W. Ramm, T. Däuwel, H.J. Kronenberger, ibidem - Verlag, Stuttgart 2000, pp. 297 - 304 R.M. Lawson: Developments in ´Slimdek´ Constructions, Theorie und Praxis im Konstruktiven Ingenieurbau, Festschrift Bode, edited by W. Ramm, T. Däuwel, H.-J. Kronenberger, ibidem - Verlag, Stuttgart 2000, p. 213 - 224 U. Kuhlmann, J. Fries, A. Rieg: Composite girders of reduced height, Proceedings of 55th Rilem annual week: Connections between steel and concrete, Stuttgart, September 2001 K. Kürschner: Trag- und Verformungsverhalten von teilweise verdübelten Verbundträgern, Internal report, Institut für Konstruktion und Entwurf I, University of Stuttgart, June 1998 M.A. Dabaon: Beitrag zur teilweisen Verdübelung bei Verbundträgern, Dissertation, University of Innsbruck, 1993 U. Kuhlmann, U. Breuninger: Behaviour of lying studs with longitudinal shear force, Proceedings of Composite Construction IV, Engineering Foundation Conference, Banff, Alberta, Canada, May/June 2000 M. Mensinger: Zum Ermüdungsverhalten von Kopfbolzendübeln im Verbundbau, Dissertation, University of Kaiserslautern, Chair for steel structures of Prof. Bode, 1999 R.P. Johnson: Shear connection – Three recent studies, Proceedings of Composite Construction IV, Engineering Foundation Conference, Banff, Alberta, Canada, May/June 2000 F. Leonhardt, W. Andrä, H.-P. Andrä, W. Harre: Neues, vorteilhaftes Verbundmittel für Stahlverbund-Tragwerke mit hoher Dauerfestigkeit, Beton- und Stahlbetonbau 1987, pp. 325-331 I. Mangerig, C. Zapfe: Ermüdungsfestigkeit von Betondübeln, Theorie und Praxis im Konstruktiven Ingenieurbau, Festschrift Bode, edited by W. Ramm, T. Däuwel, H.-J. Kronenberger, ibidem - Verlag, Stuttgart 2000, pp. 337 – 360
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[25]
[26]
[27] [28]
[29]
[30] [31]
[32]
[33] [34] [35] [36]
[37] [38]
[39] [40]
Tategami, H., Ebina, T., Uehira, K., Sonoda, K.: Shear connectors in PC box girders bridge with corrugated steel webs, Proceedings of Composite Construction IV, Engineering Foundation Conference, Banff, Alberta, Canada, May/June 2000 M. Fontana, H. Beck: Novel shear rib connectors with powder actuated fasteners, Proceedings of Composite Construction IV, Engineering Foundation Conference, Banff, Alberta, Canada, May/June 2000 H. Beck: Nailed shear connection in composite tube columns, Conference Report, Eurosteel ´99, Prague, pp. 565 – 568 F. Tschmmernegg: To the development of composite and mixed connections, Proceedings of Steel and composite structures, International conference, Delft, February 1999 D. Anderson: European recommendations for the design of composite joints, Theorie und Praxis im Konstruktiven Ingenieurbau, Festschrift Bode, edited by W. Ramm, T. Däuwel, H.-J. Kronenberger, ibidem - Verlag, Stuttgart 2000, pp. 457 – 464 ECCS: Design of composite joints for buildings, ECCS Document 109, 1999, Brussels U. Kuhlmann, M. Schäfer: Innovative verschiebliche Verbundrahmen mit teiltragfähigen Verbundknoten, Research project P505, Studiengesellschaft Stahlanwendung e. V., Düsseldorf J. Hegger, P. Döinghaus: High performance steel and high performance concrete in composite structures, Proceedings of Composite Construction IV, Engineering Foundation Conference, Banff, Alberta, Canada, May/June 2000 ENV 1993-1-1, Eurocode 3: Design of composite steel structures – Part 1-1: General rules and rules for buildings, 1991 R. Bergmann: Steel concrete composite beams and columns, Proceedings of Steel and composite structures, International conference, Delft, February 1999 H. Schmackpfeffer: Typenentwürfe für Brücken in Stahlverbundbauweise im mittleren Spannweitenbereich, Stahlbau 68, April,1999 Straßenbauverwaltung Baden-Württemberg, Regierungspräsidium Tübingen: BW1 Feldwegunterführung, Straßenkl. u. Nr. B30, OU. Ravensburg, Design Rittich, Bornscheuer u. Partner GmbH, Stuttgart M. Hagedorn, U. Kuhlmann, H. Pfisterer, J. Weber: Eine Neuentwicklung im Stabbogenverbundbrückenbau - Die Amperbrücke - , Stahlbau 66, July 1997 U. Kuhlmann: Design, calculation and details of tied-arch bridges in composite constructions, Proceedings of Composite Construction III, Engineering Foundation Conference, Irsee, Germany, June 1996, published by ASCE 1997 G. Denzer, W. Gräßlin, G. Hanswille, W. Schmidtmann: Die Talbrücke über die Wilde Gera, Stahlbau 69, November 2000 R. Wölfel: Talbrücke über die Wilde Gera, Beton- und Stahlbetonbau 94, December 1999
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DESIGN OF LYING STUDS WITH LONGITUDINAL SHEAR FORCE Ulrich Breuninger Structural Engineers Weischede, Herrmann und Partner, Germany
Abstract Innovative composite cross sections lead to an unusual positioning of the headed studs horizontally in the thin concrete slab. The behavior of this lying studs with longitudinal shear force has been investigated. The results of experimental and numerical investigations show that the failure characterized by splitting of the thin slab is influenced by different parameters compared to vertically positioned studs. Based on the investigations a design rule is presented.
1. Introduction Composite sections of steel and concrete have a continuous connection between both parts. In standard composite beams headed studs are welded vertical on the top flange of the steel girder as shear connector.
Fig. 1 Composite beam without top steel flange
Fig. 2 Slim-floor composite beam (1)
The development of innovative composite cross sections for bridges and buildings leads to modified and new sections of composite beams. The section of Fig. 1, for example, eliminates the less efficient steel top flange by welding the headed studs directly to the web. For the final usage the concrete slabs serves as top flange. During erection
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sufficient resistance is provided by the precasted concrete web. As a second example Fig. 2 shows a slim-floor structure. Again the function of the omitted top steel flange is taken over by the concrete slab. The horizontally lying studs allow a very thin slab which is an advantage also from the architectural point of view. A strong load transmission between arch and slab for tied arch bridges is achieved by connecting the slab directly to the stiffening girder, see Fig. 3. Again studs are positioned horizontally in the slab. Additional advantages of this construction are a better corrosion protection of the transverse girders and the transverse girder acting as composite beam in its entire length.
Fig. 3 Section of a tied arch bridge with lying studs connecting the slab to the stiffening steel girder (2) In contrast to the standard composite beam section the axis of the studs in the sections of Fig. 1, 2 and 3 is not vertical anymore but parallel to the plane of the slab. Therefore studs arranged this way are called “lying studs”. cleavage cracks compression
Fig. 4 Section through the shear connection of lying studs The shear connection of composite beams is dominantly subjected to a longitudinal shear force. So every lying stud mainly has to transfer a longitudinal shear load into the slab. The concentrated shear load of the stud has to spread across the thickness of the slab thus initiating compression and tension forces vertical to the extension of the slab (Fig. 4). The tensile forces result in both a splitting action of the thin slab producing cleavage
1016
cracks parallel to the plate surface and an expansion of the concrete. The failure of these lying studs is mainly due to the splitting of the concrete. Vertical stirrups surround the expanding concrete and prevent the extension of the cracks. The design rule for headed studs in Eurocode 4 (3) is based on experimental investigations for conventional vertical studs only and therefore it does not cover the splitting failure of lying studs. To identify the major parameters for this special mode of failure and to quantify the carrying capacity of lying studs, a comprehensive research program has been carried out(4) (5) (6). In this paper the results are presented. In design practice the shear connection also can be used to transfer transverse shear load from the slab into the steel girder. The content of a prosecuted research program is presented in the next paper (7).
2. Experimental investigations
A
800
500
A
80-130
Two different situations of the shear connection with lying studs relative to the concrete slab can be distinguished. In composite girders without a top flange e.g., see Fig. 1 and 2, the shear connection is situated in the middle of the concrete slab, whereas the example of the tied arch bridge of Fig. 3 shows lying studs at the front side of the concrete slab. Therefore two test series were carried out: series I with the shear connection in the middle of the concrete slab corresponding to sections in buildings and series II with the connection at the two edges of the concrete slab corresponding to bridge sections, see Fig. 5 and 6.
lineare measure in mm
Section A-A
Fig. 5 Test specimen of series I with the shear connection in the middle of the concrete plate
1017
132
A
studs in one row 300-400
A
800
200
400
studs in two rows
100
1190
100
300
132
lineare measure in mm
Section A-A
Fig. 6 Test specimen of series II with the shear connection at the edges of the concrete slab These two series comprising altogether 51 push-out specimens were designed as variations of a so called basic sample. For a group of at least 3 specimens always only one main parameter was varied whereas the other parameters were kept constant. The following parameters were varied: · strength of concrete · thickness of concrete slab · distance, diameter and length of the studs · number, diameter and situation of the stirrups · tension or compression parallel to the shear force According to Figure 7 three failure modes were observed in the tests: a) splitting of the slab, tear off of the studs
If the reinforcement of the concrete is sufficiently strong, the carrying capacity is not reduced immediately after splitting and the lying studs suffer high deformations until finally the studs tear off.
b) splitting of the slab
For low degrees of reinforcement or small distances between stud and slab surface, the carrying capacity of the shear connection starts reducing just after the splitting of the slab has first occurred.
c) pull out of the studs
In some rare cases, when the lying studs were situated at the edge of the slab and the studs were too short, the shear connection failed because of a pull-out of the studs.
1018
a) Splitting of the plate/tear off of the studs
b) Splitting of the plate c) Pull-out of the studs
Fig. 7 Failure modes of lying studs load per stud [kN] 200 Splitting of the slab, tear off of the studs 150 Splitting of the slab 100
50 Pull out of the studs 0 0
5
10
15
20
25
30 slip [mm]
Fig. 8 Load-slip curves of different failure modes. Typical load-slip curves of these three failure modes are given in Figure 8. If lying studs fail according to mode a) or b) the load slip curve shows a high carrying capacity a
1019
ductile deformation behavior beyond. If the failure is caused by pull-out of the studs (mode c), the carrying capacity decreases and the ductility is limited.
3. Variation of the parameters Beside the experiments numerous numerical investigation were carried out. A non-linear FE program considering the size effect of concrete structures was used (8). Based on the experimental and numerical investigations the influence of the parameters on the carrying capacity can be determined Concrete strength The splitting of the slab depending on the concrete tensile strength causes the collapse of the shear connection. Because of the well known relation between tensile and compressive strength the carrying capacity can be described with an exponent function of the concrete compressive strength that is more usual (Fig. 9). Pe [kN] 180
P/Pv [-] 1.2
150
1.1
0.4
K (ar´/80mm)
120
1.0
90 0.9
Test series I-1 Test series I-2 Test series II-2 FE
2 0.4
60
K (fc/30N/mm )
Test series I-6
30
Test series II-1 0 0
Fig. 9
10
20
30
0.8 0.7 20
40 2 fc [N/mm ]
Carrying capacity Pe of lying studs dependent on the concrete compressive strength fc
40
60
80
100 120 140 160 180 ar´ [mm]
Fig. 10 Relative carrying capacity P/Pv of lying studs dependent on the effective edge distance of the studs ar´ (for different distances between the studs a)
Edge distance of the studs The carrying capacity depends strong on the effective edge distance of the studs (ar´ = the edge distance of the studs without the concrete cover and a half of the stirrup diameter) (Fig.10). The influence is big if the edge distance is small. With increasing edge distance (more than 100mm) the influence on the carrying capacity disappears. Also Fig. 11 shows with different FE models the strong influence of the edge distance on the cleavage cracks in the structure.
1020
x
deformation direction
ar´ = 30 mm
ar´ = 75 mm
ar´ = 120 mm Fig. 11 Cleavage cracks following main strains at maximum carrying capacity (black areas show a strain ≥ 5 ‰) Reinforcement of the slab Fig. 11 shows the importance of the reinforcement in the slab. The stirrups and especially the intersection between stirrups and longitudinal reinforcement is used as anchoring for the cracks. It can be concluded, that the carrying capacity increases with the amount of stirrups per stud because this leads to more anchoring points. The effect of stirrups with a greater diameter on the carrying capacity can be neglected. The longitudinal distance between the studs and the stirrups has no decisive influence on the carrying capacity. The support of the stirrups for the shear connection is still intact. This means that assembling inaccuracies are of less importance. A minimum reinforcement is necessary for the cleavage tensile forces. According to (9) and to the magnitude of strains in the stirrups of the specimens, the reinforcement should be dimensioned for the splitting force Zd d Z d = Pd 0.3 (1 ) [1] a r´ Where Pd is the longitudinal shear design force.
1021
Length of the studs If the studs are not long enough a premature pull-out failure occurs (compare Fig. 7c). This phenomena is explained very well in (10). To prevent this brittle failure the studs have to be anchored with an overlapping v behind the stirrups. The overlapping depends if the concrete is cracked or not. uncracked concrete: > ≤ 30° v ≥ 110 mm; v ≥ 1.7 ar´; v ≥ 1.7 s/2 cracked concrete: > ≤ 23° v ≥ 160 mm; v ≥ 2.4 ar´; v ≥ 2.4 s/2 [2] Further parameters Although not shown by data presented here the following additional conclusions follow from the investigations: · An increase of the diameter d of the stud leads to a higher carrying capacity of the shear connection. · If the distance a between the studs and the distance s between the stirrups increases by the same amount the carrying capacity stays on the same level. · For a concrete slab in tension, e.g. the slab of the tied arch bridges the carrying capacity of the lying stud is insignificantly lower than for the slab in compression.
4. Design rule Derived from the experimental (4), (5) and numerical (6) investigations the following design rule for the carrying capacity of lying studs with failure because of cleavage cracks is proposed. 0.3
1 æaö PRd,sp = 1.42 (f ck × d × a r ´) 0.4 ç ÷ A [3] gv èsø design resistance [kN] (index sp from german spalten) PRd,sp compressive strength of the concrete [N/mm2] fck 19 mm ≤ d ≤ 25 mm diameter of stud [mm] distance between studs and stirrups vertical to the force 50 mm ≤ ar´ [mm] 110 mm ≤ a ≤ 440 mm distance between studs parallel to the force [mm] distance between stirrups / distance between studs and s/ar´ ≤ 3 stirrups a/2 ≤ s ≤ a distance between stirrups [mm] A = 1.00 modification factor if the shear connection is situated at the edge of the slab = 1.14 modification factor if the shear connection is situated in the middle of the slab stirrup diameter [mm] ds ≥ 8 mm Cv = 1.25 partial safety factor according to Eurocode 4 (3)
1022
h d concrete cover + s 2
v
headroom of the stud
d
a
ds
ß
a'r
ar
concrete cover +
s
ds 2
section A-A
Fig. 12 Designation of the geometrical parameters of the shear connection with lying studs Formula [3] can be used under the following conditions: · The stirrups are able to bear the splitting forces according to formula [1]. · The overlapping v of the studs fulfils formula [2]. · The above limited parameters are checked. · The carrying capacity for standard studs in Eurocode 4 (3) is not exceeded. Fig. 13 compares the carrying capacity of lying studs with standard studs according to Eurocode (3) for one diameter. PRd [kN] 150 d = 22 mm
PRd [kN] 150 d = 22 mm 2
2
fuk = 500 N/mm a/s = 1 A = 1.14
120
90
90
60
60 Eurocode 4 (3) Formula [3] with ar´ = 90 mm Formula [3] with ar´ = 70 mm Formula [3] with ar´ = 50 mm
30
fuk = 500 N/mm a/s = 1 A = 1.00
120
0
Eurocode 4 (3) Formula [3] with ar´ = 130 mm Formula [3] with ar´ = 110 mm Formula [3] with ar´ = 90 mm Formula [3] with ar´ = 70 mm Formula [3] with ar´ = 50 mm
30
0 15
20
25
30
35
40
45 50 2 fck [N/mm ]
a) shear connection in the middle of the concrete plate
15
20
25
30
35
40
45 50 2 fck [N/mm ]
b) shear connection at the front side of the concrete plate
Fig. 13 Design resistance of lying studs compared to studs in standard composite sections
1023
5. Conclusion Stimulated from new composite cross sections and with the aim to support the development of further new composite constructions the carrying behavior of lying studs is investigated. First efforts are carried out to describe the carrying behaviour of lying studs for longitudinal shear. They lead to a practical design equation. Following investigations will study lying studs under vertical and combined shear force and as well as fatigue. At the moment the ”Institut für Konstruktion und Entwurf” of the University of Stuttgart is continuing the work in this field of research. I would like to thank the “Bundesministerium für Verkehr” and the “Deutsches Institut für Bautechnik” for their support. They sponsored the experimental and numerical research.
6. References 1 Muess, H. (1996); ”Interessante Tragwerkslösungen im Verbund”; Stahlbau 65/10. S. 349; Verlag Ernst & Sohn; Berlin. 2 Kuhlmann, U. (1996): “Design, Calculation and Details of Tied-Arch Bridges in Composite Construction”; Composite Construction in Steel and Concrete III, Proceedings of an Engineering Foundation Conference in Irsee, Germany, p. 359, published by ASCE 1997. 3 Eurocode 4 (1994): “Bemessung und Konstruktion von Verbundtragwerken aus Stahl und Beton, Teil 1-1: Allgemeine Bemessungsregeln und Bemessungsregeln für den Hochbau“; Comité Européen de Normalisation. 4 Kuhlmann, U.; Breuninger, U. (1999): “Liegende Kopfbolzendübel unter Längsschub im Brückenbau“; Forschungsbericht; Bundesministerium für Verkehr; Bonn-Bad Godesberg. 5 Kuhlmann, U.; Breuninger, U. (1999): “Liegende Kopfbolzendübel unter Längsschub im Hochbau“; Forschungsbericht; Deutsches Institut für Bautechnik; Berlin. 6 Breuninger, U. (Feb. 2000): ”Zum Tragverhalten von liegenden Kopfbolzendübeln unter Längsschubbeanspruchung”; Dissertation, Institut für Konstruktion und Entwurf I; Universität Stuttgart. 7 Kuhlmann, U.; Kürschner, K. (2001): “Behaviour of Lying Shear Studs in Reinforced Concrete Slabs”; Symposium on Connections between Steel and Concrete, 55th Rilem Annual Week in Stuttgart, Germany. 8 Ožbolt, J.; Li, Y.; Kožar, I. (1999): “Mixed constrained microplane model for concrete“; to publish in: International Journal of Solids and Structures. 9 Leonhardt, F. (1962): “Spannbeton für die Praxis“; Verlag Ernst & Sohn; Berlin. 10 Eligehausen, R.; Mallee, R.; Rehm, G. (1997): “Befestigungstechnik“ in: Betonkalender Teil II; S. 609; Verlag Ernst & Sohn; Berlin.
1024
STUDIES ON THE DUCTILITY OF SHEAR CONNECTORS WHEN USING HIGH-STRENGTH STEEL AND HIGH-STRENGTH CONCRETE Josef Hegger*, Gerhard Sedlacek **, Peter Döinghaus*, Heiko Trumpf** *Institute for Structural Concrete, Aachen Technical University, Germany **Institute for Steel Construction, Aachen Technical University, Germany
Abstract Both the strength of the steel used in steel constructions and that of the reinforced concrete in the concrete constructions have increased considerably in recent years (e.g. steel S460 and concrete grades C60 to C90). Making meaningful use of such considerable increases in the material strength in composite constructions requires testing the shearresistant connection in the composite joint between the steel and the concrete construction members. This article summarises the knowledge from the research project “Studies on the ductility of shear connectors when using high-strength steel and high-strength concrete” gathered within the scope of the support from AiF and provides explanatory notes on the proposals developed from the findings here for construction and design. The purpose of the series of experiments conducted was to determine the load-bearing capacity as well as the ductility of the headed stud shear connectors commonly used in high-strength concrete and to develop new shear connectors of sufficient ductility, whereby a check was also made here of the applicability of the method of evaluation used up to now for the Push-Out tests carried out according to the Eurocode 4 procedure. Recommendations have also been developed for better characterisation of the load-bearing behaviour of shear connectors.
1025
1.
Status of the research project and summary of results
Initial pilot studies into the use of high-strength steel and of high-strength concrete in composite constructions were carried out as part of the coal and steel research project (ECSC) Use of High Strength Steel S460 [1] funded by the European Union. Besides questions regarding the flexural load-bearing capacity, the behaviour of the composite joint was investigated in 18 Push-Out tests performed on headed stud shear connectors in high-strength concrete.
50
Frontal View 200
∅ 10
High Strength Concrete
∅ 10
50
200
Normal Strength Concrete Displacement
600
250
Load
Side View
150
240
110
Cross Section
150
15
15
100 150
600
100
240
150
150
∅ 10
∅ 10 150 180 200
180 200
180 200
240
150 [mm]
Figure 1: Push-Out standard test specimen and typical load-deformation curves for headed stud shear connectors in different types of concrete.
1026
This showed that the ductility criterion according to Eurocode 4 [2] – the characteristic value of the deformation capacity δuk must be at least 6 mm – was not fulfilled by any of the connector diameters which were tested (Fig. 1). On the other hand, the load-bearing capacity of the headed stud shear connector in high-strength concrete is grossly underestimated by the EC 4 method of calculation. The applicability of high-strength concrete to the design rules given in EC 4 for full and partial shear connection is therefore questionable as a result of this. Within the scope of the research project here, the headed stud shear connectors were first modified in order to obtain a more ductile behaviour by the composite joint before designing and investigating alternative connectors appearing more favourable for use in high-strength concrete. So as to be able to test a large number of different connectors, a shearing test was developed at the Institute for Structural Concrete which made a quick check possible of just one shear stud. It was possible by applying this test to recognise favourites. These were then checked by the standardised Push-Out test per EC 4. The principle differentiation was made here between single (e.g. headed stud shear connector, T-profiles) and continuous connections (e.g. combined fixing strip, T-bulb fixing strip). An explanation of the selected headed stud shear connectors and alternative connectors is given in this article in terms of the load-bearing capacity and the ductility by using load-deformation curves. The applicability of the evaluation method according to EC 4 to determine the load-bearing capacity and ductility is also reviewed. A load-bearing model for headed stud shear connectors in high-strength concrete could be developed from the experiments which were conducted. This model differs from the earlier model for connections in standard-strength concrete, and is principally suitable both for standard-strength as well as for high-strength types of concrete. The applicability of the connector characteristics to composite girders could be verified by numerical studies. Possible approaches for improving the evaluation method according to EC 4 have been worked out from the results. Only an excerpt of the results can be presented in this article; it is for this reason that reference is made to the research project report [3].
2.
Test set-up for shearing tests
2.1
The Push-Out Standard Test (POST)
The Push-Out Standard Test (POST) according to EC 4 simulates transfer of the shearing forces in the composite joint of composite girders. The dimensioning of these test specimens is matched to standard-strength concrete. By using the higher concrete-quality grades and the thereby associated reduction of the load propagation zone, the magnitude of
1027
this test specimen is no longer necessary for preventing premature failing of the concrete yet for reasons of comparability, the Push-Out Standard Test is also used where highstrength concrete is concerned. The statics of this system are not optimal. During the experiments, the steel girder shall be displaced relative to both of the reinforced-concrete belts such that the shear connectors undergo stress of the purely shearing type. Horizontal forces cannot however be avoided between the three construction members in the practical execution of the experiment. The load-bearing capacity of the connection which can be attained is however reduced by this. The test specimen was modified slightly for the Push-Out tests with the fixing strips, and was subsequently adapted to the specific requirements of the fixing strips in the highstrength concrete. The dimensions of the test specimen were determined by a truss model for the load transfer using a compression-strut angle of α=45 degrees. The reinforcement required for the horizontal tensile struts in the lower area of the test specimen was determined from the load-bearing capacity estimated for the fixing strips.
2.2
The Single Push-Out Test (SPOT)
In order to obtain the characteristic curve for a single connector, a new shearing test was developed where a single connector can be tested individually (SPOT). A test specimen had to be found where the structural stability of which is not attributable to the symmetrical construction and where the straining lines of the forces causing the shear are almost identical. Since the result of the connector’s lateral force during shearing does not however remain at a constant level, the experimental set-up should be capable of tracking such changes without loosing its stable state of equilibrium. A shoe enveloping the reinforced concrete was chosen as the solution (Fig. 2). Two additionally attached stirrups created a moment to oppose the moment from the machine’s forces (M = 0.055 m ⋅ F; 0.055 m: distance between the straining lines). This neutralising moment adapts to every load level. Even a shift in the resulting shearing force (perpendicular to the shaft of the connector) is accepted by the system without any kinematic reaction. A slight twist of the steel half-shell relative to the reinforced concrete is to be expected during the experiment. The upper stirrup of the shoe does however constitute a restriction at the same time in the horizontal path for the top edge of the steel plates. As soon as twisting has set in, the tensioned-steel nuts impact on the stirrup and form a vertical sliding bearing. As the detachment process progresses, the plate turns back to a parallel position. A falsifying influence on the load-bearing behaviour could not be seen in the series of experiments conducted. This test specimen is straightforward to fabricate, can be inserted in the tester by a single person and can be tested in a smaller hydraulic press than the test specimen for the Push-Out Standard Test. It is particularly suitable for high-strength concrete because of the limited volume of concrete. A comparison of the results from the experiments with
1028
the 18 Push-Out standard experiments and the 6 single Push-Out experiments with headed stud shear connectors with a connector diameter of 19, 22 and 25 mm respectively showed that because of the better static load transfer in the Single Push-Out Test, a generally higher carry load of between 10% and 20% is reached compared to the Push-Out Standard Test.
F 3
F
Tendons ∅ 16
3 15
Nuts Retaining Stirrup
Felt 5
0,172 F
10
33
15
Steelpanels 5 10 32
F
20
0,172 F
5
20 5
Felt F
5,5
Stirrup Tendons ∅ 16
F
F
[cm]
Figure 2: Side view of the Single Push-Out Test showing the forces which are acting.
3.
Load-bearing behaviour of headed stud shear connectors in highstrength concrete
A description of the load-bearing and deformation behaviour of headed stud shear connectors in standard-strength concrete is given by Lungershausen [4] by the four loadbearing portions of concrete compression strut force before the weld collar, bending and shearing load-bearing capacity in the lower area of the connector shaft, tensile force in the connector shaft as well as friction forces in the composite joint. There is almost no load-bearing portion for connectors in high-strength concrete from the tensile force because the bending deformation of the connector shaft due to the clamping effects of the high-strength concrete is only low here. Friction forces do occur not in the form described by Lungershausen either in standard-strength or in high-strength concrete.
1029
Beginning of Testing
a
Concrete Wedge in front of Weld Collar
b
Concrete moves relatively to the Weld Collar
Plastic Zones, Stud Failure
c
d
Figure 3: Failure mechanism for a stud shear connector in high-strength concrete. Fig. 3 shows the stages of deformation for a stud shear connector in high-strength concrete. Compression forces in the concrete develop directly in front of the weld collar (a). Increasing the load causes this force to concentrate within a compressive wedge (b). Deformation of the connector only takes place in area of the bolt weld. The highstrength concrete ensures the connector is rigidly held above this deformation zone. If the load is increased further, then the compression wedge plasticizes and the remainder of the concrete body moves away over this wedge (c). The force from the connector is still transferred over the concrete wedge and base of the connector since there are high friction forces acting in the joint between the wedge and the concrete body. These deformations lead to plasticization of the connector in the region of the base (d). Friction can not occur in the joint between concrete and steel. The external forces acting on the connector are shown in greater detail in Fig. 4 in order to illustrate the deformation behaviour. Load-Distribution at non-deformed stud
Load-Distribution at deformed stud
Reaction to Uplifting Force Concrete Front
Concrete Back
Steel
pplast
Steel Force in Concrete Cavity Wedge
Figure 4: Load distribution and deformation of the connector shaft.
1030
Cavity
Uplifting Force
4.
Experiments with shear connectors in high-strength concrete
4.1
Overview of all experiments conducted
The experimental programme was based on the following considerations: for a good serviceability of the composite girders, the range for using the load-deformation curve of the connector should be associated with a range where the slip is low. A subsequent horizontal plastic plateau or a further increase in the load indicate good and stable behaviour. Plastic rearrangement, and hence economical utilisation of the connectors in the load-bearing range, is made possible by this. Before carrying out the experiments, the basic load-bearing behaviour of the differing connector types in the high-strength concrete (fck,cube,150mm = 90 – 95 N/mm² compressive strength) was estimated. Because of the time constraints, it was unfortunately not possible to implement all the conclusions theoretically possible, e.g. the very promising increase in size of the weld collar that would be possible by using newly developed ceramic rings, adaptation of the welding parameters, etc.. Headed stud connectors of 19, 22 and 25 mm diameter without any modifications were used in the first test series. These were investigated by means of the Push-Out Standard Test and the Single Push-Out Test. Also, the first series of experiments included testing the following modifications made to headed stud shear connectors (Fig. 5): Grouping in the direction of the shearing force (double connector), Cushioning the shaft of headed stud shear connectors (two cushion variants), Elliptical shaft cross-section, Slanted headed stud shear connector (inclined at an angle of 45 degrees).
HighStrenth
Figure 5: Modifications to headed stud shear connectors. The following alternative connector types were also considered (Fig. 6):
Combined fixing strip (round recess), T-bulb fixing strip (bead-type cross-section with rectangular recess), T-shape profile (with and without cushioning), High-strength bolts (M20 8.8 HV as removable connector).
For the second series of experiments, the favourites from the series of experiments were optimised from the design and additional connector types were included in the experimental programme:
1031
T-profiles of different degrees of inclinations (HEB and IPE, 30° and 45°), Various types of cushioning, sleeves and metal rings around the shaft of the headed stud shear connector, High-strength headed stud shear connector (base material S355 J2 G3), Headed stud shear connector with profiled sheet (through-welded technique).
Figure 6: Alternative connectors. The results from the first and second series of experiments are summarised in Tables 1 and 2. The most important of these are presented in greater detail in the following. series
format
type
modification
PRk
δuk
[kN]
[mm]
evaluat.
PRd [kN]
evaluat.
1
POST
KBD 19
none
125,8
4,51
-
100,7
+
2
POST
KBD 22
none
171,8
4,89
-
137,4
+
3
POST
KBD 25
none
203,4
5,98
-
162,7
+
9
SPOT
KBD 19
none
151,3
4,19
-
121,1
+
10
SPOT
KBD 22
none
211,9
7,31
++
169,5
+
11
POST
KBD 19
none
139,7
5,68
-
111,8
+
12
POST
KBD 22
none
189,8
6,71
+
151,9
+
13
POST
KBD 25
none
189,8
7,62
++
151,8
+
14
POST
KBD 19
Double stud
132,2
7,42
++
105,8
+
15
POST
T-IPE180
none
227,4
14,85
++
181,9
-
16
POST
T-IPE200
Web cushion
240,8
12,47
++
192,6
-
19
POST
SV
none
135,3
5,80
-
108,3
O O
20
SPOT
KBD 19
Cushion (1)
136,5
8,04
++
109,2
21
SPOT
KBD 19
Cushion (2)
154,1
7,07
++
123,3
+
22
SPOT
KBD 22
Cushion (1)
226,5
10,92
++
181,3
++
23
SPOT
KBD 22
Inclined
215,2
5,22
-
172,2
+
24
SPOT
KBD 22
Elliptical
189,2
5,17
-
151,4
-
30
POST
con.-strip
w-o/w reinf.
858,8
11/20
+
344/603
+
31
POST
T-Bulb
w-o/w reinf.
995,3
32/22
++
398/593
++
Table 1: Results from the first series of experiments.
1032
series
format
type
modification
PRk
δuk
[kN]
[mm]
PRd
evaluat.
evaluat.
[kN]
17
POST
T-IPE200
45° inclined
399,8
8,82
++
319,8
++
18
POST
T-IPE200
30° inclined
313,6
15,38
++
250,9
+
25
SPOT
KBD 22
none
194,7
5,55
-
155,7
-
26
POST
THEB200
45° inclined
484,3
8,17
++
387,4
++
27
POST
KBD 19
Double stud
124,7
5,95
-
99,7
O
28
SPOT
KBD 19
Cushion (3)
133,7
8,15
++
107,0
O
29
SPOT
KBD 19
Metal ring
153,7
6,52
+
128,7
+
32
POST
KBD 19
Metal sleeve
149,3
7,11
++
119,5
+
33
SPOT
KBD 19
Metal sleeve
152,8
6,30
+
122,2
+
34
POST
KBD 19
High-strength
159,1
3,62
-
127,3
O
35
SPOT
KBD 19
High-strength
172,4
2,71
-
137,9
O
36
POST
KBD 22
Profiled sheet
116,1
3,46
-
92,9
-
Table 2: Results from the second series of experiments.
4.2
Double connector
Increasing the ductility is aimed for by using two headed stud shear connectors welded very close together, whereby a decrease in the load-bearing capacity is accepted (Fig. 7). The resistance of two headed studs connected in series is sufficiently high that the concrete compression zone plasticizes in front of the first connector such that there is displacement taking place. The first connector creates an area behind its base where the compression strains are lower so that the deformation to the following connector is lower. Frontal View
240
150
150
∅ 10 150
150
80
100 150
40 130 50
50 180 40 210
Detail
150
Detail
Side View
180
180
180
Figure 7: Arrangement of the double connector, ∅ 19 mm.
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40
Although the connector slip is the same, the distortions of the second connector are distributed over a greater height. This leads to a better upwards redistribution of the forces along the shaft and hence to further relative displacement. The wedge in front of the weld collar taking up about 20% of the ultimate load can only develop to a limited extent for the second connector. With this solution, the spacing between connectors is less than the minimum given in EC 4. This means there is a deviation from the rules EC 4 in designing the ultimate load for the connectors. The test specimen 14-1 failed early because of the too large initial load steps (Fig. 8). Compared to the single headed stud shear connectors ∅ 19 mm, an average loss in the load-carrying force of 5.4 % was given with the double stirrup. The losses are entirely attributable to the screened connector. The first headed stud shear connector can make use of its load-bearing capacity to the full and at the point in time of its failing by shearing, the second connector is not yet at the limit of its load-bearing capacity. The ductility criterion according to EC 4 is thus fulfilled (Table 3). No additional traverse reinforcement should be applied. Load [kN] 1400
Load [kN] 1400
1200
1200
1000
1000 800
800 Series 14: POST KBD 19 DD/1
600
Series 14: POST KBD 19 DD/2
400
600 Series 27: POST KBD 19 DD(2)/1
400
Series 14: POST KBD 19 DD/3 200
Series 14: POST KBD 19 DD/4
Series 27: POST KBD 19 DD(2)/2
200
Series 27: POST KBD 19 DD(2)/3
0
0 0
1
2
3 4 5 6 Displacement [mm]
7
8
0
9
1
2
3 4 5 Displacement [mm]
6
7
8
Figure 8: Results from experiments with double connector, ∅ 19 mm, left: without traverse reinforcement; right: with additional traverse reinforcement. series
test
14/2 14/3 14/4
POST POST POST
type KBD 19 KBD 19 KBD 19
Pmax [kN] 1175,7 1253,2 1293,9
PRk [kN] 132,3
δu [mm] 8,47 8,24 8,77
δuk [mm] 7,62 7,42 7,89
δuk [mm]
PRd [kN]
7,42
105,8
Table 3: Evaluating the results from experiments with the double connector ∅ 19 mm without additional traverse reinforcement according to EC 4.
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4.3
Connector-strip system (combined and T-bulb fixing strip)
The combined fixing strip designed for the series of experiments consists of a strip of sheet material with round recesses opened at the top that have been welded upright to the upper flange of the steel girder (Fig. 9). The recesses have been made by burning these out to a radius of r = 40 mm, whereby the overall depth of the cut into the sheet has been selected as h = 70 mm.
Side View
Cross Section
Detail
25
25
Figure 9: Arrangement of the T-bulb connector strip. The development of the T-bulb profile is based on the endeavour to combine the advantages of the geometry of the headed stud shear connector with the high load-bearing capacity of the fixing-strip system. The geometry of the T-bulb fixing strip is based on a standardised rolled flat-bead steel profile. As is the case with the headed stud shear connector, the concrete belt is prevented from lifting from the steel girder by a profile head being formed. It is thus no longer necessary to cut back the recesses. The centre of gravity of the profile end, and by this the position of the resulting forces which are introduced, lies more at the level of the concrete-belt centre than is the case with the combined fixing strip because of the way the head is formed. The vertical tensile forces in front of the recesses are reduced to a minimum in this way. Analogous to
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the combined fixing strip, the rectangular recess was burned out at a depth of 70 mm over a length of 80 mm. The transfer of shearing forces is the same as for the concrete connector model. Design models already exist for this that are generally known [5]. Both fixing-strip systems principally exhibit similar load-bearing and ductility behaviour. The T-bulb fixing strip did however show higher initial stiffness and a more ductile overall load-bearing behaviour. The results from the T-bulb fixing strip both with (T-bulb 1 and 3) and without (T-bulb 2) traverse reinforcement in the recess are shown in Figure 10 and are tabulated in Table 4. The influence of the traverse reinforcement can be clearly seen. The expenditure for laying is however higher as the load-bearing capacity increases.
Load [kN] 3500 3000 2500 2000 1500 T-Bulb 1
1000
T-Bulb 2 (without reinforcement)
500
T-Bulb 3
0 0
5
10 15 Displacement [mm]
20
25
Figure 10: Experimental results from the T-bulb fixing strip with and without traverse reinforcement in the recess. series
test
type
31/2 31/1 31/3
POST POST POST
T-Bulb T-Bulb T-Bulb
Pmax [kN] 2211,9 3342,4 3250,1
PRk [kN] 497,7 741,6
δu [mm] 35,5 24,5 30,9
δuk [mm] 32,0 22,0 27,8
δuk [mm] 32,0
PRd [kN] 398
22,0
593
Table 4: Evaluation of the results from experiments with the T-bulb fixing strip according to EC 4.
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4.4
T-profile from a half IPE 200 at a welding angle of 45°
The characteristics of a straight T-profile as a connector (Fig. 11) have already been determined by other research institutes [6]. In the limiting region, the end face of the profile intersects with the concrete such that a high degree of ductility is reached. The load that is carried is not however satisfactory for the amount of material in service. The projected area is increased by inclining the profile such that better use is made of the cross-section. Unlike headed bolts, the profile should contribute to the transfer of forces by its whole component height. Frontal View
140
240
Detail 100
15
5,6
180
15
120 140
80 220
Detail 10
28
116
183
10
70
84
13 0
183
84
Cross Section
100
140
Figure 11: Arrangement of the T-profile from a half IPE 200 at 45°.
Load [kN] 2000
1500
1000 POST TIPE 45°/1
500
POST TIPE 45°/2 POST TIPE 45°/3
0 0
5
10 15 Displacement [mm]
20
25
Figure 12: Results of experiments with the T-profile from a half IPE 200 at 45°.
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The flange did not change its position in the concrete bed during the experiment and neither did any parting cracks occur. This is because the forces are well-distributed over the flange’s projected surface. The displacements were taken up exclusively by the shear deformation of the web and the failure initiated by having exceeded the ductile yield on the reverse side. The values shown for the ductility in Figure 12 and Table 5 suffice according to EC 4. series
test
17/1 17/2 17/3
POST POST POST
Pmax [kN] TIPE 200 1776,8 TIPE 200 1852,8 TIPE 200 1895,8 type
δu [mm] 9,80 17,2 12,7
PRk [kN] 399,8
δuk [mm] 8,82 15,5 11,4
δuk [mm]
PRd [kN]
8,82
320
Table 5: Evaluating the T-profile from a half IPE 200 at 45° according to EC 4.
4.5
Metal sleeve and cushion around the headed stud shear connector shaft
The metal sleeve and the cushion give a certain amount of play to the headed stud shear connector and at the same time, strengthen the connector shaft (Fig. 13). The metal sleeve was pushed over the shaft and the cushions arranged on the sleeve. Greater ductility and a higher load until failure from the bending and tensile forces can theoretically be attained outside the zone of thermal influence of the headed stud shear connector by this. Load [kN] 1400 1200 1000
150
800 600 Series 32: POST KBD 19 H+P/1
400
Series 32: POST KBD 19 H+P/2
80
38 26 5,0 5,0 5,0 2,0
200
Series 32: POST KBD 19 H+P/3
0 0
1
2
3
4 5 6 7 8 Displacement [mm]
9
10 11 12
Figure 13: Arrangement of the headed stud shear connector with metal sleeve and cushion around the shaft and experimental results.
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series
test
type
32/1 32/2 32/3
POST POST POST
KBD 19 KBD 19 KBD 19
Pmax [kN] 1356 1328 1327
PRk [kN] 149,3
δu [mm] 11,0 7,90 8,12
δuk [mm] 9,86 7,11 7,31
δuk [mm]
PRd [kN]
7,11
119,5
Table 6: Evaluation of the results from the headed stud shear connector with metal sleeve and cushion around the shaft according to EC 4. The load-bearing capacities of these variants were about 10% higher than those for nonmodified connectors of the same diameter (Fig. 16). The initial stiffness was very high and the ductility criterion according to EC 4 was attained by all test specimens (Table 6). The practical execution of this system proved to be problematical due to the irregularly formed weld collar preventing the exactness in arranging the metal sleeve.
4.6
High-strength headed stud shear connector
It is appropriate to improve the shear-stress load-bearing capacity of the cold-formed headed stud shear connector so as to increase the strength of the base material by at least the same ductile yield. The following material properties were aimed for in order to obtain a better load-bearing behaviour by a high-strength headed stud shear connector: Tensile strength Yield stress Ultimate strain
Rm = Re = εu ≥
800 N/mm² 650 N/mm² 12 - 15%
Load [kN] 1600
Load [kN] 225
1400
200
1200
175 150
1000
125
800
100
600
POST KBD 19 High Strength/1
75
SPOT KBD 19 High Strength/1
400
POST KBD 19 High Strength/2
50
SPOT KBD 19 High Strength/2
200
POST KBD 19 High Strength/3
25
SPOT KBD 19 High Strength/3
0
0 0
1
2 3 Displacement [mm]
4
0
5
1
2 3 Displacement [mm]
4
5
Figure 14: Experimental results of the high-strength stud shear connector, ∅ 19 mm. The use of such materials had to be dispensed with because of the time constraints of this research project. The base material S355 J2 G3 was therefore used. The experiments with the high-strength headed stud shear connectors shown in Figure 14 give almost identical
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load-deformation curves. The sudden drop in the second experiment in the ultimate load and the increase in this again at a relative displacement of δ = 4.0 mm result from a connector failing suddenly. According to Table 7, the ultimate loads that were reached, Pmax, are about 4% higher than the limiting shearing forces determined in accordance with EC 4. The attained ductility of δuk = 3.62 mm is however completely inadequate since the ductile yield of the connector material is apparently too low. series
test
type
34/1 34/2 34/3
POST POST POST
KBD 19 KBD 19 KBD 19
Pmax [kN] 1444,6 1414,8 1438,2
PRk [kN] 159,1
δu [mm] 4,32 4,02 4,60
δuk [mm] 3,89 3,62 4,14
δuk [mm]
PRd [kN]
3,62
127,3
Table 7: Evaluation of the high-strength headed stud shear connector, ∅ 19 mm, according to EC 4. The problematical nature of an inadequate ductile yield was already recognised within the scope of the tensile tension tests according to DIN EN 10002 before carrying out the experiments. In each case, the tensile test runs were carried out after the cold-forming processes in the drawing shop using solid rods of ∅ 21.9 mm and ∅ 18.85 mm respectively. This was not the case at the RWTH University where the tensile test runs were made using standardised test specimens having a diameter of ∅ 8.0 mm. The results from the different tensile-testing experiments showed that the values determined for the tensile strength were approximately of the same magnitude (Rm,18.85 = 750 N/mm² compared to Rm,8 = 743.9 N/mm²), whereas the apparent yielding point (Rel,18.85 = 675 N/mm² compared to Rel,8 = 720.7 N/mm²) and the ultimate strain (εu,18.85 = 14.5 % compared to εu,8 = 10.0 %) differed considerably. According to this, the ductility hoped for was not reached when using S355 J2 G3 with a diameter of 23 mm as the base material for a headed stud shear connector ∅ 19 mm. The qualitative load-deformation characteristics of this connector for use in highstrength concrete are very promising and it all depends on finding the right material.
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5.
Load-bearing capacity model for headed stud shear connector in high-strength concrete
A load-bearing capacity model is presented in the following on the basis of the mechanical model presented at the beginning for headed stud shear connectors in highstrength concrete. It is assumed when calculating the load-bearing capacity that both the connector as well as the weld collar contribute to the overall load-bearing capacity of the connector. Since the connector in high-strength concrete is subjected to an almost purely shearing type of stress, the shear-stress bearing capacity of this is calculated using the full stress to failure. The concrete forces that are activated in front of the collar depend on the area projected by the weld bead as well as on the strength of the concrete (greater than 70 N/mm²). The following can only be considered as a proposal because of the limited amount of data available for this research project and the varying influencing variables as well. A systematic check and a statistical evaluation of the experiments as well as a comparison with results from other experiments and numerical calculation will soon be published within the scope of a dissertation [7].
Assumed shearing force of the shaft directly above the weld collar: FS = Rm ⋅ AS Rm: AS:
Tensile strength of the connector material used Cross-sectional area of the shaft
Concrete compression force activated by the weld collar in the concrete wedge in front of the connector: FSW = AP ⋅ ηconcrete ⋅ fck,cube,average AP : ηconcrete:
Projected area of the bead Empirical correction value to determine the multi-axial load-bearing action of the concrete in front of a shear connector (= 1.5) fck,cube,average: Mean cube compressive strength on the 150-mm cube
Assumed connector shearing force: F connector = FS + FSW Figure 15 shows a comparison of the theoretical load-bearing capacities determined using this model and the load-bearing capacities determined experimentally.
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POST 19 mm
300
Pm
SPOT 19 mm POST 22 mm
250
SPOT 22 mm
200
Pk
POST 25 mm
Pd
150 100 50 0 0
50
100 150 200 P-Calculated
250
300
Figure 15: Comparison of the theoretical and experimentally determined load-bearing capacities for shear studs in high-strength concrete.
6.
Evaluation of load-deformation curves for shear connectors
6.1
Classification of the load-deformation curves for shear connectors according to EC 4
The assessment of the deformation capacity is particularly problematical when using shear connectors in high-strength types of concrete. The load-deformation curves determined in the research project for the various connector types in high-strength concrete exhibit very differing characteristics for the curve. In simplified terms, connector characteristic curves can be classified according to three types of load-deformation curves (Figures 16a to 16c). There is no standard evaluation possible for these different curve characteristics in order to determine the load-bearing behaviour and the ductility of the connector according to EC 4. Whereas evaluation of the bi-linear load-deformation curve (Fig. 16a) can be carried out according to EC 4 as long as δelastic lies in the range of the serviceability and δplastic as the limit for ductility fulfils the criterion δuk = δelast + δpla ≥ 6 mm, evaluation of the connectors with a tri-linear load-deformation curve (in particular for the connector characteristic curve II) (Fig. 16b) is not regulated. It is questionable whether for a large elastic-plastic portion, δelastic-plastic in the building, the maximum load-bearing capacity of the connector will be reached at a plastic level
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and whether the stress of the connector could already lie in the plastic range under service loads. a)
b)
P [kN]
c)
P [kN]
Pmax
P [kN] Pmax
Pmax
I)
II) δ [mm] δelastic
δplastic
δ [mm] δelastic δelasto-plastic
δplastic
δ [mm] δelastic
δelasto-plastic
Figure 16: a) Bi-linear load-deformation curve, b) Tri-linear load-deformation curve, c) Load-deformation curve of low stiffness (very flexible). This question applies in particular in the case for high-flexibility connectors (Fig. 16c). If the connectors have been designed with 90% of the maximum ultimate load Pmax as the characteristic load-bearing capacity for the connector PRk, then they have already reached the elastic-plastic deformation range under the service loads, and this is thus associated with a large degree of slip. The question is therefore also applicable as to how large the initial stiffness should be for designs for full shear connection or for partial shear connection.
6.2
Recommendations for expanding the evaluations according to EC 4
Within the scope of the research project, non-linear composite-girder calculations for representative composite cross-sections of high-strength materials (S460 and C90) were carried out using the programme system DYNACS from the Institute for Steel Construction in order to determine the required deformations of shear connectors in various load states (SLS and ULS). The differing load-deformation curves of the connectors were thereby considered for the various degrees of connecting. The characteristic load-bearing capacity of the connector in the partial connection and the load-deformation curves of the connectors were applied in accordance with EC 4. The following recommendations for expanding the evaluations according to EC 4 can be derived from the numerical investigations performed to date:
Limiting the characteristic load-bearing capacity of the connector for service loads PRk,SLS to the elastic range of the load-deformation curve.
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Limiting the characteristic load-bearing capacity of the connector for ultimate loads PRk to approximately PRk ≤ PRk,SLS ⋅ 1.65. Limiting the characteristic load-bearing capacity of the connector for ultimate loads PRk by a maximum slip deformation of δ = 6.0 mm.
These approaches shall be verified by studying the parameters further together with numerical calculations and accompanied by series of experiments.
7.
Summary
Experiments with Push-Out standard test specimens (POST) and the newly developed single Push-Out test specimens (SPOT) for connecting high-strength concrete with highstrength steel were carried out. The load-bearing capacity of headed stud shear connectors in high-strength concrete is made up of a load-bearing portion of the connector shaft and a load-bearing portion of the connector’s weld collar. So that headed stud shear connector in high-strength concrete will exhibit ductile behaviour while retaining its ultimate load, its use can be modified to currently four different types:
Enlarging the weld collar, Strengthening the connector shaft, e.g. with a sleeve made of metal, Using a high-strength base material for fabricating a cold-formed headed stud shear connector (S460), Arrangement of double connectors without intermediate traverse reinforcement.
Coming into question as further shear connectors in high-strength concrete are slightly inclined T-profiles. These are simple to fabricate by cutting open rolled I-shaped profiles into symmetrical parts. The continuous connectors, combined fixing strip and T-bulb fixing strip can be manufactured very economically by fully automated production and welding with the composite girder. In addition to this, the fixing strips exhibit very positive curve characteristics with high ultimate loads and extremely high values for the ductility. The evaluation procedure according to EC 4 cannot appropriately measure the different load-deformation curves which are determined in the experiments. Recommendations are given for expanding the evaluations performed according to EC 4. These recommendations shall be verified by carrying out further numerical and experimental investigations. The research institutes express thanks to the AiF and participating firms for their financial support, as well as to the committee accompanying the project for their helpful suggestions.
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8.
Literature
[1] ECSC Project No. 7210-SA, Use of High Strength Steel S460, Reports, unpublished, Institute of Steel Construction and Institute for Structural Concrete, RWTH Aachen, 1996 – 2000. [2] Eurocode 4: Bemessung und Konstruktion von Verbundtragwerken aus Stahl und Beton, Teil 1-1: Allgemeine Bemessungsregeln, Bemessungsregeln für den Hochbau, Deutsche Fassung: ENV 1994-1-1: 1992. [3] Abschlussbericht zum Forschungsvorhaben „Untersuchungen zur Duktilität der Verbundmittel bei Anwendung von hochfestem Stahl und hochfestem Beton“; AIF-Nr.: 12124; Studiengesellschaft Stahlanwendung e.V.: Projektnummer P 486/25/99; Aachen, November 2000. [4] Lungershausen, H.: Zur Schubtragfähigkeit von Kopfbolzendübeln, Technischwissenschaftliche Mitteilung Nr. 88-7, Institut für konstruktiven Ingenieurbau, Ruhr-Universität Bochum, 1988. [5] Bode, H., Künzel R.: Zum Tragverhalten des neuartigen Verbundmittels der Fa. Kombi-Tragwerk GmbH. Gutachterliche Stellungnahme zur Vorlage beim Institut für Bautechnik, Universität Kaiserslautern, November 1988. [6] Galjaard, J.C.; Walraven, J.C.: New and existing shear connector devices for steelconcrete composite structures. Static tests, results and observations, First International Conference on Structural Engineering, Kunming, China, Oktober 1999, ISSN 1000-4750 . [7] Döinghaus, P.: Zum Zusammenwirken hochfester Baustoffe in Verbundkonstruktionen, Dissertation in Vorbereitung, Institut für Massivbau, RWTH Aachen, 2001. Authors of this article: Prof. Dr.-Ing. Josef Hegger and Dipl.-Ing. Peter Döinghaus Institute for Structural Concrete RWTH Aachen, Mies-van-der Rohe Straße 1, 52074 Aachen. Prof. Dr.-Ing. Gerhard Sedlacek and Dipl.-Ing. Heiko Trumpf Institute for Steel Construction RWTH Aachen, Mies-van-der Rohe Straße 1, 52074 Aachen.
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EXPERIMENTAL INVESTIGATIONS ON THE BEHAVIOUR OF STRIP SHEAR CONNECTORS WITH POWDER ACTUATED FASTENERS Mario Fontana*, Hermann Beck**, Roland Bärtschi*** *Institute of Structural Engineering, ETH Zurich, CH-8093 Zurich, Switzerland **Hilti Corp., Direct Fastening Development, Principality of Liechtenstein ***Institute of Structural Engineering, ETH Zurich, CH-8093 Zurich, Switzerland
Abstract Nailed strip shear connectors are presented as an alternative to welded headed stud connectors for composite beams. The strip shear connector has a trapezoidal shape to fit the geometry of metal decks. The strips are fixed by means of powder-actuated fasteners. The legs and the crests of the strip connector are equipped with openings to improve anchorage of the strip in the concrete plate by activating concrete dowels. By means of these openings the overall ductility of the system is improved. The connectors are designed to be used with automatic installation systems to improve installation efficiency. The objectives of the push-out tests were to derive design parameters and to optimise the geometry of the strip shear connector. The test results indicate that optimised strip shear connectors will achieve high ultimate resistance in the range of 20 kN per fastener and sufficient ductility to allow plastic beam design. Further series of push-out tests are necessary to verify this behaviour statistically and to derive the characteristic resistance.
1. Introduction Nailed shear connectors in composite beams have been an alternative to welded headed stud shear connectors for over 15 years. An example of a cold formed angle shear connector – whereby one leg of the angle is fixed by two powder-actuated fasteners driven with a powder-actuated tool – is shown in Fig. 1 (Hilti X-HVB shear connector). Compared to welded studs, nailed shear connector systems exhibit the following advantages: • They require minimum installation equipment and set-up time, therefore allowing flexible scheduling of work on site.
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Fig. 1: Hilti X-HVB
• They are efficient for small projects and for projects in remote locations. • The installation quality is not affected by moisture on site or by zinc coatings of the base material resulting in less work interruptions due to bad weather or less preparation efforts like scraping of paint at the headed stud location. However, the installation costs of nailed systems based on a “per kN basis” were up to now generally greater in comparison to welded studs. This is due to the fact that the design resistance of, for example, a Hilti X-HVB amounts to just approximately 40 percent of the design shear resistance of a 19 mm welded headed stud shear connector. To improve this situation, two different alternatives were investigated. Experimental research on the first option – the nailed shear rib connector – was begun in [1]. This paper now describes the strip shear connector as the second investigated solution. Both designs allow the use of automatic installation systems. Consequently, the installation speed increases reducing the overall costs of a nailed shear connector system.
2. Description of the nailed strip shear connector The nailed strip shear connector system consists of two components, the strip shear connector itself and the powder-actuated fasteners fixing the strip connector to the beam’s flange. First investigations on such a type of shear connecting system were reported in [2]. The strip is folded from a flat zinc-coated steel sheet with a thickness in the range of 1.0 to 2.0 mm. The use of the connector on secondary beams with a composite deck spanning perpendicular to the beam is of most practical relevance. Therefore, the distance of the two troughs of the trapezoidal strip connector must be chosen to fit to the geometry of the metal deck (see Fig. 2).
Fig. 2: Typical nailed strip shear connector system The strip connector is fixed to the beam flange by Hilti powder-actuated fasteners ENPH2-21L15 providing shear transfer between the concrete plate and the steel section. The leg of the steel strip acts as a diagonal reinforcement of the concrete rib. To improve the anchorage of the tension legs the connector strip must be higher than the metal deck. In all Stripcon push-out tests performed at the Swiss Federal Institute of Technology
1047
(ETH), Zurich, a trapezoidal deck (Vikam TR60/235) with a height of 60 mm was used combined with a strip connector of height 110 mm. The anchorage is provided by the folded shape itself and additionally improved by openings in the crests and the legs of the connector to develop a dowel mechanism within the concrete. Furthermore these openings allow reliable concrete compaction between metal deck and strip connector. The high strength nails Hilti ENPH2-21L15 allow penetration of the strip connector and the beam flange without any predrilling. The ultimate strength of these fasteners is in the range of 2,200 N/mm² resulting in a shear resistance of approximately 20 kN per fastener. Though the nails show very high strength they remain ductile due to their bainite metallurgical structure as a result of specific heat treatment during manufacturing. The ability to bend without a brittle failure is very important with regard to meeting the ductility requirements of shear connectors in composite beam construction.
3. Experimental investigation 3.1 Push-out test set-up and test procedure
Fig. 3: Push-out test specimen adapted to Eurocode 4 The geometry of the push-out test specimen and the test procedure correspond to the specifications provided in Eurocode 4 [3] except for the fact that strip connectors were used instead of headed studs. Fig. 3 shows the geometry of the standard European pushout test specimen. The vertical slip was measured by 2 gauges on each side, and additionally horizontal gauges were applied to measure the uplift movement of the concrete plates. The load protocol followed the procedure given in Eurocode 4. Before
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the actual push-out test was performed a static load of 40% of the expected ultimate capacity Vu was gradually applied followed by 25 load cycles of this load range. The push-out tests were performed deformation controlled with a speed of 0.5 mm/min. 3.2 Specimen manufacturing The strip shear connectors were fastened by ENPH2-21L15 powder-actuated fasteners using the Hilti DX750 installation tool. The nailhead stand-offs were recorded. The nailhead stand-off (NHS) as defined in Fig. 4 indicates the correct depth of penetration hnom which governs the fastening quality. In the case of the ENPH2-21L15 the Fig. 4: Nailhead stand-off optimum value of NHS is 8.5 mm. NHS is controlled by correct choice of cartridge type and tool setting. According to Eurocode 4 the concrete of each plate has to be placed in a horizontal position. Therefore the two plates of the specimen differ in age (one day for each specimen) and compressive strength. Table 1 indicates the concrete compressive strength fc of the two plates. The concrete age at the day of testing varied between one and two weeks. The plates were reinforced according to the specifications given in Eurocode 4. 3.3 Push-out test program Table 1 provides an overview of the test programme, the parameters investigated and the properties of the material. All tests were performed at ETH Zurich and are documented in reports [4], [5] and [6].
a b
Ultimate fu [N/mm²]
Yield fy [N/mm²]
panel 1
panel 2
S2
Typeb Thickness t [mm]
S1
Specimen #
Series
Table 1: Push-out Tests: Test program and test parameters Strip shear connector Concrete strength Deck type and properties fca [N/mm²]
1 4 5 6 3 4 5 6
1 1 2 3 6 7 8 8
409.8 465.4 410.4 410.4 465.4 410.4 465.4 383.1
303.0 394.0 303.0 303.0 394.0 303.0 394.0 348.4
24.8 21.1 21.1 21.1 28.3 30.6 30.6 30.6
31.6 22.0 22.0 22.0 33.6 40.4 40.4 40.4
1.5 2.0 1.5 1.5 2.0 1.5 2.0 2.0
Cylinder strength: diameter = 150, height = 300 see fig. 5
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Vikam TR60/235 • thickness: 0.88 mm, • height: 60 mm • trough distance: 235 mm • fu = 434.1 N/mm² • fy = 348.7 N/mm²
3.4 Geometry and properties of strip shear connectors All strip connectors used were made of zinc-plated steel sheets. The steel used for the strip connector in test S2.6 was specified as DX51D according to EN 10142 [7]. For all other connectors tested, steel sheets specified as S280GD according to EN 10147 [8] were used. The material properties listed in Table 1 were evaluated by standard tensile tests according to EN 10002. Fig. 5 shows the detailed geometry of the different types of strip shear connectors listed in Table 1.
Type 1: slot width = 30 mm Type 2: slot width = 15 mm Type 3: no slots
Type 6
Type 7
Type 8
Fig. 5: Geometry of strip shear connector
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The geometry of the strip connector type 1 was theoretically based on the results of 24 push-out tests performed at Hilti Corporation in 1998. The fundamental behaviour of nailed strip shear connectors, using generally Holorib HR51 as metal deck, was investigated in this test programme. From these tests, the beneficial effect of openings in the legs on the ductility of the connection was obtained. Because of the dove-tail shape of the Holorib 51, the contribution of the Holorib 51 to shear transfer was significantly greater than it would be in the case of a trapezoidal deck like the Vikam TR60/235. Provided the same type of shear connector is used, it will therefore be less stressed in combination with dove-tail metal decks. Additionally, the existence of a stiffener in the troughs of the Vikam TR60/235 influences the geometry of the strip shear connector. Therefore, the troughs of the strip connector are also made with a centre ridge to fit the shape of the metal deck. This geometrical condition is advantageous with regard to an easy positioning of the strip connector on site. However, the ridge element in the plane of the nails affects the uniform load distribution to all nails.
4. Possible failure mechanism of nailed strip shear connectors The following failure modes may potentially occur: Failure in the nailed interface:
Concrete failure:
• Shear failure of the nail shank • Pullout of nails combined with local bearing deformations in the flange
• Bearing failure of the concrete dowels • Shear failure of the concrete dowels • Shear failure of the concrete rib • Splitting of the concrete plate
Steel failure of the strip connector: • Local bearing failure in the nail interface • Net section fracture in the tension leg • Net section fracture in the nailed troughs
For greatest efficiency of a nailed shear connector system, it is important to develop an ultimate capacity close to the total nail shear capacity of all fasteners installed. However, to allow plastic design of the composite beam the strip shear connector must develop sufficient plastic deformations at a high load level. Therefore, the thickness of the sheet must not be too thick to avoid brittle nail shank fracture without local bearing deformations. On the other hand, the following conditions require a stiff strip connector sheet: • Smaller shear connecting contribution of the open trapezoidal metal deck. • Greater stress in the tension legs as four nails are fixed per trough. • Existence of the ridge in the trough, with two nails on both sides of the ridge.
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In previous tests with the dove-tail-shaped Holorib metal deck no ridge was necessary and only two fasteners were installed per trough. Strip connectors of thickness 1.0 and 1.5 mm were used. For both thicknesses ultimate loads above 20 kN per fastener with excellent ductile behaviour especially due to local bearing deformations in the interface were developed. Consequently, finding the optimum design of the strip connector for use with the open trapezoidal Vikam TR60/235 required an iterative process to finally achieve satisfying results.
5. Description of load-deformation behaviour – test results The changes in geometry from strip connector type 1 to type 8 reflect the continuous improvements based on the experience made during the test programme. For a better understanding of that process, the tests are described in their chronological sequence. The list of the push-out tests in Table 1 follows that sequence. The result of test S1.1 reflects excellent ductile behaviour, developed from plastic steel deformations in the tension leg. Failure was governed by net section fracture in the tension legs. However, the ultimate load with 14.08 kN per fastener was significantly smaller than expected from the tests with the Holorib HR51, where resistances slightly above 20 kN per fastener were observed. Therefore, changes to type 1 were made to increase the strength of the tensile legs of the strip connector. Test S1.4 used a type 1 connector shape with greater thickness (2 mm instead of 1.5 mm) and with increased steel strength. Types 2 and 3 were made of the same material in the same steel thickness as used in test S1.1, but the slot width in the tension leg was reduced to 15 mm (test S1.5) or no slot was made (test S1.6). 700 S1.4
S1.1 S1.4 S1.5 S1.6
S1.6
600
Load [kN]
500 400
S1.1
300 S1.5
200 100 0 0
2
4
6
8
10
12
Deformation [mm]
Fig. 6: Load-deformation behaviour of series S1
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14
16
18
20
However, these measures were only partially successful due to non-uniform load distribution between top and bottom rib observed in all three tests S1.4, S1.5 and S1.6. From examinations of cut specimens it was clearly seen, that the connector troughs located in the bottom rib of the plate were subjected to higher forces than those in the top rib. Furthermore, it could be seen that the nails located next to the tension leg were more stressed than those separated by the ridge in the trough. Net section fracture of the tension legs located in the bottom rib governed failure in test S1.4, whereas net section fracture of the nailed trough determined the ultimate capacity in tests S1.5 and S1.6. All three tests principally showed ductile behaviour, but again the loads achieved did not fulfil the targets (see Table 2). Therefore, the type 6 strip connector used in test S2.3 incorporated further circular openings in the crests and an additional anchor tab at its ends (cf. Fig. 5). Both measures were intended to improve the anchorage of the strip connector in the concrete, especially of the upper “free” tension leg of the strip connector. The improved anchorage finally led to a more uniform load distribution between the top and the bottom ribs resulting in a high resistance of 21.03 kN per fastener. A further adaptation in the geometry was to change the parallel slot geometry into a conical one to prevent net section fracture at the bottom of the slot. The goal was to achieve the fracture in the middle of the tension leg and improve overall ductility by utilising a greater strain length. In the last 2 tests S2.5 and S2.6 the geometry of type 6 was further modified resulting in the geometry of type 8, with slight adaptations in geometry and location of the openings in the crest and the leg. To further investigate the effect of the steel sheet strength, type 8 used in test S2.5 was manufactured of higher strength steel than for type 8 used in S2.6. 700
S2.3 S2.4 S2.5 S2.6
S2.6
600
Load [kN]
500 S2.5 400
S2.4
300 S2.3
200 100 0 0
2
4
6
8
10
12
Deformation [mm]
Fig. 7: Load-deformation behaviour of series S2
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14
16
18
20
Specimen #
Series
Table 2: Push-out tests: Summary of test results Ultimate Load Deformations δ [mm] Vu [kN]
S1 1 4 5 6 S2 3 4 5 6
total 450.4 584.5 511.5 532.2 672.8 539.0 663.8 707.2
per nail a 14.08 18.27 15.98 16.63 21.03 16.84 20.74 22.10
at Vu 4.1 6.1 5.5 6.4 7.2 6.8 7.5 7.4
δu at 0.9 Vu 17.1 7.1 8.9 8.7 7.3 9.0 8.2 11.1
δuk = 0.9 δu b 15.4 6.4 8.0 7.8 6.6 8.1 7.4 10.0
Dominating Failure Mechanism Net section fract. tension leg Net section fract. tension leg c Net section fract. trough c Net section fract. trough c Nail shear + connector bearing Nail shear + connector bearing Nail shear + connector bearing Nail shear + connector bearing
In test S2.5, the upper tension legs failed in the middle of the net sectional area. This indicates the effectiveness of the improved anchorage measures at the ends of the strip connector and in the top concrete rib and also proves the effectiveness of the slot adaptations. The achieved ultimate load per nail was 20.7 kN. Though this value is sufficiently high for an economic use of the nailed system, it does not reach the ultimate loads of up to 25.7 kN developed for the rib shear connectors reported in [1]. This difference can be explained by the existence of the ridge in the strip connector trough, which is detrimental to a uniform load distribution to all fasteners installed for the entire deformation range. Ductility and interestingly also the ultimate load were greater for test S2.6 in which the strip connector with the smaller strength was used. This behaviour indicates an improved load distribution to all fasteners installed due to earlier plastic bearing deformations in the strip in the vicinity of the fasteners. The intention of test S2.4 followed the same assumption that local bearing deformations of the thinner 1.5 mm strip type 7 might activate all nails more uniformly. In comparison with types 2 and 3 the width of type 7 was increased from 80 to 100 mm to prevent premature failure owing to net section fracture of the nailed trough. However, as indicated by Table 2 and Fig. 7, the assumed behaviour did not occur due to the reduction in connector thickness which also reduced the bending stiffness of the ridge affecting again the equal activation of all four fasteners installed on both sides of the ridge. a b
c
Total number of nails: 32 for each test. Note: According to Eurocode 4 the calculation of δuk requires 3 equal push-out tests performed and certain limits of the scatter of the 3 tests within a series. Nevertheless, as the ductility is an essential criterion, δuk is calculated here just based on the result of a single test to allow a first ductility assessment. Only occurred in the bottom rib of the concrete plate
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6. Conclusions and outlook Based on the results of this test programme on nailed strip shear connectors the following conclusions are summarised: • Optimised design of the strip shear connector results in a high resistance of the nailed connections above 20 kN per fastener. With nail shank fracture, connector bearing deformations and partially net section fracture in the tension legs, a combined failure behaviour was observed. Therefore, the resistance of the fasteners was not as high as in the case of the nailed rib shear connectors [1]. • The characteristic deformations δuk were greater than the required limit of 6 mm indicating that the connector performance allows for plastic beam design. • For the definition of design resistances further series of push-out tests must be performed. Recently, beam tests were performed by the authors to verify the behaviour observed in the push-out tests in a full scale beam situation. The results will be reported later in a future publication.
7. References 1. Fontana, M., Beck, H., ´Novel rib shear connectors with powder actuated fasteners´, (2000), Proceedings of UEF-Conference Composite Construction IV, Banff, May 2000 2. Shanit, G., Chryssanthopoulos, M., Dowling, P.J. (1990), ´New profiled unwelded shear connectors in composite construction´, Steel Constr. Today 1990, 4, 141-147 3. Eurocode 4, ENV 1994-1-1 (1992), ´Design of composite steel and concrete structures, part 1-1: General rules and rules for buildings´, October 1992 4. Knobloch, M., ´Schubtragfähigkeit von gefalteten Blechverbundstreifen mit HiltiSetzbolzen´, (2000), Studienarbeit in Konstruktion, Institute of Structural Engineering, ETH-Zurich. 5. Bärtschi, R., ´Stripcon Versuche 10-12, Schubtragfähigkeit von gefalteten Blechleisten mit Hilti-Setzbolzen´, (2000), Test Report, Institute of Structural Engineering, ETH-Zurich. 6. Fontana, M., Bärtschi, R., ´New-type shear connectors with powder-actuated fasteners´, (2000), Institute of Structural Engineering, ETH-Zurich. 7. European Code EN 10142 (1995), ´Continuously hot-dip zinc coated low carbon steel strip and sheet for cold forming – Technical delivery conditions´, August 1995 8. European Code EN 10147 (1995), ´Continuously hot-dip zinc coated structural steel strip and sheet – Technical delivery conditions´, August 1995
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DESIGN CONCEPT OF NAILED SHEAR CONNECTIONS IN COMPOSITE TUBE COLUMNS Gerhard Hanswille*, Hermann Beck** and Till Neubauer* *Institute of Steel and Composite Structures, University of Wuppertal, Germany **Hilti Corp., Direct Fastening Development, Principality of Liechtenstein
Abstract Nailed shear connections are a new alternative type of shear connection in composite columns with concrete filled circular and rectangular tubes. The main advantage of a nailed shear connection is, that it can be applied from the outside of the tube without any prefabrication efforts. Based on the behaviour derived experimentally from push-out tests, proposals for the design resistance of nails for ultimate and serviceability limit states are made, providing provisions with regards to minimum steel thickness, concrete grade and nail spacing are fulfilled. In order to get a more realistic knowledge of the deformation behaviour in serviceability limit states, the combined shear resistance of the nails and the shear strength due to bond and friction and including long-term effects has to be considered. The background of a corresponding test program will be discussed.
1. Introduction Nailed shear connection in composite tube columns was introduced in practice in 1998 and 1999 in buildings in Austria and Germany [1], [2]. The design of the nailed shear connection for these projects was based on experimental work performed within the VHF-Research Project [3], [4]. Additional tests were also performed by Hilti Corporation [5] in order to investigate the load-slip behaviour of the nailed shear connections for general conditions. The objective of this paper is to introduce the design method for nailed shear connections in buildings for a limited area of application. A design resistance for the ultimate limit state will be proposed. All the push-out tests described in [3] to [5] were performed to evaluate conservative resistances for the ultimate limit state. Therefore, the inside surface of the tube specimens was always lubricated prior to concreting, in order to eliminate load contributions of chemical bond and friction in the interface between
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concrete and steel. However, neglecting chemical bond and friction completely overestimates deformations in the serviceability limit state, leading to inefficient utilisation of the nailed shear connections. To gain a more realistic knowledge of the behaviour in the serviceability limit state, an additional test program was worked out. Backgrounds of this new program will be introduced, in addition results of ongoing creep tests will be presented. Finally the paper will provide an example of a constructional detail with the corresponding design equations for the ultimate and the serviceability limit state.
2. Nailing method High strength nails with smooth shanks are driven through the tube wall from the outside using a powder-actuated tool. No predrilling of the tube is required to enable the penetration process. The front sections of the nails protrude into the inside of the hollow tube. After the tube has been filled with concrete, the nail shank acts as shear connector between the concrete core and the hollow tube. The method is applicable for both pipes and rectangular hollow sections. Powder-actuated fastener: Hilti X-DSH32 P10 fu = 2200 N/mm² Embedment Depth Diameter = 4.5 mm Powder-actuated tool: Hilti DX750G, Power loads and tool energy settings dependent on strength and thickness of the tube to finally achieve flush installation. Fig. 1. Principle of method
3. Push-out test results Fig. 2 shows examples of typical load-slip behaviour of nailed shear connections derived from push-out tests. With regards to details of the performed test program, it is referred to [4] and [5]. At great slips a high load-bearing capacity per fastener is attainable reflecting excellent ductile behaviour. Due to concrete confinement inside the tube, the concrete develops high local compressive stresses amounting a multiple of the uniaxial concrete compressive strength. As the overall behaviour is significantly affected by local concrete deformations, the load-slip curves typically exhibit a parabolic shape. From the examples in Fig. 2 the effect of the concrete strength can be clearly observed. With increasing concrete strength, the ultimate capacity of the nailed connection increases as well as a greater initial stiffness combined with smaller initial deformation is given.
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Additional tests with specimens without nails proved that the lubrication of the inner pipe surface was completely effective as only negligible small ultimate values (in total 16.7 kN, 0.6 kN per nail) developed in these control tests. Nevertheless, the ultimate loads generally exceed significantly the total shear load capacity of all nails installed, as indicated in Fig. 2. Caused by the lateral restraint of the local concrete deformations [5], a significant local compression between the pipe and the concrete develops (see Fig. 3), which is finally responsible for the additional friction load contribution. P [kN]
Pipe: d = 508 mm, wall thickness = 8.8 mm 1100 1000 900 800 700 600 500 400 300 200 100 0
C20/25 C45/55
24 nails per specimen
Level of nail shear strength
0
2
4
6
8
10
12
14
16
18
20
Slip [mm]
Fig. 2: Examples of load-slip curves from push-out tests [5] Dark areas caused by lateral compression
Fig. 3. Inside view of push-out test specimens: Right: Detail of a bent nail; Left: Bent nails and visible dark areas of lateral compression at the location of each nail.
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4. Design concept The basic idea of the design concept is to provide constant values for the design shear strength for the ultimate and the serviceability limit states in combination with the following scope and detailing provisions: • circular and rectangular tubes with no limits in the outside dimensions, • wall thickness: 5.6 to 12.5 mm. For higher strength steel grades, the application restrictions with regards to installability of the nails have to be considered according to manufacturers provisions, • limitation of diameter/thickness ratios [6] to avoid local buckling of steel tubes, • concrete strength classes not lower than C30/37 and maximum aggregate size not exceeding 16 mm, • minimum spacing between the fasteners not less than 50 mm in vertical and lateral direction, • minimum distance of 20 cm to a possible concrete joint, • installation of the X-DSH32P10 according to manufacturers specifications. 4.1 Ultimate limit state Considering the restrictions above, the design resistance for the ultimate limit state can be based on the steel shear strength of the nails. For the X-DSH32P10 a design resistance was determined from test results in accordance with Annex Z of Eurocode 3. A characteristic value Rk = 21 kN and a design value Rd = Rk / γv = 16.8 kN per nail was evaluated [6], where the partial safety factor is given by γv = 1.25. This pragmatic conservative approach is justified as follows: • Contribution of chemical bond and large area friction between tube and concrete was virtually completely excluded in the push-out test. • In all tests in the defined scope, the ultimate loads in the push-out tests were generally significantly greater than the ultimate shear capacities of the nails. This beneficial effect is explained with local frictional forces developing owing to the restriction of the local concrete deformations in the compression area to the nail, comp. Fig. 3. • In [4] tests have also been performed with very low strength concrete (fc = 15.7 N/mm²) utilising recycled aggregates. Also in such low strength concrete, the ultimate load was in the range and beyond the total shear capacity of all installed nails. However, with regards to serviceability and also practical relevance, concrete strength Class C30/37 (fc = 30 N/mm²) was selected as minimum grade. Utilising the high ultimate loads evaluated in the tests for practical design, would require an accurate theoretical knowledge of the combined influence of the shape and dimensions of the hollow sections and the concrete strength. However, due to the significant slip, these higher values could not be utilised at the end, because serviceability requirements would govern design. Furthermore the design methods for columns are based on the assumption that the composite section remains plane.
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Therefore in the load introduction area of columns excessive slip at the interface between steel and concrete must be avoided. 4.2 Serviceability limit state With regard to serviceability limit state requirements, the slip at the interface between the steel tube and concrete must be limited. Based on the experience with other types of shear connection like headed studs or gusset plates trough the profile, slip between steel and concrete should be limited to values of approximately δ = 0.5 mm in order to avoid uncontrolled redistribution of the sectional forces of the column. The load slip curve according to Fig. 2 demonstrates that this serviceability criterion can govern the design of nailed shear connectors. In [5] a proposal was made to limit the design resistance for the serviceability limit state with 8.5 kN per nail. However, that value results in an inefficient utilisation of the nails, because it was evaluated from push-out tests in which chemical bond and large area friction was excluded due to lubrication of the inner tube surface. However, with regard to the serviceability limit state neglecting effects of bond strength and friction in the interface between steel and concrete seems to be a too conservative approach.
5. Ongoing experimental investigations on serviceability limit state 5.1 Slip at the serviceability limit state Bond and adhesion in combination with friction between steel and concrete was extensively investigated in the past (for example [7]), resulting in corresponding design provisions. Push-out tests typically show a peak load corresponding to the load at which bond and adhesion is destroyed. With increasing deformations the load drops to the remaining level of effects of friction. Because the ultimate capacity of bond and adhesion shows a great scatter, it is not considered explicitly in design. Only effects of friction can be utilised. Literature [7] further indicates, that deformations before debonding are very small. Basically no slip in the interface was measured for loads up to 70 percent of the ultimate load. Therefore, an additional test program was worked out to investigate the combined behaviour of effects of friction with the nailed shear connection. The principle set-up of series I (Fig. 4) corresponds with those in the former tests. The load will be introduced into the concrete and has to be transferred into the uniformly supported pipe. For the purpose of this investigation, the symmetric test set-up I with an axial load introduction represents the most critical practical situation. To measure realistic initial deformations, no lubrication of the inner tube surface will be made. The introduction length is selected with 2.5-times the pipe diameter following the provisions given in [8]. The load sequence is selected in such a way to describe a practical situation realistically. The primary objective of these tests is to verify a design load PSLS for serviceability limit state verifications of approximately 12 kN per nail. Therefore, the specimen will be loaded in the first step up the target working load PSLS (compare Fig. 4) and relieved to
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zero to measure remaining deformations. Afterwards 100 load cycles varying between 0.5 and 0.8-times of PSLS will be performed to simulate live loads. Then the specimen will be relieved again followed with the loading up to failure. 323,9
810
50
Pipe 323.9/ 6.3, S235
Concrete: C30/37 Air gap
X-DSH32 P10
Series I
Series II (schematic)
Type A: 16 nails: PSLS = 16 . 12 = 192 kN Type B: 32 nails: PSLS = 32 . 12 = 384 kN Fig. 4: SLS-Tests: Series I and II: Set-up and load sequence Tests with two different numbers of nails (16 and 32) will be performed. It is known from [7], that the peak strength of bond and adhesion varies in a range between 0.45 and 1.4 N/mm². That means that for the given geometry the load before debonding may vary between 350 and 1100 kN. Test series I comprises also control tests without any nails. With the results from the control tests and those from the two different nail patterns, the combined behaviour will be known for this specific configuration. Therefore, the tests serve as the experimental basis for a numerical generalisation of the combined behaviour in the service state, in which just the allowable frictional bond will be utilised. Series II differs from series I in the load introduction and the specimen support. The load introduction corresponds to the practical situation in which to load is introduced into the tube by a fillet welded vertical gusset plate. The objective of these tests is to investigate the plastic load bearing behaviour of the composite column. Specifically shall be clarified, if the actual pipe deformations are high enough to activate all installed nails. The number of nails was selected in such a way, that the plastic resistance of the composite section can be achieved.
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5.2 Long-term effects Tests have been performed in order to investigate the long-term behaviour and influence of creep of concrete of the nailed shear connections. The test set-up of the creep tests performed at Hilti Corporation is shown in Fig. 5. Additional tests have been performed at the University of Innsbruck [9] using basically the same test set-up and specimen configuration. Only four nails were used per specimen, as the specimen size had to be kept smaller with regards to test execution. In order to eliminate potential effects of bond, adhesion and friction, the inner pipe surface was again lubricated. The load was applied at an age of concrete of eight days. Spring tensioned pressure device
Centric threaded rod M 16 Circular plate d = 195
30
2 displacement gages
300
100
Plastic pipe with gap to the anchor r od
180
Lubricated inner pipe surface
4 nails X-DSH32 P10
30
20
ca. 2 cm air gap
240
M16 thread
Pipe 219 / 6,3
240
Fig. 5: Test set-up for long-term tests Table 1: Parameter and results of long-term tests Test at # fc at fc at 28 Load P Initial deformation deformation loading (8 days per nail slip after 90 after 395 days) [N/mm²] [kN] [mm] days [mm] days [mm] [N/mm²] Hilti 1 27.8 44.4 10 1.04 0.76 0.88 2 27.8 44.4 10 1.28 0.75 0.85 3 27.8 44.4 5 0.56 0.24 0.29 Innsbruck 4 na 47.2 15 na 0.03 5 na 47.2 15 na 0.03 In comparison with the measurements from the push-out tests [4], [5], the initial slips are greater. Reasons for that behaviour might be the small concrete age of 8 days at loading and the small number of just four nails. It is assumed that with increasing nail number
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the stiffness per fastener also would increase caused by the fact, that the contact area between nail and concrete is of the same order as the concrete aggregates themselves. Fig. 6 shows the development of the creep deformations. Up to approximately 10 days the deformation exhibits a parabolic shape, beyond which the development of the deformation flattens significantly. The creep deformation after 10 days amounts to approximately 75 percent of the value measured after one year of loading. Considering the range of permanent dead loads, creep deformations derived from test #3 amount to approximately 50 percent of the initial slip. 1,2 1,1
Creep deformation [mm]
1
Test #1
Test #2
Test #4
Test #5
Test #3
0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0
50
100
150
200
250
300
350
400
Duration of loading [days]
Fig. 6: Deformations derived from long-term tests #1 to #5 Interestingly the tests performed at the University of Innsbruck led to complete different results. As basically the same test equipment was used as in the tests 1 to 3, it was speculated that bond, adhesion and friction was not adequately prevented by the lubrication measurement of the inner tube surface. Therefore, the tests were stopped after 90 days to perform push-out tests with these specimens, followed by a visual investigation of the inner tube surface. From these visual comparison it was clearly seen, that bond and adhesion and large area friction was partially active. That incomplete prevention of natural bond explains that even with the greater load of 15 kN per nail basically no creep deformations were recorded. This observation is a further indication, that natural bond effects shall be considered for a realistic and economical assessment of the slip characteristics in the service state. The results of the push-out tests summarised in Table 2 further support that assumption. As natural bond was partially active the achieved loads at a slip of 0.5 mm are significantly greater than the target value of 12 kN per nail for the serviceability limit state. In these push-out tests no real load maximum was observed within the recorded slips up to 35 mm, indicating that already a few number of nails will change the characteristics of bond, adhesion and large area friction completely.
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Table 2: Result of push-out tests of creep specimen #4 and #5 Test load P [kN] per nail at slip of Test at # fc [N/mm²] 0.5 mm 30 mm Innsbruck 4 47,2 30.7 170.0 5 47,2 20.0 172.5
6. Worked design example Fig. 7 shows a typical example of nailed shear connection as part of a composite joint. The load is introduced into the column by a fillet-welded gusset plate connected on the outside of the pipe. Generally the nails can be uniformly distributed along the circumference of the pipe.
Fig. 7: Example of composite beam column joint Table 3: Summary of design equations, load introduction into steel tube Ultimate limit state (ULS) Serviceability limit state (SLS) ηULS FSd ≤ n RDSH,Rd,ULS ηSLS Fk ≤ n RDSH,Rd,SLS ηULS =
A c f cd + A s f sd N pl, Rd
ηSLS =
Npl,Rd = Aa fyd + Ac fcd + As fsd
Ac / n o + As Ai
Ai = Aa + Ac/n0 + As
Composite tube columns ∅ 508 x 6,3 S235; C45/55; 8∅28 S 500 Nails X-DSH 32 P10; Rk = 21,0 kN, RDSH,Rd, ULS = 21,0 / 1,25 = 16,8 kN Aa = 99,3 cm²
As = 49,3 cm²
Ac = 1878,2 cm²
Npla,Rd = 2121,4 kN
Npls,Rd = 2143,5 cm²
Nplc,Rd = 5634,6 kN
Npl,Rd = 9899,5 kN
no = 21000 / 3600 = 5,8
Two composite beams with ΣFG = 530 kN (permanent load), ΣFQ = 320 kN (variable load)
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FSd =1,35 ⋅530 + 1,50 ⋅320 = 1195,5kN η ULS =
2143,5 + 5634,6 = 0,79 9899,5
Fk = 530 + 320 = 850,0 kN η SLS =
1878,2 / 5,8 + 49,3 = 0,79 1878,2 / 5,8 + 49,3 + 99,3
required number of nails:
required number of nails:
nULS = 0,79 ⋅ 1195,5 / 16,8 = 56,2
nSLS = 0,79 ⋅ 850 / 12 = 56,0
ref. 3 ⋅ 20 = 60 X-DSH 32 P10 with Fk ... Characteristic value of the total support reaction FSd .. Design value of the total support reaction RDSH,Rd,ULS =16,8 kN Design resistance per X-DSH32P10 for the ULS RDSH,Rd, SLS =12,0 kN Design resistance per X-DSH32P10 for the SLS n .... total number of nails per joint Npl,Rd ... Plastic resistance to compression of a composite cross-section according to [8] Ai ... Cross-sectional area of the composite cross-section based on steel properties n0 ... Modular ratio for short term loading
7. References 1. Tschemmernegg, F., ´Innsbrucker Mischbautechnologie im Wiener Millennium Tower´, Stahlbau 68, Heft 8, (1999), 606-611 2. Angerer, T., Rubin, D., Taus, M., ´Verbundstützen und Querkraftanschlüsse der Verbundflachdecken beim Millennium Tower´, Stahlbau 68, Heft 8, (1999), 641-646. 3. Tschemmernegg, F., Beck, H. ´Nailed shear connection in composite tube columns´, (1998) March 1998 ACI Convention, Houston, Session on Performance of Systems with Steel-Concrete Columns 4. Larcher, T.Z., ´Versuche zur Krafteinleitung der Trägerauflagerkräfte bei Hohlprofilstützen mit Setznägeln´, (1997), Diplomawork at the Institute of Timber and Mixed Building Technology, Leopold-Franzens-University of Innsbruck 5. Beck, H., ´Nailed shear connection in composite tube columns´, (1999) Proceedings of the Conference Eurosteel ´99, Prague, 26-29 May 1999 6. Hanswille, G., Neubauer, T., ´Zulassungsantrag beim DIBt. Stellungnahme für die Nägel X-DSH32P10 zum Einsatz bei betongefüllten Hohlprofilen als Verbundmittel´. 7. Roik, K., Breit, M., Schwalbenhofer, K., ´Untersuchung der Verbundwirkung zwischen Stahlprofil und Beton bei Stützenkonstruktion´. (1984) Projekt 51, Institut für konstruktiven Ingenieurbau, Ruhr-Universität Bochum. 8. DIN 18800-5, ´Stahlbauten: Teil 5: Verbundtragwerke aus Stahl und Beton, Bemessung und Konstruktion´. (1999), Draft, January 1999 9. Frischhut, M., Michl, T., ´Versuchsbericht: Hilti-Nägel im Verbundbau, Langzeitverformungen und Late-Push-Out´, (2000), Test report 13.09.2000, Institute of Timber and Mixed Build. Technology, Leopold-Franzens-University of Innsbruck
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AN EXPERIMENTAL STUDY ON SHEAR CHARACTERISTICS OF PERFOBOND STRIP AND ITS RATIONAL STRENGTH EQUATIONS Ushijima Yoshitaka*, Hosaka Tetsuya**, Mitsuki Kaoru**, Watanabe Hiroshi**,Tachibana Yoshihiro**, Hiragi Hirokazu*** *Kawada Industries, Inc., Japan **Japan Railway Construction,PC. ***Setsunan University, Japan
Abstract This paper deals with the rational shearing strength equation and the slip behavior for shear connectors called the Perfobond Strip (Concrete Dowel: hereinafter, abbreviated to PBL) that is used at the continuous composite girder of railroad bridges. This PBL is the shear connector proposed by Leonhardt in Germany, and its composite effect between steel and concrete is very high due to the shearing resistance of the concrete in perforations of the steel plate. Also, the PBL shear connectors Strip is recognized having high fatigue strength. Strength evaluation equations for the design of PBL shear connectors are proposed by various investigators in the world. Existing research has clarified that the shearing strength of PBL shear connectors is very dependent on the perforation diameter and the compression strength of concrete in case of no reinforcement bars. In actual structure, however, the reinforcing bars were arranged to the neighborhood of shear connectors in most of the case. Thus, in this investigation, the authors chose the strip thickness, the distance of strips, the presence of reinforcing bars and the perforation diameter as experimental parameters. Also, from the result of a multi linear regression analysis based on data published in the world including our data, two kinds of new rational strength equations for PBL shear connectors were derived. One is a strength equation without reinforcing bars and the other is a strength equation with reinforcing bars. It became clear that these evaluation equations express data of push-out test well. The strength equations for design are also proposed, respectively.
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1. Introduction At present, the construction of continuous composite girders is being examined from the consideration of noise and vibration in the train transit-time on steel railway bridges. Much research on shear connectors of steel beam and concrete slab has been carried out until now for the multi-main girder bridge [1], [2], [3]. And, the research on 2 main I cross section girder bridges, in which the floor system span is wide, is carried out for the continuous composite railway girder in order to promote further rationalization [4], [5]. As shear connector structure in this bridge type, it is also anticipated that the necessity of arranging many horseshoe-shaped shear connectors occurs and that its arrangement becomes physically difficult, since the horizontal shearing force that has to be transmitted from the girder to the concrete slab by 2 main girders increases, when the horseshoe-shaped shear connectors in railway bridge are applied with heretofore similarly. On the other hand, one has to worry about the fatigue strength of the flange plane of steel beams at the intermediate support division of continuous girder bridges, when stud shear connectors were applied. Therefore, the development of a shear connector structure that is resistant to tensile force of bridge axial direction is required. Then, the application of PBL shear connectors developed by Leonhardt et al [6]. of Germany, which also have high durability, to the continuous composite girder is examined with the transmission force of the equivalent horizontal shearing force with horseshoe-shaped shear connectors and stud shear connectors in railway bridges. There are results which have already adopted the PBL shear connectors at intermediate support parts such as Hokuriku Shinkansen "the Hokuriku way overbrige" in Japan. In until now research, these PBL shear connectors were designed so that the concrete in the perforations was fractured by shearing stress as precondition. In the reason, the following are considered as factors influencing the ultimate strength: perforation diameter and compression strength of the concrete [6], [7], [8]. Afterwards, experimental researchs were carried out in Japan [9], [10], [11]. However, there seems to be no research yet, which clarifies the behavior of the reinforcing bars, the plate thickness of PBL shear connectors, existence of the reinforcing bars running through the perforations of PBL and the number of sheets of PBL shear connectors placed on the flange plane. Thus, in this study, test specimens of 8 types with those factors were manufactured, and static push-out shearing tests were carried out. Especially, a comparison examination was carried out for the slippage constant and failure mode. And, collection, arrangement and statistic analysis in respect of the test data (including this experiment result) for previous shear capacity were made, in order to lead to strength evaluation equations of necessary shear load-carrying capacity in the design of the PBL shear connectors. The purpose of this investigation is to arrange knowledge on the PBL shear connectors.
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2. Failure conditions In order to understand the conditions of concrete cracks after completing the tests, a concrete block part of the specimen was cut, and the final failure condition was visually observed. 2.1 Influence of strip thickness Here, specimens without penetration reinforcing bars re-bars will be observed. First, concrete in perforations of the thin 8mm-strip specimen was pulverized in the steel plate of PBL. However, concrete of the thicker strip specimens sheared on both sides of the strip. As differences in failure phenomena by strip thickness are shown in Figure 1, the small thickness causes the area of compression to be minimized and the force to be concentrated. This concentration of force is thought to have generated splitting tension. On the other hand, when the strip thickness is large, the area of compression is large, and the force is thought to dispersively work on the concrete. This dispersed force is thought to finally reach the maximum shear strength of concrete on extended lines of both sides of the strip, and subsequently cause it to shear (see Photos 1 and 2). Failures in specimens with penetration reinforcing bars re-bars will be shown later 2.2. Furthermore,
Shearing force Steel strip
Shearing force
Steel Area of 3 axial compressive stress strip Compressive area
Area of 3 axial compressive stress Compressive area Shear failure
Tension failure (a)Specimen with (b)Specimen with thin strip thick strip Figure 1. Failure conditions (Influence of strip thickness) Shearing force
Steel strip Penetration reinforcing bars
Area of 3 axial compressive stress Compressive area
Pulverized
Finished test Splitting tension is restrained or Concrete in the perforations shear resistance is improved by is pulverized by penetration reinforcing baras reinforcing baras Figure 2. Failure conditions (Influence of penetration reinforcing bars)
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3-axial compressive stress areas shown in Figures 1 and 2 were assumed to be those in which concrete does not completely generate tension (areas in the figures are assumptions). 2.2 Influence by the existence of the penetraion reinforcing bars It was clarified that final failure conditions of specimens without penetration reinforcing bars would vary depending on the strip thickness as mentioned above. 8 and 16mm specimens with penetration reinforcing bars both failed because the concrete in the perforations pulverized from compression. Factors for these specimens with penetration reinforcing bars to indicate similar tendencies in final failure conditions are thought to be the penetration reinforcing bars restraining each compressive area of Figure 1 (a) shown in Figure 2, which contributed to the improvement of shear strength at the same time (see Photos 3 and 4). Here, it was also confirmed that the specimen with penetration reinforcing bars had local deformations on the inner sides of the perforations in contact with the reinforcing bars.
3. Study on strength evaluation equations The authors of this research have decided to collect and organize previous experiment data on PBL shear connectors including experiment values of maximum shear strengths
Photo 1. Failure condition (Strip thickness: 8mm)
Photo 2. Failure condition (Strip thickness: 16mm)
Photo 3. Failure condition (Strip thickness: 8mm)
Photo 4. Failure condition (Strip thickness: 16mm)
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to obtain new rational strength evaluation equations for specimens with and without penetration reinforcing bars.
Table 3. Average values and variation range for test data of Perfobond strips d(mm)
Average Max 58.9 80.0
Min 35.0
3.1 Previous strength evaluation equations t(mm) 17.1 22.0 8.0 The influenceial factors on shear strengths of PBL fcu(N/mm2) 39.0 57.6 23.8 11.9 28.6 5.1 φst(mm) shear connectors are thought to be many, and do not fst(N/mm2) 468.1 500.0 440.0 seem to be unified. A relationship of influencing factors used by the equations (d2fcu; where, d: perforation diameter; fcu: concrete cylinder compressive strength) and experimental shear strength value per perforation in PBL (Qmax) is shown in Figures 3,4. Here, the equation proposed by Leonhardt, et al., is without consideration of penetration reinforcing bars in perforations of PBL, and as made clear by Figure 4, it can be seen that all test data were not successfully taken into account. Also, H. Andrä [7] himself proposed equation by expanding equation of Leonhardt. Also in 1994 in Japan, Ogata et al., [9] proposed equation for PBL shear connectors to be applied to bridge piers. According to the strength equations proposed previously, concrete shear failure was assumed to precede; therefore, influential factors on ultimate shear strengths were thought to be perforation diameters in PBL (d) and concrete cylinder compressive strength (fcu). Furthermore, equation (1) shown in Figures 3 and 4 include coefficients to convert cube strengths into cylinder strengths in order to have the same condition as the concrete strength used in this experiment. Later, Kraus et al., [12] proposed equation which limited the perforation diameter and strip thickness (t) of PBL (d=70mm, t=10mm), adding its thickness t to the influencing factors. Experiments were conducted, changing the number of perforations in PBL, their diameters, reinforcing bars arrangement, etc., by Taira et al., [10] in 1997, Hosaka, Hiragi, Koeda, et al., [5] and Tominaga, Nishiumi et al., [13] in 1998. Ebina et al., [11] conducted experiments on a shear connector structure to be applied to lower floor slabs of a PC bridge with corrugated web, and Uehira et al., [15] also similarly proposed equation. In addition, there are experiment reports on rigid connection structures to be applied to RC piers and steel girders in a few references [15], [16], [17]. Thus in this research, efforts were made to collect as much test data as possible, and in the experiment values shown above, only experiment results that had all definite data were selected to taken into account. And strength equation relations previously proposed on shear strength were used in an attempt to reorganize test data collected and organized for this research. 3.2 Proposal of strength evaluation equations Using previous research results, the results of the experiments conducted this time, and selecting d, t, fcu, fst, etc., as influential factors on experiment values of shear strengths for PBL (Q max per perforation), an attempt was made to propose a strength evaluation equation through a statistical analysis method shown in Reference [18]. (1) Organization based on the influence factor d 2f cu Failure conditions of the results of this experiment shown in Section 2.2 were thought to differ depending on the existence of penetration reinforcing bars. Thus, the experiment
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(kN/hole)
Shear strength per perforation
data without penetration reinforcing bars were plotted in Figure 3, and those with reinforcing bars placed were plotted in Figure 4. These figures also have evaluation equation accompanying the equations (1) proposed by Leonhardt. The correlation coefficients shown in the figures 3 and 4 are indices showing a variation in experiment values for this arranging sorting method, and data of this experiment shows a positive correlation. As a result, although experiment data without penetration reinforcing bars had a significantly high coefficient 0.935 as shown in Figure 3, it was confirmed that this coefficient varied slightly in all areas of the experiment data. This is thought to be caused by the lack of consideration for the progression of failure condition progress influenced by the strip thickness shown in Figure 1 of Section 2.1. On the other hand, data from experiments with penetration reinforcing bars shown in Figure 4 had a coefficient of 0.810, which confirmed a wide variation for this arranging method. However, the influence of penetration reinforcing bars was not considered in equation (1). Thus, it was concluded that strength evaluation equations for PBL shear connectors should be proposed in 2 types of strength equations by having or not having penetration reinforcing bars to consider failure conditions. (2) Rational strength evaluation equation without penetration reinforcing bars Correlation coefficient=0.935
800
2
Qu=1.79d fcu ----(1)
700 600 500 400 300 200
fcu:Cylinders concrete strength
100 0 0
100
Test data without reinforcing bars Profosed by Leonhardt equation (1) 200 300 400 500 2 (kN/hole) d ×fcu
(kN/hole)
Figure 3. Influence factor d 2f cu (without reinforcing bars) Qu=1.79d2fcu ----(1)
Shear strength per perforation
800 700
Correlation coefficient=0.810
600 500 400 fcu:Cylinders concrete strength fst:Tensile strength of reinforcing bars
300 200 100
Test data of with reinforcing bars Profosed by Leonhardt equation (1)
0 0
100
200 300 d2×fcu
400
500
(kN/hole)
Figure 4. Influence factor d 2f cu (with reinforcing bars)
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(kN/hole)
Shear strength per perforation
800
Correlation coefficient=0.971
700
2σ
t
600 500
d
400 300 200
fcu:Cylinders concrete strength
100
Test data of without reinforcing bars rational strength equation (2) 60 120 180 240 (kN/hole) 2 1/2 d (t/d) fcu
0 0
(kN/hole)
Shear strength per perforation
Figure 5.Rational evaluation equation (without reinforcing bars) Correlation coefficient=0.979
800
2σ
700 600 500
d
Dst
400 300 fcu:Cylinders concrete strength fst:Tensile strength of reinforcing bars
200 100 0 0
Test data of with reinforcing bars rational strength equation (4) 200 400 600 2 2 (d -Dst )fcu+Dst2fst (kN/hole)
Figure 6. Rational evaluation equation (with reinforcing bars) Failure conditions without penetration reinforcing bars were seen as bearing splitting failures besides shear failures in the experiment results of the 8mm-thick specimen. Therefore, failure conditions without penetration reinforcing bars are thought to be caused by the coupling of shear and bearing progresses. The difference between these progresses in respect of the thickness variation is thought to be influenced by the dimension effects of the perforations in PBL, i.e., the ratio between strip thickness (t) and perforation diameter (d) in PBL, although shear failure occurs at the ultimoate. Thus, a multiple regression analysis was conducted to add the influence of thickness-diameter ratio (t/d) to the equation (1) proposed by Leonhardt et al., using all test data (without penetration reinforcing bars) collected and organized for this investingation. As a result, the equation (2) was obtained as a rational evaluation equation on ultimate shear strength per perforation in PBL. 1/2 Q = 3.38d 2 t / d f - 39.0 u cu
(2)
Where, Qu: Ultimate shear strength(N) t: Strip thickness(mm) d: Perforation diameter(mm) f cu: Concrete cylinder compressive strength(N/mm2)
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Also, considering experiment values, the range of application for equation (2) is assumed to be: 22 .0 < d 2 t / d
1/2
f
cu
< 194 .0
The result reorganized by the influencing factors of evaluation equation (2) is shown in Figure 5. As a result, the correlation with the experiment values further increased compared to the expression method proposed by Leonhardt et al., and the correlation coefficient became 0.971. Here in equation (2), the thickness-diameter ratio (t/d) increased with the increase in the strip thickness, and a dominance of shear failure can be reproduced; the thickness-diameter ratio (t/d) decreased with the decrease in the strip thickness, and a tendency of bearing splitting failure dominating prior to shear failure can also be reproduced. Also, as a shear strength equation to be used for design (Qd), equation (3) shifted twice as low as the standard deviation is shown in a form including the lowest limit value of scattering experiment values. Q = 3.38d 2 (t d )1/2 f - 121.0 (3) d
cu
Here, Qd: Design shear strength(N) (3) Rational strength evaluation equation with penetration reinforcing bars With penetration reinforcing bars, it is confirmed from Figures 3-6 of Section 2.1 and Section 2.2 that penetration reinforcing bars contribute to shear strength. Thus, a multiple regression analysis similarly mentioned above was conducted by adding the penetration reinforcing bars diameter (Dst ) and its tensile strength (fst) as influence factors. As a result, the relation shown in Figure 6 was finally obtained. Here, the experiment value Dst shown in the figure was the diameter of a penetration reinforcing bars inserted into a perforation of PBL, and for the case, that not all perforations had reinforcing bars, a reinforcing bar diameter converted into diameter per perforation in PBL was used. As a result, equation (4) was obtained as an evaluation equation for ultimate shear strength per perforation in PBL.
{(
)
}
Q = 1.45 d 2 - Dst 2 f cu + Dst 2 f st - 26.1 u
(4)
Where, Dst: Penetrating re-bar diameter(mm) f st: Penetrating re-bar tensile strength Also, considering the experiment values, the range of application is of equation (4) assumed to be:
(
)
51.0 < d 2 - Dst 2 f cu + Dst 2 f st < 488.0
The first item bracketed { } in equation (4) is the shear strength for the actual area of concrete between perforations in PBL and penetration reinforcing bars (the value which subtracted the reinforcing bar cross section area subtracted from the perforation area in PBL), and the second item is the factor equivalent to the tensile strength of the penetration reinforcing bars. Superimposing these factors lead to obtaining an arranging method with a high correlation and even a correlation coefficient of 0.979, which resulted in supporting the explanation of failure conditions shown in Figure 2. Also, as a shear strength equation for PBL to be used for design, equation (5) shifted twice as low
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as the standard deviation is shown in a form including the lowest limit value of scattering experiment values.
{(
)
}
Q = 1.45 d 2 - Dst 2 f cu + Dst 2 f st - 106.1 d
(5)
From the results above, it can be judged that a rational evaluation equation with a high correlation was obtained on ultimate shear strengths for PBL shear connectors with and without penetrating re-bars.
4. Conclusion In this paper, special attention was paid to important factors of Perfobond Strips such as strip thickness, existence of penetration reinforcing bars and the number of strips, to describe results of basic push-out tests. Also, based on existing previous results including the our present results, a rational strength evaluation equation for PBL was proposed. Main results obtained in this experiment are summarized below. (1) This experiment made it possible to propose a rational shear strength evaluation equation (Qu) on PBL without penetration reinforcing bars. This evaluation equation was derived considering the influence of dimension effect (thickness/diameter ratio) to methods of expression obtained in the previous research. In addition, a shear strength evaluation equation for design (Qd) was proposed. (2) It became possible to propose a rational shear strength evaluation equation (Qu) on PBL shear connectors with penetration reinforcing bars. This evaluation equation was derived, based on relation expressions obtained in previous research, from adding shear strength in the actual area of concrete between perforations in PBL and penetration reinforcing bars (a value which subtracted the reinforcing bar area from the perforation area) and the tensile strength of penetration reinforcing bars. Also, a shear strength evaluation equation for design (Qd) was proposed. Considering the application of wide span floor slabs to 2 continuous composite Isectional main girder systems on railway bridges, and based on this research, it is intended to conduct further fatigue experiments on the PBL shear connectors subject to uplift action from a floor slab.
5. References [1]Abe.H: Experimental Investigation of Shear Connectors for Railway Composite Bridges , Railway Technical Research Report , No.961,1975.(in Japanese) [2] Abe.H, Nakajima.A, Hirohi.H:Efect of Division of Slabs in Composite Girder and Development of Flexible Connectors, Journal of Structural Engineering, Vol.35A , pp1205-1211,1989. (in Japanese) [3]Hosaka: Attempt of Economical Steel Railway Bridge, Proceeding of The 1st Symposium on Steel Structures and Bridges, pp89-97,1998. (in Japanese) [4]Ushijima, Hosaka, Tachibana, et al: An Experimental Study on Cracking Behavior in Continuous Concrete and Steel Composite Girder Bridge, Proceedings of the 52th Ananual Conference of the Japan Society of Civil Engineers, I-A123,1997. (in Japanese)
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[5]Hosaka, Hiragi, Koeda, Tachibana, Watanabe: An Experimental Study on Characterristics of Shear Connectors in Composite Continuous Girders for Railway Bridges, Journal of Structural Engineering, Vol.44A , pp1497-1504,1998. (in German) [6]Leonhardt Fritz , Wolfhart Andrä , Hans-Peter Andrä and Wolfgang Harre : Neues , vorteilhaftes Verbundmittel Für Stahlverbund-Tragwerke mit hoher Dauerfestigkeit, Beton-und Stahlbetonbau , Heft , 12/1987. (in Japanese) [7]Hans-Peter Andrä : Economical Shear Connectors with High Fatigue Strength , IABSE SYMPOSIUM , 1990. [8]Wayne S . Roberts and Robert J . Heywood : An Innovation To Increase The Competitiveness of Short Span Steel Concrete Composite Bridges , Developments in Short Medium Span Bridge Engineering , 1994. [9]Ogata, Murayama, Okimoto, Imanishi: Study on Adhesion Characteristic of Steelmade Element and Concrete, Proceedings of Third National Concrete and Masonry Engineering Conference, Vol.16, No.2,1994. (in Japanese) [10]Taira, Amano, Ootsuka: Fatigue Characteristic of Perfobond Strip, Proceedings of the 52th Ananual Conference of the Japan Society of Civil Engineers, Proceedings of Third National Concrete and Masonry Engineering Conference, Vol.19, No.2, pp150311508,1997. (in Japanese) [11]Ebina, Takahashi, Uehira, Yanagisita: Basic research on Perfobond Strips under Shear Strength, symposium of the eighth times thesis collection, Proceedings of The 8th Symposium on Developments in Prestressed Concrite, pp31 -36,1998. (in Japanese) [12] Dieter KRAUS and Otto WURZER : Bearing Capacity of Concrete Dowels , Composite Construction-Conventional and Innovative , 1997. [13] Tominaga, Nisiumi, Muroi, Furuichi: Shear Strength of Perfobond Rib Shear Connector Under The Confinement, Proceedings of the 53th Ananual Conference of the Japan Society of Civil Engineers, I-A323, pp646 -647,1998. (in Japanese) [14]Shintani, Ebina, Uehirai, Yanagisita: To the method of uniting a wavy steel board and the concrete floor version Concerned experimental research, Proceedings of The 8th Symposium on Developments in Prestressed Concrite, pp91-96, 1999. (in Japanese) [15]Taira, Furuichi, Yamamura, Nishiumi: Study on Strength of Perfobond Strip, Proceedings of the 53th Ananual Conference of the Japan Society of Civil Engineers, IA324, pp648-649,1998. (in Japanese) [16]Nagata, Akehashi, Watanabe: An Examination on Pull out of Perfobond Strip in, Science lecture lecture outline collection of the 54th time of engineering works academy annual and I-A149 and pp298-299,1999. (in Japanese) [17]Suzuki, Ueda, Furuucti:Base Concerning Push Out Shearing Strength of Perfobond Strip, Proceedings of the 54th Ananual Conference of the Japan Society of Civil Engineers, I-A150, pp300-301,1999. (in Japanese) [18] Hiragi Hirokazu, Matsui Shigeyuki, Fukumoto Yuhshi: Derivation of Equations of Headed Stud Shear Connectors -Static Strengths-, Journal of Structural Engineering, Vol.35A , pp1221-1232,1989. (in Japanese)
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BEHAVIOR OF LYING SHEAR STUDS IN REINFORCED CONCRETE SLABS Ulrike Kuhlmann, Kai Kürschner Institute of Structural Design, University of Stuttgart, Germany
Abstract As a basis for innovative composite structures with horizontally lying headed studs in thin reinforced concrete slabs results of investigations about the carrying behavior under vertical shear and combined vertical and longitudinal shear are presented. The significance of the reinforcement and the influence of various other design parameters for the carrying capacity and the deformation behavior are demonstrated and assessed. A design method for the application of lying shear studs in practice is illustrated.
1. Introduction Some new interesting composite cross sections for buildings and bridges lead to a horizontally lying arrangement of headed studs partly with only a small distance ar,o to the upper surface of the thin reinforced concrete slab (see Fig. 1.1). (a) Position of the Shear Connection
Section A-A (Without Reinforcement)
A a r,o
A
(b) Cracking Action
A Edge Position
A Middle Position
Due to Longitudinal Shear
Due to Vertical Shear
Figure 1.1 Position of the Shear Connection and Cracking Action due to Shear In contrast to the common arrangement of studs perpendicular to the steel flange the transfer of the longitudinal shear by horizontally lying studs causes a splitting action in the direction of the slab thickness producing cleavage cracks parallel to the slab surface /1/, /2/, /3/. In practice however often not only longitudinal shear but also vertical shear
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due to vertical loading is often acting on this kind of connection. In contrast to standard composite girders there is no upper steel flange which may transmit the vertical shear to the steel web by contact pressure. The stud is subjected to an additional shear action. Basically two different positions of the shear connection relative to the reinforced concrete slab exists: at the edge or in the middle of the slab (see Fig. 1.1). Analogous to the strut-and-tie models for the longitudinal shear action /1/, /3/, due to different stiffness conditions the position of the shear connection influences the carrying behavior of horizontally lying studs subjected to vertical shear action. For the transfer of vertical shear the following two simplified strut-and-tie models are developed (see Fig. 1.2). Middle Position of the Shear Connection
Edge Position of the Shear Connection T/2 T
T T/2
Reinforced Concrete Slab
Steel Web
Tension Compression
Figure 1.2 Strut-and-Tie Models for the Transfer of the Vertical Shear Action In both cases the vertical reaction force of the slab is induced in the steel web by an inclined spatial compression field. The resulting inclined strut may be resolved in its horizontal and vertical component. For the shear connection in the middle of the slab the horizontal components on both sides of the steel web are adjusted in equilibrium by themselves. Friction and bearing stress are expected to result in an increase of the vertical shear resistance. For the shear connection at the edge of the slab the geometry and stiffness do not enable a direct compensation of the horizontal components. As a consequence due to anchorage of the headed stud the reinforced concrete slab is subjected to an additional tensile stress. To identify the major parameters of failure and to quantify the carrying capacity of horizontally lying studs under vertical and combined vertical and longitudinal shear at the edge of the slab a research project has been carried out /4/.
2. Experimental Outline The test series is subdivided into ten test groups. Altogether 22 pushout tests under vertical shear and four tests under combined vertical and longitudinal shear have been carried out. According to Table 2.1 within each test group of two up to four specimens only one design parameter is varied whereas the other parameters are kept constant.
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Test Group
Number of Tests
Variation of Design Parameters
R1
Concrete Strength C 20/25 → C 30/37 → C40/50
3
R2
Thickness of the Slab 300 mm → 350 mm → 400 mm
2
R3
Horizontal Distance Between the Studs 110 mm → 165 mm → 220 mm
2
R4
Stirrup Reinforcement per Stud 1∅10 → 1∅12 → 2∅10 → 2∅12
3
R5
Diameter of the Longitudinal Reinforcement ∅12 → ∅14 → ∅16
2
R6
Position of the Studs Relative to the Centre Plane of Slab below → concentric → upside
2
R7
Horizontal Distance Between the Studs (two rows but not parallel) 110 mm → 165 mm → 220 mm
Stud ∅ 22, dc = 400 mm
R8
Number of Stirrups per Stud (studs in two rows) 1∅12 → 2∅12
2
Stud ∅ 25, dc = 300 mm
R9
Horizontal Distance Between the Studs 125 mm → 187,5 mm → 250 mm
3
Stud ∅ 22, dc = 300 mm
R10
Combined Vertical and Longitudinal Shear 0 → 0,25 → 0,45 → 0,55 → 0,75 → 1
4
Stud ∅ 22, studs in one row (except for R7), dc = 300 mm (except for R2)
22
3
4
Remark: The underlined design parameters corresponds to the basic specimen B.
Table 2.1 Allocation of the Test Groups to the Design Parameters R10
SectionA-A
Side View
B
165 165 165 402.5
1300
a a
a
1300
a = 110 to 250
A Section B-B
A
300 to 400
Section A-A
150 150
A B
A
300
800
402.5
800
70
Top View
70
R1 to R9
All Dimensions in mm
Figure 2.1 Geometry of the Specimens Subjected to Vertical Shear (R1 to R9) and Combined Vertical and Longitudinal Shear (R10)
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To be able to compare one basic specimen B is identified and included in each test series with the exception of R7, R8 and R9. The four specimens of the test group R10 are produced identically. The geometry of the specimens subjected to vertical shear only (R1 to R9) and combined vertical and longitudinal shear (R10) is given in Figure 2.1. The test procedure was chosen as consistent as possible with the specifications in Eurocode 4 /7/. During the tests the slip, the displacement between the steel web and the front face of the slab and diverse strain measurements have been documented.
3. Vertical Shear 3.1. Experimental Investigations See Figure 3.1 for a typical load-slip behavior of a stud subjected to vertical shear only. After 25 load cycles the loading was applied at a very slow displacement rate until the specimen failed. After exceeding the carrying capacity a relatively high residual load capacity remained. The high ductility of the shear connection is ensured by the reinforcement close to the front face of the concrete slab. Load Pe,Q per Stud [kN] 100
Carrying Capacity
80
Maximum Load per Stud 60
Load per Stud at Termination of the Test
40 20 0 0
5
10
15
20
25
30
35 40 45 Vertical Slip [mm]
Figure 3.1 Typical Load-Slip Behavior The following three failure modes were observed in the tests: Concrete For low degrees of reinforcement close to the shear connection the concrete edge above the studs broke out gradually. Concrete/Stud For higher degrees of reinforcement at first the concrete edge above the row of studs broke out gradually. This gradual concrete failure came along with high deformations of the stud shanks until a slip deformation of more than 35 mm led to a shear off of the studs. Stud Shear off of the studs just above the welds. For 91 % of the tests concrete failure was predominant.
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3.2. Parametrical Study The experimental studies as well as the additional numerical investigations indicate, that the following design parameters influence the carrying capacity: – concrete strength, – effective distance between the stud and the upper surface of the slab, – number of stirrups per stud, – diameter of the longitudinal reinforcement, and – diameter of the headed stud. Moreover the investigations show that the horizontal distance a between the studs and the stirrup diameter ds,Bü do not decisively affect the carrying capacity. Concrete Strength The investigations reveal, that the failure of the shear connection is initiated by an intense cracking formation. Therefore the tensile strength of the concrete, which is directly related to the compressive strength fc of the concrete, is of significance for the carrying capacity (see Fig. 3.2). An increase of the concrete strength leads to a distinct rise of the carrying capacity. Effective Upper Edge Distance Between the Stud and the Surface of the Slab If the shear connection is subjected to vertical shear primarily the concrete above the studs but within the reinforced part of the slab – defined by the effective upper edge distance ar,o′ between the stud and the surface of the slab according to Eq. (3.1) – offers resistance against the splitting forces in the direction of the slab thickness (see Fig. 3.3). ar,o′ = ar,o – nom cv – ds,Bü / 2
(3.1)
The carrying capacity increases significantly with rising effective distance between the studs and the stirrups at the upper slab surface. Pe,Q [kN]
Trend: Pe,Q ~ (fc)
0,5
Pe,Q' [kN]
100
0,7
100
80
R6/1
80
R1/3 B1
60 40
Trend: Pe,Q' ~ (ar,o')
R2/3 R2/2
60 B1
R1/1
40 R6/3
FE Tests
20
FE
20
0
Tests
0
20
25
30
35
40
45
50 55 2 fc [N/mm ]
25
Figure 3.2 Carrying Capacity Pe,Q per Stud Depending on the Compressive Cylinder Strength fc of Concrete
1080
50
75
100
125
150 175 ar,o' [mm]
Figure 3.3 Carrying Capacity Pe,Q′ per Stud Depending on the Effective Upper Edge Distance ar,o′ between the Studs and the Stirrups
Number of Stirrups per Stud In contrast to an increase of the stirrup diameter an increase from one to two stirrups per stud leads according to Fig. 3.4 to a distinct rise of the carrying capacity. The increase of the carrying capacity is caused by a more homogenous embracement of the front face of the slab. For example a doubled number a/s of stirrups per stud causes also a doubling of the edge points of the stirrups thus improving the support of the compression struts at the reinforcement. In addition due to the refined distribution of the stirrup reinforcement the stirrups cut the cracks at an earlier stage of the cracking process.
Pe,Q' [kN] 120 100 80 60
Mean Trend: Pe,Q' ~ (a/s)
0,4
R8/2 R8/1
R4/3
B1
R4/4
R4/1
40
FE Tests
20 0 0
1
2
3 a/s [-]
Figure 3.4 Carrying Capacity Pe,Q′ per Stud Depending on the Number a/s of Stirrups per Stud
A higher amount of stirrups per stud leads to a significant increase of the resistance. Diameter of the Longitudinal Reinforcement and Diameter of the Headed Stud Only a small rise of the carrying capacity of the shear connection may be achieved by an increased diameter ds,L of the longitudinal reinforcement and by an increased diameter dDü of the shank of the stud. The first is due to a higher flexural stiffness, the latter a result of a slightly increased width of force transition.
3.3. Results Model of Structural Behavior According to Fig. 3.5 the vertical load, to be transmitted into the steel web, is mainly introduced to the headed shear stud by two struts. (a) Flow of Force
(b) Cracking Formation
Figure 3.5 Flow of Force and Cracking Formation Close to the Shear Connection The vertical load is partly transferred by an inclined strut, which is supported by the lower edge point of the stirrup. The further flow of force can be explained by the specified strut-and-tie model. Additionally a part of the vertical load is transmitted by an even more inclined strut, directly supported by the shear stud. Due to anchorage of the headed
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stud the horizontal components of the struts cause tensile stresses in the reinforced concrete slab. With increasing slip deformation combined shear and tensile forces are acting on the headed stud. In spite of cracking formation mainly on the front face of the slab the break-out of a nearly conical concrete block is prevented by the reinforcement which embraces the edge of the concrete slab (see Fig 3.5). Carrying Capacity and Design Rule On the basis of experimental and numerical results an equation describing the carrying capacity of horizontally lying studs subjected to vertical shear has been derived. Pt,Q = 0,0396 ⋅
f c ⋅ d s,L ⋅ (dDü ⋅ a/s)0,4 ⋅ (ar,o′)0,7
assumptions for design: 22,2 N/mm2 ≤ fc ≤ 50,2 N/mm2 1 ≤ a/s ≤ 2 110 mm ≤ a ≤ 250 mm 12 mm ≤ ds,L ≤ 16 mm 49 mm ≤ ar,o′ ≤ 249 mm 22 mm ≤ dDü ≤ 25 mm where: Pt,Q fc ds,L dDü a s ar,o′ ar,o nom cv ds,Bü av hDü
(3.2) 10 mm ≤ ds,Bü ≤ 12 mm av ≥ 100 mm hDü ≥ 150 mm
carrying capacity [kN], compressive cylinder strength of the concrete [N/mm2], diameter of the longitudinal reinforcement [mm], diameter of the shank of the stud [mm], horizontal distance between the studs [mm], horizontal distance between the stirrups [mm], effective upper edge distance according to Equation (3.1) [mm], upper edge distance [mm], nominal vertical concrete cover [mm], diameter of the stirrup [mm], vertical distance between the studs in the case of two rows of studs [mm], and length of the stud [mm].
The geometrical parameters of the shear connection are given in Figure 3.6. Considering some simplifications the design resistance of a stud to vertical shear can be determined from: PRd,Q = 0,385 ⋅ where:
f ck ⋅ (a/s)0,4 ⋅ (ar,o′)0,7 / γV
(3.3)
γV = 1,25 partial safety factor according to Eurocode 4 /7/
Equation (3.3) has been developed for the edge position of the shear connection. As explained in Chapter 1 the results are applicable also for the position in the middle of the slab because this situation is less critical.
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h Dü
a'r,o
ar,o
d s,Bü 2
nom c v
A
nom c v +
a'r,o
A
nom c v
ds,Bü 2
d s,Bü 2
nom c h +
h Dü
ds,Bü 2
nom c h +
ds,Bü 2
nom c v +
ds,Bü 2
A
A
Section A-A studs in one row
studs in two rows d Dü
studs in two rows and not parallel a
av
a'r,o,unten
av
a'r,o,unten
a'r,o
ds,L
s
a'r,o,oben
a a'r,o,oben
a
s
s
Figure 3.6 Geometrical Parameters of Shear Connections with Horizontally Lying Studs Figure 3.7 shows a satisfying conformity of the test results with the theoretical resistance, the characteristic and design resistance of headed studs subjected to vertical shear. Pe,Q [kN] 140
PRd [kN] 120
Arrangement of Studs:
120
one row two rows
100 80
100 250 mm
Pt,Q
PRk,Q
80
200 mm
60
150 mm
40
100 mm
60 PRd,Q
40 20
20
0
0
0
20
40
60
ar,o' = 50 mm Vertical Studs Lying Studs
15
80 100 120 140 Pt,Q [kN]
Figure 3.7 Comparison of the Test Results Pe,Q with the Theoretical Resistance Pt,Q , the Characteristic and Design Resistance PRk,Q and PRd,Q
20
25
30
35
40 45 50 2 fck [N/mm ]
Figure 3.8 Design Resistance of Horizontally Lying Studs according to Equation (3.3) Compared to Vertical Studs (Assumption: a/s = 1)
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Figure 3.8 compares the design resistance of horizontally lying studs subjected to vertical shear according to Equation (3.3) with the design values of vertical studs according to Eurocode 4 /7/. The shear resistance of vertical studs is considered to form an upper limit for the resistance of horizontally lying studs.
4. Combined Vertical and Longitudinal Shear 4.1. Experimental Investigations The load-slip behavior features a good correspondance to both cases of longitudinal shear only /1/, /2/, /3/ and vertical shear only (see Chapter 3). After exceeding the carrying capacity a distinct ductile behavior was observed. The following failure mode occured: Concrete/Stud For the carrying capacity the concrete failure was decisive. Depending on the ratio of acting forces a combination of splitting of the slab /1/, /2/, /3/ and break-out of the concrete edge determined the failure. The gradual concrete cracking came along with high deformations of the stud shanks until the studs sheared off.
4.2. Results A combination of vertical and longitudinal shear acting on the horizontally lying stud leads to a mutual interference of the resistances, so that the single resistances have to be reduced (see Fig. 4.1). For design the combination of forces should satisfy the following condition: (Fd,Q / PRd,Q)1,2 + (Fd,L / PRd,L)1,2 ≤ 1
(4.1)
where: Fd,Q , Fd,L PRd,Q , PRd,L
ηL =
Pe,L' / PRk,L' [-]
1,2 B2 R10/1
1,0 0,8
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R10/3
Elliptical Interaction Relation with k = 1,2
0,6
R10/4
0,4 Linear Interaction Relation
0,2
design vertical and longitudinal shear force respectively, corresponding design vertical and longitudinal shear resistance of the stud according to Equation (3.3) and /1/, /2/, /3/.
R10/2
B1
0,0 0,0
0,2
0,4
0,6 ηQ
0,8 1,0 1,2 = Pe,Q' / PRk,Q' [-]
Figure 4.1 Interaction Diagram for Horizontally Lying Studs Subjected to Vertical and Longitudinal Shear
5. Conclusions and Outlook Considering the present investigations a significant step forward to clarify the load transmission of shear connections with horizontally lying studs is almost concluded. In near future the results presented are completed by further investigations considering the shear connections in the middle of the slab /5/. On the basis of both research projects a common design rule is intended. For applications in bridge design fatigue tests for horizontally lying studs under longitudinal shear are performed at the moment /6/.
Acknowledgements The authors gratefully acknowledge the financial support of their research by the Bundesanstalt für Straßenwesen and the Deutsches Institut für Bautechnik /4/, /5/, /6/.
References /1/ Breuninger, U.: Zum Tragverhalten liegender Kopfbolzendübel unter Längsschubbeanspruchung, Dissertation, Institute of Structural Design, University of Stuttgart, No. 2000-1, January 2000. /2/ Breuninger, U.: Design of Lying Studs with Longitudinal Shear Force, 55th Rilem Annual Week: Connections between Steel and Concrete, Stuttgart, September 2001. /3/ Kuhlmann, U., Kürschner, K., Breuninger, U.: Zum Tragverhalten von liegenden Kopfbolzendübeln, Institute of Structural Design, University of Stuttgart, No. 200114X – Article in “Festschrift zu Ehren von Prof. Dr.-Ing. H. Bode”, September 2000. /4/ Kuhlmann, U., Kürschner, K.: Liegende Kopfbolzendübel unter Quer- und Längsschub im Brückenbau, Institute of Structural Design, University of Stuttgart, No. 2001-1 – Report on Project financed by the Bundesanstalt für Straßenwesen, February 2001. /5/ Kuhlmann, U., Kürschner, K.: Liegende Kopfbolzendübel unter Quer- und Längsschub im Hochbau, Institute of Structural Design, University of Stuttgart – Report on Project financed by the Deutsche Institut für Bautechnik, in Process. /6/ Kuhlmann, U., Kürschner, K.: Ermüdungsbeanspruchte liegende Kopfbolzendübel unter Längsschub im Brückenbau, Institute of Structural Design, University of Stuttgart – Report on Project financed by Bundesanstalt für Straßenwesen, in Process. /7/ CEN: ENV 1994-1-1 Eurocode 4, Part 1-1: Design of Composite Steel and Concrete Structures: General Rules and Rules for Buildings, February 1994.
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COMPOSITE BRIDGE WITH COMPRESSION JOINT CONNECTION CONCRETE END SLAB TO STEEL GIRDER FINITE ELEMENT METHOD M.V. Lammens Mercon Steel Structures B.V., Netherlands
Abstract To prevent concrete deckslabs in steel-concrete bridges from cracking, a new technique has been developed by three Dutch companies. The benefits of using a composite solution in bridge design are enlarged with this technique which is called “hydraulic compression joint”. In the introduction a short summary of this technique is given. For all ins and outs of this technique a reference is made to the paper of Mr. D. Tuinstra in these congress proceedings [4]. In chapter 2 of this paper the use of the hydraulic compression joint in statically undetermined bridges is explained. The hydraulic compression joint gives the opportunity to reach a high compression force in the concrete slab at the mid support without using high-tensile strands or bars. The anchor plates through which the compression force of the hydraulic joint is exerted as a tensile force and a bending moment to the steel girder are part of a follow up investigation at the TU Delft [3]. Results of this investigation in which finite element methods are used are showed in chapter 3 of this article.
1. Introduction: The hydraulic compression joint The hydraulic compression joint is developed by Beton Son, Mercon Steel Structures B.V. and Iv-consult. This innovative technique is a result of a project “composite bridges”. The objective of this project was to develop a general suitable design for composite bridges with spans between 50 and 100 meters, which is economical as well as build for permanence. The emphasis is put on the efficiency in use of materials, a short construction time and a low level of maintenance costs. Studies in Germany, France and Austria showed cracking in concrete bridge decks as the
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reason for requiring early maintenance. It was decided, for that reason, to look at the possibility of a monolithic deck compressed in two directions and without the pockets for connection with the steel girders. The objective of in this project was achieved by making a design that incorporated a high level of prefabricated elements. By using prefabricated elements, due to fabrication in shop rather than on site, a high quality could be achieved and the construction time on site could be reduced considerably. With the hydraulic compression joint, for which a patent is granted, a concrete slab of prefabricated elements can be pre-stressed in the perpendicular direction to the span direction of the joints. A flattened steel pipe is locked in the joints between the elements. This “joint pipe” (fig.2) is put under a high pressure (about 400 bar). The pressure is transmitted to the concrete elements and compresses the concrete up to 10 N/mm2 from support to support (fig. 1). The principle of the hydraulic compression joint is that of a hydraulic jack. The elements are connected to the Figure 1: Test of compression joint steel girder by sliding guides. The first and the last elements (end plates) are connected to the steel girder by anchor plates. The end plates make up the rigid endpoints towards which the other elements can be compressed. Through the end plates the compression force of the hydraulic joint is exerted as a tensile force and a bending moment to the steel Girder. Applying this method with its resultant forces allows the support steel to be reduced in weight by 15% over normal Figure 2: Cross section joint methods. The concrete elements are individually prestressed in their length in the factory using standard methods. The compression force in both directions in the concrete slab prevents cracking of the concrete. The compression from the hydraulic joint is maintained by an innovative method of filling the joint. The filling sequence is showed in the figures below (fig. 3). Joint (up)
Joint (down)
Rubber profile
A: inflating of tube
B: filling of joint (up and down)
Figure 3: Filling sequence of hydraulic joint
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C: injecting the tube
In accordance with the graduation at the Faculty of Civil Engineering and Geosciences in Delft follow up investigation is being done on this innovation [1]. The investigation deals with two subjects, the possibility of reducing the thickness of the concrete slab [2] and the detail calculation (by FE-analysis (fig. 4)) and optimization of the anchor plate [3].
Figure 4: Stress in end plate in longitudinal direction
2. Statically undetermined system The benefits of using the hydraulic compression joint are not limited to statically determined bridges only. The hydraulic compression joint gives the opportunity to compress the concrete deck slab at the middle support on a much higher and different level as in the field. Using this method, tensile stresses in the concrete deck slab can be reduced with 100% in all design phases and of additional reinforcement or high tensile steel is not necessary. The building sequence is explained in the figures below (fig. 5 to 12). Stage 1: 7
Fig. 5: Starting point
Fig. 6: Placing the steel girders
The U-shaped steel girders are positioned on the bearing pads, one after one (fig. 6). (Girders on two supports, statically determined) Stage 2: First the end slab is fixed in position and the steel connection between the slab and girder is welded (fig. 7). jack
Fig. 7: Placing the end slab
Fig. 8: Placing the deck slabs
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Next the precast intermediate deck slabs are positioned one after the other, while a steel tube is placed in the joint before the next slab is placed. A rubber strip, glued at one side of a slab closes the vertical joint. The slabs are pressed against each other and positioned by jacks (fig. 8). The pressing of the jacks also makes that the rubber strip is sufficient pressed to keep the joint closed after filling the tube under high pressure. The rubber strip is required to allow filling of the joint with mortar. The slabs are still unconnected with the steel girder, only a fixing to avoid buckling of the deck during compressing is present. The positioning of the intermediate slabs always starts from the end of a steel girder, because the end slab is used to press the other slabs against to. Stage 3:
Fig 9: Situation before filling the joints
Fig. 10:
Situation after filling the field joints
After all slabs are positioned, all tubes are connected to each other (fig. 9), water is pumped into the tubes under very high pressure (fig. 10). When sufficient compression force is present in the slabs, the joint is filled with mortar and after hardening of the mortar the water pressure is released and replaced by a filling of mortar under pressure. The joint is ready; the pressure is still present in the deck. The open space between the groove in the deck slab and the top flange of the steel girder, where the perfobond strips are, will be filled with mortar. Each of the two spans is a separate composite construction, now statically determined. Stage 4: At the middle support, the top flanges of the steel girder of the two separate spans are connected to each other by welding (fig. 11). "pumpj oInt" support
connecti on top f langes
Fig. 11:
Connecting the top flanges
Fig. 12:
mortar
Filling the joint at the support
Subsequently a slab is positioned at the middle support. To be able to position the slab and the tube precisely, some extra space is needed. This space will be filled after positioning the slab with a special mortar. After hardening of the mortar the steel tube in the joint is directly filled with mortar under pressure (fig. 12). After hardening the webs and the bottom flange of the steel U-shaped girders are connected by welding (fig. 13).
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The bridge is now a continuous girder with a fully working composite construction, statically undetermined. Stage 5: Finishing the bridge and ballasting if necessary.
connection steel girder
Fig. 13: Situation after finishing and ballasting plate at mid-support compression force joint ‘field’ stage 3
compression force joint ‘support’ stage 4 dowel plate end plate
steel- girder
mid support
investigated area
Fig. 14: Forces on end slab connection
3. Finite element research on concrete end slab An essential element in the steel-concrete bridge with hydraulic compression joint is the end plate. The end plate forms the connection between the compressed deck slab and the tensioned steel girder (fig. 14). To get a better view of the stress distribution in the end plate in all (assembly-)phases and the influence of connection type and connection stiffness in the stress distribution, a follow up investigation is being done. The finite element program Mark and postprocessor Mentat has been used in this investigation. A case study has been made on the ‘Westrandbridge 511’. The alternative steel-concrete design of this bridge consists of two U-shaped statically undetermined steel girders. The bridge is about 16 meters wide (fig. 15). Due to symmetry in this design a calculationmodel of only 1/16th of the complete bridge had to be made.
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Figure 15: Cross section
A comparison of several steel-concrete connection types has been made. In the end a dowel connection has been chosen in the design model. The dowels are welded in large numbers on the top of a steel plate. The steel plate is positioned in the mould before casting the concrete slab (fig. 16). The connection between end-slab and steel girder, by welding the steel plate and the girder together, is essential for the structural capacity of bridge system and is executed before compressing of the deck takes place. Springs in three directions represent the model of a dowel (fig. 17). The vertical spring represents the tension stiffness of the dowel, the other two springs represent the bending stiffness. The bending stiffness is based on the results of deformation tests on dowel connections (fig. 18). The (bending) stiffness of the dowel connection strongly depends on factors like dowel diameter, dowel length, concrete quality. Concrete end slab Kh (x-direction) 0,5mm
Kh y direction.
z
Dowel plate
Embedded Dowel plate
Plug welding
Figure 16: Connection dowel plate to top flange girder
Kv (z-direction)
y
x
Figure 17: Model of a dowel
To get a better view at the influence of the dowel stiffness on the stress distribution in the end plate, calculations have been made with two different stiffnessmoduli. Solid elements, for the concrete deck slab and the upper flange of the steel girder are used to calculate the stresses in the end plate (fig.19). Plate elements are used for the steel girders bottom flange and web, which are loaded in plain.
Figure 18: Results of deformation tests
Further details concerning applied edge conditions and calculation methods reference is made to relevant literature [3].
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o Results of FE-study 4. The main goal of the FE-study was getting a true view at the stresses and stress distribution in the end plate. The distribution of forces in the dowel plate connection and the relation between the force distribution over the dowels and the stresses in the end plate are investigated and put into graphics. Some of these graphics are presented in this chapter. Figure 20 shows the dowel displacement in the end plate connection. On each dowel plate 5 rows of 21 dowels are welded. Dowel(row) 1 (in the graphic) is the dowel(row) at the field side, dowel(row) 21 the Figure 19: Modelling of the deck slab one at the support side. The figure shows two different lines each corresponding with a different stiffness modulus. The calculations results shown in the graphic are easy to explain and according with the expectations. The dowels at the front deform more than the dowels near the end. All displacements are within the linear elastic range. The distribution of forces (= displacements) is not linear due to elastic behavior of the material between the connection points. The calculated displacements in the model with the stiffer dowels are, according with the expectations, less. In figure 21 the dowel forces are presented in a graphic. The figure shows that the distribution of forces does not depend on the stiffness of a dowel. Only the ‘peak’ forces in the front row in the stiffest dowel connection are higher. Dowel forces in the end plate
Dowel displacement in the dowel plate 0,60
160.00
dowel (K=240e3) dowel (K=480e3)
0,40 0,30 0,20
dowel (K=240e3) dowel (K=480e3)
140.00 Dowel forces (kN)
Dowel displacement (mm)
0,50
120.00 100.00 80.00 60.00 40.00
0,10
20.00 0.00
0,00 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 Dowel number
Dowel number
Figure 20: Dowel displacement in end plate
Figure 21: Dowel forces in end plate
The dowels are connected in the mod to the bottom side of the end slab. The dowel forces produce a stress distribution (in longitudinal direction) at the bottom site of the end slab, presented in figure 24.
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Figure 22: Stresses at the bottom site of the end slab near the mid support
Figure 23: Stress introduction in steel girder
In perpendicular direction the compression forces result in tensile stresses at the front of the end slab. Prestressing in this direction using high tensile steel prevents the end slab from cracking reducing these tensile stresses. The behavior of the end slab is similar to the behavior of a high fixed wall. Similar results are found by mr. D. Tuinstra in his graduation study of the end plate connection [4]. The stress distribution in the steel girder is shown in figure 23. The difference between the stresses at the bottom side and the upper side of the end plate can be explained by the fact that the dowels are connected only to the bottom side of the end slab. Stresses in perpendicular direction of the end slab
stress (N/mm2)
12 10
Bottom side
8
Upper side
6 4 2 0 -2 -4 -6 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
x-coordinate (m)
Figure 24: Perpendicular stresses in end plate
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2.00
2.25
5. Conclusions A comparison between different end plate connections show that the dowel connection has the benefit of many variation possibilities (diameter, length, number, position). The introduction of forces in the end plate can be send easily through the parameters mentioned. The dowel has also the benefit that many experiences are present with this type of connection. It is proven that the use of alternative connection types also can give reliable solutions. Several connection types are tested in the Stevin Lab of the Delft University of Technology. For more details about these connection types and the results of the tests, a reference is made to the paper of ing. S.J. Poot “Perfo-bond connections and tests” [5]. The results of the FE-calculations show that the influence of the stiffness of the modeled dowels in the distribution of forces in the end plate is minor. The stiffer connection shows a little more concentration of forces at the front dowel rows. In general the results show a concentration of forces at the front rows. The stresses in the end plate mostly depend on the equability of the distribution of forces. Strength and stiffness of the dowel connection must be chosen in such a way that on the one side a more ore less equable distribution of forces is achieved. On the other hand the number of dowels and the displacement (plastic deformation) of the dowels must be reduced to a minimum.
6. References 1.
2.
3.
4.
5.
Lammens, M.V., ‘Staal-beton-bruggen met pompvoeg, Deelrapport 1: Literatuurstudie’. University of Civil Engineering and Geosciences, March 1999 Lammens, M.V., ‘Staal-beton-bruggen met pompvoeg, Deelrapport 2: Onderzoek naar de toepassing van een gereduceerde dekplaat’. University of Civil Engineering and Geosciences, March 1999 Lammens, M.V., ‘Staal-beton-bruggen met pompvoeg, Deelrapport 3: Ontwerp en dimensionering van een eindverankeringsconstructie voor een brug met pompvoeg’. University of Civil Engineering and Geosciences, March 1999 Tuinstra, D., ‘Composite bridge with compression joints Connection concrete end slab to steel girder - Dowels divided in groups’ Conference proceedings symposium Stuttgart September 2001 Poot, S.J.,‘Composite bridge with compression joints Perfo-bond connections and tests’ Conference proceedings symposium Stuttgart September 2001
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PERFO-BOND CONNECTION AND TESTS Simon Poot Beton Son B.V. NL
Abstract This paper outlines the first set up of the connection of precast deck slabs on steel girders for a new type of composite bridge in the developing stage. According to the published results about the perfo-bond connection in Beton- und Stahlbetonbau 12/1987 [1] calculations and a test set-up are made for the perfo-bond connection of the in between slabs and tested according to chapter 10 of ENV 1994-1:1992 (EuroCode 4-1).
1. Introduction The prestressed steel – concrete bridge is one of the latest developments. Beton Son B.V., Mercon Steel Structures B.V. and Iv-Infra are the inventors of the system. The development concept combines the strengths of the materials steel and concrete more as usual, while the in situ construction activities are limited. It is an innovative system, for rapid assembling and constructing activities at the building site. The deck structure consists of concrete precast prestressed deck-slabs, supported by steel U-shaped girders. The key of the system is the prestressing of the structure by prestressing the joint between these deck-slabs. High water pressure is expending a steel tube positioned between the deck-slabs. By grouting the joint the pressure is kept on level. The prestressing force changes both the stress distributions and the deformations. The system is able to resist normal as well as railroad transport actions.
2. The concept of the construction In the separate paper of ir D. Tuinstra [2] the concept is fully explained. The connection of the end slabs to the steel girders is part of his master thesis at the Technical University of Eindhoven. An other separate paper of ir. M.V. Lammens [3]contents the results of a
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numerical analysis of the connection of the end slab to the steel girder as a part of his master thesis at the Technical University of Delft. This paper deals with the connection of the intermediate slabs. End-slab
Concrete slab
St eel U-girders
Figure 1:schematic overview of the bridge system
3. Perfo-bond connection 3.1 The deck-slabs The concrete deck-structure consists of monolith precast slabs, prestressed with strands, in the longitudinal direction of the slab, during the slab production in the factory. The width of the slab is 3.0 meter; transportable with a lorry without too much trouble. The slab is provided with profiled sides to shape the joint between the adjacent slabs and provided at the bottom side with ‘perfobond strips’ in a groove running in the transverse direction of the slab, which means in the longitudinal direction of the bridge.
Figure 2: top view of the deck slab with cross-sections
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The cast-in part of the perfo-bond strips is cammed to place the reinforcement and strands. For easier production the strips are placed as one item in each groove.
Figure 3: cammed perfo-bond strip (combi-strip) 3.2 The perfobond strips on top of the steel girders On the steel flanges of the girder two perfo-bond strips are welded at a small distance of each other. The shear force does not require these strips over the complete length. Figure 4 shows a practical approach.
Figure 4: three strips per slab width (3 m) Instead of round perforations slotted holes allow to bring reinforcement bars in the connection without special attention to the position of the strips. 3.3 The connection The structural connection is completed and effective when the open joint-space is grouted and the grout has been hardened. See Figure 5.
Figure 5: Grouted connection
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A rubber profile, present at both sides of the groove, closes the opening during the grouting operations and will not be removed afterwards. The openings in the strips are filled with strong mortar. The mortar acts like a dowel and via the perfobond – mortar connection forces can be transferred from the deck to the slabs and visa versa.
4. Tests Although the publication about perfo-bond [1] was already from 1987, not much more information was available 10 years later. Part of the development of the bridge system was external research. At that time research on shear connections was running and a suitable test rig was available in the Stevin Lab of the University of Technology at Delft to test the perfo-bond as designed for the connections of the slabs between the end slabs. 4.1 Considerations for the test set up In the factory of Betonson a daily production cycle of prestressed elements such as box girders, I-shaped beams and double T-elements, and intensive use of floor space has been made possible by a separate prefabrication of reinforcement packages in which bars, stirrups and strands are combined. The cast-in part of the perfo-bondstrip therefore is designed with cut-ins. For the parts to be grouted for the connection with the steel girder a cammed version (combi-strip)should be compared with a perforated perfo-bond version. The welded strips on the top flange should have sleeve-shaped perforations to make it possible to place reinforcement bars through the perforations in the double flange strips and the slab strip in between.
Figure 6: combi-, perforated- and top flange version of perfo-bond strips for the tests. The space between the concrete slab and the steel flange must allow placing of such bars from the internal of the U-shaped steel girder before tightening the space with a rubber profile (see figure 5).
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4.2 Test specimen Specimen dimensions within 650 x 650 x 650 were possible in the test rig and a compressive force of 5000 kN was the maximum. From the combi version as well as from the perforated version 4 specimen were tested without reinforcement bars and only one of each type with reinforcement bars through the perforations in the grout, just to have an indication of the influence of those bars. The steel flange was simulated as a 40 mm thick steel plate with a connection on each site. Figure 7 shows the specimen.
Figure 7: top-, side- and cross views of the test specimen
In the concept of the bridge design the concrete slabs are prestressed Prestressing of the small specimen is expensive. To avoid slip of the short reinforcement bars in the concrete of the specimen parts a special end construction is designed. This detail is showed in figure 8. Figure 8: end detail reinforcement bars
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4.3 Test results Tests are executed according to chapter 10 of ENV 1994-1:1992 (Eurocode 4-1) with the exception of the geometry of the specimen. The geometry is in accordance with the designed connection for the bridge concept. Force-displacement diagram combi strip
Figure 9: force-displacement diagram of combi-strips Force-displacement diagram perfo-bond strip
Figure 10: force-displacement diagram of perfo-bond strips
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Figure 11: pictures of the top of the specimen, the cams of the combi-strip, the sleevestrips and the perfo-bond strips after testing.
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5. Comparison (pre-calculations and tests) When we started with the test set up we made some calculations to define the dimensions of the strips. Guideline was the article of Fritz Leonardt, Wolfhart Andreä, Hans-Peter Andreä and Wolfgang Harre in Beton- und Stahlbetonbau 12/1987 [1]. The 5 concrete dowels Ø45 have a total cross-section of 7.948 mm2. The concrete quality of the specimen was B75 and of the grout B55. The shear force for the specimen is 2*7.948*0,9*0,075=1073 kN and for the grout 2*7.948*0,9*0,055=787 kN. The steel cross-section of this strip over the dowels 6*35*12=2.520 mm2. Shear force of the strip 1,44*2.520*0,235=835kN. This matches concrete dowels B60. Each welded strips on the steel top flange has 4 sleeve-shaped concrete dowels with a total surface of 11.226 mm2. There are 2 strips, with only 1 active cross-section. If we compare the 7.948 mm2 with the 11.226 mm2 the dowels in the central strip, the central strip is normative. The steel cross-sections of the welded strips are 3.000 mm2, so also for steel the central strip is normative. According to these calculations the needed force in the test rig for B55 will be 2*787=1574 kN. If we compare the situation for which these calculations are valid with the test specimen in this paper, we may conclude that there is not much equality. The grout around the central strip is not a part of a monolithic concrete piece, but implied between two other strips, the steel top flange and the bottom sleeve of the concrete deck slab. An other difference is the aggregate size. For the grout only sand is used with a grading 0-4 mm. The concrete quality of the specimen at the moment of testing is not exactly known but control cubes of the same mixture show a quality of 75 MPa. It was self compacting concrete. The grout was Pagel V 40. The specimens were grouted and tested 4 days later. Measured on prisms 160x40x40 the average bending strength was 10,2 MPa and the average compressive strength on 80x40x40 was 65,8 MPa (calculated was 55 MPa). The calculated force for the test rig is 1860 kN for B65. Pu Combi-strip 1 1393 Combi-strip 2 1417 Combi-strip 3 1284 Combi-strip 4 1359 With reinforcement 1491 Table 1: results of combi-strip tests
Prk
δu
δuk
1156 1156 1156 1156
34,26 34,25 18,01 34,47
16,2 16,2 16,2
The average force of the combi-strip tests without reinforcement is 1363 kN.
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Pu Perfo-bond 1 1333 Perfo-bond 2 1631 Perfo-bond 3 1437 Perfo-bond 4 1364 With reinforcement 2022 Table 2: results of perfo-bond tests
Prk
δu
δuk
1200 1200 1200 1200
23,42 31,91 26,52 18,01
16,2 16,2 16,2 16,2
The average force of the perfo-bond strip tests without reinforcement is 1441 kN. This is 77,5 % of the calculated value according to [1].
6. Conclusions The scatter of the different tests is very low. The first cracks in the concrete connection are for the combi-strips a little lower as for the perfo-bond strips. The mechanism of deformation after the cracks for both types of connection is different if we look at the deformation of the cams of the combi-strips and the grooves of the broken aggregate on the nearly deformed perfo-bond strips. For the combi-strips it is a combination of shear off of the concrete between the cams and in the sleeves, hook resistance of the aggregate, cracks in the concrete structure and deformation of the cams. In figure 9 the highest curve is the combi-strip with reinforcement. The curve after the top is similar to those without reinforcement. For the perfo-bond it is a combination of shear off of the concrete in the perforations and hook resistance without much cracks of the concrete structure. The reinforcement bars have significant influence on the behaviour of the connection, but not before the top of the connection without reinforcement bars. Even at the end of the displacement the force is still rising. Since only one test is made with reinforcement bars in each connection the results are only indicative. The dimensions of the strips and concrete dowels were designed for a first failure of the dowels in the central strip. Because of the higher concrete quality as calculated some deformation of the central strip was expected. The results show for this system a reduction of about 25 % of the maximum force of direct cast-in strips in reference. According to ENV 1994-1 90 % of the highest failure load of the lowest test value is the characteristic value Prk. For the combi-strip that is 1156 kN and for the perfo-bond strip it is 1200 kN. With δuk = 16,2 and characteristic values Prk = 1156 respectively 1200 kN the connections are very ductile.
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An important aspect for the results is the retaining of the grout in the slotted hole of the slab. Test series with welded steel dowels were part of the research, but not included in this paper because of a not retained grout filling. The graphs showed an increase of the forces after the first cracks in the joint but a quick fall of the forces followed after 4 mm displacement.
7. Recommendation Cost calculations are made and the perfo-bond system for the slabs in intermediate slabs has been abandoned. For the heavily prestressed end slabs however perfo-bond might be a preferable connection above welded steel dowels.
8. References 1
Fritz Leonardt, Wolfhart Andreä, Hans-Peter Andreä and Wolfgang Harre "Neues, vorteilhaftes Verbundmittel für Stahlverbund-Tragwerke mit hoher Dauerfestigkeit" Beton- und Stahlbetonbau 12/1987
2
Dimitri Tuinstra "Composite bridge with compression joints Connection concrete end slab to steel girder - Dowels divided in groups" Symposium Stuttgart 2001
3
Michel Lammens "Composite bridge with compression joints Connection concrete end slab to steel girder - Finite Element Method" Symposium Stuttgart 2001
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DEVELOPMENT AND APPLICATION OF SAW-TOOTH CONNECTIONS FOR COMPOSITE STRUCTURES Jörg Schlaich University of Stuttgart, Germany Schlaich Bergermann und Partner, Consulting Engineers, Stuttgart, Germany
Abstract High-capacity saw-tooth connections, as against those with headed studs, enable the highly concentrated transmission of large forces between steel members and slender concrete slabs. The connection is made from a welded or cast steel bar provided with a saw-tooth shaped geometry along the interacting face of the connection. The geometry of the teeth is universally applicable for most sorts of connections and ensures a very high fatigue strength of the connection. In this paper the initial typical engineering approach to this development and its early practical applications are described as well as its later application based on an improved geometry of the teeth. With respect to its detailed scientific investigation resulting in this improved new geometry, reference is made to the work of Volker Schmid and his paper [1] also submitted for this Symposium and a more extensive joint paper [2].
1. Early Applications of Saw-Tooth Connectors 1.1 A footbridge suspended from a hotel-building The two main cables of this self-anchored suspension bridge with 2.5 MN each have to be anchored on either side of the 28 cm thick deck slab (Fig. 1). The vertical components of the cable force are held down by pendula. For the load transfer of the predominant horizontal components into the concrete slab saw-tooth connections made from cast steel were developed (Fig. 2) [3] following the type as shown in figure 12b.
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Fig. 1: View and plan of the bridge
Fig. 2: Anchorage of the main cables at deck with saw-tooth connections and vertical tie on either side of the deck slab
Since to the knowledge of the author, this was the first time such saw-tooth connection was explicitly used for the transfer of a high concentrated load from steel into concrete, its genesis is described in some detail here. This is also a good example for the fact that strut-and-tie-models are not only valid for a design check but may also be successfully applied in the conceptual design by consequently materialising a smooth flow of forces. This case itself has been worked out by M. Jennewein [4] – [7].
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Fig.3: Step-by-step design of the horizontal cable forces´transfer into the concrete shell
In figure 3 the transfer of the horizontal components S of the cable forces into a concrete deck slab is discussed. Figure 3a describes the problem. For generalisation or clarification the forces S are assumed to act outside the contour of the slab as seen in plan. At the separation lines between the D- and B-regions the axial stresses in the concrete slab are clearly known (Fig. 3b) and from there the basic strut-and-tie models directly follow (Fig. 3c). One straight forward solution would be to follow this model by joining the two cable ends directly with the concrete slab, this assuming the role of a cable saddle (Fig. 3d). The more common solution (Fig. 3e) will work only for small cable forces, because it provides only a very short length for the anchorages or bond of the cross-ties. Therefore one might prefer to introduce steel elements there, to which these ties can be welded (Fig. 3f). It is to be observed that the front of these elements is sloped in the direction of the struts. This is very helpful, because if not done, a very complicated strut-and-tie model (Fig. 3g) is needed to take care of the cantilevering moment, and accordingly a difficult reinforcement layout results (Fig. 3h). To avoid this moment we return to figure 3f. To ensure a safe load transfer into the concrete, the stresses σc in figure 3f need to be checked. If they are excessive, one choice would be to increase the width of these steel elements (Fig. 3i); they become sort of dowels penetrating the slab. The model describing their flow of forces (Fig. 3i) and also the corresponding reinforcement layout is again rather intricate (Fig. 3k). The improvement due to the increased width is eaten away by a cantilevering moment which is now larger
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than in figure 3g, asking for an additional longitudinal reinforcement. This finding already leads into the right direction. In order to reduce the concrete stresses σc in figure 3f it is more reasonable to increase the length instead of the width of the steel elements and to provide them with saw-teeth (Fig. 3l). Accordingly the strut-and-tie model develops along the length of the deck slab and the struts and transversal ties distribute. Obviously by increasing the number and decreasing the size of the teeth the flow of forces becomes more smooth and harmonic (Fig. 3m). The depth of the teeth should reflect the diameter of the concrete’s aggregate, i.e. be in the order between 20 and 50 mm. Their inclination of Θ = 30° was kept constant throughout. The length of the connectors was calculated from fc = α x fck/γc in the inclined compression stress field, without a further reduction factor for transversal cracking, because the height h of the teeth was chosen to be 1/3 of the slab thickness only, permitting on the other side an increase for this partially loaded concrete surface. For the sake of completeness it should be added that in case of this footbridge the sawtooth connection as shown in figure 3m, having a constant width there and looking rather clumsy, was visually improved with the tooth-connector itself hidden in the concrete and the cable anchorage projecting out (Fig. 2). Unfortunately this results in a cantilever moment characterised by the lever arm or eccentricity e (Fig. 3n). To understand this new situation, it is helpful to subdivide it into two cases 3o and p. For the cantilevering moment alone (Fig. 3o) we find again the above quite complicated strut-and-tie model, requiring a local transversal tie at the end of the corbel; therefore, obviously this corbel should not be too short along the deck. The second case (Fig. 3p) is again smooth. The superposition results in the reinforcement as shown in figure 3p, certainly still preferable to the solution shown in figure 3h or k, and finally in the configuration as built (Figs. 2 and 4). The transversal reinforcement was welded onto the cast-steel teeth connectors. Comparing in retrospective this early teeth geometry (Figs. 2 and 4: continuous teeth with slope 30°/60°) with the later optimised one by V. Schmid [1][2][8] (Fig. 13, discontinuous teeth with slope 70°) for a stress field with Θ varying from 20° to 70°, one finds that the early configuration holds good for Θ = 20° if a minor friction value of 10° is accepted at the interface of steel and concrete, whereas for Θ = 70° there remains as small triangle (shaded in figure 4) which appears to be not in equilibrium. This (minor) problem – which of course disappears if instead of the theory of elasticity we apply the theory of plasticity – may not only be overcome by choosing the optimised teeth but also with an “open” and from point of manufacture even simpler teeth connector as shown in figure 5.
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Θ = 70°
10°
Θ =20°
Fig. 4: The early teeth connector from Fig. 2 for Θ = 70° and 20°
10°
Θ = 70°
Θ =20°
Fig. 5: An open teeth connector, welded from steel plates, which satisfies 20°< Θ < 70°
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1.2 Some other Self-Anchored suspended Foot-Bridges [9] For two bridges built in Stuttgart at Nordbahnhof, the same type of anchorages of the main cables was successfully repeated (Fig. 6). Further the cable-anchorage at the abutment is shown which follows the approach as shown in figure 3d.
Fig. 6: Movable and fixed anchorages of self-anchored suspension bridges at Stuttgart Further for a bridge in Pforzheim the tied-down anchorage was varied or simplified (Fig. 7). The teeth are welded onto a vertical steel plate which at its one end provides the anchorage for the main cable, at its other end for the holding down pendulum. The cable anchorage at the abutment again makes use of a typical tooth connection.
Fig. 7: Movable and fixed anchorages of a self-anchored suspension bridge at Pforzheim
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1.3 The Evripos Cable-Stayed Highway Bridge [10] The deck of this bridge with a main span of 215 m and two side spans of 90 m each is 14.14 m wide and made of a solid concrete slab with a mean thickness of 45 cm. This slab is monolithically connected to the concrete pylons, since these are high enough between the foundation and the deck level to respond elastically to the temperature expansion of the deck. Only at the ends movable supports are provided. The benefits of such a monolithic connection are an increased overall robustness, including an improved ductility with respect to seismic attack, and savings in cable steel, because the deck loads enter the pylon base directly and avoid the detour through the cables and the top part of the pylons. Concerning the cable anchorages at the concrete pylon heads of this bridge, in order to achieve a very smooth and direct flow of forces and to avoid any prestress or sophisticated reinforcement, the inner faces of the “chamber” or slotted mast heads are lined with steel plates (Fig. 8). The pairs of cross-bars, provided to support one cable socket each, transfer their loads to these plates in which the horizontal components of the cable forces can easily balance in tension whereas the merging vertical components are transferred to the concrete through horizontally arranged block-dowels with welded loop reinforcement. This results in a very compact arrangement of the cable anchorages, very close to the ideal fan-geometry with minimised mast bending. On the other side, since the flower-pot shape is desirable anyhow to accommodate the steep cables close to the mast, there is no difficulty to keep sufficient clearance between the sockets to accommodate hydraulic jacks for cable-adjustment and prestress there. This makes it very convenient to stress all cables from within one chamber at each mast head without the need to move the jacks over long distances.
Fig.8 Cable anchorages at pylon heads
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Fig. 9: Cable anchorages along the 45 cm deck slab (right) and of back-stays (left)
Since with that there is no need anymore to stress the cables at their anchorages along the deck, the bottom anchorages can be really simple and made from completely prefabricated welded steel elements (Fig. 9). Their vertical plate provides for the cable anchorages: teeth welded to it introduce the horizontal components of the cable forces into the deck; the horizontal bottom plate provides for the vertical support. The transversal tension is taken by prestress to avoid cracks passing the compressive stress fields which would reduce its strength. This anchorage could easily be expanded to serve for the back-stays which include pendulum eye-bars to hold down the vertical components of the back-stays, permitting horizontal movements simultaneously (Fig. 9). 1.4 The Cable-Supported Highway Bridge at Ingolstadt [11] This is by definition not a composite bridge, though it incorporates concrete and steel, but these are not combined to act jointly but independently to their best (Fig. 10). This bridge is included here because it makes use of a typical teeth-connection for the anchorages of its main cables at the abutments. The two bundles of four locked coil ropes of 118 mm diameter each carry an ultimate load of 4 x 15 = 60 MN to their anchorages. There they are supported by steel boxes with teeth ribs at their bottom face, which are embedded into the concrete of the abutments. The vertical tension is taken by prestressed tendons. If the concrete slab underneath the teeth is sufficiently thick to provide ample length and space for the anchorages of these tendons, this is a satisfactory solution (Fig. 11).
Fig. 10: The cable-supported highway bridge at Ingolstadt, 1998 Overall view with the location of the cable anchorage discussed here
Fig. 11: Teeth-shaped anchorage of 4 locked coil ropes ∅ 118 mm at an abutment
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2. First Application of improved Saw-Tooth Connectors 2.1 The basic types Saw-tooth connectors may project into the interior of a concrete slab (Fig. 12a) or be applied to its sides (Fig. 12b).
a)
b)
Fig. 12: Saw-tooth connections for concentrated load transfer a) projecting into the interior of the concrete slab (see Fig. 14b) b) applied to the sides of a concrete slab (see Figs. 2, 6, 7, 9)
In both cases all efforts should be made to fit the axis of the saw-tooth connector with that of the concrete slab and both of them with the resultants of the applied loads, i.e. of
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the point of intersection of the diagonals in figure 12a or of the suspension/holdingdown cables in figure 12b. This guarantees that the load transfer solely happens with transversal tension in the plane of the slab, i.e. transversal reinforcement but no vertical tension, i.e. without the need for stirrups (as against that see figure 15). 2.2 The improved Geometry In his dissertation [8] as well as in his paper [1] included in the proceedings of this symposium, V. Schmid has shown that a teeth-geometry as shown in figure 13 leads to better results as that of the early applications shown above, see also [2].
b)
Fig. 13: a) best teeth geometry field (see also figure 5)
b) all possible inclinations of the compression stress
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2.3 The Bridge over the Nesenbachtal at Stuttgart [12]
Fig. 14: The Bridge over the Nesenbachtal, Stuttgart, 1999 a) view and plan b) teeth-connectors, made from cast-steel, project into the concrete slab This innercity highway bridge (near the venue of this symposium) offers a number of innovations which can be listed but not discussed in the context of this paper (Fig. 14): - The concrete deck slab is supported by a tubular steel truss on “tree-columns” - All tubular joints are made from cast-steel to avoid the direct intersection and welding of the tubes. This results in more robust, easy to maintain and more appealing joints. - The concrete bridge deck has no lateral joints but is monolithically connected with the adjacent tunnels on either side. It is provided with sufficient reinforcement to ensure a good crack distribution when acting in tension at low temperature. (One of the less mentioned advantages of such composite bridges is that their concrete section and with that their restraint forces under such circumstances are minimised.) Since also the deck, the truss and the columns are monolithically joined, this bridge has neither any bearing nor any joint! This is not only favourable from
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-
the point of view of robustness and durability – no bearing is the best bearing – but also avoids the noise usually emitted from expansion joints when passed by trucks. Noise avoidance was a key issue of this bridge situated in a residential area. Arches with movable panels, but always open on one side, envelop the traffic, with a foot-/bicycle path on top.
For the locally concentrated connections of the concrete slab with the tubular truss at the top intersection of its diagonals the investigations and experience described in this paper were brought forward and the saw-tooth connections, as described above, applied in principle. Since at the time of the final design of this bridge, the research work of V. Schmid [1][8] was still under way, the geometry of the teeth as proposed in figure 13 was not yet fully available and therefore the one used for this bridge is slightly different (Fig. 14b) but, as shown in figure 5, the load transfer is not very sensitive in this respect. On the other side, eccentricities have to be followed up carefully (Fig. 15). As long as the intersection of the diagonals coincides with the centreline of the teeth-connector but does not match that of the slab (eA ≠ 0), no moment will build up between the slab and the connector. Therefore in this case the vertical ties in the slab can be covered by stirrups which need not to be welded to the connector (eL ≠ 0), a moment is produced calling for vertical reinforcement, which is to be welded to the connector (Fig. 15 below). This situation should be and can be always avoided in most practical cases. In case of this actual bridge, the situation as described in figure 15 in fact occurred out of its given special boundary conditions. Nevertheless the bridge was built without difficulties and behaves satisfactorily.
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Fig. 15: Teeth-connectors with eccentricities eA (above) and eA + eL (below)
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References 1.
Schmid, V., Geometry, behaviour and design of high capacity teeth connectors. Paper included in the Proceedings of the Symposium on ‘Connections between Steel and Concrete’, 55th Rilem Annual Week, Stuttgart, Germany, Sept. 9-12, 2001 2. Schlaich, J., Schlaich, M. and Schmid, V., Composite Bridges – Recent Experience – The Development of Teeth Connectors, Proceedings of the 3rd International Meeting on ‘Composite Bridges’, Madrid, Spain 3. Schlaich, J. and Bergermann, R., Hotel in Stuttgart trägt Fußgängerbrücke, Betonund Stahlbetonbau 86 (1991), Verlag Ernst und Sohn, Berlin 4. Schlaich, J. and Schäfer, K., Konstruieren im Stahlbetonbau, Beton-Kalender 1998, pg. 791-985, Verlag Ernst und Sohn, Berlin 5. Schlaich, J., Schäfer, K. and Jennewein, M.: Towards a Consistent Design of Structural Concrete, PCI Journal May/June 1987, Vol. 32 No. 3 6. Jennewein, M., Zum Verständnis des Tragverhaltens von Stahlbetontragwerken mittels Stabwerkmodellen, Dissertation Universität Stuttgart, 1988 7. Schlaich, M.: Computerunterstützte Bemessung von Stahlbetonscheiben mit Fachwerkmodellen, Dissertation ETH Zürich, 1989, Verlag der Fachvereine Zürich 8. Schmid, V.: Hochbelastete Verbindungen mit Zahnleisten in Hybridtragwerken aus Konstruktionsbeton und Stahl, Dissertation Universität Stuttgart, 2000, Verlag Grauer, Stuttgart 9. Schlaich, J., Bergermann, R., Fußgängerbrücken, Katalog zur Ausstellung an der ETH Zürich 10. Bergermann, R. and Stathopoulos, S.: Design of the Evripos Bridge in Greece, Cable-stayed Bridge Seminar, Bangalore, India 1988 11. Schlaich, J., Schlaich, M. and Werwigk, M.: Die neue Glacisbrücke Ingolstadt, Beton- und Stahlbetonbau 94 (1999), Verlag Ernst und Sohn, Berlin 12. Schlaich, J., Pötzl, M., Beiche, H., Ehrke, E. and Decker, U.: Die Brücke über das Nesenbachtal im Zuge der Ostumfahrung StuttgartVaihingen, Beton- und Stahlbetonbau 95 (2000), Verlag Ernst und Sohn, Berlin
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GEOMETRY, BEHAVIOUR AND DESIGN OF HIGH CAPACITY SAW-TOOTH CONNECTIONS Volker Schmid Institute for Structural Design II, University of Stuttgart, Germany
Abstract High-capacity saw-tooth connections enable the highly concentrated transmission of large forces between steel members and slender concrete slabs. The connection is made from a welded or cast steel bar which has a saw-tooth shaped geometry along the interacting face of the connection. The geometry of the teeth is universally applicable for most sorts of connections and ensures a very high fatigue strength of the connection. Based on the investigations carried out in the Institute for Structural Design II, University of Stuttgart, with Prof. J. Schlaich, the paper presents the most important results of the research on the behaviour and design of saw-tooth connections. The paper describes the flow of forces in the connection area and explains the interdependent factors which govern the dimensioning of the connection. Emphasis is laid on the new geometry of the teeth, which is derived from a close look into the stress distribution in front of a single tooth using non-linear analyses. Reference is made to Prof. J. Schlaich’s paper [1] also submitted for this Symposium and a more extensive joint paper [2].
1. Introduction The use of different materials such as steel and reinforced concrete within one design enables very efficient and interesting structures. The common problem of connecting the steel elements to the reinforced concrete is usually solved using headed studs. Differing examples are the self anchored pedestrian suspension bridge (Fig. 1a) and the road bridge made from a steel girder and a concrete deck (Fig. 1b), both designed by J. Schlaich [1] [3]. For the anchorage of the steel cable or the steel truss at the slender concrete deck a special high capacity saw-tooth connection was developed which allows the transmission of huge and highly concentrated forces from the steel element into the concrete slab.
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concrete slab
Steel truss concrete slab
cable
Fig. 1: a) Anchorage of a steel cable at the edge of a thin concrete slab
b) Anchorage of a steel girder within a thin concrete slab
Fig 2: Arrangement of saw-tooth connections and corresponding strut-and-tie models for a saw-tooth connection a) at the edge of the slab b) within the slab
2. Arrangement of saw-tooth connections The anchorage of the steel cable at the edge of the rc-slab is shown in Fig. 2a. The plan of the connection area includes a simplified strut-and-tie model. The cable is fixed to a welded or cast steel bar which distributes the tangential forces along a sufficient length, reducing the stress concentration within the interacting surface to a level which is appropriate for the rc-slab. The deviation of the cable forces into the slab requires tension forces perpendicular to the edge of the slab. Therefore reinforcement bars, or even better post-tensioned tendons, have to be positioned along the connection. The inter-acting face of the steel bar has a saw-tooth shaped geometry. The teeth prop the inclined compression struts within the concrete slab. If the connection has about the same height as the slab the forces within the slab will be uniformly distributed over the height of the connection and will not cause any splitting forces perpendicular to the slab plane. Fig 2b shows the anchorage of a steel truss within a thin concrete slab. Neglecting the relatively small vertical force in the slab the two axial forces in the steel diagonals equal the horizontal force in the rc-slab. The most efficient geometry of the connection is
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obtained if the centre lines of the steel truss and the slab coincide in one single point as shown in Fig 2b. Therefore the saw-tooth connection should be arranged perpendicular to the slab plain. This arrangement allows to carry the forces from the steel diagonals to the centre of the concrete slab within the steel section. From there compression forces spread horizontally into the concrete slab. To prevent the concrete from vertically splitting the height of the saw teeth connection should be close to the height of the slab. Sometimes it is not possible to achieve this favourable geometry. Examples for other arrangements of saw teeth connections are explained in [4].
3. Structural behaviour and detailing of saw-tooth connections The load capacity of a saw-tooth connection as well as the amount and arrangement of the reinforcement can only be determined using a strut-and-tie model (see Fig 3). Following [5] the model has to be adapted to the results of a linear elastic FE-Analysis which provides the distribution of the forces per meter vf and nf transmitted in tangential and perpendicular direction along the connecting surface between steel and concrete. Assuming the cracks propagate parallel to the main compressive stresses at stage 1, the angles θ of the compression struts can be derived from the FE-analysis as well. The angles range from approximately 20° at the tip to 70° at the end of the connection. The forces Ccw,i and Ti [MN] in the struts and ties related to a discrete area ∆lL,I may be derived from the equations given in Fig. 3.
Fig 3: Strut-and-tie model for the anchorage of a tangential force at the edge of a slab
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Following a conservative assumption the load capacity of the connection is reached as soon as one concrete strut fails in compression. At the interacting face the maximal compression stress σcw(x) in the concrete struts depends on the shear forces vf(x) [MN/m], the height h [m] of the saw-tooth connection and the angle θ(x) (see Fig 4): σcw(x) = vf(x) / (h sinθ(x) cosθ(x)) Notice: θ(x) = 45° ⇒ σcw(x) = 2,00 vf(x) / h θ(x) = 20° or 70°⇒ σcw(x) = 3.11 vf(x) / h Fig 4: Interdependence of shear force vf, concrete compression stress σcw and angle θ For concrete struts with cracks parallel to the struts the maximal effective concrete strength fc,eff [MN/m2] may be estimated as follows: fc,eff = 0.8 f1c = 0.68 fck
f1c: uniaxial compressive strength; f1c = 0.85 fck
Different arrangements of saw teeth connections require different strut-and-tie models. In [4] further models are described such as the model shown in Fig 2b, which is suitable for the anchorage of a steel truss within a concrete slab.
4. Influences on the load capacity of saw-tooth connections
shear force per meter vf(x) [MN/m]
As described above, the connection’s load capacity depends most of all on the distribution of the shear forces vf(x) [MN/m] along the connecting surface. The following parameters have a major influence on vf(x) and have been examined in [4] using strutand-tie models as well as physically non-linear FE-Analyses with the program “Sbeta”.
loaded area [m]
Fig 5: Distribution of the shear forces vf(x) along connections of different length
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The relationship between the stiffness of the rc-slab and the stiffness and length of the saw-tooth connection is of great importance. Based on a parameter study [4] gives rules of thumb for reasonable values. Fig 5 shows the distribution of the tangential forces vf along three connections with equal stiffness but different length and exemplifies why there is an under-proportional correlation between the connecting length and the load capacity. This diagram explains why this kind of connection can neither be detailed by using the theory of plasticity nor by employing a certain average “shear resistance”. The strain in the rc-slab has a great influence on the load capacity of a connection. Different strains in rc-slabs occur e.g. in bridges as shown in Fig. 1b, where the slab acts in tension above the columns and in compression in mid span. A Comparison shows that the load capacity of a saw-tooth connection arranged in the tension zone of the slab may be up to 40% less than the load capacity of a connection arranged in the compression zone. Cracking of concrete reduces the stiffness of the rc-slab in the cracked areas, which is of minor importance for saw-tooth connections within the rc-slab (see Fig 2b). But cracking may have a considerable influence on the load capacity of connections situated at the edge of the slab (see Fig 2a). The non linear FE-analysis of a 15m long saw-tooth connection taking into account cracking shows the uneven redistribution of the shear forces vf [MN/m] as the cracked areas increase during the loading process (Fig. 6 and 7). This analysis results in a load capacity of FLk = 41.3 MN which is 17% less than according to a strut-and-tie model based on a linear elastic FE-Analysis with FLk = 49.9 MN.
Ultimate Load
Fig 6: Development of cracks during the loading process of a saw-tooth connection of 15m in length
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shear force per meter vf(x) [MN/m]
Fig 7: Change of shear forces per meter vf(x) as loading FLk [MN] increases To compensate for the negative effects due to cracking it is recommended to use posttensioned tendons perpendicular to the connection. Prestressing prevents large areas from cracking and causes a more uniformly distribution of the tangential forces. As a result the load capacity increases by 35% to FLk = 55.7 MN (see Fig. 8 and 9).
Fig 8: Development of cracks during the loading process of a saw-tooth connection of 15 m in length with post-tensioned tendons
Fig 9: Change of shear forces per meter vf(x) as loading FLk [MN] increases
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Using a curved layout of the tendons as shown in Fig. 10 may even increase the load capacity by 75% up to FLk = 72.3 MN.
Fig. 10: Development of cracks during the loading process of a saw-tooth connection of 15 m in length with curved post-tensioned tendons
5. Geometry of the connection surface 5.1 Principal idea The concrete stresses within the compression field in front of the connection govern the load capacity of the connection. For this reason it is crucial to support the concrete struts uniformly, avoiding an increase of the compression stresses in front of the connection which would inevitably result in a reduction of the connection’s load capacity and resistance to fatigue. Therefore the front of each steel tooth is arranged perpendicular to the struts (see Fig. 11). Furthermore the steel tooth should be fabricated to almost the same height as the concrete slab. As a result of this geometry the concrete stresses in front of the saw-tooth connection do not exceed the effective compressive strength fc,eff which ensures an unrestricted load capacity and resistance to fatigue.
Fig 11: Fan shaped compression field propped by teeth which provide a front perpendicular to the struts
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5.2 Geometry of the teeth The teeth’s changing geometry along the connection (see Fig. 11) is difficult to construct and requires a lot of steel. Therefore a casted steel tooth was shaped which allows to prop the arbitrarily inclined concrete struts using only one single geometry for all teeth (see Fig. 12).
Fig. 12: Optimised geometry of the teeth made from casted steel Teeth with this geometry perform in the same way even for changing load directions and don’t rely on friction forces between steel and concrete. Therefore the following investigations were carried out neglecting friction. A simplified model with compression fields (Fig. 13) explains the principal structural behaviour of the saw tooth connection for struts inclined at an angle of 20°, 45° and 70° degrees. Here the local stresses σf at the surface of the teeth and within the nodes are equal to the stresses σcw in the concrete compression struts. These connections are designed so that the stresses σc in the adjacent compression field do not exceed fc,eff = 0.8 f1c = 0.68 fck (see 3.) whereas the allowable stresses in compressive nodes exposed to biaxial compression reach up to 1.2 f1c = 0.96 fck (see [5]).
steel teeth
Fig 13: Compression fields with different angles ? and forces ncw [MN/m] in front of the teeth
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concrete failure cracks cracks
Fig. 14: Single tooth and compressive strut inclined with θ = 30°: Areas with concrete failure and cracks
Fig 15: Group of teeth and compression field inclined with θ = 45°: Areas with concrete failure and cracks
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These figures suggest that failure of the concrete in between the teeth will not occur. This is verified by non-linear FE-analysis of a single tooth propping struts with different inclinations. The most unfavourable example with θ = 30° is shown in Fig 14. The concrete failure occurs distant from the tooth, resulting in a load bearing capacity of 1.16 fc,eff . The black areas in front of the teeth indicate the compression failure of the concrete. Analysis of entire compression fields inclined by angles of 20°, 45° and 70° resulted in a load bearing capacity of 1.22 fc,eff , 1.18 fc,eff and 1.24 fc,eff . Fig. 15 shows the results of a compression field inclined by 45°.
6. Conclusion Saw-tooth connections are suitable for the concentrated transmission of large forces into thin concrete slabs. Their design has to be carried out using strut-and-tie models orientated on the results of a linear FE-analysis. A close look into the flow of forces within the connecting area leads to an optimised geometry of the teeth. This geometry ensures that the load bearing capacity along the connecting surface is higher than the effective strength within the slab.
References [1] Schlaich, J (2001): Development and Application of Teeth Connectors for Composite Structures. Proceedings of the Symposium on “Connections between Steel and Concrete”, 55th Rilem Annual Week Stuttgart, Germany, Sept. 9th – 12th, 2001 [2] Schlaich, J.; Schlaich M.; Schmid, V. (2001): Composite Bridges – Recent Experience, The Development of Teeth Connectors. Proceedings of the 3rd International Meeting on “Composite Bridges”, Madrid, Spain, 2001 [3] Schlaich, J.; Bergermann, R. (1992): Fußgängerbrücken. Katalog zur Ausstellung an der ETH Zürich, 1992 [4] Schmid V. (2000): Hochbelastete Verbindungen mit Zahnleisten in Hybridtragwerken aus Konstruktionsbeton und Stahl. Dissertation am Institut für Konstruktion und Entwurf II, Universität Stuttgart 2000 [5] Schlaich, J.; Schäfer, K. (1998): Konstruieren im Stahlbetonbau. 721-895 in: BetonKalender 1998, T.2, W. Ernst und Sohn, Berlin
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COMPOSITE BRIDGE WITH COMPRESSION JOINT. CONNECTION CONCRETE END SLAB TO STEEL GIRDER - DOWELS DIVIDED IN GROUPS Dimitri Tuinstra* Iv-Infra B.V., The Netherlands
Abstract A new prestressing system for composite bridges with precast concrete deck slabs is introduced. The prestressing system focuses on low costs and a long lifecycle through the economic use of materials, prefabrication and short construction periods. In the bridge system precast deck slabs on top of a steel girder are prestressed by a hydraulic compression joint. The bridge deck is prestressed before the composite connection has been made. The force is transferred to the steel girder by concrete slabs at both ends of the span. In order to do so, the end slabs are connected to the upper flange of the steel girder with dowels. In this paper the distribution of the prestressing force over the dowels is determined, using a simplified analytic model. The study is part of the author's master thesis at the Technical University of Eindhoven.
1. Introduction In today's society with severe traffic problems, short construction periods and the least possible hinder, are almost a must. The prestressed composite bridge is one of the latest developments by Beton Son b.v, Mercon Steel Structures b.v and Iv-Infra b.v. The main goal of the system is to develop a bridge system that causes the least possible obstruction by limiting the construction activities on site and long lifecycle with low maintenance costs.
*
Prof.ir.H.W.Bennenk, Prof.ir.H.H.Snijder and ir.H.Janssen Faculty of Building Technology, Technical University of Eindhoven
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In chapter 2 the bridge system and the hydraulic compression joint are introduced. In chapter 3 the stresses in the end slab due to prestressing are explained. The stiffness of the shear connection between the end slab and the steel girder is of great influence on the stress level in the end slab. The connection consists of a large amount of dowels. A relation between the stiffness of the concrete slab, the steel girder and the dowels is retrieved. The study results in a design approach for the end slab connection of a single span bridge.
2. The prestressed composite bridge system The bridge system consists of steel girders End-slab Concrete slab supporting a concrete deck. The deck is built up with prestressed precast concrete slabs. The first and last deck slab are different from the rest because they transfer the prestressing force to Steel U-girders the steel girders during construction. The end slab has other dimensions and is prestressed in Figure 1 Schematic overview of the bridge its longitudinal direction to a higher rate as system. normal deck slabs. Figure 1 shows the schematic overview of the bridge. The substructure of the bridge system consists of U-shaped steel girders as shown in figure 2 The number of girders depends on the width of the bridge and the loading situation. The upper flange of the steel girder acts as the support of the concrete deck and the spacing between the girders can be chosen in such a way, that the Figure 2 The steel U-shaped girders. concrete deck slabs are optimised in transverse direction. The abutments at both sides of the bridge support the steel girders. Apart from the self weight, the steel girders carry the dead load of the concrete deck in the construction stage and, as part of the composite structure, they partly carry the additional loading.
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3000 mm
perf obondst rips
prestressed strands Open space Perf obond strip
3000 mm
Figure 3 Prestressed precast deck-slabs provided with cast-in ‘perfobond strips’.
The concrete deck consists of monolith precast slabs (figure 3). During slab production in the factory, the slabs are prestressed with strands in the longitudinal direction of the slab. The width of the slab is limited to 3.0 metres because of maximum allowable transportation dimensions with a lorry. The length of the slab depends on the desired width of the deck. The sides of the slab are provided with a groove to shape the compression joint between the adjacent slabs. The longitudinal sides of the slab are thicker in order to support the slab during construction. In the transverse direction of the slab, after construction this will be the longitudinal direction of the bridge, ‘perfobond strips’ are cast in at the bottom side. The perfobond strips are perforated steel strips that will act as shear connectors. Concerning the performance of this type of shear connectors reference is made to the paper of Mr. S.Poot in these proceedings [1]. The strips are present at both the upper flange of the steel girder and the Concrete slab concrete deck slab as shown in figure 4. The cavity between the steel and concrete will be filled with mortar. A Rubber profile Perfobond strips rubber sealing at both sides of the Upper flange and w eb flange prevents mortar from being of steel girder spilled. The openings in the perfobond Figure 4 Connection of steel girder and deck-slab via the strips are filled with mortar. After hardening of the mortar the strips will ‘perfobond strip’ be able to transfer shear forces. End-slab
The precast and prestressed end slabs have the same length and width but are St eel dow els thicker than the deck slabs (figure 5). Steel plat e The end slab is prestressed in Welded at the side longitudinal direction in the factory to Figure 5 Cross-section of end-slab supported and welded a higher level than the deck slabs. on the top of the steel girder. Other than the intermediate deck slabs,
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the end slab is connected to the steel girder with dowels. The dowels are welded to a steel plate which is positioned in the mould before casting the concrete. The connection between end slab and steel girder, by welding the steel plate and the girder together, will be essential for the structural capacity of bridge system and is executed before any prestressing of the deck takes place. In chapter 3 the action of the end slab during prestressing will be explained more elaborately. 2.1. The hydraulic compression joint The key of the system is the hydraulic compression joint. This is a flattened steel tube that acts like a jack in the joint between the deck slabs. Each tube is connected with all other tubes. When all tubes are present and connected with each other, water under very high pressure is pumped into the joints. The tube expands and acts as a force on the deck-slabs (figure 6A). Under maintaining the water pressure, the joint is grouted with rapid hardening and high strength mortar. When the mortar strength is sufficient the water pressure is lowered, the present prestressing force will be transferred to the mortar in the joint (figure 6B). Grouting mortar is pressed into the empty tubes under a relatively high pressure. After the grout in the tube has hardened, the stress is levelled over the height of the joint (figure 6C). Joint (up)
Joint (dow n)
Rubber profile
A: inflating of tube
B: filling of joint (up and down)
C: injecting the tube
Figure 6 The execution of the prestressed joint step by step
At the time of prestressing the deck slabs are not connected with the steel girder. However, the deck slabs are closed in by the end slabs and because of restricted deformation the concrete deck is prestressed in longitudinal direction of the bridge. The prestressing force loads the end-slab, which is connected with the steel girder. This introduces a tensile force at the upper flange of the steel girder. The vertical eccentricity of the tensile force introduces a upward bending moment. The prestressing force changes both the stress Figure 7 The action of the prestressing distributions and the deformations of the structure. force in the joint on the bridge system The actions are shown in figure 7. 2.2. The stress distribution in general terms The prestressed steel concrete bridge system is constructed in stages, which means that the stress distribution follows the construction activities step by step.
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Stage 1: The dead load of the steel girders and deck-slabs is acting on the steel U-shaped girder alone. The centroidal axis is positioned rather low in the cross-section. The stress distribution is shown in figure 8. The dead load causes compressive stresses in the upper flange of the steel girder. end slab
end slab concrete deck w ithout pressure
cent roidal axis st eel girder
pressure
pressure
t ension
t ension
centroidal axis
Figure 8 Stress distribution in steel girder, due to dead load.
Stage 2: The deck is prestressed. The centroidal axis is still low positioned. The prestressing force acts as a tensile force in the steel girder and the eccentricity causes a constant upward bending moment in the girder. The deck slabs compressed. The stress distribution is shown in figure 9. Due to the bending moment and the normal tension force in the steel girder, the upper flange of the steel girder is loaded with tensile stress. concrete deck under pressure caused by inf lated t ubes excent ricity cent roidal axis st eel girder
bending moment and t ension in st eel girder
pressure
t ension
pressure
t ension
cent roidal axis
Figure 9 Stress distribution caused by the prestressing force in the deck structure.
Stage 3: The connection between the steel girder and the deck-slabs is fixed by grouting the cavity with the perfobond-strips. From this moment the structure acts as a composite bridge. The centroidal axis is now at a higher position in the total cross-section of the bridge. The additional permanent load and live load causes positive bending moments. The stress distribution due to the permanent load is shown in figure 10. centroidal axis composite
pressure
tension
pressure
tension
centroidal axis
Figure 10 Stress distribution in the composite structure, due to permanent load and live load.
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After construction stages the resulting stresses in the cross section are shown in figure 11. The compressive forces in the upper flange of the steel girder due to dead load can be counterbalanced. Depending on the level of prestressing, this can result in a complete cross section under tensile stress. Due to the prestressing of the deck the compression stress in the deck tends to be higher than normal composite structures. centroidal axis composite
pressure
tension
pressure
tension
centroidal axis
Figure 11 Stress distribution after construction stages.
3. End slab connection During prestressing the steel girder acts as a tension member for the concrete deck. The end slab transfers the prestressing force to the upper flange of the steel girder by means of a shear connection as shown in figure 12. The shear connection is 3 metres long and over this length it has to transfer the prestressing force to the steel girder. End slab
Shear connection
Prestress from compression joint
Steel girder
Figure 12 Isometric view of the end slab during prestressing.
Other than the deck slabs, the end slab for a statically determined span is loaded from one side only. For action of prestressing in a statically undetermined system reference is made the paper of Mr. M.Lammens in these proceedings [2]. The prestress acts in the plane of the slab. Because of the ratio of the width of the plate to its length the slab is considered to act as a wall element. This means that stresses due to prestressing will not be divided equally over the slab. A probable distribution of stresses over the length of the shear connection is shown in figure 13. For the origin of this image of stresses reference is made to "Wandartige Träger" [3]. At the left side stresses perpendicular to the direction of prestressing are shown. Shear forces in the slab are shown at the right side.
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11250 mm 3000 mm
5250 mm
500
Upper flange End slab
Prestress
3000 mm
tension pressure
Normal st ress
Shear stress
Figure 13 Top view of the stresses in the end slab during prestressing in case of rigid shear connection.
In the image the shear connection is assumed to be rigid. As a result the prestressing force will be transferred to the steel girder at the front (bridge) side of the slab. This will inevitably lead to high tensile and shear stresses in the slab. This concentration of stresses could lead to cracking of the concrete and possible rupture of the shear connection. To reduce the stresses in the slab and the connection the aim is to distribute the force over the total length of the connection.
This can be achieved through the use of a flexible connection. In the design under consideration dowels are used to transfer the prestressing force to the steel girder. Dowels are easy to apply and capable of taking large deformations before failing. By deforming, the dowels next in line will be loaded during prestressing. Once the prestressing force is equally distributed over the length of the connection a stress distribution in the slab as shown in figure 14 will occur. Again at the left side transverse normal stresses and at the right side shear forces in the slab. This will result in a considerable tension reduction of peak stresses, as well tensile as shear tresses. The level pressure of transverse prestressing and Shear stress Normal stress posttensioning of the end slab can be reduced to a minimum and the Figure 14 Top view of the stresses in the end slab during chance of failure of the connectors prestressing in case of flexible shear connection. is reduced. Because of the flexibility of dowels the shear connection is made of dowels. Dowels are easy to weld to steel and are readily available in all sizes and strengths. The dowels are welded on a steel plate which is placed in the concrete formwork of the end slab in the factory before the concrete is poured. As soon as the concrete is hardened it is prestressed with pretensioning strands in the factory in its longitudinal direction (transverse direction of the bridge). On site the end slab is welded to the upper flange of the steel girder as shown in figure 15.
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Transverse w eld dow elplat e flangeplate
dow elplate
propw eld
f langeplate
Upper f lange
Figuur 15 Transverse and longitudinal cross section of the shear connection.
Research has been done to retrieve a relationship between the stiffness of the shear connection and the distribution of the prestressing force over the shear connectors. This has been done with a model in which the shear connection has been simplified to a one dimensional problem as shown in figure 16. Deck slab
End slab
group3
group2
concret e steel
group1
Upper flange
F Prestressing force
concret e st eel
Figure 16 Longitudinal cross section of the end slab and schematisation for the analytical model.
In the model the dowels are divided into three groups, first (front side) second (middle) and third (rear end) in line. These groups are represented by longitudinal springs connecting the steel girder and the concrete end slab. The steel and concrete are modelled as pinned beams, only capable of taking axial force. The prestressing force coming from the hydraulic compression joint is acting on the concrete as a concentrated force. The model is supported on only one side where the steel girder is cut off in the model. This does not influence the results because deformation of this part of the steel girder causes the model to translate but does not influence the behaviour of the connection. Formulas have been deducted for this model where all dowel groups have equal stiffness. These formulas have been input in a spreadsheet program. With this program it is possible to vary the ratio of stiffness between the three actors in the model and derive the influence on the distribution of the prestressing force over the groups of dowels.
4. Results The reference value for the dowels has been set to 1.0 representing the elastic behaviour of a group of 24 dowels with a 22 mm diameter. These values have been implemented in
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the first model, with equal stiffness of the dowel groups, and varied from 0.01 to 100 times the reference value. Results are shown in figure 17. The horizontal axis represents the stiffness of the dowel groups, relative to the reference value. The vertical axis indicates the percentile part of the prestressing force taken by the dowel groups.
in de kracht Share of theaandeel prestressing force
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
groep 1 groep 2 groep 3
0,01 0,02 0,04 0,12 0,35 1,00 2,86 8,16 23,30 66,54 relatieve stijfheid dowel deuvelgroepen Relative stiffness groups
Figure 17 Distribution of the prestressing force over the dowel groups with equal dowel stiffness.
The stiffness is of great influence on the distribution. The reference value for the stiffness of the groups results in overloading of group 1, taking 55% of the force. Enlarging the stiffness of the groups causes divergence of the results. Reducing stiffness to 0.3*reference leads to equal distribution. The corresponding strain of the groups can only be met with plastic deformation of the dowels [4]. In this region the model is invalid and the structure has no backup strength.
aandeel in de kracht Share of the prestressing force
As reducing dowel stiffness is not sufficient the effect of varying the stiffness of the steel is studied. In this study the stiffness of the dowels is kept constant and the stiffness of the steel girder is varied. Results are shown in figure 18. The horizontal axis represents the stiffness of the steel girder, relative to the reference value of a flange thickness of 30 mm. The vertical axis indicates the percentile part of the prestressing force taken by the dowel groups. The influence of the stiffness of the 100% steel is visible. Increasing the 90% groep 1 stiffness (thickening the upper 80% groep 2 70% flange) leads to more equal groep 3 60% distribution over the dowel groups, 50% 40% reducing the steel stiffness leads to 30% divergence of the results. The figure 20% shows that doubling the steel 10% 0% stiffness does not lead to equal 0,09 0,16 0,27 0,46 0,77 1,30 2,20 3,71 6,27 10,60 17,92 distribution over the dowel groups. relatieve stijfheidsteel stalenbeam ligger Relative stiffness
A different design approach has been chosen in the second case, where the stiffness between the groups of dowels is variable. In the former study the dowels at the front side of the connection attracted a larger part of the prestressing force. By increasing the number of the dowels towards the end of the Figure 18 Influence of the stiffness of the steel girder on the distribution of the prestressing force over the dowel groups.
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connection by increasing the number of the dowels. This will cause the rear end of the shear connection to attract more force. As a cause of prestressing with the compression joint the end slab is pressed and the steel flange is . The difference in deformation is forced upon the dowels. This deformation can be determined by assuming that the force is equally distributed over the dowels. In this situation the end slab transfers an equal part of the prestressing force over the length of the connection. From this fact the deformation of the end slab can be derived. The deformation of the steel girder can be determined by assuming that the force increases from 0 at the rear end of the connection to the entire prestressing force at the front end. The deformation of the dowels is determined as the sum of the deformation of the end slab and the steel girder. Knowing that the dowels transfer an equal part of the prestressing force over the length of the connection the stiffness of the dowels can be derived. With this information the number of dowels can be determined.
5. Conclusions With a simple analytical model the number of dowels in the shear connection can be determined. By increasing the stiffness of dowels towards the end of the shear connection the prestressing force can be equally distributed over the dowels. This reduces the maximum shear stress in the end slab to an acceptable level. The peak stresses in the end slab in transverse direction of the span are reduced and tension can be avoided by prestressing the end slab in the factory.
6. References 1. 2.
3. 4.
"Perfo-bond connection and tests", S.J. Poot. Symposium on Connections between Steel and Concrete, September 2001, Stuttgart. "Composite bridge with compression joints. Connection concrete end slab to steel girder - Finite Element Method", M.V. Lammens, Symposium on Connections between Steel and Concrete, September 2001, Stuttgart. "Wandartige träger", Förster/Stegbauer. Werner-Verlag 1974. "Statisch onbepaalde betonliggers", CUR-rapport 4, 1987.
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THE FATIGUE BEHAVIOUR OF THE SHEAR CONNECTION IN THE HOGGING REGION OF STEEL AND CONCRETE COMPOSITE CONTINUOUS BEAMS UNDER REALISTIC LOADING Helmut Bode, Andreas Leffer Department of Steel Constructions, University of Kaiserslautern
Abstract At Kaiserslautern University four large-scale tests on two span continuous composite beams have been performed [1,2]. The tests were aimed at investigating the fatigue behaviour of the shear connection in the hogging region under approximately realistic conditions. Therefore a new experimental simulation of the crossing of vehicles over bridges has been developed using two alternating hydraulic cylinders. It is shown that the studs’ flexibility and the cyclic cracking of the concrete directly adjacent to the stud influence the fatigue behaviour significantly. Both cannot be taken into account using the basis of design provided by the European standardization [3] or by the new national codes [4]. It turned out that some parts of the structure do not show elastic behaviour under service loads. Considerable shear force redistribution takes place along the connection and it seems probable that the fatigue phenomenon cannot be described in a sufficiently exact manner with the classical load-life fatigue approach.
1. Introduction Headed studs are normally used as shear connectors in steel and concrete composite structures. In bridge constructions repeated non-static loading occurs originated by lorries or trains. Therefore special attention has to be paid to the fatigue phenomenon. Due to the harmonization of the European Codes a standardized proof of the fatigue strength for the shear connectors is required [3] and partly simplifying national codes, for e.g. [5], will be replaced. In [3] the classical load life approach is used, like it is the same as the high cycle fatigue concept for steel elements. The concept is based on nominal stresses and uses a fatigue strength curve, the so called Wöhler curve, to determine the expected number of load cycles for the connectors. In general, the load life approach is limited to the elastic behaviour of all structural components under non-static (service-)loads. In that case, the fatigue resistance mainly
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depends on the amplitude of the load. Because of that in [3] the longitudinal shear per unit length has to be calculated by elastic theory, a complete shear connection has to be provided and the size and spacing of the studs should be such that the maximum shear force does not exceed 0.6*PRK. Furthermore a full interaction between structural steel, reinforcement and concrete is assumed, so that the redistributions of shear forces along the connection can be neglected. The characteristic value of the fatigue strength curve (eq. 1) [6] and the derived design value of the Wöhler curve (eq. 2) [3] are drawn up from a statistical re-evaluation of international data from stress controlled push-out tests. log N = 25.340 − 9.2 ⋅ log ∆ τR ”Characteristic fatigue strength curve“ [6] (1) log N = 22.123 − 8.0 ⋅ log ∆ τR “Design fatigue strength curve” [3] (2) Because of the very low inclination of the fatigue strength curves the lifetime prediction is very sensible to inaccurately calculated shear forces. In the hogging region of composite beams it is very likely that concrete cracking occurs. This can be taken into account according to [3] by considering the tension stiffening effects. Because of the concrete cracking the neutral axis descends into the web of the steel profile and causes considerable amplitudes of normal tensile stresses in the upper flange. Fatigue cracks in the flange may develop when shear connectors are welded over the centre support and the so-called fatigue failure mode “C” can occur, which causes a global failure of the beam. For this case a functional interaction relationship is proposed in [3] according to eq. (3). ∆ τE , c ∆ σE ≤ 1,3 + γ Mf , v ⋅ (3) γ Ff ⋅ γ Mf ,a ⋅ ∆ σc ∆ τc In reality even for low load levels significant shear force redistributions along the connection take place, which are not constant over the course of time. Besides concrete cracking in tension this is mainly due to the following two effects: 1. In principle the shear connection with headed studs is not rigid. Even for very low values of the load, the load-slip relationship is non-linear. Plastic deformations occur which are strongly developed for the first load cycle [7]. 2. The concrete directly adjacent to the feet of the headed studs is subjected to very high multiaxial stresses. Therefore a progressive cyclic crushing of concrete occurs and the slip at the steel-concrete interface steadily increases. The headed studs are more and more subjected to bending, which further amplifies the redistributions caused by the cyclic concrete crushing. As a matter of fact, after each load cycle an increment of slip is accumulated due to the progressive damage both in the concrete adjacent to the stud and in the shank of the stud [8,9]. Because of that larger areas of the shear connection are subjected to alternating cyclic loads, which cannot be estimated in a sufficiently exact way using linear calculation methods. Besides that these alternating amplitudes cannot be judged regarding the fatigue damage caused because the fatigue strength curve is derived from push-out tests subjected to unidirectional cyclic loads.
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2. Large scale tests on two span continuous composite beams In the past, the most common method to perform beam tests where the fatigue behaviour of the shear connection in the hogging region has been investigated was to carry out tests on single span beams with an inverted test set-up. This means that the specimens were turned upside down and therefore the hogging region was isolated from the whole structure. Besides that the tests were usually carried out as single range tests. In literature, for e.g. [10], other test set-ups can also be found but most of them have the single range loading in common. Fig. 1 shows the test set-up chosen at Kaiserslautern University.
2,41 m
1,59 m
1,59 m
2,41 m
Figure 1 Test set-up Within the scope of two research projects at Kaiserslautern University [1,2] tests on two span continuous composite beams have been performed. The simulation of the crossing of vehicles was approximated using two alternating hydraulic cylinders which were synchronized. The crossing was approximated by a “run over” in five steps. It turned out that the fatigue behaviour under more realistic loading conditions differs significantly from single range (beam-) tests. Only under more realistic conditions the various different sections along the shear connection in real structures can be modelled. Fig. 2 shows the scheme of the simulation. One load cycle took one second, which results in a test frequency of 1 Hz.
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Eigengewicht
Synchronisation of the Cylinders Synchronisation of Cylinders 450,0
maxF1
Cylinder 1 Cylinder 2
400,0
Force [kN]
Eigengewicht
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0,0 0,00
0,20
0,40
0,60
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1,00
Time [s] Time [s]
1,20
1,40
1,60
1,80
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Figure 2 Scheme of the simulation In the Constructional Engineering Laboratory at Kaiserslautern University it is not possible to carry out large-scale tests on real bridge girders. Therefore girders on a reduced scale were tested. The first two (T7_1 and T7_2) of four specimens were performed to robtain an idea of the fatigue behaviour under realistic loading. The major aim was to realize the desired, very complicated synchronisation. The third (T7_3) and fourth (T7_4) tests, which will be mainly referred to in the discussion of the test results, can be distinguished from the first two tests by an improved arrangement of shear connectors, the width of the concrete slab and the ratio of reinforcement (table 1 and 2). Those parameters were determined by a linear predesign based on elastic analysis. The cracking of the concrete and the tension stiffening effects were taken into account according to [3]. The main difference to normal design methods was, that no design values were used, but characteristic, predicted material properties (table 3). When the longitudinal shear forces are determined the cracking of the concrete has to be considered. This results in three different values for the stud spacing according to fig. 3: • e1 within the length L1 • e2 within the length (L3-L1) and • e3 within the length L4. The obtained values are given in the following tables. The studs directly over the centre support are subjected to alternating cyclic loads (Load step 2 + Load step 4) whereas all the other shear connectors are theoretically subjected to unidirectional amplitudes of shear forces (Load step 1 + Load step 3). The spacing of the shear connectors was chosen so that the required boundary conditions in [3] for non-static loads are satisfied and therefore the design concept mentioned should be theoretically applicable to determine the lifetime of the shear connectors as well as for the whole structure, by means of a safe lifetime prediction.
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EI2
EI1
L4
L3
EI1 L4
Stiffnesses
L3
minF1
minF2 Loadstep 1 (LS1)
L2
L1
L2
L1
maxF1
minF2 Loadstep 2 (LS2)
maxF1
maxF2 Loadstep 3 (LS3)
minF1
maxF2 Loadstep 4 (LS4)
Figure 3 Structural System of the predesign, linear shear forces (schematic) and designations Table 1 Dimensions and results of the linear predesign Test T7_3 T7_4
lTOTAL [m] 8,20 8,20
l0 [m] 4,10 4,10
Fmax [kN] 400 400
Fmin [kN] 20 20
l1 [m] 2,51 2,51
l2 [m] 1,02 1,02
l3 [m] 0,57 0,57
e1 [cm] 31 31
Table 2 Cross sections and ratios of reinforcement Test
T7_3 T7_4
Concrete width bc [cm] 80 80
Concrete depth hc [cm] 12,5 12,5
Steelprofile
µ l1 [%]
µ l2 [%]
µ l3 [%]
HE300A HE300A
0,63 0,63
1,1 1,1
1,1 1,1
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e2 [cm]
e3 [cm]
12,5 15
25 24
Table 3 Expected and real material properties Test
T7_3 T7_4
fy fy fck,cube fck,cube expected test expected test [N/mm2] [N/mm2] [N/mm2] [N/mm²] 300 362 40 42,2 300 362 40 47,4
fsk KD fsk expected test [mm] [N/mm2] [N/mm2] 500 540 22 500 561 22
3. Test results [1,2,11] 3.1. Global beam failure All tests including T7_1 and T7_2 finally failed according to failure mode „C“. The number of load cycles achieved in comparison to the number of cycles calculated using eq. (3) is displayed in table 4. It seems to be obvious that the design concept for the global beam failure underestimates the lifetime significantly. The functional relationship regarding the interactive effects in the hogging region seems to give very conservative results. The fact that the maximum values for ∆τ and ∆σ do not coincide, which is the regular case in real bridge girders, obviously influences the fatigue behaviour positively. Table 4 Comparison of the calculated number of load cycles for failure mode „C“ (ncalc) with the real number (ntest) Test
Failure mode
ncalc for type “C”
ntest for type “C”
T7/3
Type „C“
153.695
797.000
5.19a
T7/4
Type „C“
185.845
803.000
4,32a
n test n calc
3.2. Shear stud failure and slip development Regarding the pure shear stud failure and neglecting interaction effects, the four test specimens showed some similar results. The concrete slab was opened after the beams finally failed. It turned out that in all beam tests large areas of the shear connection had already failed due to fatigue effects. In beam tests it is quite difficult to determine the moment of stud failure exactly. In literature [7,10] there are some different proposals how to measure the moment of failure or even the moment where a fatigue crack starts to develop. Most of these proposals are based on specific applications of strain gauges or ultrasound scans. These methods were also applied in the first two tests but this was more or less unsuccessful. Those methods are very sensible, some experience is required and sometimes “luck” is required. The estimated value of load cycles for the first stud failure by evaluating secondary test data of T7_1 and T7_2 was 200.000. Preparing the tests T7_3 and T7_4 new test methods were developed to determine the moment of shear stud failure exactly [11]. Fig. 4 and fig. 5 show the comparison of the number of load cycles reached for each row of headed
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studs with the number calculated using eq. (2). In both tests the shear studs over the centre support failed first. They are subjected to high amplitudes of alternating shear forces (fig. 6). After that a successive failure from the inside to the outside occurs. Table 5 shows the total number of failed shear studs and the comparison of the moments for the first real stud failure (nfirst,real) with the calculated number for these studs (nfirst,calc). Table 5 Shear stud failure Test No. of studs No. of studs between failed between loaded points loaded points T7_3 42 26 T7_4 38 28
nfirst (Real)
Position (Real)
nfirst,calc (Calc.)
Position (Calc.)
348.000 254.250
Centre Centre
456.000 664.000
Centre Centre
Test T7/3 8,E+05
Number of load cycles n
7,E+05 6,E+05 5,E+05 4,E+05 Real stud failure 3,E+05 Calculated stud failure 2,E+05 F
1,E+05
F
0,E+00 2,5
2,75
3
3,25
3,5
3,75
4
4,25
4,5
4,75
5
5,25
5,5
Longitudinal axis [m]
Figure 4 Comparison of the calculated lifetime for pure shear stud failure with the lifetime obtained in test T7_3 By neglecting the tensile stresses in the upper flange of the steel profile (pure stud failure, no interaction effects) the extreme sensibility of the lifetime prediction for inaccuracies in the calculated shear forces becomes obvious. Regarding fig. 4 the curve representing the real stud failure always shows smaller values than the dashed curve which represents the results from the linear predesign. For the stud arrangement in T7_4 only the lifetime of the studs over the centre support is overestimated (fig. 5) although the differences in the stud arrangement were very small (table 1, table 5).
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Test T7/4 Real stud failure
8,E+05
Calculated stud failure
Number of load cycles n
7,E+05 6,E+05 5,E+05 4,E+05 3,E+05 2,E+05 F
1,E+05
F
0,E+00 2,5
2,75
3
3,25
3,5
3,75
4
4,25
4,5
4,75
5
5,25
5,5
Longitudinal axis [m]
Figure 5 Comparison of the calculated lifetime for pure shear stud failure with the lifetime obtained in test T7_4 In T7_4 there is only one pair of shear studs less near the two loaded points within (L3L1) (e2 = 15cm instead of 12.5cm) than in T7_4. This results in a total of 38 instead of 42. However the fatigue behaviour of the shear connection was in fact significantly influenced. Regarding the final failure of the beam no significant difference occurred (797.000 load cycles instead of 803.000), but the stud failure started much earlier in the more flexible, “weaker” beam T7_4. Both tests have in common that the shear studs over the centre support -the studs with the largest amplitude of alternating shear forces- failed first and earlier than expected. After that a successive stud failure occurs which runs faster the weaker the whole connection is. Regarding fig. 6 and fig. 7 some important notes have to be pointed out: • The studs over the centre support are subjected to alternating cyclic loads (fig. 6). • An initial slip occurs at the very beginning of the tests. The value is dependant on the friction on the steel-concrete interface, the peak of the shear force, the concrete compressive strength, the flexibility of the shear connectors and the stiffness of the whole shear connection (fig. 7). • After that only small and slow changes in the system take place. A slow but almost linear slip growth occurs. This is mainly due to the cyclic cracking of the concrete adjacent to the stud. Towards the end of the test a strong and faster slip growth occurs but the shear studs have already failed (fig. 7).
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•
The slip growth is stronger the less stiffness is provided in the whole shear connection from the very beginning (fig. 7). • The faster the slip develops the earlier the failure occurs. The value of slip determines the failure. • Small changes in the stiffness of the shear connection affect the lifetime of several studs significantly. • The studs fail due to fatigue for very small amplitudes of slip (fig. 6, fig. 7). These values are not comparable to the slip amplitudes obtained from stress controlled push-out tests. Nevertheless, the general course of the slip development (fig. 7) is quite similar, but in beam tests the moment of failure generally occurs before the major slip growth takes place. Slip hysteresis throughout several load cycles for T7/3 and x = 4,10 m (centre support)
Slip hyteresis throughout several load cycles for T7/4 and x = 4,10 m (centre support)
700
700
Loadstep 3
600
Load cell centre support [kN]
Load cell centre support [kN]
n=100
∆s ~ 0.3mm for moment of failure
500 400
Loadstep 4
Loadstep 2
300
n=1000 200
n=325600 100
n=378000
Loadstep 5 0
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
n=797000 0,6
∆s ~ 0.4mm for moment of failure
Loadstep 3
600
n=280.000 n=576.000
400
Loadstep 4
n=1000 n=100.000
500
Loadstep 2
300 200 100
Loadstep 5 0
-0,6
-0,4
-0,2
-100
0
0,2
0,4
0,6
-100
Slip s [mm]
Slip s [mm]
Figure 6 Slip development with a load cycle over the centre support (Alternating cyclic load) Maximum and minimum values of slip for T7/3 and x=4,10m (centre support)
Maximum and minimum values of slip for T7/4 and x=4,10m (centre support)
0,6
0,6
0,2
0,4
∆s~0,3mm for moment of failure Initial slip
0 0,E+00
1,E+05
0,2
2,E+05
3,E+05
4,E+05
5,E+05
6,E+05
7,E+05
8,E+05
9,E+05
-0,2
-0,4
-0,6
Slip s [mm]
Slip s [mm]
0,4
∆s~0,4mm for moment of failure Initial slip
0 0,E+00
1,E+05
2,E+05
3,E+05
4,E+05
-0,2
Loadstep 2 Loadstep 4
"Linear" slip growth
Load cycles n
-0,4
-0,6
5,E+05
6,E+05
7,E+05
Loadstep 2 Loadstep 4 "Linear" slip growth
Load cycles n
Figure 7 Boundary curves for the slip over the centre support over the course of time Regarding all shear studs between the loaded points it can be shown that the amplitudes of shear forces range from a pure alternating cyclic load to pure unidirectional cyclic loads. Fig. 8 shows the slip hyteresis and the boundary curves for a pair of shear studs between the loaded points and the centre (x=3.235m). For unidirectional cyclic loads the (one-sided) initial slip is usually greater than for alternating amplitudes (for comparable amplitudes), because it is strongly dependant on the peak of the cyclic load. The slip
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growth throughout the first cycles is mostly larger, although this is heavily influenced by the stiffness of the whole shear connection. Maximum and minimum values of slip for T7/3 and x=3,235 m (~80 cm left from centre)
Slip hysteresis througout several load cycles for T7/3 and x = 3,235 m 700
0,5
∆s ~ 0.40 mm for moment of failure
500
0,4
Loadstep 4
300
n=1000 n=70000
200
n=150000 n=557000
100
n=797000 0
-0,1
0
0,1
0,2
Loadstep 3 Loadstep 4
0,3
400
0,3
0,4
0,5
0,6
0,7
0,8
Slip s [mm]
Load cell centre support [kN]
Loadstep 3 600
0,2
∆s~0,40 mm for moment of failure
Initial slip
0,1 0 0
100000
200000
300000
400000
500000
600000
-0,1 -0,2 -0,3 -0,4
"Linear" slip growth
-0,5
-100
Slip [mm]
Load cycles n
Figure 8 Slip hysteresis and boundary curves for a pair of shear studs arranged 80cm left of the centre support in test T7_3 Summary This paper deals with results of testing done on two span continuous composite beams under cyclic loading. The special feature is the realistic loading situation, realized by two alternating, synchronized hydraulic cylinders. Therefore especially the hogging region could be investigated under more or less realistic conditions. It must be pointed out that the existing design concept for preventing the global failure of the beam (failure mode “C”) delivers very conservative results. It became obvious however that with the existing design models the real fatigue behaviour of the shear connection in the hogging region under realistic (service-) loading cannot be described in a sufficiently exact manner. Concrete cracking has to be considered, but it was shown that the flexibility of the shear connection, which is not taken into account in the European standardization, also influences the fatigue behaviour significantly, also under service loads. The headed studs over the centre support are subjected to large amplitudes of alternating shear forces and a considerable number of shear studs failed due to fatigue a long time before the whole beam failed according to failure mode “C”. It is important to point out that the shear connectors fail for very small amplitudes of slip (some tenth of a millimetre) and for a greater part of the lifetime of the beam the shear connection is interrupted. By neglecting the interaction effects and regarding the pure stud failure the sensibility of the existing design format to inaccuracies in the calculated shear forces becomes obvious. This is due to the very flat inclination of the fatigue strength curve. On the other hand it turned out that the moment of failure for a single shear stud is almost unpredictable. The high cycle fatigue concept, transferred from pure steel constructions, which assumes a constant relationship between the applied (service-) loads and the resulting fatigue-stress-amplitudes seems to be hardly applicable. There are ongoing and significant shear force redistributions along the shear connection, which are mainly due to the studs’ flexibility and the cyclic crushing of the concrete adjacent to the studs. Both are neglected in the existing design concept if the constructive requirements
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mentioned in the introduction are satisfied. It turned out that the slip at the steel-concrete interface, which is heavily dependant on the stiffness of the whole shear connection determines the moment of fatigue failure. Further research activities at Kaiserslautern University are dealing with the question if a strain-life approach which assumes a correlation between the slip and the resulting lifetime of the shear connectors may be more applicable.
4. References [1] Bode, H.; Mensinger, M.; Leffer, A.: Verdübelung von Verbundträgern unter nichtruhender Belastung im Brückenbau; AIF Forschungsbericht Nr. 11266, Düsseldorf 2000. [2] Bode, H.; Leffer, A.: Die Übertragungsfunktion beim Nachweis der Betriebsfestigkeit von Stahlverbundbrücken im negativen Momentenbereich unter besonderer Berücksichtigung einer nachgiebigen Verdübelung. DFG-Forschungsprojekt BO 733/11 (in progress). [3] ENV 1994-2, Eurocode 4, Teil 2: Bemessung und Konstruktion von Verbundtragwerken aus Stahl und Beton, Teil 2: Verbundbrücken; Deutsche Fassung, 1. Entwurf, Mai 1999. [4] EDIN 18800-5: 1999-01: Verbundtragwerke aus Stahl und Beton, Bemessung und Konstruktion (Entwurf, November 1999). [5] Richtlinie für die Bemessung und Ausführung von Stahlverbundträgern, März 1981; Ergänzende Bestimmungen zu den Richtlinien für die Bemessung und Ausführung von Stahlverbundträgern, März 1984. [6] Roik, K.; Hanswille, G.: Hintergrundbericht zu EC 4: Nachweis des Grenzzustandes der Betriebsfestigkeit für Kopfbolzendübel; Bericht EC4/11/90; Bochum,1990. [7] Mensinger, M.: Zum Ermüdungsverhalten von Kopfbolzendübeln im Verbundbau; Dissertation, Kaiserslautern 1999. [8] Gattesco, N.; Giuriani, E.; .Gubana, A.: Low-Cycle fatigue test on stud shear connectors, Journal of Structural Engineering, Vol. 123, No. 2, February 1997. [9] Gattesco, N.; Giuriani, E.: Experimental study on stud shear connectors subjected to cyclic loading, Journal of Constructional Steel Research, Vol. 38, No. 1, pp. 1-21, 1996. [10] Leonhardt, F.; Andrä, W.; Andrä, H.-P.; Saul, R.; Harre, W.: Zur Bemessung durchlaufender Verbundträger die dynamischer Belastung, Der Bauingenieur 62 (1987), S. 311-324. [11] Leffer, A.: Zum Nachweis der Betriebsfestigkeit von Stahlverbundbrücken im negativen Momentenbereich unter besonderer Berücksichtigung der Nachgiebigkeit der Verdübelung, Dissertation, Kaiserslautern (in preparation).
1151
INFLUENCE OF FATIGUE LOADS IN TENSION ON SHORT CAST-IN-PLACE ANCHORS IN CONCRETE Ezio Cadoni Istituto Meccanica dei Materiali, Switzerland
Abstract In the modern civil engineering field the anchorages play a very important role. In fact, the standardization of industrial process, like precasting industry, puts in evidence the need to develop modular elements. For the connections of these elements can be used: anchoring industrial systems (chemical anchors, undercut anchors, ecc.), cast-in-place anchors (designed before the casting of concrete). These anchors are often short cast-inplace anchors. They are used for fixing anchored panels, for fixing other elements to structure (publicity panels for example), or for fixing operating machine to ground. The anchors are subjected to cyclic loads. In particular, in the case of blocking operating machine, problematic of fatigue is present and can be predominant. In this paper the fatigue behaviour of three types of short cast-in-place anchors is described. For this research have been used: anchor bolt, ribbed and rod bar. The experimental results permit to describe the evolution of some variables like displacement, stiffness, dissipated energy during the fatigue life. The correlation between the load-displacement curve during the static pull-out test and the cyclic behaviour of anchor is also discussed.
1. Introduction The great development of anchor bolts and their direct appliance in the field of structural engineering, has pointed out the necessity of knowing their behaviour under not usual loading case. In particular with the appearing of new types of structures (off-shore, high towers, ecc.) the anchors are often subjected to fatigue load. A short anchor is usually defined as one whose embedded length is insufficient to develop tensile yield in the bolt. They are normally used in the connection between structural members. For this research [1] have been used: anchor bolt, ribbed and rod bar. Cast-in-place steel anchors, threaded rods with nuts and washers at the bottom, which are widely used
1152
throughout the world, are here considered as the short anchor to study the fatigue behaviour of concrete. The ribbed and rod bar have been chosen in order to emphasize the diffused damage and bond failure, respectively. The fatigue failure of these anchors has been investigated through pull-out tests carried out on concrete slabs by applying sinusoidal shaped loading cycles to anchors previously embedded in the casting.
2. Experimental technique The tests were performed on 40 anchors embedded, before the casting, in as many concrete slabs sized 500*500*150 mm. Only one type of micro-concrete, having the composition and mechanical properties given in Table 1, was tested. Compressive strength, R, was evaluated on standard cubes. The determination of secant modules, E, and fracture energy, Gf, were performed on 160*160*500 mm prism and 100*100*840 mm notched prisms, respectively. Table 1 - Material Composition: • cement CEM I 42.5 • alluvional sand with 0-8 mm diameter • water/cement ratio Compressive strength, R Young's modulus, E Fracture energy, Gf
400 kg/m³ 1700 kg/m³ 0.50 25 MPa 20.4 GPa 62 N/m
Before the tests, the slabs and tests pieces were kept for 30 days at a temperature of about 20°C at a relative humidity of approx. 65%. The pull-out tests were performed by means of an MTS with maximum load of 250 kN by imposing a constant velocity of the • load application point of η = 5 ⋅ 10 − 6 m/s. Instantaneous displacement, η, was calculated as the arithmetical mean of η1 and η2 values measured by two LVDT (linear variable displacement transformer) transducers placed in a diametrically opposed position with respect to the anchor bolt. The measuring points of the transducers on the surface of the slab and on the testing machine were chosen so as to minimize possible displacement errors due to play in the mechanical connection or elastic strains in the materials. A large diameter contrast ring (500 mm) was used so as not to affect the cracking surface. The fatigue tests were carried out by applying a sinusoidal loading cycle with a frequency of 1 Hz. Maximum load, Pmax, was kept constant throughout the test. Load-displacement diagrams were recorded keeping the load increase rate constant at the first loading/unloading cycle and after N0, N1, N2, ....Ni fatigue cycles. The anchor bolts were embedded at 40 mm while the rod and ribbed bars were embedded at 60 mm. All three types had a nominal diameter of 16 mm.
1153
3. Failure mode of short cast-in-place anchors The potential failure modes of a short anchor bolt can be of four kinds according to the materials and geometrical characteristics. The first mode is obtained by the pulling out of the rod and it depends exclusively on the interface quality between the two materials, the inadequate anchor length and the absence of the washer at the bottom. The second mode is the typical one which shows the concrete frustum cone shape failure. The third mode is half way between the two and mixed-mode named. In the fourth we finally have the threaded rod failure. This occurs in case of high anchor lengths or high resistance concretes. There is another ‘structural’ failure mode that is the splitting of the member due to the loading anchor. In the typical failure (extraction of cone) of anchor bolts, due to axial-symmetric conditions, the crack more over enucleate at the top edge of the washer. As is known, in pull-out tests involving a contrast ring of considerable size compared to bolt depth, concrete failure is caused by a tensile stress field localised at the end of the bolt head, as born out by the fact that is the area where both the main crack and the micro-cracking zone are initiated. Moreover, the stress field produced by support reactions turns out to be negligible compared to the stress field close to the stem. In this case, a tensile stress field around the bolt heads triggers off the crack and, when static tests are considered, brittle behaviour is observed during collapse. The load-bearing capacity depends on the fracture energy and the tensile strength of concrete. By using smaller diameter contrast rings or different types of anchorage, such as those commonly used in the building industry, a brittle-ductile, or ductile behaviour is observed instead, that is to say, friction or hooping phenomena, due to the presence of reinforcement, or interlocking effects, etc. occur alongside with diffused micro and macro-cracking that enhance the ductility of the material [2]. The presence of a head or lateral pressure in short anchor permits a more uniform distribution of the shear stress and a better transferring of loads. The drawback is that this type provokes a brittle failure of concrete. In the rod and ribbed bar the transferring of loads depends on hardly to the interface condition between anchor and concrete but in the case of short anchor it is ever present the slipping failure (that is more o less brittle). In the case of anchor bolts, the fatigue collapse process evolves in two states: the initial phase, in which appears little local crack that arriving to a sufficient dimension develops, and a second phase in which the last one increases up to failure. In the case of ribbed bar, it should take into account that during the fatigue life the stress are not uniformly distributed along the anchorage; this fact implies a new stress distribution during the load sequence and to failure with high interlocking effect. The geometry of anchors is very important for the failure analysis of anchors.
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4. Evolution of the mechanical behaviour during fatigue life of anchors During the fatigue life the short anchor shows a variation of some variables that indicate a progressive damage [3-4]. The variables chosen as tool for checking the fatigue process were the energy dissipated of cycles, compliance and displacement of anchorage. The fatigue process can be subdivided in three zone corresponding to the three known states. Considering the displacement of anchors as variable the state can be defined as follows: • State I is the rapid increase of displacement up to 10% of the life • State II is the stable growth between 10% and 80% of the life • State III is the rapid increase up to failure In Fig. 1 the dimensionless displacement versus dimensionless number of cycles (fatigue life) is shown. 1 III phase
Displacement / displacement at failure
0.9
0.8 II phase 0.7
0.6 I phase 0.5
0.4
0.3
0.2
0.1
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
N° cycles / N° cycles at failure
Fig. 1 - Dimensionless displacement vs. dimensionless number of cycles The fatigue effect on anchors depends on several factors as anchorages type, the concrete around, the presence of stress state or reinforcements near the anchors, the confinement, the load history of loads in time, the maximum stress and so on. The shape of cycles change a little bit for each cycle. In Figs. 2, 3, 4 the variation of cycles shape for the three types of anchors are shown.
1155
30
25
N=2 ED=100% N/Nf= 0%
Load [kN]
20
N=3000 ED=85% N/Nf= 8.8%
N=30000 ED=161% N/Nf= 88%
15
10
5
0 0
0.5
1
1.5
2
2.5
Displacement [mm]
Fig. 2 - Evolution of the cycle shape during fatigue life (anchor bolts)
Analysing the variation of the cycle is possible to study the evolution of the variable chosen for the damage process in fatigue. In Figs. 5 and 6 are shown the displacement of anchor bolt and ribbed bar, respectively. In Figs. 7 and 8 are described the evolution of the compliance and the energy dissipated per cycles during the fatigue life of anchor bolts. The energy dissipated per cycles in the case of anchor bolts decreases during the firsts cycles, and increases steadily thereafter, up to failure. For the rod and ribbed bars, this does not occur. The same behaviour was observed for the compliance of anchorage. The displacement of anchorage seems to be the most suited feature that can be used as variable to check the fatigue process.
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30
25
N=2 ED=100% N/Nf= 0%
Load [kN]
20
N=50'000 ED=15% N/Nf= 6.5%
N=332'500 ED=12.5% N/Nf= 46%
N=700'000 ED=13% N/Nf= 95%
15
10
5
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Displacement [mm]
Fig. 3 - Evolution of the cycle shape during fatigue life (ribbed bar) 5
4.5
4
N=2 ED=100% N/Nf= 0%
3.5
N=40'000 ED=74 % N/Nf= 12 %
N=302'240 ED=140 % N/Nf= 95 %
Load [kN]
3
2.5
2
1.5
1
0.5
0 0
0.02
0.04
0.06
0.08
0.1
Displacement [mm]
Fig. 4 - Evolution of the cycle shape during fatigue life (rod bar)
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0.12
0.14
9 T7
T4
T5
Displacement / Diplacement at first cycle
8
7
6
5
4
3
2
1
0 0
1
2
3
4
5
6
Log N° cycles
Fig. 5 – Displacement/displacement at first cycle vs. log number of cycles curves of anchor bolts
Displacement / displacement at first cycle
3
2.5
2
1.5
1
0.5
0 0
1
2
3
4
5
6
Log. number of cycles
Fig. 6 – Displacement / displacement at first cycle vs. log number cycles curves of ribbed bar
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7
0.0007 T7
T4
T5
0.0006
Compliance [mm/daN]
0.0005
0.0004
0.0003
0.0002
0.0001
0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Log N° cycles
Fig. 7 – Compliance vs. log number of cycles curves of anchor bolts
Dissipated energy / Dissipated energy of 2nd cycle
2 T7
1.8
T4
T5
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Log N° cycles
Fig. 8 – Energy dissipated per cycle vs. log number of cycles curves of anchor bolts
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5. Correlation between static and cyclic behaviour of anchor bolt. The displacement, more generally the deformation, gives the possibility to understand if the fatigue process is in a stable or an unstable zone. Does exist a link between the static and cyclic deformation? The answer can be positive. The same conclusion [5] was reached through a theoric-experimental study that described a local approach to fatigue concrete. The descending branch of the load-displacement curve of static pull-out test could be the boundary for the displacement in fatigue tests. As it has been reported before, the load-displacement curve during the cycles shows damage that consists of a decrease of slope with respect to the displacement axis hence, increase of compliance for the whole system. The failure occurs when the cyclic load-displacement intersects the descending branch of the static pull-out curve. It should be considered that is necessary to make some comments before verifying this hypothesis. It is difficult to know the exact pull-out curve for each type of anchor. In fact, each anchor possesses its own curve, in the sense that this depends on numerous factors as the concrete composition, the disposition of particular aggregate near the anchor, the modality of extraction and so on. It must be considered that the deduction and the hypothesis are referred to a mean behaviour; therefore, with a statistic dispersion that in some cases can be elevated, more caution is necessary. The same difficulties are encountered when one wants to establish the bearing capacity of anchor or the displacement at failure. The displacement that corresponds to the displacement of maximum load in static pullout load has been considered as the end of linear growth of displacement, after the non linear growth begins up to reach the point of intesection with descending part of static pull-out test where the failure occurs. The same hypothesis for the description of τ-slip law of bars embedded in concrete [6] was also used. The tests on anchor bolts have shown a behaviour similar to Hordijk’s observations. Therefore, it is possible to define a failure criterion based on displacement because a relationship between the static and dynamic deformation (or displacement) recorded in static and cyclic tests respectively exists. As a result of this hypothesis, it is possible to point out the fundamental features that govern the cyclic behaviour by means of the static pull-out test. The maximum displacement is represented by the intersection of the line at predetermined percentage of load and the descending branch of the static pull-out test. However, in the fatigue life of anchor it is better not to exceed the displacement at static failure because in this case the process of fatigue is in the unstable zone.
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6. Conclusion The type of anchor have to be considered when it is subjected to cyclic load. The experiments have shown a non linear damage of anchorage during the fatigue life. The damage is influenced by anchor geometries thus one needs to consider this aspect in anchor type choice, especially if subjected to cyclic load . By comparing the evolution of load cycles it is possible to say that the most suited feature for the control of fatigue process is the displacement. The relationship between displacement in static and cyclic tests exists, therefore, by the load-displacement recorded during the static pull-out test, it is possible to point out the fundamental features that govern the cyclic behaviour. As result, the anchor fatigue life may be predicted more effectively through a relationship based on the increase in the displacement of the load application point as a function of the number of cycles rather than through a relationship based on the crack propagation velocity as a function of the number of cycles as in metals [2].
7. References. 1. 2. 3. 4. 5. 6.
E. Cadoni. ‘Sul comportamento a fatica degli ancoraggi nel calcestruzzo’, Doctoral Thesis, , Politecnico Torino, (1994) P. Bocca, E. Cadoni, S. Valente. ‘On concrete fatigue fracture in pull-out tests’, in “Fracture and Damage of Concrete and Rock”, Chapman & Hall, (1993) 637-646. E. Cadoni. ‘Tension fatigue failure of short anchor bolts in concrete’, in ‘Anchors in Theory and Practice’, ed. Widmann, A.A. Balkema, (1995) 405-410. E. Cadoni. ‘Fatigue behaviour of anchor bolts in concrete’, in ‘Fracture Mechanics of Concrete Structures’, Wittmann editor, Aedificatio, 2, (1995) 1555-1565. Hordijk, D.A. Local approach to fatigue of concrete. Doctoral Thesis, Technische Universiteit Delft: Delft (1991). Balazs, G.L. Bond behaviour under repeated loads. Studi e Ricerche. 8, (1986) 395430.
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A TEST PROPOSAL FOR FATIGUE EXPERIMENTAL STUDIES ON STUD SHEAR CONNECTORS Gattesco Natalino* and Ezio Giuriani** *Dipartimento di Ingegneria Civile, Università di Udine, Italy. **Dipartimento di Ingegneria Civile, Università di Brescia, Italy.
Abstract A new fatigue test for stud connectors able to represent as confidently as possible the actual behavior of the stud in a composite beam is herein proposed. This test method avoid most of the shortcomings of the standard push-out test and allows to perform easily reverse cyclic loading with either load or displacement control procedure. The specimen is arranged with one single connector so to allow on the one hand to survey the local behavior of the stud during fatigue life and on the other hand to permit to draw analytical relationships under cyclic loading (cyclic load-slip relationship). Some monotonic and fatigue tests evidenced the reliability of the test method proposed.
1. Introduction The push-out test was devised in the early nineteen-thirties to determine the transfer capacity of spiral type shear connectors; since then, it has been used widely to study the behavior of different types of connectors. Although the stress conditions in the concrete block of the push-out specimen do not truly represent the stress conditions which occur in an actual composite beam, push-out test permits to obtain reliable load-slip characteristics of connectors in case of monotonic loading. For cyclic loading, the different stress conditions in the concrete of the specimen and some intrinsic shortcomings of the test [1] may influence significantly both the cyclic load-slip relationship of the connector and its endurance resistance. Moreover it is not easy to perform reverse cyclic loading using the push-out test. Most of the studies on connection fatigue available in the literature [e.g. 2, 3, 4] are focused to low-intensity cyclic loads leading thus to the connection failure in a large number of cycles (high-cycle fatigue). In these cases the endurance depends markedly to the load range while the dependence to the ratio between the minimum and maximum load is almost negligible [3]. For such a reason, the majority of the experimental cyclic
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test results available were performed using standard push-out specimens subjected to unidirectional loading cycles [2, 3, 4]. The reference endurance curves (Wöhler curves) present in the codes of practice were obtained from these experimental results [5]. The complex load histories of bridges include also cyclic loading of high intensity which involve in the stud significant nonlinear deformations at each cycle, so that the endurance depends both to the load range (amplitude) and to the load ratio (min/max load ratio). For high intensity cyclic loads, then, it is necessary to evaluate the stud endurance using the strain control approach, suitable for low-cycle fatigue. Moreover, for the check of connection fatigue using this approach, it is necessary to determine the cyclic load-slip relationship of the connector for any loading condition. Moving loads on bridges causes also cyclic loading with opposite sign in the connectors so the test method has to allow reverse cyclic loading. Some researchers conducted reverse cyclic loading using either push-out specimens arranged in a purpose built reaction steel frame [6] or doubling specularly the specimen with respect to its base [7]. These techniques allowed to perform reverse cyclic loading tests, using either a load controlled or a displacement controlled test procedure, without excessive experimental difficulties; but most of the shortcomings of the standard push-out test are still present. The scope of this research work is to discuss in detail a specific test proposal to carry out experimental investigations on the fatigue of stud connectors; the test herein presented is a refinement of that illustrated by the authors in some preceding papers [1, 8]. In particular this method aims to correctly represent the actual stud behavior in the beam, so to remove the shortcomings of the push-out test, and to allow easily carrying out reverse cyclic tests, so to determine the cyclic load slip curve of the single connector.
2. Stud features in the composite beam The study of the behavior of connectors subjected to cyclic loading requires specimens and test procedures able to simulate as confidently as possible the actual behavior of the stud in the structure. In fact, small behavior divergences of the specimen can accumulate at each cycle leading to quite different responses, with respect to the beam, after a significant number of cycles. It is then important to firstly analyze the actual forces and boundary conditions applied to the stud in the beam. A composite beam with a single row of equally spaced studs is considered. Each stud is submitted at its base to a shear force Q and a moment M (Fig. 1a). The force Q is transmitted to the concrete slab by longitudinal shear flow q acting on both sides of the element surrounding the stud, as illustrated in Fig. 1a,b. The longitudinal compression of the slab, due to the bending moment in the beam, is normally very low because where the connection shear force has great values the moment tends to zero (e.g. close to supports in simply supported beams subjected to uniformly distributed loads).
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Fig. 1 – Concrete element surrounding the stud: (a) longitudinal view in the beam, (b) assonometric view, (c) forces acting on the element.
Fig. 2 – Equilibrium forces in push-out test: base of concrete blocks (a) laterally restrained and (b) laterally free. The shear force Q, the stud moment M and the shear flow q do not satisfy the rotation equilibrium of the element (Fig. 1 c); it is needed a couple of vertical shear forces V*. No axial forces are involved in the stud. As a matter of fact the flexural deformability of the slab between two studs may cause the uplift of the slab and consequently a tensile force in the connector; however such a force becomes appreciable only when very large slip values occur at the interface (second order effect on the stud).
3. Push-out test considerations As stated above, the push-out specimen do not truly represent the actual behavior of the stud in the beam. The concrete block of the specimen, simulating the concrete element surrounding the connectors in the beam (Fig. 1a,b), is subjected to different forces causing diverse stress conditions in the studs.
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Shear forces Q and Q’ are equilibrated by bottom reaction force Fv acting on the concrete block (Fig. 2). Such a force, that is not aligned with shear forces Q and Q’, causes a stress distribution inside the block according to the schematic strut-and-tie systems shown in Fig. 2, with some struts thrusting against the steel element surface. Thrusts cause an additional force δQ, due to the friction between the steel flange and the concrete blocks, so that a greater stud capacity than the actual one is obtained. This additional force is different whether the concrete blocks of the specimen are at the bottom restrained or free to move laterally (Fig. 2a,b). In the latter case, moreover, the lower connectors are also subjected to a tensile force (Fig. 2 b), so the studs of the specimen are differently loaded (Q ≠ Q’). This difference cause a diverse fatigue damage in the connectors, yielding to collapse the studs of the bottom row appreciably earlier than those of the top row [2]. It has also to be noted that the deformability of the concrete member between the two rows of studs is in general greater than that of the steel member, so again bottom and top groups of connectors are subjected to a different shear force. The push-out specimen has a double symmetry from a geometric point of view, but an asymmetric mechanical response may occur due mainly to the unavoidable inhomogeneity of the concrete surrounding each stud. For this asymmetry may occur relative rotations between the steel element and the concrete blocks, both in the plane of concrete-steel interface and in the plane of the steel web. These rotations do not allow to obtain the local slip and the shear force of each connector, but only average values; that is the cyclic load-slip curve of the single connector can not be determined with this test. Another important issue concern the casting direction of concrete in the specimen. In fact, it was pointed out by many researchers (e.g. [9]) that placing concrete in the direction perpendicular to the stud axis causes significant static and fatigue resistance reduction, because beneath the connector bleeding water accumulates leading to local softer concrete. It is then necessary to place concrete in the direction of stud axis, as occurs in the concrete slab of composite beams. For such a problem some researchers proposed to cast the two concrete blocks of pushout specimens in two times (the latter when the former hardened), with the disadvantage that each specimen is cast from a separate concrete mix (likely have slightly different properties); some others proposed to use two plates, with the studs welded to them, to cast the concrete blocks against the plates, taking the studs with vertical axis and, after concrete has hardened, the plates are mounted with bolts to the flanges of an I-shaped steel member [6].
4. Proposed Test Method A specific test method, able to avoid most of the shortcomings of the push-out test listed above, is presented and discussed in detail in the follow. In order to obtain a good agreement with the situation of Fig. 1c, a direct shear test, based on the scheme of Fig. 3, is herein proposed. In this test the action lines of the opposite forces Q have a relative distance equal to e so to nullify the vertical shear forces V* (Fig. 1c). The distance e is
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obtained from the relationship e=M/Q, where M is the moment corresponding to the force Q in the hypothesis that the stud is considered as a beam resting on a cohesionless elastic foundation with one end restrained to rotation. The occurrence of different values of the moment M, with respect to that predicted, needs forces R1 and R2 for rotation equilibrium of concrete block. Steel ties were used to resist eventual tensile values for forces R1 or R2. Compressive values induce a friction action which is negligible in comparison with the shear force Q. A U-shaped concrete block is used so to simulate the concrete element in the beam (Fig. 1a,b,c), which is subjected to a longitudinal shear flow q for equilibrating the shear force Q. In fact, the force Q, applied to the concrete ribs, equilibrates the opposite force Q, transmitted to the slab element by the connector, through a shear flow q at slab-rib interfaces (Fig. 4), similarly to scheme of Fig. 1b. In detail the proposed specimen concern the U-shaped concrete block (a) and the Tshaped steel element (b). In the flange of the steel element a single stud connector (c) is welded and embedded in the concrete block. The concrete block is 340 mm wide, 400 mm deep and 130 mm thick; the longitudinal ribs (wings of the U) are 70 mm wide and 90 mm thick. The steel flange is 70 mm wide and 20 mm thick while the web is 170 mm wide and 15 mm thick (Fig. 5). The concrete block is pierced through longitudinally so to allocate four threaded bars (d) for fixing the specimen to the contrast frame of the loading system or to an adequately designed steel device to allow the specimen to be clamped to the grips of a common testing machine. Moreover six transversal steel ties (e), (f) are needed to prevent relative rotations between the steel element and the concrete block; four ties (e) are in the interface plane and two ties (f) are perpendicular to the interface (see Fig. 3). Large elliptic holes are provided so to avoid any lateral interaction (flexure and shear) between ties and concrete (Fig. 5). To reduce friction at steel-concrete interface a thin layer of stearic acid was interposed. A stiff L-shaped steel device (g) is bolted to the web of the steel element with high-strength bolts so to prevent slip. In the top of such a device a big nut is welded, which is needed to fix the specimen to the hydraulic actuator, or alternatively a device to be clamped to the grips of a common testing machine.
Fig. 3 – Forces acting on the specimen which simulates the actual behavior in the beam.
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Fig. 4 – Shear flow in test specimen in assonometric view.
Fig. 5 – Specimen details.
Fig. 6 – Gauge arrangement. The size of concrete block is important in push-out tests because it influences the capacity of the connection. In fact, when the concrete block is of limited width a low ultimate load may be obtained because cracking of concrete involves the entire block. In the proposed test the single connector produces limited stresses in the concrete block so that no macroscopic cracks may develop up to the connection failure, as confirmed by experiments. Hence, in the proposed test the width of the concrete part is of minor importance.
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The specimen proposed allows to perform both load and displacement controlled tests. Specimens may be subjected to tension, compression and reverse cyclic loading by simply using a common dynamic testing machine. The slip between the concrete block and the steel element is measured by means of two inductive transducers LVDT (A) (Fig. 6). The check of the effectiveness of steel ties (e) and (f) (Fig. 5) against the relative rotation between concrete and steel elements can be done by means of dial gauges (B) and (C), or alternatively other inductive transducers. In all tests carried out up to now, the rotation was always negligible.
5. Application of the test method The test method was applied to study the behavior of single studs subjected to monotonic and cyclic loading. In the first case the maximum capacity, the maximum slip at failure and the load-slip relationship were determined. In the latter case tests were carried out at constant load amplitude; the fatigue endurance and the cyclic load-slip relationship were determined. For the concrete of specimens was used Portland cement and river aggregate (15 mm maximum size). The water-cement ratio was fixed to 0.5 and 3 l/m3 of superplasticizer (MAC – Reobuild 716) was added to obtain a good workability. After casting, the concrete was cured under moist sacks for one week and then the specimens were stored in air at 20 °C until subjected to test. The compressive strength of concrete was determined on cylinders (100x200 mm) and cubes (150 mm), cast and cured under the same conditions as the concrete of specimens. The cylindrical and cubic compressive strength at testing of specimens were on the average of 43.5 MPa and 58.5 MPa, respectively. Stud connectors with a shank diameter of 19 mm and a height of 110 mm were used; the yielding stress and the ultimate strength were 415 MPa and 547 MPa. 5.1 Monotonic tests Four specimens were subjected to monotonic loading; the tests, identified with letter A, were performed at displacement control imposing a constant slip rate of 0.001 mm/s. The average values of the maximum shear resistance and of the slip at failure were 109 kN and 8.70 mm, respectively. The failure of all specimens was reached by shearing of the shank of the stud just beyond the weld collar. This stud capacity was used as reference static resistance in the cyclic test program. In Fig. 7, the shear load Q is expressed as the ratio of the ultimate load Qu in order to make the comparison possible among results from different mechanical characteristics of concrete and steel of studs. The curve of specimen A1 is compared with some other results available in literature [1, 10, 11]. 5.2 Fatigue tests For fatigue tests a load controlled procedure was adopted varying the load sinusoidally between the fixed limits (constant amplitude). Cycle frequency was kept constant during the test and equal to 1.0 Hz. The peak values of the slip at each cycle were recorded as
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well as the entire load-slip curve for a certain number of cycles (1,2,...,10,20,..,etc.), so to avoid excessive amounts of data. All the tests concern reverse cyclic loading. The specimens identified with B, C, D refer to a load ratio equal to –0.1, the specimens E, F, G refer to a load ratio equal to –0.5 and the specimens H, I, L refer to the complete reverse loading (load ratio equal to –1.0). Moreover, the specimens B, E, H are subjected to a load range approximately equal to 44% of the static resistance Qu, the specimens C, F, I to a range of 67% of Qu and the specimens D, G, L to a range close to 88% of Qu. A couple of each specimen type was studied. The details concerning cyclic loading are summarized in Tab. 1.
Fig. 7 – Comparison of monotonic test results with results in the literature [1,10,11]. Tab. 1 – Fatigue test results. Spec. Ident. B1 B2 C1 C2 D1 D2 E1 E2 F1 F2 G1 G2 H1 H2 I1 I2 L1 L2
Fatigue load Max Min/max [kN] 43.9 43.9 65.6 65.6 85.4 85.4 33.1 33.1 49.5 49.5 64.8 64.8 27.8 27.8 36.6 36.6 46.5 46.5
-0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0
Fatigue/static max load ratio
Loading range [kN]
0.40 0.40 0.60 0.60 0.78 0.78 0.30 0.30 0.45 0.45 0.60 0.60 0.26 0.26 0.34 0.34 0.43 0.43
48.3 48.3 72.2 72.2 93.9 93.9 49.6 49.6 74.2 74.2 97.2 97.2 55.6 55.6 73.2 73.2 93.0 93.0
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Slip max first cycle Ultimate [mm] [mm] 0.176 0.159 0.125 0.191 0.225 0.241 0.120 0.103 0.188 0.170 0.195 0.206 0.078 0.089 0.116 0.105 0.210 0.173
3.35 3.02 3.67 3.73 3.81 4.26 3.90 3.18 3.90 3.67 3.83 4.18 1.69 1.89 2.46 2.66 4.07 3.79
Fatigue life [cycles] 65997 48532 3980 4922 618 1019 91600 69730 6452 8105 790 492 36500 47133 2400 2982 491 339
200 Q
Load range (kN)
∆Q
t
100 80 60
Headed studs 19 mm
40
20 1E+2
EC4 fatigue curve Qmin /Qmax = -0.1 Qmin /Qmax = -0.5 Qmin /Qmax = -1.0 1E+3
1E+4
1E+5
Number of cycles
Limits of cyclic slip (mm)
Fig. 8 – Experimental endurance limits compared with the fatigue curve proposed in [5]. 4.0 Headed studs 19 mm 3.5 Q /Q = -1.0 L1 max min 3.0 smax I1 smin 2.5 2.0 H1 1.5 1.0 0.5 0.0 -0.5 0.0 0.2 0.4 0.6 0.8
1.0
Cycle ratio
Fig. 9 – Cyclic slip versus cycle ratio for completely reversed cyclic tests. The fatigue life as well as the maximum slip at first and ultimate cycles are also reported in Tab. 1. The maximum slip at failure was almost always lower for the smallest loading range considered, independently to the value of the load ratio. In Fig. 8 the experimental endurance limits are plotted against the load range. The rhombi, squares and triangles refer to specimens tested with a load ratio equal to -0.1, -0.5 and -1.0, respectively. The solid line represents the endurance curve of high-cycle fatigue [5]. It can be noted that the endurance of specimens with a load range greater than 60% of the static capacity Qu (spec. C, D, F, G, I, L) is, as expected, notably lower than that predicted by code curve. Moreover, for greater load ranges the dependence to the load ratio is more pronounced. The values of the peak slip values at each cycle are plotted in Fig. 9 in function of the cycle ratio (ratio between current number of cycle and number of cycles at failure), for specimens H1, I1, L1. In the figure thick lines refer to the maximum slip while thin lines refer to the minimum slip. Such a plot evidences large variations of the slips with cycles for specimens I and L due to the significant nonlinear deformations involved in the stud. For such cases fatigue check need to be based on the strain life approach [8].
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6. Concluding remarks The push-out test do not represents consistently the actual behavior of studs in composite beams; this inconsistency may influence significantly test results when cyclic loading are carried out. The direct shear test proposed was devised in the purpose to correctly represent the actual stress conditions that characterize the steel-stud-slab system in the composite beam. The test method allows to perform easily monotonic and cyclic tests operating either with a load control or a displacement control procedure. The specimen has a single connector so that the actual load-slip relationship of this stud can be obtained. Some monotonic and cyclic tests evidenced the reliability of the test method proposed. Moreover, fatigue tests results showed that for a loading range greater than 60% of the static resistance the strain life approach has to be used to study the connection fatigue.
7. References 1.
Gattesco, N. and Giuriani, E., ‘Experimental Study on Stud Shear Connectors Subjected to Cyclic Loading’, J. Constr. Steel Res., 38 (1), (1996), 1-21. 2. Slutter, R.G. and Fisher, J.W., ‘Fatigue Strength of Shear Connectors’, Highway Research Record, 147, (1966). 3. Mainstone, R.J. and Menzies, J.B., ‘Shear Connectors in Steel-Concrete Composite Beams for Bridges: part 1. Static and Fatigue Tests on Push-Out Specimens’, Concrete, 1, (1967), 291-302. 4. Oehlers, D.J. and Foley, L., ‘The Fatigue Strength of Stud Shear Connections in Composite Beams’, Proc. Inst. Civil Eng., Part 2, 79, (1985), 349-364. 5. ENV 1994-2 : 1997, Eurocode 4: Design of Composite Steel and Concrete Structures. Part 2: Bridges, (1996). 6. Taplin, G. and Grundy, P., ‘Incremental Slip of Stud Shear Connectors under Repeated Loading’, Proceedings of the International Conference – Composite Construction – Conventional and Innovative, Innsbruck, (1997), 145-150. 7. Leonhardt, F., ‘Critical Remarks on the Testing of Fatigue Strength of Shear Studs for Composite Girders’, (in German), Bauingenieur, 63, (1988), 307-310. 8. Gattesco, N., Giuriani, E. and Gubana, A., ‘Low-Cycle Fatigue Test on Stud Shear Connectors’, J. Struct. Engrg., ASCE, 123 (2), (1997), 145-150. 9. Maeda, Y., Matsui, S. and Hiragi, H., ‘Effect of Concrete Placing Direction on Static and Fatigue Strengths of Stud Shear Connectors’, Technology Reports of the Osaka University, 33 (1733), (1983), 397-406. 10. Menzies, J.B., ‘C.P. 117 and Shear Connectors in Steel-Concrete Composite Beams Made with Normal-Density or Lightweight Concrete’, Struct. Engr., 49 (3), (1971), 137-154. 11. Johnson, R.P. and Molenstra, N., ‘Partial Shear Connection in Composite Beams for Buildings’, Proc. Institution Civil Engrs., Part 2, 91, (1991), 679-704.
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INNOVATIVE INTERFACE SYSTEMS FOR STEELGIRDERS/CONCRETE-DECK CONNECTION Maher K. Tadros, Sameh S. Badie, Amgad M. Girgis University of Nebraska-Lincoln, USA
Abstract Shear studs used in composite steel bridge construction are typically 19.1 mm or 22.2 mm in diameter. This paper presents the development and implementation of the 31.8 mm stud diameter. Because the 31.8 mm stud has about twice the strength and higher fatigue capacity than the 22.2 mm stud, fewer studs are required along the length of the steel girder. This would increase bridge construction speed and future deck replacement and reduce the possibility of damage to the studs and girder top flange during deck removal. Studs also can be placed in one row only, over the web centerline, freeing up most of the top flange width and improving safety of field workers. This paper provides information on the development, welding, quality control, and testing of the 31.8 mm stud. Information on the first bridge built in the state of Nebraska with the 31.8 mm studs is provided.
1.
Introduction
Composite members in bridges consist of a reinforced concrete slab supported on steel or concrete girders where the two elements act together as a unit under live and superimposed dead loads. Shear connectors are used to resist the horizontal shear at the girder-deck interface caused by the superimposed loads. Composite construction is an economical and efficient way to increase the span, girder spacing, or live load capacity of a bridge. Girders in composite construction are shallower and lighter than those of non-composite construction. The headed steel stud system is the most common type of shear connectors used on steel girders. In this system, headed studs are welded to the top flange using an arc-welding process. Two sizes of studs, the 19.1 mm and 22.2 mm diameter, are typically used. In high shear areas of steel girder bridges, as many as four 22.2 mm diameter studs per row are used to satisfy design requirements. The relatively high number of studs has
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many disadvantages. Among them are: 1) long installation time, 2) difficult deck removal that may damage the studs as well as the girder top flange, and 3) the construction workers are left with little room on the top flange to walk, which raises safety concerns. For these reasons, a girder-to-deck connection that reduces the number of shear studs could be advantageous. Since a 31.8 mm diameter circle has almost twice the cross sectional area of a 22.2 mm diameter circle, using a 31.8 mm stud would reduce the number of studs by 50%. This paper discuses the development and application of the 31.8 mm diameter stud in steel girder bridges. This paper covers the following items: 1. Stud welding and quality control programs conducted to establish the most suitable steel material for the stud and the most economic, efficient way to weld and test the stud for quality control; 2. Feasibility of applying equations given by the AASHTO Standard Specifications (1996) [1] and the AASHTO LRFD Specifications (1998) [2] in the design of the large stud; and 3. A demonstration project, where the 31.8 mm studs were used on a three-span continuous bridge in Nebraska.
2.
Stud Material and Geometry Development
Although the use of 31.8 mm studs is not entirely new (Viest 1956)[3], no convenient method of stud welding or testing of welding quality of these large studs has been developed. No evidence also was found in the literature search that this stud size of studs has been used in bridge applications. The researchers conducted a search in cooperation with stud manufacturers in order to find the steel grade that can be used in producing the 31.8 mm stud. The study revealed that the Society of Automotive Engineering (SAE) 1008 steel, currently used for the 22.2 mm studs, or SAE 1018 steel could be used for the 31.8 mm stud. Table 1 gives a comparison of the mechanical properties between the SAE 1008 and SAE 1018 steel grades. Table 1: Mechanical Properties of SAE 1018 and 1008 SAE 1008 SAE 1018 Specified minimum properties Tensile Strength, Mpa 340 440 Yield strength, Mpa 290 372 Elongation, % 20 15 Reduction in area, % 45 40 Brinell hardness 95 126
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Figure 1 shows the dimensions of the 31.8 mm stud. The stud head can be produced by creating an integral head, similar to the 19.1 mm and 22.2 mm studs, using a hot forge process; or by threading the top part of the stud and adding a hexagonal nut.
3.
Stud Welding Technique
The researchers determined that the arc stud welding process that is currently used in welding the 19.1 mm and the 22.2 mm studs could be used for the larger stud, because of its availability, productivity, and familiarity. During this welding process, a controlled electric arc is used to melt the base of the stud and a portion of the base metal. The stud is thrust automatically into the molten metal and a high quality fusion weld is produced. Figure 2: Welding of the 31.8 mm Stud The "chuck" of the welding gun that grips the stud was modified to fit the large stud diameter, as shown in Figure 2. Many welding trials were conducted to determine the factors that may affect the welding quality. Three factors were the slope of the stud chamfer; amount of flux; and power supply. During early welding trials, it was evident that steeper chamfer and more flux than those used with the 22.2 mm studs would facilitate the welding process and lead to high quality welding. Thus, the 31.8 mm stud was provided with a steep chamfer and the amount of flux material was tripled compared to that used with the 22.2 mm studs.
Since the 31.8 mm stud has a larger cross sectional area than the 22.2 mm studs, it was expected that welding would require a power source with higher amperage. Welding trials showed that a power source with minimum amperage of 2,400, which is available
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from commercial vendors, would produce enough heat to melt the stud base and lead to good welding quality. Note that welding the 22.2 mm stud usually requires amperage in the range of 1,800 to 2,000. With the above modifications, excellent welding quality was achieved.
4.
Quality Control
Bridge owners require testing of studs for quality assurance. Most specifications require that studs welded to the steel girders be bent at a 45o angle without failure at the weld. The researchers determined that it was not practical to bend the large stud. Thus, they developed a portable hydraulic jacking system that could be used in the shop or in the field for testing pairs of studs. The device, shown in Figure 3, consists of two collars placed around two adjacent studs, a small hydraulic jack and a top tie. The collar consists of two steel blocks tied together with four screws. By tightening the four screws, the collar is in full contact with the stud. The base of the collar is chamfered to accommodate the weld at the stud base. A hydraulic jack is placed between the collars to provide lateral shearing force at the stud base. The top tie, which consists of two hooks and a turnbuckle, is used to protect the studs from bending. Figure 3: Quality Control Setup The quality control test was conducted by applying a horizontal force to cause a tension failure in the stud. The force was calculated by analyzing the studs with the top tie as a frame structure, where the studs are fixed at the base and hinged at the top. By equating the principal stresses at the stud base with the stud yield strength, a relation between the applied force and the stud yield strength was derived. In order to protect the stud from damage during the quality control test, an appropriate factor of safety may be applied.
5.
Experimental Program
The experimental program comprised three parts: 1) twenty push-off specimens for ultimate strength investigation; 2) twenty-five push-off specimens for fatigue resistance investigation; and 3) one full-scale beam test.
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5.1 Ultimate Strength Investigation Twenty push-off specimens were tested in the ultimate strength investigation. In all specimens, studs were welded on the top flange of a W-steel beam and a cast-in-place concrete slab was then poured on top of the steel beam. Equation 6.10.7.4.4c-1 of the AASHTO LRFD Bridge Specifications [2] is used to determine the ultimate strength for studs. Equation 6.10.7.4.4c-1 is as folow: Qn=0.5Asc
( f c' Ec ) <= Asc Fu
Where
f c' = specified 28-days compressive srength (MPa) Asc = cross-sectional area of stud shear connector (mm2) Ec = modulus of elasticity of concrete, (MPa) Fu = specified minimum tensile strength of astud shear connector, (MPa) From the ultimate investigation, it has been found that the AASHTO LRFD Equation 6.10.7.4.4c-1 can be safly applied for the designe of the 31.8 mm stude. Also it has been found that confinement of the concrete around the stud affects the ultimate stud capacity. A high level of concrete confinement is usually achieved in bridge decks by using continuous top and bottom transverse reinforcement over the girder lines. This issue is recognized by the empirical deck design of the AASHTO LRFD Specifications (1998) [2], which mandates the use of continuous top and bottom transverse reinforcement over the girder lines. 5.2 Fatigue Resistance Investigation Twenty-five push-off specimens were tested, eleven specimens were built with 22.2 mm headed studs and fourteen specimens were built with 31.8 mm headed studs. From the fatigue investigation, the authors came up with the following equations for the fatigue stud capacity: Zr = Alpha d2 >=
38 2 d 2
(1)
where: Zr = stud capacity in fatigue N = number of cycles Alpha (MPa) = 278.8 – 31.4 Log (N)
For the 31.8 mm studs
(2)
AASHTO LRFD Bridge Specifications [2] gives the following equations for fatigue stud capacity Zr = Alpha d2 >=
38 2 d 2
(3)
1176
Where Alpha (MPa) = 238.0 –29.4 Log (N)
(4)
Figure 4 gives a comparison of the Alpha-value between the AASHTO LRFD Specifications (1998) [2], and the current testing program. From the comparison, the following conclusions can be drawn Figure 4: Comparison of the Alpha-values
1. 2.
3.
4.
5.
It is conservative to use the Alpha-values given by the AASHTO Specifications to calculate the allowable range of horizontal shear force for the 31.8 mm. Designers are encouraged to use Equation 2 developed in this research. Using these equations will reduce the amount of studs by about 30%, which will reduce the initial cost of a bridge as well as the cost of future deck removal. If Equation 2 is used, it is expected that one row of 31.8 mm studs over the girderweb location, spaced at 150 mm or more, will be adequate to maintain full composite action for the majority of bridges. This will ease deck replacement in the future and will increase safety of the construction workers. Equation 2 for the 31.8 mm studs is perhaps too conservative for stress-range of 110 MPa or less. That is because no failure was observed in this testing program at this stress range, even after as many cycles as about 7,000,000 cycles. It is recommended to use the 31.8 mm stud with a flange with a minimum thickness of 12 mm.
5.3 Full-Scale Beam Test A full-scale beam was tested to evaluate the performance of 31.8 mm studs in a flexural beam test. A 12.2 m long W36x160 rolled section, with alternate headed and headless 31.8 mm shear studs spaced at 152.4 mm, were used in the test. A 1.22-m wide and 203mm thick concrete deck was placed on the top of the girder. The beam was tested in
1177
fatigue for 4,800,000 cycles under HS-25 truck loading positioned at the critical shear section as specified by AASHTO Specifications. The truck load was then moved to the midspan section and run for another 4,800,000 cycles. Figure 5 shows the test setup of the beam. Figure 5: Full-Scale Beam Test
Slippage between the concrete deck and the steel beam is given in Table 2, where the maximum slippage was as 0.049 mm Linear stress distribution over the beam height due to live load was observed before and after applying the fatigue load. Fatigue testing showed no loss of composite action between the concrete deck and the steel beam or distress in the concrete deck due to the use of 31.8 mm studs. The researchers could not test this beam to failure because of the limited capacity of the structural floor of the laboratory. For more information, please refer to Kakish (1997) [4].
Table2: Slippage Measurements of the Full-Scale Beam Test Slippage at Slippage at Cycles x 106 Section #1 Section #2 Load position Mm mm Zero 0.0370 0.0152 Section #1: 1.76 0.0389 0.0153 Shear Critical Section 4.80 0.0494 0.0206 Section #2: 4.80 0.03971 0.0206 Midspan Section
6.
Demonstration Project
The Nebraska Department of Roads (NDOR) assigned a three-span continuous bridge in western Nebraska to implement the 31.8 mm stud. The bridge, on Highway 71 in Gering South, Nebraska, consists of three continuous spans of 13.7, 18.28, and 13.7 m. The cross section of the bridge consists of five W30x99 rolled steel girders spaced at 2.67 m supporting a 190 mm thick cast-in-place composite slab. Total width of the bridge is 12.60 m. Preliminary design of the composite action included three 22.2 mm studs per row at spacing from 254 to 407 mm. NDOR decided to use the 31.8 mm studs on the South
1178
span, and 22.2 mm studs on the center and North span. This arrangement was chosen to give NDOR the opportunity to compare the structural performance of the 22.2 mm and 31.8 mm studs. After letting the project, NDOR called for a change order from 22.2 mm studs on the other exterior span to 31.8 mm studs. Use of the 31.8 mm studs resulted in using one stud per row welded directly over the girder web with spacing from 177 to 254 mm. Tri-Sales Associates, Omaha, Nebraska, produced the 31.8 mm studs the steel fabricator, Capital Contractors, welded them in their shop. An electric source of 2,500 Amps was used in welding the studs. Welding of the studs on the steel girders proceeded at a rate of 40 seconds per stud without any problems. The quality control test previously described before was conducted at three locations of each girder. Even though a factor of safety of one was used in the quality control test, no welding failure was observed in the quality control test. Figure 11 shows the 31.8 mm studs after welding. Since this was the first time the 31.8 mm studs were used in bridges, and since the fatigue investigation was underway when the bridge was being constructed, NDOR’s bridge designers decided to use only headed studs and to add a washer to the stud assembly. The washer was 4.8 mm thick with an outside diameter of 76 mm, and was tack welded to the stud head. It was added to the stud assembly to ensure sufficient confinement of the concrete around the stud. However, upon completion of the fatigue resistance investigation, it was evident that providing continuous top and bottom reinforcement in the deck slab can provide adequate confinement to the concrete. Thus, the researchers have advised NDOR not to add the washer to the stud in future projects. Figure 6 The 31.8 Stud after Welded on the Girder Figure 6 shows the steel girders with 31.8 mm studs installed in the field. The bridge construction was completed in the fall of 1999. The researchers and NDOR designers took deflection measurements of the bridge using a three-axle dump truck. Deflection measurements were taken at the maximum positive moment section of the center girder of the exterior spans. Both exterior spans showed the same amount of deflection, 3
1179
mm. Visual inspection of the bridge deck showed no cracks or distress on the South span where the 31.8 mm were used. The bridge contractor commented that using one line of studs provided the construction crew with a higher level of safety during deck construction. He also noted that welding the studs in the steel fabricator shop increased the construction speed and produced high welding quality for the studs. The bridge was opened to traffic in August 2000. Figure 7 Steel Girders with the 31.8 mm Studs installed in the Field
7.
Conclusions
This paper presents the development and application of 31.8 mm studs to steel girder bridges. The new stud has almost double the cross sectional area of the 22.2 mm stud. It can be produced using 31.8 mm SAE 1008 or 1018 rods that are commercially available and can be produced as headless or forged headed studs. The research showed that arc stud welding current practice, used in welding 19.1 mm and 22.2 mm studs, can be used in welding the proposed stud. However, a 2,400 minimum Amperage is recommended for welding. The quality of stud welding can be checked by shearing off two adjacent studs using a small hydraulic jack. Use of the 31.8 mm studs will significantly reduce the number of studs needed to achieve full composite action with the concrete deck. This will increase construction speed, ease deck replacement and reduce the possibility of damaging studs and girder top flange during deck removal. It also will enhance the safety factor for construction workers because more space on the steel top flange will be available for the construction workers. The ultimate strength testing program of the proposed stud showed that: 1) stud capacity can be safely determined using the equation given in the AASHTO LRFD Specifications (1998); 2) prior cyclic loading up to 2,000,000 cycles has no detrimental effect on the stud capacity; and 3) a composite member built with the proposed stud has less slippage than that of a member built with 22.2 mm studs.
1180
Fatigue testing showed that current α-values included in the AASHTO Standard (1996)[1] and AASHTO LRFD Specifications (1998)[2] can be conservatively used with 31.8 mm stud. However, the designers are encouraged to use the α-values developed in this research. This will reduce the number of studs by about 30% compared to the AASHTO Specifications. It is also recommended to weld the 31.8 mm stud on steel plates that are thicker than 12.7 mm. The full-scale beam test showed that full composite action could be achieve even up to 4,800,000 cycles. Also, it showed that using alternate headed and headless 31.8 mm (22.2 mm) studs has no harmful effect on the slippage or deflection of the beam. Further research is warranted for using only headless 31.8 mm stud.
8.
Acknowledgments
The research reported herein was performed under NCHRP Project 12-41 titled “Rapid Replacement of Bridge Decks” and Nebraska Department of Roads (NDOR) Project SPR-PL-1(35)P516 titled “I-Girder/Deck Connection for Efficient Deck Replacement.” Additional support was provided by the University of Nebraska-Lincoln, Center for Infrastructure Research, Kiewit Construction Company and HDR Engineering Inc. Special thanks goes to Hussam F. Kakish, Darin L. Splittgerber, Mantu C. Baishya, University of Nebraska for their help in conducting the testing program.
9. 1.
2. 3. 4.
References AASHTO Standard Specification for Highway Bridges (1996), 16th Edition, American Association of State Highway and Transportation Officials, with 1997, 1998, 1999 Interims, Washington D.C. AASHTO LRFD Bridge Design Specifications (1998), 2nd Edn, American Association of State Highway and Transportation Officials, Washington D.C. Viest, I. M., ‘Investigation of Stud Shear Connectors for Composite Concrete and Steel T-Beams’, Journal of the American Concrete Institute, (1956) 875-89. Kakish, H. F., ‘Composite Action in Bridge I-Girder Systems’, Dissertation presented to the Faculty of the Graduate College of the University of Nebraska in Partial Fulfillment of Requirements for the Degree of Doctor of Philosophy, Nebraska. (1997).
1181
NON-LINEAR ANALYSIS OF STEEL-CONCRETE COMPOSITE BEAMS: A FINITE ELEMENT MODEL Ciro Faella*, Enzo Martinelli* and Emidio Nigro* * Dipartimento di Ingegneria Civile, Università di Salerno, Fisciano (SA), Italy
Abstract In the scientific literature several models devoted to non-linear analysis of steel-concrete composite beams are already available. Utilising finite element models generally based on classical displacement approach, some problems may occur, as relevant discontinuities in the nodal forces, especially when non-linear behaviour of both shear connection and structural materials are considered. In this case the necessity of very fine discretization of the structural members arises. In the present paper a different non-linear procedure is proposed, based on a finite element model derived by the extension of the “exact” solution of the Newmark’s model to the composite beam with mechanical characteristics variable along the axis. A “modified Newton-Raphson approach” is used to achieve the convergence considering also the non-linearity of shear connection, concrete and steel. Some comparisons with other numerical procedures and experimental results, both available in the scientific literature, are also proposed and, finally, a brief discussion on the solution convergence varying the number and the types of beam-element subdivision is reported, in order to point out the effectiveness of the proposed procedure.
1. Introduction The behaviour of steel-concrete composite beams at serviceability and ultimate states depends on the shear connection between steel profile and concrete slab, which influences both the distribution of the internal stresses over the cross-section and the distribution of the internal forces in statically indeterminate beams. Several finite element models denounce some problems concerning discontinuities in the internal forces, due to the assumption of usual shape functions, as remarked also in [1] and [2]. The proposed finite element model takes its advantage by starting from an “exact” elastic finite element, based on the solution of the Newmark’s differential equation [3]. The elastic finite element model has been extended in [4] in order to introduce both the non-
1185
linear behaviour of the shear connection between concrete slab and steel profile and the cracking of the concrete slab: so the important topic of the assessment of the beam deflections due to service loads has been widely investigated. In the present paper this finite element model is rearranged in order to consider also the nonlinear behaviour of the materials (steel and concrete) and to reduce the number of elements per beam, as it is useful in the analysis of complex structures: the aim is to utilise up to a single element per member considering all the non-linearities without lack of accuracy. Each element is characterised by mechanical properties variable along the axis, due to the non-linearity of the shear connection, concrete slab and steel beam properties (see pars. 3 and 4). The solution of the whole mechanical problem is reached iteratively, by means of a procedure similar to the “modified Newton-Raphson Approach”, as described in par. 2.
2. A non-linear procedure for the analysis of steel-concrete composite beams with flexible shear connection: description of the general algorithm The general solution procedure is within the displacement approach, based on the knowledge of the stiffness matrix and the vector of the equivalent nodal forces of the structure. Due to the various mechanical non-linearities, the mathematical problem may be written in the “pseudo-linear” form
K (s) ⋅ s = Q − Q 0 (s) ,
(1)
where the stiffness matrix K (s) and the vector Q 0 (s) depend on the internal forces over the element and hence on the actual displacements s, still unknown. The solution procedure is obviously iterative and two level of iterations may be distinguished: - external iteration: it regards the whole structure and allows to evaluate the increments of nodal displacements due to the un-balanced residual nodal forces deriving by previous iteration; - internal iteration: for each element it allows to evaluate the nodal forces which correspond in the non-linear field to the current nodal displacements by means of the stiffness matrix of the element. With regard to the external iteration, applying the “modified Newton-Raphson Approach”, for a single load step, the total displacements s of the structure is obtained iteratively by the superposition of several increments of displacement due to the unbalanced residual nodal forces R i−1 , each deriving by the previous iteration (Fig. 1a): ) R i −1 = Q − Q i(−NL 1 ,
(2)
s i = s i−1 + ∆s i−1 = s i−1 + K −1R i−1 ,
(3)
1186
( NL) In the previous formulas the vector Q i− 1 contains the nodal forces which correspond to the prescribed displacement s i −1 taking account of the non-linear behaviour of the structural members, while K is the initial tangent stiffness matrix of the whole structure. The convergence of the iterative procedure, especially for load levels which lead to wide non-linear behaviour of the structure, may be improved if the stiffness matrix K, utilised in (3) for the iterations of the generic load level, is updated at the end of the iterations of the previous load step (Fig. 1b). R(s)
R(s) ∆s1
∆si-1
Q3
Q Ri-1
Q(NL)i-1 R1
∆Q2
R2
Q2
Q(NL)i
∆Q1 Q1
K1
K3 s1
s2
si-1 si
sn
s
K1 K2
sn
s
Fig. 1a,b: Modified Newton-Raphson Approach Mj
Mi j
i
Fi
Fj
Tj
Ti
si sj
vi i
ϕi
j
vj
ϕj
Fig. 2: Nodal forces and displacements of composite beam with flexible shear-connection. For a steel-concrete composite beam-element with flexible shear-connection (see Fig. 2), the vectors of nodal displacements and nodal forces are respectively s h = ( v i ϕi s i v j ϕ j s j ) T and Q h = (Ti M i Fi T j M j Fj ) T . The vector of nodal
forces Q ( NL) of the whole structure is obtained assembling the vectors of nodal forces of each h-th element, Q h , which correspond in non-linear field to the current nodal displacements s h by means of the stiffness matrix K h of the element:
1187
Q h = K h s h + Q 0, h
(4)
being Q 0,h the vector of the equivalent nodal forces of the h-th element. The evaluation of the nodal forces Q h of each element is iterative (internal iteration): at each step of the iterations, K h and Q 0,h vary due to non-linear behaviour of the component materials and shear connection. This topic is explained in the following paragraphs.
3. The element “composite beam with flexible shear connection” with mechanical characteristics variable along the beam The non-linear σ−ε constitutive laws of concrete and steel, the cracking of the concrete in tension and the non-linear relationship P-s of the shear connection between the concrete slab and the steel profile are introduced in an internal procedure, which utilises the subdivision in segments of the beam-element, each part having mechanical characteristics depending on the current internal forces. As previously said, for a steel-concrete composite beam with flexible shear-connection (see Fig. 2), the vectors of nodal displacements and nodal forces are respectively:
(
s h = v i ϕi s i v j ϕ j s j
)T
,
(
Q h = Ti M i Fi T j M j Fj
)T
(5)
In respect of usual beams, a composite beam with flexible shear-connection is characterised by interface slips s(z) between concrete slab and steel profile, related to the longitudinal shear force per unit length F′(z): F′(z) = k (z ) ⋅ s(z) (6) The presence of interface slips prevents from defining a moment-curvature relationship of the cross-section: instead of express it by algebraic relations, as it is usual for Bernoulli’s beam, it is possible to derive the curvatures along the beam solving the wellknown Newmark’s differential equation [3]: χ′′ − α 2 χ = −
k ⋅ d ⋅ ε sh q M − α2 − EI abs EI full EI abs
(7)
being α2 =
EI full kd 2 EI full − EI abs EI abs
(8)
where k is the shear connection stiffness, EIfull and EIabs are the two values of the flexural stiffness evaluated for full and absent shear connection, respectively, d is the distance between concrete slab and steel profile centroids. Obviously, in presence of non-linear behaviour, the stiffness parameters EI abs , EI full , k and α are variable along the beam-element and then equation (7) may be utilised to obtain the curvature in a finite number of segments, in which the beam-element is subdivided, by solving algebraically the problem (7).
1188
The h-th beam-element is subdivided in n segments, each one characterised by the stiffness parameters k k (shear connection stiffness), EI abs,k (flexural stiffness with absent shear connection), EI full,k (flexural stiffness with full shear connection), being k=1,…,n . For a simply-supported beam with prescribed values of nodal forces and external loads, the curvature along the whole beam is assessed on the basis of the local expressions of the curvatures χ k (z k ) , being z k the local abscissa (see Fig. 3) χ k (z k ) = C 2k −1 ⋅ cosh (α k z k ) + C 2k ⋅ sinh (α k z k ) + χ 0,k (z k )
(9)
The 2n constants (C 2k −1 , C 2k ) k =1,...,n are determined solving a system of 2n linear equation, derived imposing the following boundary conditions at the external nodes of the beam-element and at the internal points between the segments: F1 (0 ) = −Fi
z=0 ⇒
F (∆z ) = Fk +1 (0) z = k∆z ⇒ k s k (∆z ) = s k +1 (0 ) z=L ⇒ Fn (∆z ) = Fj
(10)
In (10) Fi and Fj are the external nodal forces of the beam-element, while the local values of the longitudinal shear force Fk (z k ) and the interface slip s k (z k ) are related to the curvature χ k (z k ) by means of the following formulas: M(z k ) − χ k (z k ) ⋅ EI abs,k
Fk (z k ) =
d
Fk′
s k (z k ) =
kk
=
1 d M(z k ) − χ k (z k ) ⋅ EI abs,k ⋅ k k dz k d
(11)
q Mi
Mj 1 0
Fi i
1
z
k
2
∆z
2
n-2
zk
n
n-1
n
n-1
Fj
j
si
sj ϕi
ϕj
Fig. 3: Subdivision of the beam-element in n segments with different mechanical characteristics
1189
{C m }m=1,...,2n
As the constants
and the curvatures χ k (z k ) are known, the nodal
displacements (rotations and interface slips) at the end of the beam-element are deduced by means of the following formulas: n ∆z
ϕi = −
∑ ∫ χ k (z k ) ⋅ 1 −
(k − 1) ⋅ ∆z + z k ⋅ dz
n ∆z
ϕj =
∑ ∫ χ k (z k ) ⋅
(k − 1) ⋅ ∆z + z k
k =1 0
L
k =1 0
L
⋅ dz k
,
k
,
s i = s1 (0 )
(12)
s j = s n (∆z )
(13)
being the interface slips obtained directly by the second of (11), whereas the rotations are deduced applying the Principle of Virtual Works. The previously described procedure may be utilised also in order to determine, for a beam-element with mechanical characteristics variable along the axis, the reduced 4×4 flexibility matrix D h ,r , which relates the vector of the nodal displacements s h , r = (ϕi s i ϕ j s j ) T with the vector of nodal forces Q h , r = (M i Fi M j Fj ) T : s h , r = D h , r ⋅ Q h , r + s 0, h , r
(14)
being s 0,h ,r the vector of the nodal displacement due to the external loads. In fact, each column of the D h ,r matrix may be deduced by applying to the beam the corresponding set of nodal forces, with one force equal to 1 and the others equal to 0, solving the equation system (10) and evaluating the nodal displacement by means of (12) and (13). In a similar way the terms of the vector s 0,h ,r , due to the external loads, may be also determined. By inverting the reduced flexibility matrix D h ,r , the reduced 4×4 stiffness matrix of the simply-supported beam K h ,r and the 4×1 vector of equivalent nodal forces Q 0,h ,r may be obtained:
(
)
Q 0, h , r = − D h , r −1 ⋅ s 0, h , r = −K h , r ⋅ s 0, h , r
(15)
The stiffness matrix K h and the vector Q 0,h of the beam-element with three degree of freedom per joint may be easily deduced, as explained in [3].
4. “Internal iterations” for each composite beam-element in non-linear field As previously said, the internal iterations allow to determine, for each beam-element, the nodal forces Q h which correspond in non-linear field to the current nodal displacements (see eq. (4)). With this aim, the previously described solution of the simply-supported composite beam with stiffness characteristics variable along the axis may be utilised.
1190
Starting from the current nodal forces, evaluated applying (4) and utilising the current K h and Q 0,h , the solution of equation system (10) allows to known the curvatures χ k (z k ) , the longitudinal shear forces Fk (z k ) and the interface slips s k (z k ) , whose values at midpoint of each segment are:
χ k = χ k (∆z 2) ; Fk = Fk (∆z 2) ; s k = s k (∆z 2) (16) The equivalent mechanical characteristics are assessed on the base of the non-linear constitutive relationships for each segment. With regard to the shear connection, assuming a P−s law (longitudinal shear forceinterface slip), as suggested by Johnson and Molenstra ([5])
(
P(s) = Pmax 1 − e −β c s
)
αc
(17)
the equivalent stiffness of the shear connection is defined as kk =
(
)
αc P( sk ) Pmax = 1 − e −β c s k i c sk i c sk
(18)
being i c the distance between the shear connectors, α c and βc two constants depending on the type of the connectors. Moreover, in order to evaluate the equivalent stiffness parameters EI abs,k ed EI full,k of the k-th segment, the axial strains ε c,k ed ε a ,k in concrete slab and steel profile are evaluated on the basis of the current values of the axial stiffness EA c,k ed EA a ,k ε c, k =
Fk EA c,k
; ε a ,k =
Fk EA a ,k
(19)
and then the strain path of the midpoint cross-section of the segment may be determined utilising also the curvature χ k (see Fig. 4). For the σ−ε constitutive relationships of the materials (see Fig. 5) the Saenz’s law for concrete in compression and an elastic-plastic-hardening law for steel are assumed. A nonlinear relationship for concrete in tension, whose softening branch takes account of tension stiffening effect, is also considered. εc,m s'
dc x
εa,m
da
εay
y
fay
Fig. 4: Stress and strain paths along the cross-section
1191
Utilising the σ−ε relationships, the stress paths are immediately deduced starting from the strain ones; hence, the resulting internal forces ( N c,k , N a , k ) and bending moments ( M c,k , M a ,k ) may be assessed by means of the usual equilibrium equations. The equivalent mechanical characteristics of the concrete and steel components related to the current internal forces hold: E A c, k = E I c, k =
N c,k
E A a ,k =
,
ε c, k M c, k
EI a ,k =
,
χk
N a ,k ε a ,k
(20)
M a ,k χk
which allow to define the secant flexural stiffness EI abs,k and EI full,k of the k-th segment of the composite beam: EI abs, k = EI c, k + EI a , k ,
EI full, k = E I c, k + E I a , k +
E A c, k ⋅ E A a , k E A c, k + E A a , k
d2
(21)
The values of the secant flexural stiffness of the segments allow to define the stiffness matrix K h and the vector Q 0,h of the beam-element applying the method described in the previous paragraph; hence, the nodal forces Q h , taking account of the non-linear behaviour, may be deduced by (4). The internal iterations in each beam-element are stopped when the nodal forces Q h , corresponding to the prescribed displacements s h , do not differ, unless a little tolerance, by the ones of the previous iteration. 45
σa
fc 40
35 30 25
σu
20 15
σy
Esh
10 5 -0,002
-0,001
0 -50,000
εc1=0,0022
0,001
0,002
0,003
εcu=0,0035
0,004
E
-10
εy
εsh
εu
εa
Fig. 5: Constitutive relationships of concrete and steel
5. Some comparisons with numerical analyses and experimental results and discussion about the convergence The non-linear procedure described in the previous paragraphs is now compared with other theoretical procedures and available experimental tests.
1192
The first comparisons refer to two simply-supported beams with two different degrees of shear connection ( N / N f = 1.0 and 0.55), subjected to a midspan concentrated force and analysed by Aribert and Labib in [6]. With regard to Fig. 6a,b, it may be observed that the agreement between the two numerical procedure is good, both for low load levels and in non-linear field. Moreover, some theoretical-experimental comparisons are performed with the experimental results provided by Ansourian in [7], which refer to two-spans continuous beam loaded by concentrated forces applied at midspan: also in this case a good agreement may be observed. Fig. 7a shows also the influence of the beam subdivision, as well as the number n of segments per element, on the result accuracy. The represented load−deflection curves are obtained dividing each span in two elements (N=2), as it is necessary due to the concentrated force applied at midspan, and assuming different segment subdivisions for each beam-element (n = 3,4,5,6). It may be observed that the experimental results are well fitted with a number n = 5 or 6; moreover, the numerical results do not change significantly when the number of internal subdivisions is greater than 6. 400
400
350
350 P
300
300 P
250
200
P [kN]
P [kN]
250
N/Nf=1.0 150
200 150
Proposed simulation
N/Nf=0.55
100
100
Aribert-Labib [1982]
Proposed simulation
50
50
0
0 0
2
4
6
8
10
12
14
16
18
20
Aribert-Labib [1982]
0
2
4
6
f [mm]
8
10
12
14
16
18
20
f [mm]
Fig. 6a,b: Comparisons with theoretical analyses of Aribert and Labib ([6]). 600
500 400
400
3 4 5 6
200
Ansourian [1982] Beam CTB4
300
F [kN]
F [kN]
Ansourian [1982] Beam CTB4 Experimental
200
n
100
N=2
n=6
N=4
n=3
N=12 n=1 Experimental
0
0
0
20
f [mm]
40
60
0
5
10 f [mm] 15
20
25
Fig. 7a,b: Comparison with experimental tests of Ansourian ([7]) and influence of the beam subdivision (number of segments per element)
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Finally in Fig. 7b different types of “external subdivision” of the beam are compared: the cases (N=2 , n=6) , (N=4 , n=3) and (N=12 , n=1) for each span are considered, all characterised by the same number of “total parts”. The obtained results, deriving from different discretizations, are quite coincident, but the total dimension of the mathematical problem is significantly different: this leads to an increment of the computing time about 50% in the third case with respect to the first one. Therefore, it may be remarked that the proposed solution of subdividing the beam-element in internal segments represents an useful tool.
6. Conclusions In the paper a non-linear procedure able to analyse steel-concrete composite beams with flexible shear connection is proposed. The model starts from the an “exact” finite element model, previously presented by the authors, and allows to avoid also in nonlinear field the discontinuity of the nodal forces, which classical finite element models based on displacement approach denounce. The proposed model takes into account the non-linearity of the shear connection and of the component materials in a finite number of segments, which each beam-element is subdivided in: in such a way the global problem is characterised by a reduced number of unknown nodal displacements. This represents an useful result when structures with a large number of joints have to be analysed in non-linear field.
References [1] Ayoub A., Filippou F.C.: Mixed Formulation of Nonlinear Steel-Concrete Composite Beam-element, A.S.C.E. J. Struct. Eng., 2000, vol.126, n. 3, pp.371-381; [2] Reza Salari M., Spacone E., Benson Shing P., Frangopol D.M. (1998): Nonlinear Analysis of Composite Beams with Deformable Shear Connectors, A.S.C.E. J. Struct. Eng., vol. 124, n. 10, 1148-1158; [3] Faella C., Consalvo V., Nigro E.: An “Exact” Finite Element Model for the Linear Analysis of Continuous Composite Beams with Flexible Shear Connections, Fourth International Conference on Steel and Aluminium Structures, ICSAS ’99, Espoo, Finland, June 20-23 1999, pp.761-770; [4] Faella C., Martinelli E., Nigro E.: Inflessione di travi composte acciaio-calcestruzzo con connessione deformabile: proposta di una formulazione semplificata, IV Workshop Italiano sulle Strutture Composte, Palermo, 23-24 novembre 2000; [5] Johnson R.P., Molenstra I.N.: Partial shear connection in composite beams for buildings, Proc. of the Institutions Civil Engineers, Part 2, 1991, 91, Dec., pp.679-704; [6] Aribert J.M., Labib A.G.: Modèle de calcul élasto-plastique de poutre mixtes a connexion partielle, Costrution Métallique, n°4, 1982, pp.3-51; [7] Ansourian, P.: Experiments on continuous composite beams, Proc. of the Institutions Civil Engineers, Part 2, 1981, 71, Dec. pp.25-51; [8] Eurocode 4: Design of composite steel and concrete structures - Part 1: General rules and rules for buildings , 1994. Acknowledgements: This work has been partially supported by Research Grant PRIN 1999
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CONNECTIONS BETWEEN PRESTRESSED CONCRETE BRIDGE DECKS AND COMPOSITE BRIDGE DECKS – HYBRID CONSTRUCTION Dirk Jankowski*, Oliver Fischer**, Manfred Matthes** *AJG Ingenieure GmbH – Abelein Jankowski Gebbeken, Consulting Engineers BYIK,VBI, Munich / Germany **Engineering Department, Bilfinger + Berger Bauaktiengesellschaft, Munich / Germany
Abstract Bridges that can be constructed with prestressed concrete decks economically might lead to difficulties in some spans. These difficulties for example can be river-crossings. Here the question arises what is the best concept for the superstructure. The rigid connection between prestressed concrete bridge decks and composite bridge decks lead to economical solutions. Two applications are given: The new Isarbridge in Dingolfing/Bavaria shows the combination of prestressed concrete bridge decks in the approaches and composite bridge decks in the river area. In the approach-parts the decks are constructed with prefabricated pc-beams and the plate structure is cast in place. The longer spans are built as composite constructions. For the plate structure of the composite part semi-prefabricated concrete elements are used. While the Isarbridge is a beam bridge in both parts of the decks the river Donaubridge in Vilshofen/Bavaria connects prestressed concrete bridge decks with an arch bridge deck in the middle span. The topics of this article are the special problems in the connection zone.
1. Introduction Trend setting constructioning is increasingly ruled by the optimised choice of materials according to the structural necessities. Moreover, the designing engineer has the advantage to use the achievements of research and development of recent years. This gives the opportunity to assemble new materials, improved material properties, and optimised connectors to newly formed structural elements. This is helped by the growing together of German and also European code regulations for the different materials. In the following, "hybrid structures" are explained by applications in the field of bridge construc-
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tioning using different materials and systems. Besides the description of the general applicabilities in bridge construction, examples of constructions are given.
2. Intensions and effects of hybrid constructions The basic idea of hybrid constructions is the appropriation of occurring stresses to suitable structural material. Hence, the conventional approach in engineering applies cheap concrete for compressive stresses, whereas for tensile stresses steel is used. The composite steel-concrete is the best example in this context. In particular for the development of the double composite the stress distribution is obvious. Extending this approach to the whole structure suggests a combination of different structural systems. Especially in bridge constructioning the design is chosen to build the whole superstructure with the same system. So, for short and medium spans the reinforced or prestressed concrete is preferred, whereas for long spans steel constructions or composite steel-concrete is used. In the case of largely varying spans or because of other limiting conditions, such as river crossings and approaches, or for distribution of loads the combination of reinforced and prestressed concrete with steel or composite structures is conceivable. Some structures even become practicable only by applying hybrid systems. Furthermore, due to the optimisation process these structures are highly cost efficient.
3. Choice of applications in bridge constructioning The commonly used connectors between steel and concrete are headed studs. They are, in particular for bridge constructioning, used to transmit shear forces only. This way of stress transmission is used for the linking of steel and concrete. Figure 1 shows one example of such a connecting part. Here, top and bottom flange, and web of the steel beam are equipped with headed studs in a way that load transmission is possible for the appropriate forces (tension, compression, shear). Special treatment is necessary to transfer the stresses within the concrete. Therefore appropriate reinforcement is required. This demands for a careful spatial reinforcement design, since the high reinforcement ratio for different kinds of reinforcement in different directions needs tight fitting. New developments in composite construction - like the connectors given in Eurocode 4 and e. g. perfobond strips - may yield better solutions for design details of this kind. Another question by joining several elements is the choice of coupling points. Generally, there are two main possibilities, first the coupling with cross beams at the support points and second in the zone of zero bending moments. The coupling by transverse beams gives the opportunity to use nearly any kind of structural elements and cross sections.
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Most suitable are open cross sections and plate structures as well as prefabricated concrete elements. The coupling at the zones of zero bending moments is suggested for prestressed box girders. Thereby, longitudinal tensional forces are taken over by prestressing tendons. Especially with unbonded external post-tensioning this construction is advantageous because no cross sectional areas are intersected.
Figure 1: Coupling point at the cross beam
4. Examples of applications The application of hybrid structures in the way of combining prestressed concrete with concrete-steel composite is explained by examples of the bridge over the river Isar in Dingolfing and the Donau crossing in Vilshofen. 4.1 Isarbridge Dingolfing The bridge was built in 1999 and 2000 as a part of the newly planed eastern by-pass of the small city of Dingolfing over the meadows of the river Isar and the river itself. The road has a standard 11.5 m wide two-lane cross-section (RQ 11,5). The height over the terrain is relatively low and the outline is mostly straight with a slight curvature to the right at the southern end. The structure is a nine-span continuous beam designed as deck bridge with the length of 296 m.
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The specified design in the invitation to bid suggested spans between 25 m and 46 m with a box girder at a constant depth of 2.30 m. This should have been longitudinal prestressed either by post-tensioned internal tendons or alternatively by external tendons. The substructure was conceived as piled panels and shallow founded box piers.
Figures 2 and 3: Views of the Isarbridge Dingolfing During the tender preparation, the design concept with its rigid superstructure, governed by only one span length of 46 m, was considered to be uneconomical. In addition, the superstructure would have been built on false work in sections with a large number of coupling points. Thereby, the crossing of the river would have been most complicated. The search for a together economic and pleasing design lead to a combination of two multiple side spans made of prefabricated prestressed girders supported by pairs of round columns and steel composite beams used for the two spans over the river. All sections were connected to assure a continuous spanning beam. The different surface and colour design of the two river spans emphasise their technical and geometrical characteristics. The special location of the middle pier is especially outlined by the increasing construction height to 2.30 m from 1.70 m at standard cross section. This greater depth is beneficial for structural purpose too, after all during construction as it functions as a two-span beam. Further, the installation of the concrete bottom plate over the middle pier (double composite) was another advantageous application of hybrid design. The choice of steel in sectional change with prestressed concrete made it possible to extend the structure harmonically over the river, even though the length of the spans enlarged to 42 m. Moreover, the assembly of the girders was possible with cranes located at the riverbanks. The economical usage of steel composite structures - especially in exchange with conventional cross sections of reinforced and prestressed concrete - is met by the permissibility of prefabricated form plates according to the "Allgemeines Rundschreiben Straßenbau Nr. 42/1998" (ARS 42/1998, German circular for road constructioning), because it avoids expensive formwork systems or formwork carriers. Here, the 10 cm thick form plates overhang on both sides and are statically efficient with its full cross section in transverse direction. To resist the compression stress in longitudinal direction
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mainly the 23 cm thick in-situ concrete is supplemented. The bonding results from headed studs of 175 mm length and a diameter of 22 mm, which are concentrated in gaps of the form plates.
Figure 4: Coupling point of steel girder
Figure 5: View into the cross beam
The rigid connection of the two-span steel composite structure to the side spans formed from prestressed concrete was desired out of the following reasons: -
statical relieving of the long spans avoiding of additional joint constructions horizontal connection of the whole superstructure whose longitudinal fixed bearings are located at the middle piers.
The cross beams on top of the bank piers are the transition zones between the different structural systems. These beams are design purely of reinforced concrete and consist of a 35 cm thick prefabricated base whereon the prestressed prefabricated beams as well as the longitudinal steel girders during the construction process were placed. The webs of the cross beams where the load is mostly transmitted were filled with concrete afterwards. Parallel to the hardening of the concrete the statical connection is established continuously. This makes the time of concreting become most relevant. For this construction the cross beams were formed when the deck slab of the side spans had nearly reached the coupling cross beams, whereas on top of the formwork girders only formwork panels where placed. The connection of the structural elements before pouring the
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in-situ concrete in the river spans lead to a release of the steel beams due to partially fixed-ends. Therefore, smaller cross sections could be used. For compensation of the fixed-end moments the resistance to the tensional forces needed to be assured structurally.
Figures 6 and 7: Coupling of cross beam with load transmission plate The tensional forces were transferred via horizontal blades with headed studs to the cross beams on the level of the top flange. There, reinforcement loops take the load within the deck slab. To take effect early, not only the webs of the cross beams were filled with concrete, but also a 2 m long slab strip with included support reinforcement was concreted. The compressional forces were treated alike with bottom blades and headed studs. Shear was taken by vertical plates in extension of the webs. The additional in-situ concrete affects the nine-span continuous beam structure without composite action, whereas service loads, live loads, and compulsion act on the final composite structure. 4.2 Donaucrossing in Vilshofen Another example for the combination of post-tensioning and composite action is the newly built bridge over the river Donau near Vilshofen, Germany. After the expansion of the clearance width for ships from now 49 m to 90 m, a renewal of the existing eight-span road bridge including the demolition of two piers in the river (reduced number of spans) was announced. According to the design concept provided by the client the existing deck bridge, an orthotrope steel structure built in 1978, was apriori slided transversely to auxiliary supports. This enabled a continuous traffic crossing over the river during construction time. The design suggested a steel arch structure for the large span with a length of 116 m. It was further intended to rigidly connect the new composite steel superstructure to the south approach with two short spans of 25,80 m.
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Figures 8 and 9: Models of the Donau crossing in Vilshofen [1] To the north of the steel arch an existing part, despite of its smaller width, was meant to be redesigned as a three-span structure and connected by an expansion joint. It should have been moved back to almost its initial location. And again, an alternative tender proposal, introduced by Bilfinger+Berger Bauaktiengesellschaft, with hybrid constructions was less costly and finally built. Starting with the new large middle span with its 15° inclined double steel arch and a hanging composite steel roadway, the northern as well as the southern post-tensioned concrete parts were rigidly joint to the roadway slab of the arch. Despite of the abandonment of 800 m² of existing bridge area with its restricted width and the instead newly built 1100 m² area bridge deck, the design of the structure outside the arch with precast prestressed girders proofed to be very economical. The advantages of the hybrid solution of coupling prestressed girders with the arch structure are for this example: -
minimisation of costs uniform roadway geometry for the whole length of the bridge no reduction of the roadway from 3 to 2 lanes due to restrictions of the existing structure no expansion joint at the end of the arch reduction of road closing time due to the left out of the sliding back of the existing bridge part.
The arch structure is connected to the adjacent parts at the end of the arches near the cross girders. These are primarily the end cross connectors of the arch and therefore steel composite elements on deck level. Secondary, a massive in-situ concrete part is added to mainly transfer the forces from the three longitudinal deck girders of the arch structure to the five webs of the prestressed girders. The sectional optimisation of the longitudinal structural elements leads, as a matter of course, to additional stresses in the joints such as torsional moments and splitting tensional stresses due to change of force direction.
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Fig. 10: Detail of the end cross girder
Fig. 11: Part of post-tensioned concrete girder
Here, the cross beam between the main span and the approach have a width of 1.80 m with 40 cm designed as torsional rigid steel box and the rest executed with B 55 concrete. The normal and shear forces are again transferred by studs. The normal forces in the top and bottom flanges may alter from tension to compression and vice versa due to changing traffic load moments. Negative moments at support are usually absorbed by reinforcement within the deck slab. The structural analysis showed that, because of the stiffness ratio of the arch and the adjacent parts, larger positive moments at support occurred for traffic loads on half of the arch. These moments had to be transferred to the prefabricated longitudinal girders within the cross beams. Therefore, in the bottom zone additional threaded bars (Gewi Ø 32 mm) were placed to connect tensional reinforcement (see figure 11). The design of the steel parts of the cross girder with the required diaphragms and studs can be seen figure 10. For this combination it becomes obvious that a unification of the standards for concrete construction on one hand, and for steel construction and steel-concrete composite construction on the other hand is desperately needed. According to the current German standards the question arises whether the concrete encased end cross girder of the arch span is treated as a concrete structure (factor of safety is 1.75) or treated as a steel composite structure (factor of safety is 1.4)? With the introduction of the new generation of standards this contradiction would be solved.
5. Final statement This report shows how the combinations of reinforced and prestressed concrete, as well as steel and composite elements yield hybrid structures for bridge constructioning. These structures are characterised by its robust load bearing behaviour, low maintenance demand, and its high efficiency. The use of similar structures will increase in the future.
6. References [1]
Freistaat Bayern, Straßenbauamt Passau: Neubau der Donaubrücke Vilshofen, 2000
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ANCHORAGE BEHAVIOR OF 90-DEGREE HOOKED BEAM BARS IN REINFORCED CONCRETE WALL-BEAM INTERSECTIONS Osamu Joh, Yasuaki Goto and Atsunori Kitano Graduate School of Engineering, Hokkaido University, Japan
Abstract Experiments were conducted to determine anchorage performances of 90-degree hooked beam bars in a joint at which a beam intersects a structural wall at right angles. Seven wall-beam joint specimens that had some variations in the arrangements of wall reinforcement and L-shaped beam bar anchorage were used in the experiments. All of the specimens subjected to pullout loading on the beam bars failed in beam bar anchorage. The anchorage strength increased as the amount of wall reinforcements increased, especially when the wall reinforcement was arranged in the direction of thickness as tie bars. The following results were obtained: (1) the inclusion of many tie bars made the zone of transmission stress become wider and the anchorage strength increase, (2) the anchorage strength of hooked bars without tie bars increased by only 10% even though spacing of wall bars was reduced by 50%, and (3) accurate estimation of anchorage strength was possible by considering the dowel action of wall bars.
1. Introduction In a reinforced-concrete structure, when a beam is connected to one face of a structural wall at right angles, the main bars of the beam are anchored into the wall usually with 90-degree hooks. We have been experimentally investigating anchorage behaviors of steel bar hooks arranged in exterior beam-column joints with a rotated T shape for a middle story of a building [1] and with a reversed L shape for a roof story [2], and we have proposed formulas for evaluating anchorage strengths. Based on our previous experimental results, failure modes of a 90-degree hooked-bar anchorage in a beam-column joint can be divided into three types: 1) side split failure, in which the concrete covering the bend portion of the beam bars in a joint peels away, leaving dish-shaped depressions on both sides of the joint; 2) local compression failure, in which a small amount of concrete adjoining the inside part of the 90-degree-bent portion of each beam bar is crushed; and 3) raking-out failure, in which a concrete block,
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approximately the same size as the inside dimensions of the hooked bar, is raked out toward the beam side of the column, and all beam bars simultaneously lose their resistance. Raking-out failure is caused by the use of many beam bars and/or a short horizontal development length inside the joint. From the results of our previous experiments, it became clear that the anchorage strength of the raking-out failue mode depends on the number of hoops in the joint and the horizontal development length (Ldh ). This length is the lateral distance between an inside face of the column and an outside face of beam bar tails and it consists of horizontal bar length of a straight portion in the joint, radius of bar bent and diameter of the bar. Judging from the anchorage behaviors in a beam-column joint, it can be easily predicted that the mode of anchorage failure of a beam-wall joint depends on raking-out and that the anchorage strength of hooked beam bars in this joint is lower than that in a beamcolumn joint because the depth of the wall is smaller than that of the column and there is no lateral reinforcement in the depth direction. Most structural design codes, however, do not prescribe any special requirement for reinforcement. The purpose of this study was to clarify anchorage behaviors of 90-degree hooked beam bars in a beam-wall joint intersecting each other at right angles. For this purpose, experiments in which specimens were subjected to pullout loading on the beam bars were carried out. The results were compared with results of anchorage strengths in beam-column joints obtained from our previous experiments.
2. Experiment 2.1. Test specimens Nearly actual sized specimens, which were simulated tensile beam bars with 90-degree hooks anchored into a beam-wall joint, were used (see Figure 1). Beam concrete or compressive beam bars was not used in order to simplify the production of specimens. The dimensions of the specimens were identical: 2700 mm in height (the distance between two reaction points on the wall being 2300 mm); 900 mm and 250 mm in wall width and thickness, respectively; and 250 mm and 600 mm in imaginary beam width and depth, respectively. The beam bars were two threaded deformed bars of 19 mm in nominal diameter (db), the wall bars were deformed bars of 16 mm or 19 mm in diameter, and the tie bars were deformed bars of 10 mm in diameter. These bars were arranged in the specimens as shown in Figure 1 and in Table 1. A total of seven variables were used: 1) two horizontal development lengths (Ldh) (distance from the critical section of the beam to the center of the tail), 2) two vertical development lengths (Ldv) (distance from the tip of the tail to the center of the lateral beam bar), and 3) three spacings of wall-tie bars. Specimen WA25-1A was a standard specimen, and the other specimens differed from the standard specimen in only one or two test variables. 2.2. Mechanical properties of materials Only beam bars made from high-strength steel were used in order to generate anchorage failure. Wall bars and tie bars made from normal-strength steel were generally used, but
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Tb
Vertical section WB25-1A
59.5 Tb
59.5 131 WA25-1BP2
100
100 50
100
Steel plate of Reaction
Virtual beam
Compression corner
Upper wall Beam-wall joint
Ldh=155 Ldv=539
Ldv=295
102
WA25-1A
Ldh=83
900
100 50
WA25-1AP3
100
@200
925 200
Elevation WA25-1AP2
R2 74
Lower wall
Walltie bar
60
Tb
200
450 600
200
In 385 side 385 130 Horizontal section 250
90
In side
Out side
R1
2700 450
925
Qw
74
250 77 96 77
900 Out side
@100
250 58 134 58
60
WB25-3A
60 130 WA25-1BP2 (-1B)
Figure 1. Diagrammatic representations of specimens
those made from high-strength steel were used for specimens having high anchorage strength in order to avoid premature failure in yielding of the bars. Concrete strength varied from 34.5 MPa to 41.2 MPa. The mechanical properties of the steel bars and ypical concrete used in the specimens are shown in Table 2. The aggregate used was crushed stone with a maximum diameter of 20 mm, which was normal size to match the actual scale of specimens. Table 1. Specification of specimens beam-bar (2-D19) wall-bar wall-tie bar (D10) Specimen spaceing spaceing d L dh L dv grade grade b 155 295 SD490 D16a @200 WA25-1A non － 155 539 SD490 D16a @200 WA25-3A non － 83 295 SD490 D16a @200 WB25-1A non － 155 295 SD490 D16a @100 WA25-1B non － 155 295 SD490 D16a @200 @200 WA25-1AP2 SD295 155 295 SD685 D16b @200 SD685+(SD295) @100+@200 WA25-1AP3 155 295 SD685 D16b @100 SD685+(SD295) @100 WA25-1BP2 [Notes] D : diameter of reinforcing bar, a / b : distinction of strength, D16 : deformed bar of 16mm in normal diameter
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reinfocing bars beam-bar
D19
wall-bar
D16a D16b
wall-tie bar σB
D10 σt
concrete (MPa) (MPa) 39.1 3.17
SD490 SD685 SD345 SD345 SD295 SD685
Pin support Qw
σy
εy
σ max
(MPa) 558 788 421 372 364 729
(%) 0.34 0.50 0.25 0.26 0.20 0.40
(MPa) 749 967 583 556 557 889
ε max
Ε 1/3
(µ) 2520
(GPa) (GPa) 30.4 26.1
Ε 2/3 Pin support
[mm]
R1
Cantilever-type measuring instrument
Roller support 25 100 125
Figure 2. Steel frame for measurement
Steel frame
Virtual beam
Table 2. Measured propaties of materials
Tb
R2 Beam-bar Roller support
2.3. Instrumentation for loading and measuring Tensile load (Tb), controlled so as to distribute the increasing pull-out displacement equally between two beam bars, was supplied horizontally to both bars. In order to simulate a moment diagram in actual beam-wall joints, the following loading system was used. An apparatus supported by a pin and an apparatus by a roller were set on the compression zone of an imaginary beam and on the reflection point at the bottom of the wall, respectively, and another load (Qw) applied to the top of the wall was controlled at Qw = 0.19 Tb so as to generate the same shear forces in the upper and lower parts of the wall. Reaction R1 was generated in the compression zone of the imaginary slab crosssection by a steel plate with a height of 180 mm and a width of 900 mm, and reaction R2 was generated at the bottom of the wall by a steel plate with a height of 100 mm and a with of 900 mm, as shown in Figure 1. Using a steel frame for measurement attached at the top and bottom reflection points of the wall, relative displacements were measured in the direction of out-plane of the wall and lateral displacement of each beam bar was also measured as relative displacements from the mid depth of the wall, as shown in Figure 2.
3. Test results 3.1. Behavior of Failure Figure 3 is a schema showing a typical crack pattern that appeared on the inside faces of specimens. Failure was dominated by three types of cracks: radially oriented UV and DV cracks caused by the formation of a shallow cone, the top of which was located at the position of the beam bars, due to expansion of the wall; and a C crack that formed along the circumference on the side opposite the tails. The C crack was a shearing crack oriented inward from the bent part of the bar and upward at an angle of 45-degrees. The properties of this crack are the same as those of a diagonal crack occurring in a beam-
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R1
C
EH
C
UV
WF TH
Tb
TV DV
EH
Figure 3. Crack pattern
Figure 4. Circumstances of failure after testing
column joints due to raking-out anchorage failure. Figure 4 shows photographs of specimens taken after the loading test. 3.2. Relationship between load and displacement The existence of tie bars and the number of wall bars affect the relationship between load and displacement as shown in Figure 5. (1) Specimen WA25-1A (with no tie bars and with wall bar spacing of 200 mm): First, the initial stiffness in the relationship was decreased by the occurrence of WF cracking (shown by ▲ in Figure 5). Next, the stiffness in the relationship was greatly decreased again by the occurrence of UV cracking (V in Figure 5). Finally, the occurrence of C crack led to maximum strength or to strength just before maximum strength. (2) Specimens WA25-1AP2 and -1AP3 (with tie bars and wall bar spacing of 200 mm): The stiffness of each specimen was decreased remarkably by the occurrence of WF cracking, and the occurrence of C crack led to maximum strength. (3) Specimens WA25-1BP2 and -1B'P2 (with tie bars and wall bar spacing of 100 mm): Since the small spacing of tie bars and wall bars generated a truss mechanism that could effectively transmit local compressive stress from the bar bent to the supporting points, anchorage strength increased after the occurrence of C cracking. These specimens reached maximum strength due to the occurrence of TV cracking (shown by ◇ in Figure 5) or EH cracking (shown by ◆ in Figure 5). 400
Table 3 Results of experiment Specimen WA25-1A WA25-3A WB25-1A WA25-1B WA25-1AP2 WA25-1AP3 WA25-1BP2
σ B T d T d ' Crack (MPa) (kN) (kN) at T d 34.5 38.9 38.8 38.8 37.3 37.8 38.3
116 105 51 96 119 140 121
124 105 51 96 122 142 122
WF WF WF WF WF WF WF
Tu (kN) 153 155 93 172 179 224 377
Tb(kN)
WA25-1BP2
T u' WA25-1AP3 (kN) 300 WA25-1AP2 WA25-1B 163 200 WA25-3A 155 93 179 100 WA25-1A 183 WB25-1A Db(mm) 228 0 5 10 15 380 Figure 5. load vs. disp. relationship
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3.3. Strength at degradation of initial stiffness The test results of strengths are shown in Table 3. The value Td is the strength at degradation of initial stiffness (shown by ▲ or V in Figure 5) expressed by total tensile force in the beam bars, and the value Tu is maximum strength. The values Td' and Tu' were normalized by the average compressive strength of concrete (=39.1 MPa) using Equation (1) in order to eliminate the differences in concrete strengthσB among the specimens. All of the specimens except WB25-1A had almost the same strength Td'. This means the strength at degradation of initial stiffness does not depend on the spacing of wall bars and tie bars, but it is proportional to the lateral development length. Td’ or Tu’ = Td or Tu・√(39.1/σB).
(1)
3.4. Factors affecting maximum strength (1) Spacing of wall bars In the standard specimen (WA25-1A) with no tie bars and with wall bar spacing of 200 mm, the resistance against pull-out loading on the beam bars is thought to consist mainly of sliding resistance of the concrete on a plane along the shear crack (C crack) and a dowel action caused by wall bars intersecting the crack plane. When the spacing of the wall bars was decreased to 100 mm (the same as that of specimen WA25-1B), the enhancement of maximum strength was limited to about 10% because the wall bars were not confined in the direction of wall thickness due to the absence of tie bars. However, when the spacing was decreased and the tie bars were added (as in specimen WA251AP3), maximum strength was greatly enhanced. (2) Number of tie bars The relationship between normalized maximum strength (Tu’) and tie-bar ratio (Pb) is shown in Figure 6. The tie-bar ratio is the ratio of the total cross-sectional area of tie bars arranged in a unit area of the wall surface. The maximum strength increased in proportion to Pb for each wall bar spacing, as shown by ▲ for spacing of 100 mm and 400
Tu'(kN)
R1
350
WA25-1BP2
300 WA25-1B
250 200 150
Tb
WA25-1AP2 WA25-1A
100
Wall-bar spacing ▲ @100 ◆ @200
50 0
Tb
WA25-1AP3
Pb(%) 0.5
1
Truss mechanism
R2 Strut mechanism
1.5
Figure 6. Maximum strength (Tu’) and wall-tie bar ratio (Pb) relationship
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Tt(kN) 40 30 20 10 0
LH (mm) 200 40 30 20 10 0 -200
100 LV(mm)
-100
-300
WA25-1AP2 : measured values
200 100
40 30 -100 20 10 0 -200 150
0
0
0
300
200 100
100 0 -100-200 -300
WA25-1AP3 : surmised values
-100 50 -50 -150-250
-200
WA25-1BP2 : beam bar position
Figure 7. Distributions of wall-tie bar stress Tt (kN)
by ◆ for spacing of 200 mm in Figure 6. The maximum strength increased because the route of shear stress transmission through both the truss and strut mechanisms (see Figure 6) was formed by the inclusion of tie bars, because the tie bars could transmit shear stress from the inside to the outside of the wall. 3.5. Performance of tie bars Stress distributions of tie bars in some specimens are shown in Figure 7. When the tie bars were arranged with a smaller spacing (100 mm), the effective area of stress transmission through the tie bars spread widely around the beam bar tails by generating the truss mechanism. When the tie bars were arranged with a larger spacing (200 mm), the tie bars near the tips of the tails did not work effectively. Thus, the effective area of tie bars with spacing of 200 mm was smaller than 300 mm within the tail side. 3.6. Validity of our previously proposed equation for anchorage strength We previously proposed the following equation for estimating anchorage strength in a beam-column joint that has failed in raking-out [3]: calTu
= kN ( calTc + calTw ),
(2)
where calTc is the horizontal resistance of concrete (= kh・kc・bce・L1’・σe), calTw is the horizontal resistance of lateral reinforcement ( = kw・kb・aw・σwy), andσwy is the axial stress modification factor ( = 1 + 0.020σo). The definitions of the terms in the above equation are as follows: kc : effective factor for sliding resistance of concrete (= 0.85 when the bar tail is bent toward the beam compressive zone, and = 1.20 when the bar tail is bent toward the wall-supporting point)
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kw : effective hoop stress factor (= 0.8 when the bar tail is bent toward the beam compressive zone, and = 0.9 when the bar tale is bent toward the wall-supporting point) kb : effective factor by the thickness of cover concrete (= 1.0 when Co ≦0.8 Ldh ) bce : effective column width (= bs + 0.53 bc ) L1’: diagonal crack length measured along the horizontal plane (= Ldh – db – Cc ) aw : total cross-sectional area of lateral reinforcement crossing failure planes bs : distance between extreme beam bars bc : total thickness of cover concrete on both sides Cc : thickness of cover concrete on extreme beam bar Dc : depth of beam db : diameter of beam bar σo: column axial stress (not larger than 0.08σB) σe: sliding strength of concrete (= √σB ) σwy: yield strength of lateral reinforcement A comparison of the calculated and experimental results is shown in Table 4 and Figure 8. The values of the variables in Equation (2) were calculated on the basis of the assumption that the tie bars within the effective area of the walls (the walls of the specimens considered as being wide columns) correspond to lateral reinforcement of the equation. In case in which tie bars were used, Equation (2), which is the sum of concrete resistance (calTc ) and lateral reinforcement resistance (calTw ), could be used to estimate anchorage strength of beam-wall joints, since the ratio of calculated values to experimental values for all of the specimens with tie bars (except for specimen WA25-1AP2, which had the smallest tie-bar ratio) were in the range of 0.85 to 0.96. However, further study is needed to determine the reason for the minimum value (0.85) in specimen WA25-1AP3, in which tie bars were alternately spaced at 100 mm and 200 mm. When tie bars were not used, the calculated values (calTu) were less than the experimental values (expTu) because these calculated values were obtained by only the concrete resistance Tc and the dowel action of wall bars was disregarded in the calculation. Lateral resistance by the dowel action maybe is estimated as the difference TΔ between the calculated and experimental strengths of WB25-1A (TΔ＝92-6＝86 MPa), which had the smallest value of calTc among all specimens because it had the smallest horizontal Table 4 Comparison of calculated and experimental values [kN] cal T c cal T w cal T u exp T u exp/cal cal Tu ∆ exp/cal Specimen 60 － 60 153 2.55 146 1.05 WA25-1A 64 － 64 155 2.43 150 1.03 WA25-3A 6 － 6 93 14.47 93 1.00 WB25-1A 63 63 172 2.73 149 1.15 － WA25-1B 62 47 109 179 1.64 195 0.92 WA25-1AP2 63 201 264 224 0.85 WA25-1AP3 modified value 65 327 391 377 0.96 WA25-1BP2 =86.2(kN) (fixed)
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lL ua
cal Tu
Eq
300
in e
0%
expTu (kN)
12
400
cal Tu∆
80
%
200
100 cal Tu (kN)
0
100
200
300
400
Figure 8. Comparison of the calculated and experimental results
development length Ldh. Using modified strength calTuΔ, which is the sum of the original calculated value calTu and the dowel resistance T Δ , the ratios of expTu to calTu Δ for specimens without tie bars and for specimen WA25-1AP3 ranged from 0.92 to 1.15, and the experimental and calculated values showed good agreement. However, the ratio for WA25-1B, which had a large number of wall bars, was the largest value (1.15) because the effect of the number of wall bars was disregarded. The phenomena mentioned above indicated the following results: in the case of no tie bars, dowel resistance predominated in total resistance and it depended on the number of wall bars; in the case of using many tie bars, resistance of tie bars at yielding predominated; and in the case of using few tie bars, both of the resistances needed to be considered to estimate anchorage strength.
4. Conclusions The anchorage behavior of beam-wall joints using wall panels with 90-degree hooked beam bars at right angles as study specimens was examined. The test variables of the specimens were horizontal and vertical development lengths, lateral reinforcement ratio of tie bars, spacing of wall bars. The conclusions based on the experimental results are as follows. (1) The inclusion of many tie bars in walls around beam bars, especially around tails, made shear-stress transmission zone become wider and anchorage strength increase, because of the generation of the truss mechanism. (2) The anchorage strength of hooked bars without tie bars increased by only 10% even though the spacing of wall bars was reduced to by 50%, but the strength was greatly enhanced by inclusion of tie bars.
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(3) Our previously proposed equation for estimating anchorage strength in beam-column joints could be applied to estimation of anchorage strength in beam-wall joints with tie bars, dowel resistance caused by wall bars crossing shear crack planes needed to be included in the calculation in order to get good agreement with experiment results.
Acknowledgements The authors gratefully acknowledge the financial support provided by the Japanese Ministry of Education, Science and Culture (Grant-in-Aid for Scientific Research No.11450201) and the experiments carried out by students of Hokkaido University.
References 1. Joh O., Goto, Y. & Shibata, T., ‘Anchorage of Beam Bars with 90-Degree Bend in Reinforced Concrete Beam-Column Joints’, Proceedings of Tom Paulay Symposium on Recent Developments in Lateral Force Transfer in Building, La Jolla/California, September, 1993 (American Concrete Institute, 1995), SP-157, 97-116 2. Joh, O. & Goto, Y., ‘Anchorage behavior of 90-degree hooked beam bars in reinforced concrete knee joints’, Proceedings of Second International Symposium on Earthquake Resistant Engineering Structures, Catania/Italy, June, 1999, (2) 33-42 3. Joh O. & Shibata, T., ‘Anchorage Behavior of 90-Degree Hooked Beam Bars in Reinforced Concrete Beam-Column Joints’, Proceedings of the 12th World Conference on Earthquake Engineering, Acapulco, June, 1996, CD-ROM-3
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EMBEDDED STEEL BEARINGS INSTEAD OF CONCRETE NIBS Matthias R. Kintscher Pfeifer Seil- und Hebetechnik GmbH, Memmingen, Germany
Abstract The steel bearing which is equivalent to a steel cantilever embedded in concrete and anchored by an rebar anchored in the stemm of the TT is transfering the dead load from a TT-beam to a supporting beam. The supporting beam can have a rectangular shape so that no intrusive and work intensive nibs are necessary. This provides technical as well as architectural advantages. Additional reinforcement together with the steel cantilever of the steel bearing helps to transfer the live load to the supporting beam so that the whole construction works together between steel and concrete. The whole design provides the user with a couple of advantages which are discussed in the following article.
1. Introduction Often there is a deep mistrust within the precast industry against welded steel constructions. But assembles of steel buildings demonstrate that the methods of the steel industry are very fast and in times of decreasing programme requirements for building situations the advantages of the erection methods of the steel industry are slowly approaching the precast industry. Connecting precast elements, bolts and nuts or other steel construction tools get more and more fashionable. A typical example is the steel bearing for TTImage 1: Hot rolled steel bearing with beams (image 1) which is equivalent to a steel screwable anchor bar and centring cantilever embedded in concrete (image 2) and anchored with an anchor bar. bearing plate
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Therefore, this steel bearing is transferring the dead load from a TT-beam to a supporting beam. The big advantage is that there is no neoprene pad necessary to be mounted in situ on the supporting beam. Everything is prepared in a precast company. The supporting beam can have a rectangular shape so that no intrusive and work intensive nibs are necessary. This provides also architectural advantages (image 3).
Image 2: Steel bearing embedded in TT- Image 3: TT-beam on rectangular beams supporting beam gives a clear architectural view Additional reinforcement together with the steel cantilever of the steel bearing helps to transfer the live load to the supporting beam so that the whole construction works together between steel and concrete. The whole design and engineering is done easily in load selection tables. The tables and the design scheme have a German type approval. From the quality management point of view, there is a big advantage as no work has to be done by a non skilled person on the site. The TT-beam has only to be placed on the supporting beam and that is all. This accelerates the installation of the TT-beams by one third of the time so that the biggest advantage is given if one considers the whole procedure from producing the TT-beams, the rectangular shaped supporting beams and the erection work. By using the embedded steel bearing there is a reduction of cantilever arm for the supporting beam. That means the torque moment is less than with nibs at the supporting beams and this helps to prove the stability of the supporting beams on the corbels of the columns without any braces necessary under the TT-beams or the supporting beams. To get this benefit it is necessary to overcome the mistrust of the precasters against welded steel construction and it is necessary to see the thing not only from the eyes of the purchaser but also from the general manager who is responsible for the whole costing process.
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2. Advantages using embedded steel bearings instead of concrete nibs The traditional way of building load bearing constructions with TT-beams is shown on image 4 and 5 as a view from the underside and and a cross section. Greatest disadvantage is the complicated cross section of the supporting beam with nibs. A more straight forward way of achieving the same result is shown on image 6 and 7 but that requires far more height. The steel bearing combines the two advantages: a low building height and a simple shaped supporting beam, shown on image 8 and 9.
Image 4: Underside view of TT-beam on supporting beam with nibs
Image 5: Cross section of TT-beams on supporting nibs
Image 6: Ineffective height with TT-beams Image 7: Cross section of TT-beams on upon rectangular supporting beam rectangular supporting nibs costs height
Image 8: Optimized construction: TTbeams sustained rectangular supporting beam with steel bearing
Image 9: Cross section shows the steelbearings reducing height and making the design easier
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The formwork for a supporting beam with 2 nibs on the sides is normally very complicated. If a supporting beam system formwork is used, plywood extension boxes must be used in order to achieve this nib cross section shape (image 10). Also, the reinforcement is less complicated if only rectangular shaped supporting beams are adopted, as shown on image 11. If nibs are necessary much more reinforcement is necessary, specificially a second layer of stirrups in transverse direction will be required.
Image 10: Complicated formwork and reinforcement for supporting beam with nibs
Image 11: Straight forward formwork for rectangular supporting beam
A lot of money can be saved if the supporting beams are built rectangular. From the transportation view point the rectangular shaped beams obviously have a reduced dead weight compared with the lateral nibs. Dispite the reduction of concrete volume, the supporting beams can be built rectangular. Therefore, the costs for the steel bearings are compensated by the reduced costs of concrete, the reduction of reinforcement and the reduced formwork costs.
Image 12: Large eccentricity with nibs at the supporting beam
Image 13: Minimal load eccentrictiy with steel bearing
One of the main disadvantages of the nib shaped supporting beam is that it creates a relatively high eccentricity for the load bearing. In comparison with this the centered load bearing plate of the steel bearing gives a critical reduction in eccentricity for the
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load bearing (images 12 and 13). Due to the fact that the eccentricity is significantly reduced the sequence of assembling the TT-beams into the building is no longer of importance. Previously the site manager had to ensure that the TT-beams on the opening sides of the supporting beam were assembled in the correct sequence so that no rotation of the supporting beam could take place. This was associated with the requirement to use 2 cranes to move 1 crane from one side to the other which caused additional costs. To avoid these effects very often strong and high braces were used to support the supporting beams (image 14) under the nibs but nowadays with the utilisation of a TT-beam steel bearing this is no longer a consideration as the reduced eccentricity also reduces the torque moments and the rotation of the supporting beam is eliminated (image 15). Previously once rotation had taken place by means of friction it could not be reversed.
Image 14: Beams with nibs supported by braces
Image 15: Assembling on one side of the beam without any worries about the sequences by using steel bearings
This positive effect of reducing the torque moment helps also to cope with edge conditions. Previously it was extremely complicated to construct edge zones such that the forces were balanced.
Image 16: Complicated edge situation
Image 17: Easy done edge with steel bearing
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3. How it works The reinforcement necessary in the area around the steel bearing may look initially a little complicated but it is not actually the case. The philosophy of the load bearing behaviour is very simple, as shown on image 18. The steel bearing bears the whole dead weight of the precast element, the TT, and the additional weight of the liquid concrete which is poured upon the table of the TT as a top layer. For this load condition the steel bearing works like a cantilever arm and transfers the loads over bending and shear from the anchor bolt to the hot rolled beam and to the load centering plate.
Image 18: Superposition of transferring mechanisms: Precast element dead weight and liquid concrete weight transferred by steel bearing and live load transferred by reinforcement plus concrete
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The hot rolled beam works in conjunction with longitudinal reinforcement with hooks at the front end. As the concrete around the beam and the reinforcement is hardened, this area of concrete incorporating additional reinforcement (longitudinal rebars as well as the vertical stirrups) transfers the live load to the supporting beam. This combination affects the transferance of the live load over the concrete element as well as transferring of the dead weight by means of bending and shear of the steel bearing working together in such a manner that the flection of the components are equal. Only this solution offers the possibility to use this construction without cracks and other damage.
Image 19: The essential reinforcement required with the steel bearing Most of the elements shown make up that the rebar cage around the steel bearing is not necessary for the steel bearing itself but only for the anchorage of the prestressing strength or such like. There is an additional link with an angle of inclination which helps to avoid cracks in the stem or the table, where the stem ends accross the internal corner. The forces would like to unfold this sharp corner so that some cracks could occur but by using this inclined rebar the unfolding forces are nutralized, so that no cracks will occur there.
Image 20: Prestressed TT-beam with a pitch in the middle and an angle of inclination at the end at the steel bearing due to the curvature
The bearing situation without a neoprene pad poses the question, whether the loads can be securely transferred to the supporting beam, especially if the TT-beam has an
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inclinded angle at its end. This could result for instance from the prestressing procedure. Image 21 demonstrates what can happen. We take into account that we have a span of 16 meter and a pitch of 5 centimeters. This gives an angle of inclination of 0,143 degrees. This causes a gap of 0,2 millimetres at the outer end of the bearing plate which should center the load. It is clear that 0,2 millimeter is much less than the roughness of the concrete surface. Thus, such an angle of inclination will not influence the load bearing behaviour.
Image 21: Detail view on the steel bearing at the end of a curved prestressed TT-beam
Image 22: The position of the steel bearing totally embedded in concrete and the narrow gap gives sufficient fire protection (F90). The gap is too narrow to allow hot fumes transfer to the steel bearing.
Fire protection is also provided with this steel bearing construction as the whole steel bearing is embedded totally into concrete. The hot fumes can not come into direct contact with the steel so that the critical temperature of 500 ° will not be reached within a time limit of 90 minutes. The only location where the steel bearing is slightly closer to the surrounding air, is where the stem ends. There is a gap between stem and the supporting beam under the table of the TT-beam but this gap has a limited width of 20 mm (image 22), so that the hot fumes transferred to the table will come into contact on the surface of the stem or the supporting beam beside the gap. Through this contact the fumes will be cooled down so that no critical temperature will be transferred to the table where the steel bearing is embedded and has the lowest protection.
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4. Practice in the precast industry Image 23: Prepared rebar cages incorporating steel bearings to be set into the formwork
Image 25: Freshly cast in steel bearing held down from a fixing timber bar
Image 24: Installed steel bearing, properly fixed to the formwork, with additional longitudinal reinforcement and links
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Image 25: Assembled TT-beams ready to be reinforced and to be cast with the top concrete
5. Conclusion It is not possible to demonstrate every advantage that can be offered in conjunction with the steel bearing. However, it is clear that considerable economic benefit can be gained from the use of steel bearings as an alternative to concrete nibs in the design process. Simplified design of the elements is reflected through production drawings. In turn the precaster is able to produce less complicated formwork and use less reinforcement and save on labour costs by simplifying the transportation of the supporting beams. The reduced weight and volume of the units allows for easier assembly on site. In this way it is conceivable that savings of more than 30 % can be achieved during the erection process. In order to obtain the greatest advantage the whole system should be considered from design through production to the construction process on site. In this way the design engineer can influence the quality of precast concrete structures and the problems of in situ concrete and offer fast-track construction previously only associated with steel framed buildings.
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ANCHORAGE ZONE IN A STEEL-CONCRETE COMPOSITE SLAB WITH UNBONDED TENDONS Heli Koukkari VTT Building and Transport, Finland
Abstract At VTT Building and Transport, Finland, the composite action between the concrete part and steel sheet of a composite slab with unbonded tendons was investigated by fifteen column tests simulating a load-balanced state. The results from the column tests showed that the transfer lengths were between 350 and 400 mm. They were in agreement with the previous results that the length of an anchorage zone is between the slab thickness (presented for a solid concrete slab) and two times the column side (as for composite columns). The tests showed also that the location of anchors influences on the transfer length of the compressive force to the sheet and on the resistance of the concrete end block.
1. Foreword This presentation is based on the experimental results in two research programs that dealt with prestressing of steel-concrete composite floor construction. The National Technology Agency of Finland, TEKES, the Rautaruukki Company and VTT Building Technology financed the projects. 2. General A steel-concrete composite slab with unbonded tendons is a new type of structure that combines the benefits of composite construction and prestressing. Prestressing induces a stress state mainly counteracting the effects of permanent loading. It is a method to improve the performance of a composite slab particularly under service loads because cracking of concrete can be eliminated or substantially reduced. The increase of the flexural stiffness can be utilized in span lengths and slab thickness.
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A post-tensioned steel-concrete composite slab is a combination of prefabricated steel sheets, in-situ concrete with its reinforcement and a post-tensioning system (Fig. 1).
A
C
B
A
C
B
B-B
A-A
concrete steel sheet
C-C
anchor tendon
Fig. 1. A post-tensioned composite slab with unbonded tendons. The composite action between concrete and steel sheet relies mainly on the joint detailing but also on the profile of the sheet. Typical joint details are embossments or perforations. The shapes, heights, depths, locations and inclinations from the longitudinal axis vary in great ranges. Compared to an ordinary reinforced slab, the joint details are usually flexible. A great variety of ribbed sheet products for composite slabs can be found on the market. The total cross-sectional steel area is about 1000 - 1500 mm2/m depending on the type of the sheet. The heights of the sheets vary commonly from 40 to 55 mm. Deep profiles to 210 mm are also on the market for the purpose of minimum propping during construction. A post-tensioning system with unbonded tendons contains the tendons in their sheathings, active and passive anchor assemblies and tensioning jacks. The tendons will be lengthened and then fixed to the surrounding hardened concrete only at their anchors. The lubricating material between the sheathing and tendon allows for free movement of the tendon. In concrete slabs with unbonded tendons the long-term compressive stresses are typically between 1.5 and 2.5 N/mm2. The behaviour of the joint depends mainly on the location, mechanical resistance and ductility of the joint details made in the sheets. The basic requirement for a composite slab suitable for post-tensioning is that the joint between concrete and steel sheet has enough strength and ductility to resist the actions in different loading situations. In a ductile joint, the shear stresses at ultimate limit state can reach the same strength value over a length that is called a shear span. All sheet types for composite slabs on the market are experimentally proved to have composite action in normal loading conditions. Brittle behaviour is also accepted with an additional safety factor. Posttensioning causes a concentrated force in the joint at the slab ends.
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3. Analysis of a composite slab with unbonded tendons The behaviour of a post-tensioned steel-concrete composite slab depends upon the deformation and strength properties of the steel and concrete parts and of the joint between them. The composite slab is commonly analysed as a one-way slab due to the geometry of a sheet. A post-tensioned steel-concrete composite slab remains uncracked or slightly cracked in most design cases and the deflections will increase linearly as the loading increases. The elastic theory will be used to calculate the stresses and deformations due to loading and post-tensioning. The strains and stresses are calculated based on the Hooke´s law, Bernoulli´s hypothesis and principle of force equilibrium. 3.1 Cross-sectional values The notation used in analyses is given in Fig. 2.
A c Ec I c centroid of concrete
h
h
ec
centroid of the slab
c
ea e
y ha da ds
centroid of sheeting
Aa E a I a
Ap Ep A s Es
Fig. 2. Notation for the cross-sectional values: Aa Ac Ea Ec Ia Ic dc da e ea ec ep h ha hc na
effective area of the steel sheet in tension, compression or flexure gross area of concrete (including the area of the tendons) elastic modulus of steel elastic modulus of concrete effective second moment of area of the sheet second moment of area of concrete distance from the centroidal axis of concrete to the bottom fibre of the slab distance from the centroidal axis of the sheet to the bottom fibre of the slab distance from the centroidal axis of concrete to that of the sheet y- co-ordinate of the centroidal axis of the sheet y- co-ordinate of the centroidal axis of the concrete component y- co-ordinate of the centroid of the tendons total thickness of the composite slab height of the steel sheet thickness of concrete above the upper flange of the sheet modular ratio of structural steel to concrete
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ecl
ep
eal
dp
In calculations, the nominal measures and characteristic values are used in general. For steel sheet, the thickness of the steel core and effective cross-section is used. The crosssectional values of a composite section transformed into concrete are sums of those of the components with respect to the centroidal axis of the slab:
Am = ∑ n k Ak
(
I m = ∑ n k I k + nk A e where nk is
2 k k
(1)
)
(2)
modular ratio Ek/Ec.
The effective area of a sheet under tension is different from that under compression or flexure. The steel sheeting in compression is not taken into account in the cross-sectional values at the internal support. However, when the anchorage zone is treated, the sheet is taken into account in the axial stiffness. 3.2 Effects of the tendon force A tendon is usually curved or otherwise shaped along the length in order to counteract the effects of permanent loads, including the self-weight. The magnitude of the tendon force depends on the cross-section and time of consideration. The losses due to friction between the curved sheathing and the tendon can be ignored in slab design. The tendon force will also be reduced by the anchorage slippage just after the fixing, by creep and shrinkage of the concrete and by the relaxation of the steel with the time. The force P in a curved tendon can be divided in horizontal and vertical components, Phor and Pver, respectively: Phor = Pcosβ ≅ P Pver = P sinβ
(3)
where β is the angle between the horizontal axis and the force P. The horizontal component is roughly equal to P in a slab as the length L is large compared to the thickness h, and the angle β is small. When the vertical loads on the concrete due to post-tensioning equal to the external loads, the slab is load-balanced presuming that the tendon is anchored at the centroidal axis of the composite slab. The external loads include here the self-weight of the slab. Such a composite slab is uniformly compressed due to the horizontal component, when there are no stresses induced by restricted deformations.
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3.3 Anchorage zone The anchors of the tendons cause concentrated loads on the concrete at the ends of the composite slab. A zone with both tensile and compressive stresses is induced. Splitting of the concrete may take place due to the bursting stresses. Additional reinforcement is needed to ascertain the resistance with respect to the concentrated load. However, accurate determination of the stresses in the vicinity of anchors is complex and expensive, especially when the anchors are closely spaced. In practice, empirical design equations are used for the cracking load. No special consideration of the strength of the concrete is needed, when the recommendations of the suppliers of the post-tensioning systems are followed in applications with profiled steel sheets. The horizontal component of a tendon force produces uniformly compressed crosssections in a load-balanced slab. The length of the anchorage zone is determined as a distance where a uniformly compressed cross-section takes place. At the slab ends however, a part of the force at anchorage is transferred by shear stresses in the joint from the concrete to compressive force of the sheeting. For this reason, two anchorage zones are defined. Anchorage zone 1 is defined to represent a plain concrete and 2 composite slab with a little longer anchorage zone (Fig. 3).
anchorage zones anchor
uniform compression
1 2 concrete
P hor
compressive stresses
Pc P a
P sheet
Fig. 3. Anchorage zones from an anchor to the concrete (1) and composite section (2). The tendon force Phor≅P on the anchor is divided into a force Pa of the sheeting and a force Pc of the concrete following where na and Am are calculated according to the formula (1). Pa = PAana/Am Pc = PAc/Am
(4)
The length of the transferring area of the Pa is not known by calculations. The exact length of the anchorage zone of concrete is difficult to determine by calculations, too. Consequently, experimental methods are seen preferable to study the anchorage zone of a composite slab.
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4
Column tests
4.1 Specimens and testing arrangements The composite action between the concrete and steel sheeting was investigated by fifteen column tests simulating a balanced composite slab. The specimens were short concrete columns with steel sheets on two opposite surfaces. Nine columns were composed of so called shallow sheets which have a ductile joint behaviour in most common loading cases (Finnish SteelComp sheets). No stirrups were placed in those specimens P1 – P9 because the calculated failure load was higher than the force needed to induce a high compressive stress 7 N/mm2 (about 720 kN), which seldom is used in post-tensioned structures. Six columns had deep steel sheets with handmade embossments in webs (Finnish RAN120 sheet), and stirrups were placed at the ends (Fig. 6 and Table 2). Table 1 gives data about the specimens P1-P9. In those tests, strains of concrete and sheet and slips of the sheet were measured. The strains were measured over a length of 200 mm or 300 mm by transducers in all tests and by strain gauges in two tests. After first tests, the points of measurements were moved on the narrow flanges (bottom of the trough) located inside the concrete. The compressive force was introduced on a steel plate of an area 320x120 mm2 located in the middle of the columns P1- P9. The testing and measuring arrangement of the tests P1-P6 is presented in Fig. 6. The same arrangement as in Fig. 6 b was used in the tests P7-P9, too.
steel sheet embossments in flange
150
320
concrete
300
117 steel sheet
a)
231.6
b)
320
Fig. 4. Cross-sections of test columns. a) P1-P9, b) P10-P13
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300
a)
b)
P
P
Steel plate
50
2
0
50
50
2
0
22
10 (12)
50
20
200
or
200
300 4 (5)
7
7
6
23
5
4
21
6
11 (13)
50
3
1
50 3
50
1
50
P
P
Fig. 5. The loading arrangements and measurements in the column tests (see Table 1). a) Specimens P1, P2, P4, P5, b) specimens P3 and P6. The numbers in parenthesis refer to the opposite side. Table 1. Specimens in the column tests P1-P9. The length of a column is Lc, the nominal thickness of the sheet t0, the distance between the measurement points Lm and the distance of the measurement point to the end of a column dm. SPECIMEN
Lc mm
P1 P2 P3
to mm
Lm mm
dm mm
500 500 500
0.7 0.7 0.7
300 300 200
100 100 150
P4 P5 P6
500 500 500
0.9 0.9 0.9
200 200 200
150 150 150
P7 P8 P9
1000 1000 1000
0.9 0.9 0.9
200 200 200
400 400 400
The measurement arrangement is presented in Fig. 6.
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Remarks
strain gauges on wide flanges transducers on narrow flanges
strain gauges on wide flanges transducers on narrow flanges transducers on narrow flanges transducers on narrow flanges transducers on narrow flanges
P
P10, P12
P14
987
SIDE C
8 6 5 4
10 11 12
500 600 400
250
10 11 12
6 5 SIDE B 4
Sivu D 1
SIDE A
3 2 SIDE A
123
P11, P13
250
9
SIDE B
SIDE D
SIDE C 7
P15
3
3
4
2
4
2
1 1
P
Fig. 6. Measurements in tests P10 – P15 (see also Table 2). Table 2 gives data about the specimens P10-P15. In those tests, the deformations of concrete and sheets were measured by the aid of transducers in the middle of the specimen. The distance between the measurement points were 400, 500 and 600 mm in specimens P10 and P14 and 500 mm in other tests as presented in Table 2. Table 2. Specimens in the column tests P10-P15. The length of a column is Lc, the nominal thickness of the sheet t0, the distance between the measurement points Lm, and the distance of the measurement point to the end of a column dm. SPECIMEN
P10 P11 P12 P13 P14 P15
to
Lc mm
mm
Lm mm
dm mm
1200 1200 1200 1200 1200 1200
0.9 0.9 0.9 0.9 0.9 0.9
400, 500 and 600 500 500 400, 500 and 600 500 500
400, 350 and 300 350 350 400, 350 and 300 350 350
The compressive force in tests P10-P15 was divided on two steel plates of an area 75x150 mm2 that were located in different ways with respect to the troughs.
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3.2 Results of column tests The strains of the sheet and concrete increased almost equally in the tests, where the distance of strain measurement points to the column end was long enough to cover the anchorage zone in the concrete and the transfer length of the compressive force Pa to the sheet. One example of the measured strains is presented in Fig. 7.
1400
1200
FORCE P, kN
1000
800
600 4, concrete 5, concrete 6, sheet 7, sheet
400
200 P9
-0,800
-0,700
-0,600
-0,500
-0,400
-0,300
-0,200
-0,100
0 0,000
STRAIN, %o
Fig. 7. Measured strains of concrete and sheet in the specimen P9. In the tests P1-P9 the failure of a specimen took place in the concrete and not in the joint. The forces at the failure are presented in Table 3. In all the column tests P10-P15 failure of the specimen took place in the concrete. However, in the tests P10-P13 the sheet broke off on one side of a specimen. Table 4 presents the forces at failure of the joint and that of concrete in the tests P10 – P15. Table 3. The ultimate forces Pu in column tests P1-P9 at the failure of the concrete. Pu ,kN
P1
P2
P3
P4
P5
P6
P7
P8
P9
1070
1035
1135
987
950
1075
1175
1268
1250
1231
Table 4. The force Pub at the beginning of buckling, Puj at joint failure and Puc at the failure of concrete in column tests P10 – P15. P10 Pub, kN
P11
P12
P13
P14
P15
1075
1187
930
-
-
Puj , kN
1350
1266
1740
1199
-
-
Puc , kN
1375
1338
1905
1745
1510
1553
The column tests showed that at the distance of the anchorage length the compressive force is transferred into the steel sheeting and the parts have equal strains at least in the location of the embossments. Summary of the measuring lengths in columns and results are presented in Table 5. Table 5. The agreement of strain measurements on sheets and concrete surface at different transfer lengths Lt. Projected breadth of a sheet is bs and distance between the outer flanges in P1-P6 and inner flanges in P7-P9 is bc. Lt mm 100 150
Test P1, P2, P4, P5 P3, P6
bs .bc, mm2 320x320 320x320
300 350 400 400
P10, P12 P10, P11, P12, P13 P7, P8, P9 P10, P12
295x300 295x300 320x320 295x300
Remarks No correlation No correlation in strain gauges Weak correlation of results from transducers (narrow flanges) Increasing differential strain Good or excellent correlation Good or excellent correlation Good or excellent correlation
5 Conclusions The share of the sheet Pa from the total tension force is from 11.5 kN to 28.7 kN, when the concrete compressive stress was from 1.5 to 2.5 N/mm2 (concrete grade K30, na 7.67. This force caused a shear stress in the joint that is from 0.04 to 0.1 N/mm2 supposing that the transfer length is 300 mm. These shear stresses are low compared to the characteristic shear strength values of the products on the market, in general. The results from the column tests showed that the specimen lengths 1000 and 1200 mm were suitable. The transfer lengths 350 and 400 mm gave a good agreement of the measured strains of concrete and steel sheets. The results of column test showed that post-tensioning can be applied to a composite slab with a ductile joint. The tests undertaken on columns with a high profile also showed that the sheet type having lower ductility but strength enough could be used in post-tensioned slabs. The column tests are recommended in verification of joint resistance for a post-tensioned slab, as the effects of a compressive force on the joint and sheet are different from those of bending.
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CONNECTIONS FOR CONTINUOUS FRAMING IN PRECAST CONCRETE STRUCTURES G.Krummel PEIKKO GmbH, Waldeck, Germany
Abstract Connections for continuous framing in precast concrete structures have been a problem almost impossible to solve. A frame system is more economical in comparison with to the standard system for precast concrete elements, consisting of a rigid column to foundation connection and a jointed beam to column connection. But the rigid beam to column connection was difficult and expensive to realise. Therefore an easy and economical bolt system has been developed. This system allows a fast assembling of the column to the foundation and a fast assembling of the beam to the column, independent of weather conditions. The roots of this system are in Scandinavia / Finland.
1. Introduction The economical aspect and the details of precast concrete frames have been researched and tested in the ELECON [1] project. The most common ways of rigid column to foundation and column to beam connections in Europe have been compared with a bolt system to screw the precast concrete elements together. Two bolted rigid frame systems were studied to clarify how big material savings can be obtained. Finally the assembling time of the different frame types was compared. The static calculations have been proceeded according to ENV 1992, the anchoring of the headed bolts is calculated according to concrete capacity (cc-designing).
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2. Bolt based frame system 2.1 Column-foundation connection 2.1.1 Details The common ways for rigid column anchorage have been socket bases and grout –sleeve bases.
Figure 1: Socket foundation
Figure 2: Grout sleeve base These systems are expensive and costly. The socket requires a deep foundation. The column is fixed by wedges during assembling time and might need a support (tall columns). The grout- sleeve base carries the loads by overlapping in the foundation and has to be supported during assembling time until the grouting is hardened. The bolted connection consists of the following parts: 1. Anchor bolts (base bolts), which are placed to right position before casting. 2. Column shoes, which transmit forces from the column to the anchor bolts. There can be 4 shoes in every corner and shoes in the middle, too. The shoes are placed entirely inside the column thus the formwork can be done easily. 3. After the column has been erected and the anchor bolts are tightened, the gap between column and foundation is grouted with non shrinkage mortar.
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Figure 3: Bolted column foundation connection The connection is also suitable for column to column joints. 2.1.2 Load transfer The column shoes transmit the loads normally by overlapping with the longitudinal reinforcement of the column. The load transfer after grouting can be calculated according to ENV 1992. The compression force is taken by the mortar and the bolts, the tensile force from the bending moment is taken by the bolts. The stiffness of the joint depends on the size of the cross section and the diameter of the bolts. The shear force can be taken by the bolts, the concrete section or an extra shear dowel. During assembling time all loads can be taken by the bolts. The anchoring of the bolts depends on the dimensions of the foundation. Anchor bolts with headed studs can be calculated according the German approval (HPM/L, PPM/L anchor bolts) or a truss and tie model. Other anchorings like overlapping etc. according ENV 1992 are also possible (HPM/P, PPM/P anchor bolts). A special software to calculate the load transfer and the anchoring is available.
Figure 4: Column shoe
Figure 5: HPM/L anchor bolt
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2.1.3 Assembling A levelling plate is adjusted in the right level on the foundation. The lower nuts are screwed under the right level, the column is screwed with the upper nuts in the right direction. After that the lower nuts are tightened to the base plate of the column shoe. It is a rigid connection already during assembling state and no extra support for the column is needed. Finally the gap between the foundation and the column is grouted with an non shrinkage mortar. 2.2 Beam to Column connection 2.2.1 Details The connection between column and beam was basically realised by welding joints or grout –sleeves. Both systems are difficult during assembling time and can be very expensive. The bolted joint consists of the following parts 1. Anchor bolts with or without muffs cast in the column 2. Beam shoes cast in the beam (similar like column shoes) 3. Corbel for shear force- if required 4. Niches on the columns face and the end of the beam for shearforces 5. After the beam has been erected and the anchor bolts are tightened, the gap between column and beam is grouted with non shrinkage mortar.
Figure 6: Bolted connection
Three different connections are mainly used:
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•
Connection between a column and a precast beam: Figure 7: The beam is screwed to the column, the beam shoes can have a long hole. The top connection is realised by bolts with muffs or couplers.
•
Connection between a column and a half precast beam: Figure 8: The beam is screwed to the column, the upper connection is realised by couplers and are casted in situ, depending on the floor system (f.e. filigran floor system).
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•
Connection between column and precast top beam Figure 9: The top beam is assembled in the same way as the column to column or column to foundation connection. The bars of the column shoes can be bent according to the structure of the top beam.
2.2.2 Load transfer The beam shoes carrying the normal forces by overlapping with the longitudinal beam reinforcement. The bolts are screwed with the beam shoes and transfer the loads inside the column. The shear forces are normally taken by corbels, depending on loads. Niches in the column and in the beam are also possible to take shear forces after grouting with non shrinkage mortar. The anchoring is mainly calculated to ENV 1992 (f.e. overlapping , anchor plate). The usage of headed studs for anchoring the tensile forces has been tested . Mainly it can be calculated according to cc- method and the tie and truss model. 2.2.3 Assembling A levelling plate is adjusted in the right level on the corbel. The beam is seated on the levelling plate, the nuts are tightened. The gap and the niches are casted with non shrinkage mortar.
3. Economical aspects When the elements have been screwed together, the connection is rigid and need not to be braced. The assembling is independent of weather conditions. The hardening time of the grout is not critical. The erection time of two one storey high frames (bolted system and socket foundation) has been compared [1] , 35% savings of assembling time are possible to reach with a bolted column foundation connection in comparison with a socket foundation.
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The assembling time for the bolted system to fix a beam rigidly to a column is much shorter than the welding joints or the grouted sleeves. The erection is independent of weather conditions, the system is rigid during assembly time. The material savings for a frame system have been tested and researched [1]. The amounts of concrete and steel can be reduced by up to 30% with a rigid frame system in comparison with the common system with hinged beam to column connections. The material saving starts with the foundation. The quantity of topsoil which has to be removed is smaller in comparison with to the socket foundation, the length of the column can be shorter. The rigid beam to column connection reduces the bending moment for the column foundation connection in comparison with the hinged joint.
4. Conclusion Bolted rigid frame systems for precast concrete elements offer an economical and fast are more than an alternative to the common connections for precast concrete elements. These systems allow an easy and economical assembling for rigid column to foundation and rigid column to beam connections. The assembling advantages for steel constructions are translated to precast reinforced concrete constructions.
5. References 1. 2. 3.
ELECON project: Research project for bolted connections (Bolt based connection for precast frames) 1996, Tampere University of Technology Deutsches Institut für Bautechnik (DIBt), Berlin 1997: Bemessungsverfahren für Teräspeikko Ankerbolzen HPM/L Technical data PEIKKO GmbH
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STANDOFF SCREWS AS SHEAR CONNECTORS FOR COMPOSITE TRUSSES: PUSH-OUT TEST RESULTS AND ANALYSIS J.R. Ubejd Mujagic*, W. Samuel Easterling**, Thomas M. Murray** *Pinnacle Structures, Inc., USA **Virginia Polytechnic Institute and State University, USA
Abstract Composite trusses, or joists, are structural members that have become increasingly popular in the last several years due to economical and functional considerations. These members typically consist of a steel truss and composite slab that are connected by welded headed shear studs. The trusses are specifically designed for the composite application. Composite slabs are constructed using steel deck, topped with normal or lightweight concrete. Typically, welded, headed shear studs are used to connect the slab and top chord of the truss. Welding studs in the field can present problems if the chord angles, or other structural shape, are relatively narrow or thin. An alternative type of shear connector has been under investigation at Virginia Tech for several years. The shear connector is a standoff screw that has a self-tapping, self-drilling point. A number of push-out tests and full-scale composite truss tests have been conducted to evaluate the performance of the shear connector. Results from the push-out tests and related analysis are described in this paper.
1. Introduction Along with improvements and innovations in composite construction in general, specific improvements in composite floors have been made in recent years. One development that continues to gain popularity in the U.S. is the composite open-web joist. Open web joists are prefabricated steel trusses in which the top and bottom chords usually consist of
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double angle sections, and web members are either double angles, single (crimped) angles, or continuous round rods. (Hereafter, the composite joists will be referred to as composite trusses.) Composite trusses have several advantages when compared to other types of floor framing. These advantages include the ability to span large openings, thus providing large column free areas. Also, the open web structure permits HVAC ducts and utilities (plumbing, electrical, telecommunications) to be placed within the depth of the truss. Using the most popular form of shear connector, the welded shear stud, can be problematic for certain trusses. This is particularly true for shorter-span members, which generally use relatively thin angles for the top chord. Specifically, problems can arise with welding of headed shear studs to the double angle top chords. The double angle section is narrow and thus presents a target that is difficult for the stud installer to hit when welding the studs. The requirement used for limiting the ratio of stud diameter to base metal thickness is given in the AISC specifications1 as 2.5. This criterion sometimes limits the use of composite trusses because the top chords must be increased in size to accommodate the welded shear stud, resulting in a loss of economy. These circumstances warrant the need for a different shear connector that satisfies the strength requirements, is functional and easy to install, and at the same time does not govern the size of the truss chord to the extent that welded shear connectors do. The development of a ductile shear connector, which can be screwed into the top chord, would solve the problem of strict welding requirements and also eliminate the need for sizeable welding equipment and the necessary energy sources at the job site. This new shear connector would also be simple to install, not requiring the presence of trained and expensive welding personnel. The new connector would potentially be ideal for smalland medium-sized construction jobs where lighter trusses with thinner top chords could be used in composite floors. 14
In response to this need, there has been ongoing 11 10 research at Virginia Tech for the last several years. The researchers have focused on the 1.25 development of a shear connector that would make trusses even more practical and appealing 38 7 7 for use in composite floors. Earlier work on 67 similar types of connectors was reported by El2.5 The ongoing Shihy2 and Moy, et al3. investigation has narrowed the possible choices down to a standoff screw, a schematic of which Fig 1. Standoff Screw Schematic is shown in Fig 1. The screw has a self-drilling, self-tapping point and is manufactured from ASTM Grade 8 material with a minimum specified tensile strength of 1034 MPa.
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The standoff screws have been evaluated in three different types of tests: push-out tests; full-scale short span truss tests; and simple shear and tension tests. Push-out tests are the primary way of evaluating the strength of standoff screws due to the relative simplicity and economy, as compared to full-scale tests. The role of full-scale tests has been primarily to verify the results obtained from the push-out tests. Simple shear and tension tests were used to determine material properties for the screws. Only push-out test results and related analyses are presented in this paper. Detailed results can be obtained from the project reports.4-9
2. Push-out Tests A total of 254 push-out tests were conducted using the Grade 8 screws. Specimen fabrication and test procedures did not differ significantly between the various studies. Specimen configuration included variations in slab construction (solid concrete slab or composite deck slab), deck depth, base material thickness, concrete strength, number of screws per specimen, and screw height above the deck. Detailed descriptions of specimen fabrication, instrumentation and test set-ups for each specific series are presented in the project reports.4-9 A schematic of the typical push-out test configuration is shown in Figure 2. The push-out specimens were subjected to a vertical load that simulated the load at the steel concrete interface. Elastomeric bearing pads were placed under each slab to insure that the slabs were uniformly loaded along their bottom surfaces. The swivel and the loading plates, which were placed atop the steel section, insured that the load from the hydraulic ram was evenly distributed between the two halves of the specimen, and that the axial load indeed remained axial. The hydraulic ram used to apply the axial load was fixed to the loading frame. A normal load apparatus was used to simulate the application of gravity load in a composite truss and to prevent premature separation of the concrete and steel. The apparatus consisted of a hydraulic ram and two beam sections that were used to distribute normal load along the length of top chords. The three quantities measured during the test were axial load, normal load, and slab vs. top chord relative slip. The axial load was measured with a load cell placed between the hydraulic ram and crosshead, as shown in Figure 2. Normal load was measured with a load cell that was placed between the normal load distribution frame and the hydraulic ram. Movement between the steel and composite slab was measured using linear potentiometers at four evenly distributed locations on each slab. The loading scheme for all the tests was relatively similar. Axial load was applied in increments of 22-45 kN with the normal load kept at 10% of the magnitude of the applied axial load. After each loading application, the system was left to stabilize for about three
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minutes, at which point all the measurements were recorded, and the next higher load applied.
500 Kip Load Cell
Cross-head located between cross beams Hydraulic Ram
Loading Plate
50 Kip Load Cell
Normal Load Distribution Frame Reaction Floor
Elastomeric Bearing Pad
Fig 2 Typical Test Setup (Alander et al.5)
3. Analysis of Results 3.1 Ribbed Slab Analysis The tests evaluated in this section are those constructed with formed steel deck used to simulate the condition in which the deck is perpendicular to the steel member. Three types of failures were identified in the tests performed: screw pullout, screw shear, and concrete rib shear. Screw pull-out is the failure of the shear connection where localized yielding of the base material around the screws occurs, causing severe deformation of the base material, allowing the screw to slip out of the angle with the threads experiencing minimal or no damage at all. Screw shear is any kind of failure where the section failed due to screws breaking through their threaded portion. Rupture may occur due to shear or a combination of shear and tension. Concrete rib failure is any type of failure where the specimen failed due to the separation of a concrete rib from the rest of the slab before breaking of the screws or screw pull-out
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occurs. Although a distinction was made in the past between concrete rib failure and concrete cone pull-out, concrete rib failure is used herein to cover both types of failure. Previous studies by Hankins et al.4, Alander et al.5, and Webler et al.7 focused on predicting the strength of the standoff screws at a slip of 5 mm. The choice of this slip magnitude was based on the notion that standoff screws should exhibit behavior similar to that of headed shear studs. Another motivation to use the slip of 5 mm was that the behavior of the test specimens was generally consistent up to that point. The researchers experienced difficulty in consistently predicting ultimate strengths that occurred at slips greater than 5 mm. Thus, it was felt that the strength corresponding to the 5 mm displacement would be more reliably calculated. A negative aspect of this approach is that the screws typically exhibit significant strength beyond the level attained at the 5 mm displacement. Thus the need to develop strength calculation models for the ultimate strength of the screws. The push-out test results were grouped based on their mode of failure and three separate analyses performed. This resulted in three different models to predict the shear strength for each individual mode of failure, with the smallest being the controlling value. The following variables were identified as important in determining the mode of failure and strength of a given configuration: Screw Pullout Failures - screw height, rib height, top chord thickness, bottom rib width Screw Shear - top chord thickness, screw tensile strength, screw cross-sectional area Concrete Rib Failure - concrete compressive strength, length of shear plane, number of screws per rib, bottom rib width Test results confirmed that screw pull-out failures occur in specimens with relatively thin top chord angles. Specifically, angles with thickness ranging from 3 to 3.5 mm exhibited screw pull-out. Specimen parameters, other than top chord angle thickness, that were determined to influence pull-out strength are listed above. These parameters primarily affect screw rotation and thus the pull-out strength. The strength model was developed using regression analysis techniques. If the thickness of the top chord angle is large enough to prevent a screw pull-out failure, then a screw shear or concrete rib failure will occur. The screw shear failures observed in the push-out tests were often thought to be a combination of shear and tension. Depending on the combination of specimen parameters, rotation of the screw/rib/top chord angle occurred. Thus, the screw was not in direct shear, but rather a combination of shear and tension. This influence was evaluated through regression analysis.
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The shear plane, depicted in Figure 3, represents the plane through which the applied shear force is transferred. This plane is highly dependant on screw height and deck geometry. The vertical distance between screws in a rib containing more than one screw is a part of the shear plane length and is also depicted in Figure 3 along with other variables.
Fig 3 Shear Plane in Concrete Rib Failures Several expressions for the effect of concrete compressive strength were investigated. In one of the models considered, it was suggested that the square root of the product of concrete compressive strength and corresponding concrete modulus of elasticity adequately accounts for the effect of concrete shear strength.10 However, based on statistical analysis of the models investigated and the available test data, it appeared that the effect of concrete compressive strength was best represented by a constant multiple of ln (f ’c). This, along with other variables noted, was used in a regression analysis to develop the strength equation for concrete rib failure. 3b. Solid Slab Analysis Push-out tests were conducted using screws in solid slabs. The number of screws per half specimen ranged from 14 to 26, and the screw spacing ranged from 51 to 102 mm. The only mode of failure observed in this type of configuration was screw shear. The equation for calculating screw shear in the solid slabs is the commonly used shear rupture criteria based on a von Mises failure theory. 3c. Strength Prediction Model The equations below represent the strength prediction model for the standoff screws evaluated in this study. Based on the range of experimental variables and the fact that statistical analyses were used in the development of the equations, the equations are applicable for concrete compressive strengths of 21 to 48 MPa, 1 to 12 screws per rib and angle thickness of 3 to 6.5 mm. The first equation in the deck rib perpendicular to truss case represents the strength in the screw pull-out mode, the second screw shear and the third concrete rib. Note that all the
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equation variables are identified in United States Customary (USC) units. This is because of the coefficients generated in the statistical analyses. The solid slab equation is the commonly used shear rupture criteria based on a von Mises failure criterion. This is expression is obviously applicable as is in either USC or SI units. Deck rib perpendicular to the truss: H 36.71 (t tc )1.61 s hr CA sc Fut
φ Rn = φ
0.75
0.13 0.18 (ln f ' c)L sp w r1 0.74
N
min
(1 - 0.15w
2 r1
+ 0.98w r1
)
(1) ( 2) (3)
Solid slab: φR n = φ
A ts Fut
(4)
3
A reliability analysis was conducted to determine the strength reduction factor, φ, for use in a load and resistance design factor design (LRFD) format. The analysis was performed separately for each component of the strength equation, using the approach proposed by Galambos and Ravindra.11 Based on a target reliability index of 3.5, the range of φ factors calculated for the three strength equations ranged from 0.82-0.89. A single φ factor of 0.85 was determined to be appropriate. 3d. Simplified Strength Prediction Model A simplified strength prediction model was developed. As will be noted, the simple model is not as accurate as the model in section 3c., however the simple model benefits from a more mechanistic based development, and thus it is easier to visualize. As in Section 3c, the first equation below represents screw pull-out, the second screw shear and the third concrete rib shear. Also because certain coefficients are statistically based, the expressions are given in USC units. The screw pull-out expression was based on statistical analysis of screw shear tests in which the only variable was the base metal thickness. This is the same relationship used in the more elaborate equation of Section 3c for the base metal thickness. The difference in the two is that the influence of other parameters was ignored due to their relatively minor affect on the strength. The second equation is the commonly used shear rupture criteria based on a von Mises failure criterion.
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The third equation represents a concrete rib failure. An analogy is made to reinforced concrete corbels in which the shear friction concept is applied. Only the concrete shear strength portion of the concept is applied here. An area of concrete defined by Lsp x 1.67 Lsp is multiplied by 0.3 ksi. The length of the shear plane perpendicular to the rib of the deck, Lsp, is defined quantitatively in Section 5 and can visualized in Fig. 3. The failure surface of the rib, particularly the length along the rib, is a quantity that varies significantly in push-out tests. The choice of a 1.67 multiple of the Lsp value appeared to give reasonable results. Deck rib perpendicular to the truss: 130 t1tc.6
(5)
A ts Fut
(6 )
φR n = φ
3 0.5 L2sp
(7 )
N
min
The calculations for the strength reduction factor, using the simplified equations, continue to be evaluated at the time of this writing. Preliminary calculations indicate that a strength reduction factor of 0.8 is applicable. 3e. Comparison of Models for Deck Rib Perpendicular to Truss A graphical comparison of the two models for the deck rib perpendicular to truss case is presented in Fig. 4. As can be noted from the figure, the distribution is smoother for the more detailed model than for the simplified model. Additionally, the coefficient of variation is lower for the more detailed model. 45 39
40
Screw Prediction Model
35
Simplified Prediction Model
Standoff Screw Strength Prediction Model C.O.V. = 0.105 No. of Tests = 163 Mean = 1.018
Number of Tests per Range
31 30
Simplified Strength Prediction Model C.O.V. = 0.155 No. of Tests = 163 Mean = 1.026
28 26
25 21
21 19
20
17 15
15
12
11
10
10
11
10
9
8
7
6
5
4
3
5 0
0
1
0
1
0
4 1
1
0
1
2
1
2 0 1.40-1.45
1.35-1.40
1.30-1.35
1.25-1.30
1.20-1.25
1.15-1.20
1.10-1.15
1.05-1.10
1.00-1.05
0.95-1.00
0.90-0.95
0.85-0.90
0.80-0.85
0.75-0.80
0.70-0.75
0.65-0.70
0.60-0.65
0.55-0.60
0
Experimental/Predicted Strength Ratio Range
Fig. 4. Comparison of Strength Ratios for Standoff Screw Calculation Models
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4. Summary and Conclusions Results from an on-going study of the behavior and strength of a new type of shear connector for use in composite design were presented. The connector consists of a standoff screw with a self-tapping, self-drilling point, made from ASTM Grade 8 material. Push-out test results, obtained from a wide variety of specimen parameters, were used to develop strength calculation equations for configurations in which the steel deck was oriented perpendicular to the truss. These equations represent three modes of failure: screw pull-out, screw shear, concrete rib shear. Two sets of equations were presented, one relatively simpler than the other. Strength reduction factors were calculated based on the models and test data. The models developed provide an acceptable means by which the shear connector strength can be calculated for use in design of composite trusses. Both forms of the model provide acceptable accuracy for design as reflected in Fig. 4, with means of experimental/predicted strengths of 1.018 (c.o.v. of 0.105) and 1.026 (c.o.v. of 0.155). A strength reduction factor of 0.85 was determined to be applicable for use with the more detailed strength model. Additional work is required to arrive at a final recommendation for a strength reduction factor for the simplified calculation procedure. Further studies are required to evaluate the applicability of the solid slab test results to the configuration in which the steel deck ribs are parallel to the flexural member.
5. Nomenclature φ = strength reduction factor Asc = gross area of the screw, in.2 Ats = tensile stress area of the screw, in.2 = 0.7854(D – 0.9743/n)2 C = top chord thickness coefficient = (2/5) for ttc ≤ 0.205 in. = (2/3)(1-2ttc) for ttc > 0.205 in. D = screw diameter f ‘c = concrete compressive strength, psi Fut = screw tensile strength, ksi hr = rib height, in. Hs = screw height, in. ls = vert. dist. between screws in rib, in.
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Lsp = length of the shear plane perpendicular to deck rib, in. 2
n N Rn ttc wr1 wr2
w −l = 2 r 2 s + (H s − h r ) 2 + ls 2 = number of threads per inch = number of screws per rib = shear strength per screw, kips = top chord thickness, in. = bottom rib width, in. = top rib width, in.
6. Acknowledgements The research described in this paper was sponsored by Nucor Research and Development and the ELCO division of Textron. The authors are grateful for the assistance provided by David Samuelson and G. Wayne Studebaker of Nucor R&D and Mike Janusz of ELCO.
7. References 1.
Load and Resistance Factor Design Specifications for Structural Steel Buildings (1993). American Institute of Steel Construction, Chicago, Illinois. 2. El-Shihy, A.M. (1986). “Unwelded Shear Connectors in Composite Steel and Concrete Structures.” Ph.D. dissertation, University of Southampton, Southampton, United Kingdom. 3. Moy, S., Jolly, C., and El-Shihy, A. (1987). “Unwelded Shear Connectors for Composite Joists.” Proceedings of the International Conference on Steel and Aluminum Structures, Cardiff, UK, July 8-10, 1987. 4. Hankins, S.C., Gibbings, D.R., Easterling, W.S., and Murray, T.M. (1995). "Standoff Screws Functioning as Shear Connectors in Composite Joists.” Report CE/VPI-ST 94/16, Virginia Polytechnic Institute and State Univ., Blacksburg, VA. 5. Alander, C.C., Easterling, W.S., and Murray, T.M. (1998a). "Standoff Screws Used in Composite Joists." Report No. CE/VPI - ST 98/02, Virginia Polytechnic Institute and State University, Blacksburg, VA. 6. Alander, C.C., Easterling, W.S., and Murray, T.M. (1998b). "Data Report for Standoff Screws Used in Composite Joists." Report No. CE/VPI - ST 98/03, Virginia Polytechnic Institute and State University, Blacksburg, VA. 7. Webler, J.E., Easterling, W.S. and Murray, T.M. (2000). "Further Investigation of Standoff Screws Used in Composite Joists." Report No. CE/VPI - ST 00/18, Virginia Polytechnic Institute and State University, Blacksburg, VA. 8. Mujagic, U., Easterling, W.S., and Murray, T.M. (2000a). "Further Investigation of Standoff Screws Used in Composite Joists (Addendum.)" Report No. CE/VPI - ST 00/19, Virginia Polytechnic Institute and State University, Blacksburg, VA. 9. Mujagic U., Easterling, W.S., and Murray, T.M. (2000b). "Further Investigation of Short Span Composite Joists." Report No. CE/VPI - ST 00/20, Virginia Polytechnic Institute and State University, Blacksburg, VA. 10. Grant, J.A., Fisher, J.W., and Slutter, R.G. (1977). “Composite Beams with Formed Steel Deck.” AISC Engineering Journal, 14 (1). 11. Galambos, T.V. and Ravindra, M.K. (1976). Load and Resistance Factor Design Criteria for Composite Beams. Research Report No. 44, Washington University, St. Louis, MO.
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EXPERIMENTAL STUDY ON A NEW JOINT FOR PRESTRESSED CONCRETE COMPOSITE BRIDGE WITH STEEL TRUSS WEB Kousuke Furuichi**, Masato Yamamura*, Hiroyuki Nagumo* and Kentaro Yoshida** *Civil Engineering Design Department, Kajima Corporation, Japan ** Technical Research Institute, Kajima Corporation, Japan
Abstract A composite truss bridge has been developed that comprises concrete upper and lower slabs and steel truss as the web. This structure rationalizes structural performances, reduces weight and labor costs. A structure is proposed to simplify the cantilever construction, and to utilize both steel and concrete effectively to realize a new composite joint structure for a composite truss bridge. This joint structure is achieved by inserting the diagonal tubular steel into a box-shaped steel structure called a steel BOX made from welded perforated steel plates. The force flow in this joint structure was expected to be complicated. Therefore, static destructive tests were carried out using scale models to conceive their force propagation conditions and ultimate strengths, and to obtain basic data for designing. These tests confirmed that the force was propagated in the steel BOX until shear cracks occurred at the joint. At this point, re-bars in the joint carried some of the forces. It was thus confirmed that varying both quantity and placement of re-bars could control the ultimate strength at the joint.
1. Introduction Hybrid bridge structures have recently been developed that utilize the advantages of both steel and concrete 1), 2). These structures have enabled cost saving by rationalizing structural performances, and reducing bridge weight and labor costs. An example of this type of hybrid structure is shown in Fig. 1.
Fig.1 PC Composite Bridges with Steel Truss Web
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引張斜材
圧縮斜材
Tensile Diagonal Member
Compressive Diagonal Member Joint of Compressive Diagonal Member Rings of Rebar
Concrete Slab
Main Re-bars
Steel BOX
Stirrups
Fig.２ Joint Structure
Fig. 3 Object Bridge
This is a composite truss bridge comprising concrete upper and lower slabs and steel truss as the web. This structure draws a bead on decreasing bridge weight while maintaining high rigidity against live loads, and reducing labor costs. The concrete web is replaced with steel truss, because it contributes little to the resisting moment in a PC box girder. Applications of this structure are found in the Albore Bridge, the Loars Bridge, etc. However, in this type of bridge, there is a possibility of brittle failure of the total system due to breakdown of the joints between concrete slabs and steel truss members. Therefore, it is necessary to develop the joint structure that can propagate the required forces. Various joint structures have been proposed, but authors have developed a new joint structure 5), 6), 7), 8) which is compact and has sufficient strength, as shown in Fig. 2. This joint is easy to construct during the cantilever construction, and effectively utilizes steel and concrete to produce joint with a composite structure. This joint structure is achieved by inserting tensile and compressive tubular steel diagonal members into a box-shaped steel structure called a steel BOX. The steel BOX is made of welded perforated steel plates. The steel BOX and the tensile diagonal members are welded to form an integrated structure. The compressive diagonal members and the concrete in the steel BOX are unified by the effect of bonding of the re-bars, which are welded along the internal perimeter of the tubular steel. This paper reports static loading tests using scale models of the joint to conceive the force propagation conditions and the ultimate strengths of the joint structure, and to establish a concept of designing. And further more, it proposes the equation of shear strength derived from test results.
D13
Steel BOX ｔ＝6.0 Hall of Diameter 25.0 Pith of Hall 50.0
Tensile Diagonal Member φ＝165.2 ｔ＝7.1
50
[email protected] 50 D10 50 50 3@75=225 50 50 50 50 5@65=325
Compressive Diagonal Member φ＝165.2 ｔ＝7.1
a) No.1 Specimen
425
50
100
2500 2350 2@32=64 33 33 6@125=750 6@125=750 100 4@65=260 4@65=260 D10
D10
D13
1361
D10
425
D10
1361
50
[email protected] 50 D10 50 81
[email protected]=163 81 50 50 50 5@65=325 D13
2500 2350 18@125=2250 68°68°
Tensile Diagonal Member φ＝165.2 ｔ＝7.1
b) No.2 Specimen
Fig.4 Aspect of Specimen
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Steel BOX ｔ＝6.0 Hall of Diameter 25.0 Pith of Hall 50.0 Compressive Diagonal φ＝165.2 ｔ＝7.1
2. Test outline
4@50=200
35 195 5035
Table 1 Material Properties of Steel Tubular and Steel BOX Tensile Strength
Yield Point
Elastic Modulus
Elongation
N/mm2
N/mm2
×103N/mm2
%
Steel Tubular
450
408
207
39
Steel BOX
532
361
207
26
250
80
250
50
162.5
2.1 Specimens Dimensions of specimens and applied design loads for the specimens were determined to simulate the φ25.0 111 joint with a 1:2 scale model of the bridge, as shown t=6，SM490 φ25.0 315 325 in Fig. 3. Fig. 4 and 5 show the configurations of the specimens and the steel BOX, respectively. Two specimens were tested. The first specimen (No.1) was used to evaluate the shear strength of the 313 152 5@50=250 152 joint. In the second specimen (No.2), the quantity of re-bars in the joint is approximately doubled to Fig.5 Steel BOX prevent failure in the joint before failure in the other members. The diagonal tubular steel has an outside diameter of 165.2 mm and a wall thickness of 7.1 mm (diameter-thickness ratio 23). To unify the joint of the compressive diagonal members with the slab, re-bars with diameter of 6 mm were welded along the perimeter of the steel pipe at 30 mm pitch in three stages. This design referred to results of previously implemented axial compression element tests. 24 perforations of 25.0 mm diameter were aligned at 50.0 mm spacing on the side steel plates of the steel BOX taking into an account of the integration with the slab concrete and of filling capability during the concrete placement. Table 1 shows the mechanical properties of the diagonal tubular steel and the steel plates of the steel BOX. The slab concrete was determined as 42.5 cm high and 42.5 cm wide. For the 1/2 scale model, the maximum grain diameter of coarse aggregate was set to be 10 mm. Table 2 shows the material properties of the concrete. Re-bars with diameter of 10.0 mm and 16.0 mm were used in the slabs. Table 3 shows the material properties of the re-bars. Table 2 Material Properties of Concrete No.1:21days No.2:25days No
Compressive Strength
Elastic Modulus
N/mm2
×103N/mm2
No.1 Specimen
39.7
25.7
No.2 Specimen
41.4
26.2
Table 3 Material Properties of Reinforcement D10 No
No.1 Specimen
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Tensile Strength Yield Strength Elastic Modulus Tensile Strength
Yield Strength Elastic Modulus
N/mm2
N/mm2
×103N/mm2
N/mm2
N/mm2
×103N/mm2
512
349
18.8
508
356
18.9
No.2 Specimen
2.2 Test method A horizontal load was applied at the end of the concrete slab using the apparatus shown in Fig.6, so that it was precisely transferred to the joint, tensile diagonal member and compressive diagonal member. In order to determine the horizontal load P, the linear frame
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反力壁
2950
3000
P（ｋN）
5500
2500
580 230195 Specimen
2000kN Load cell
1500 1000 600
Result of Linear Analysis
Fig.6 Side View of Load Carrying
Maximum Load 983．5ｋN Displacement 51.1mm Specimen No.2
Maximum Load 931.4ｋN Displacement 31.3mm Load of S er viceability Condition×３（P=663kN）
Shear P=839.0ｋN
Specimen No.1
Load of Ult imat e C ondition Displacement 59.4mm (P=377kN） viceabilityy C Load of S er viceabilit (P=221kN）
0
600
500
1378.5
Hydrauric 球座 Jack
1978.5
2000
700
2500
1100 1000 900 800 700 600 500 400 300 200 100 0
10
20
30
40 50 60 δ（mm）
70
80
90 100
Fig.7 Load-Displacement Relationship
analysis was conducted separately to evaluate the relationship between the axial forces in the diagonal members and the axial forces in the subject bridge. The following static repeated loads were applied: 1) the design load (P=221kN), 2) the design ultimate load (No.1: P=584kN, No.2: P=671kN), and 3) the maximum load and load conformable to maximum load to confirm the conditions of developed displacements. The design load and design ultimate load were specified to originate the axial force in the tensile diagonal member identical to the axial force for each loading state based on the separately conducted linear frame analysis. The measured parameters were horizontal load (load cell), specimen displacement (displacement meter), open width between concrete and diagonal tubular steel (cantilever type displacement meter), diagonal tubular steel strain (strain gauge), slab concrete strain (strain gauge and mold gauge), and re-bar strain (strain gauge).
3. Test Results and discussions 3.1 Horizontal load – horizontal displacement Fig. 7 shows the relationship between horizontal load P and horizontal displacement δ for the specimen No.1 and No.2. Both specimens showed an increase in displacement of about 2.8 mm at the beginning of the loading. This is caused by the margin at the hinge that fixed the specimen on the platform. Thereafter, the gradient of P-δ (rigidity) became larger and the relationship was linear up to P=550 kN, which was larger than the design ultimate load (P=377 kN). The gradient (rigidity) up to that point was almost the same as that of the gradient obtained from the linear frame analysis, which took into account the rigid connection of nodes and the eccentricity of the joint. In the process, both specimens showed a similar trend up to P=931.4 kN (the maximum load of specimen No.1), indicating that increase in displacement was gradually enhanced. For specimen No.1, the width of the shear crack at the joint increased and at the same time the load started to decrease at the maximum load of P=931.4 kN (δ=31.1 mm). The load rapidly decreased after P=839.0 kN (δ=59.4 mm) due to the shear failure, and thereafter specimen No.1 reached its ultimate strength. For specimen No.2, the load increased beyond the maximum load for specimen No.1 (P-931.4 kN). It reached a maximum at P=983.6 kN (δ=51.1 mm), and specimen No.2 reached its
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upper view
upper view
Load
Load
side view
side view
Load
Load
lower view
lower view Load
Load
b) Specimen No.2
a) Specimen No.1
Fig.8 Specimen Cracking after Loading ultimate strength due to full plastic buckling of the compressive diagonal member. 3.2 Cracking patterns Shear cracking occurred in both specimens at a force P of about 600 kN. There were no signs of cracking at the design load and design ultimate load. Fig.8 shows the cracking patterns observed at the completion of tests. In specimen No.1, cracking occurred on the side face of the joint in an angle of 45 degrees. The crack development was also observed along the main re-bars. On the upper side, the crack extended from the center to the periphery of the steel BOX. This is probably caused by the fact that the compressive diagonal member was trying to extrude the steel BOX to the upper side. In specimen No.2, shear cracking occurred on the side face of the joint as for specimen No.1. However, unlike specimen No.1, the cracks were concentrated on the side face of the steel BOX. More cracks induced by the diagonal tubular member were found on the lower side of specimen No.2 than that of specimen No.1. The joint in specimen No.2 has higher shear strength and shear rigidity owing to the increased number of re-bars. As a result, the larger forces were converged at the joint between the tubular steel and the concrete slab for specimen No.2 than that of specimen No.1 causing more cracks at that point. 3.3 Strains in tubular steel Fig. 9 shows the axial strains and the bending strains of the tubular steel. It is found that no portion of either specimen reached yield strain at design ultimate load (P=377 kN). Strains of the two specimens were almost identical up to the maximum load of specimen No.1. For specimen No.2, it was observed that at around the maximum load of specimen No.1, the middle-stage bending strain of the compressive diagonal member was released and the other strains were greatly increased. Therefore, it was possible to confirm that the full plastic buckling in the compressive tubular member occurred around this point. The smaller strains took place in the upper stage than in the other stages because the upper stage was situated inside of the slab concrete and the force was propagated through the concrete in the tubular steel.
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① Allowable Strain (667μ) ② Nominal Yield Strain (1143μ) 1100
①②③
1100 Upper
1000
Lower
900
600
P（ｋN）
P（ｋN）
500
500
Load of Ultimate Condition (P=377kN）
300
Load of Ultimate Condition (P=377kN）
400 300
Load of Serviceability Condition （P=221kN）
200
200
100
100
0
Load of Serviceability Condition （P=221kN）
Positive
0 0
2000
4000
6000
8000 ε（μ）
10000
12000
14000
16000
0
2000
4000
6000
8000
10000
12000
14000
16000
ε（μ）
a) No.1 Specimen (Axial Strains of Tensile Tubular Steel) ③②①
b) No.1 Specimen (Bending Strains of Tensile Tubular Steel) ①②③
1100
1100
1000
Upper
800
Lower
1000
Lower
900
Upper
900 800
Middle
700
Middle
700 P（ｋN）
Load of Serviceability Condition×３ (P=663kN）
600
P（ｋN）
Load of Serviceability Condition×３ (P=663kN）
700
600
400
500 Load of Ultimate Condition (P=377kN）
400 300
Load of Serviceability Condition×３ (P=663kN）
600 500
Load of Ultimate Condition (P=377kN）
400 300
Load of Serviceability Condition （P=221kN）
200
200
100
100
Load of Serviceability Condition （P=221kN）
Positive
0 -16000
0
-14000
-12000
-10000
-8000 ε（μ）
-6000
-4000
-2000
0
0
2000
Lower
10000
12000
14000
16000
Middle
1000 900
900 800
8000
①②③
1100 Upper
6000
d) No.1 Specimen (Bending Strains of Comp. Tubular Steel)
①②③
1000
4000
ε（μ）
c) No.1 Specimen (Axial Strains of Comp. Tubular Steel)
Lower Upper
800
Middle
700
700 Load of Serviceability Condition×３ (P=663kN）
600
P（ｋN）
P（ｋN）
Middle Upper
800
Middle
Load of Serviceability Condition×３ (P=663kN）
700
1100
Lower
900
800
③ Actual Yield Strain (1916μ)
①②③
1000
500 Load of Ultimate Condition (P=377kN）
400 300
500
300
200
200
100
100
4000
6000
8000 ε（μ）
10000
12000
14000
16000
a) No.2 Specimen (Axial Strains of Tensile Tubular Steel)
0
2000
4000
Load of Serviceability Condition （P=221kN）
6000 8000 ε（μ）
10000
12000
14000
16000
b) No.2 Specimen (Bending Strains of Tensile Tubular Steel)
③②①
1100
Positive
0 -2000
0 2000
Load of Ultimate Condition (P=377kN）
400
Load of Serviceability Condition （P=221kN）
0
Load of Serviceability Condition×３ (P=663kN）
600
①②③
1100
1000
Lower
1000 Lower
900
Upper
900
800
Upper
800 Middle
700
Load of Serviceability Condition×３ (P=663kN）
600
P（ｋN）
P（ｋN）
700
Middle
500 400 300
Load of Ultimate Condition (P=377kN）
Load of Serviceability Condition×３ (P=663kN）
600 500
Load of Ultimate Condition (P=377kN）
400 300
Load of Serviceability Condition （P=221kN）
200
Load of Serviceability Condition （P=221kN）
200 Positive
100 0 -16000
100 0 -14000
-12000
-10000
-8000 ε（μ）
-6000
-4000
-2000
0
c) No.2 Specimen (Axial Strains of Comp. Tubular Steel)
0
2000
4000
6000
8000 ε（μ）
10000
12000
14000
d) No.2 Specimen (Bending Strains of Comp. Tubular Steel)
Fig.9 Load-Steel Tubular Strain Relationship
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16000
a) Main Re-bar
b) Stirrups
Fig.10 Strain Distribution of Reinforcements on the Joint
3.4 Reinforcing bar strains Fig.10 shows the strain distributions of the main re-bars and stirrups in the joint when the load equivalent to the design load (P=200 kN) was applied and after cracking took place (P=900 kN). Neither shear cracking nor strain was observed in the re-bars at P=200 kN for either specimen. However, strains were observed mainly at the joint in the main re-bars and in the stirrups at P=900 kN. In specimen No.2, the strains in the re-bars were small and were more evenly distributed than in specimen No.1. The strains in the main re-bars were found to be evenly distributed over the height of the steel BOX and the strains in the stirrups were found to be concentrated near the intersection with the centroid of the tension compression diagonal member. 引張 圧縮
3.5 Steel BOX strains Fig.11 shows the principal strains (P=200 kN and P=900 kN) occurring in the steel BOX. On the side face of the steel BOX, diagonal compressive strains and diagonal tensile strains occurred at an angle of 45 degrees at P=200 kN. At P=900 kN, the principal tensile strains were lateral. Furthermore, the principal tensile strains wee vertical at near the compressive diagonal member. This is considered to be the result of the constraint of the concrete in the steel BOX and the resistance against slipping-out of the compressive diagonal member to the upper face. It is noted that the principal strains on the side face of
50μ
1000μ
50μ
引張 圧縮
a) No.1No.1試験体（200KN） Specimen (P=200kN)
1000μ
引張 圧縮
b) No.1No.1試験 Specimen (P=900kN) 体（900KN）
tension 引張 compression 圧縮
50μ
c) No.2 Specimen (P=200kN) No.2試験 体（200KN）
1000μ
d) No.2 Specimen (P=900kN) No.2試験体（900KN）
Fig.11 Principal Strains of Steel BOX
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the steel BOX were smaller than the yield strain even at P=900 kN. On the upper side of the steel BOX, tensile strains were directed toward the center of the tensile diagonal member, because the steel Box was welded to the tensile diagonal member. Although the principal tensile strains exceeded the yield strain at P=900 kN, they were smaller than the allowable strain for three times the design load (P=663 kN). In the steel member connected to the side face of the steel BOX, the tensile strains were about 450 μ and 200μ on the tensile side and the compressive side, respectively. The steel member on the tensile side had larger strains.
4. Discussions and points to be clarified for joint design method 4.1 Force distribution in joint The strain distributions of the re-bars (main re-bars and stirrups) placed in the joint, and of the steel Box showed a difference between the force distributions of the joints before and after cracking when design load was applied. With the design load, almost no reinforcement strains were observed. The force is considered to be propagated mainly in the steel BOX. In contrast, the re-bar strains increased after cracking took place. At this point, the surface of the steel BOX would be contributing to the strength. The following re-bar strain distributions were observed at that time. The main re-bar strains ranged over the height of the steel BOX and, the stirrup strains occurred at the intersection of the centroids of the diagonal members. It is considered that this can be used as a reference to determine the range of the contributing re-bar when estimating the ultimate shear strength of the joint. The principal strains on the side face of the steel BOX resulting from the shear are decisive with the design load. As the load level increases after shear cracking, the rigidity of the joint decrease and the amount of deformation increases. It is therefore considered that, as well as the effect of shear, the constraint of the concrete inside the steel BOX, slipping-out of the tensile diagonal member and the rotation effect due to the extrusion of the compressive diagonal member influenced this behavior. Therefore, additional analyses or experiments are necessary to clarify the ambiguities for further improvement in the detailed designing for the configuration of the steel BOX, arrangement and size of the perforations, etc.
5. Equation of Shear Strength 5.1 Relationship between the applied horizontal force and shear force at the joint To formulate the equation of shear strength, the relationship between the applied horizontal force and shear force at the joint is calculated by using the frame analysis. From results of the frame analysis, an applied horizontal force of 100kN results in 103kN of force at the joint. Fig.12 Shear-Strain Diagram of Steel BOX
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5.2 Formulating the equation of shear strength Fig.12 shows the shear-strain diagram of a steel BOX with applied horizontal force of 931kN. All gages attached on the surface of the steel BOX show that all of the strains exceeds the shear yield strain of 2078μ. As a result, the shear-stress distribution may be assumed as a rectangular shape. Fig.10-b) shows the transition of strains measured from the gages attached on stirrups. Consequently, if the applied horizontal force is large enough to bring the steel plate to the point of shear yield, stirrups would also yield. The shear strength at the joint is sum of shear strengths of the concrete, stirrups, and steel BOX. Therefore, the equation of shear strength at the joint can be described as Vnd = Vcd + Vstd + Vssd Vnd: nominal shear strength at joint Vcd: nominal shear strength provided by concrete at joint Vcd = βd・βp・βn・fvcd・bw・d fvcd = 0.23√fcd βd =4√1/d βp =3√100pw βn = 1.0 fcd: compressive strength of concrete bw: web width d: distance from extreme compression fiber to centroid of tension reinforcement pw = As/(bw・d) As: area of tension reinforcement Vstd: nominal shear strength provided by stirrup at joint Vstd = Aw・fyd・z / s s: pitch of spiral reinforcement Aw: total amount of area of shear reinforcement over the interval z: distance from compression resultant to centroid of tension reinforcement fyd: design yield strength of tension reinforcement Vssd: nominal shear strength provided by steel BOX at joint Vstd = 2・ｔ・ｈ・σsy / √3 t: thickness of surface steel plate h: height of surface steel plate σsy: allowable tension stress
Table 4 shows both experimental and calculated shear strengths of specimen No.1 and 2. Table 4 Comparison of Experimental and Calculated Shear Strengths Unit:kN No.1 Specimen No.2 Specimen Vcd 82 82 Vstd 130 508 Vssd 623 623 Vnd 835 1213 978 1356 Experimental Value: Vn Vn / Vnd 0.854 0.895
Comparing with experimental values, calculated values are fairly good and are 80% of that of experimental values. Farther analysis such as a non-linear analysis would be carried out in a
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future to clarify both shear transfer capacity and system of applied load endurance, and to decide whether using equation to calculate the shear strength is proper way to do. The restraint of the concrete in steel BOX makes the actual shear strength provided by the concrete larger than that of the calculated one.
6. Concluding remarks Destructive tests were conducted using scale models. The object of the tests was the joint structure made by inserting tensile diagonal members and compressive diagonal members into a steel BOX made of welded perforated steel plates. The acquisitions obtained from the tests are summarized as follows: a. By actually destroying the joint, properties of shear failure in the joint were conceived. b. No abnormalities such as shear cracking were found under the design loading. c. It was confirmed that the joint was safe at over three times the design load. d. The force propagation conditions in the joint were conceived from the strain distributions in the re-bars (main re-bars and stirrups) of the joint and in the steel BOX. e. The force propagation conditions in the joint of the compressive diagonal members were conceived. f. The equation of shear strength was derived from the tests results. It is planned to conduct additional analysis and tests to confirm the current test results and to improve and refine the designing method of full-scale joint structures.
APPENDIX. REFERENCES 1) Keiichiro Sonoda, “Hybrid Structures”, Bridge and Foundation, pp23-29, 1997 2) Atsuo Ogawa, and Norio Terada, “Composite Bridges in J.H.”, Bridge and Foundation, pp48-55, 1997 3) Express Highway Research Foundation of Japan, Report on Investigation of Prestressed Concrete Composite Bridges, 1997 4) Yasuo Inokuma, et al., “Scheme of Tomoe-gwa (Prestressed Concrete Composite Bridge) ”, Proceedings of the 51st Annual Conference of the JSCE, pp514-515, 1996 5) Yasuo Inokuma, et al., “Analytical/Experimental Study of a joint in Prestressed Concrete Composite Bridges with Steel Truss Web”, Proceedings of the Prestressed Concrete Symposium, pp73-78, 1999 6) Hiroshi Miwa, et al., “Experimental Study on the Mechanical Behavior of Panel Joints in PC Hybrid Truss Bridges ”, Journal of Structural Engineering, pp1475-1484, 1998 7) Masaaki Hoshino, et al., “Experimental Study of a Panal Joint in Prestressed Concrete Hybrid Truss Bridges”, Journal of Structural Engineering, pp1423-1430, 1999 8) Kyoji Niitani, et al., “Experimental Study on a Joint in Prestressed Concrete Composite Bridges with Steel Truss Web”, Journal of Structural Engineering, pp1509-1516, 1999 9) Youhei Taira, et al., “Investigation of Connecting Steel Pipe and RC member Using Dubel ”, Proceedings of the 54th Annual Conference of the JSCE , pp288-289, 1999
1259
DESIGN AND CONSTRUCTION OF A CONCRETE-FILLED STEEL TUBE JOINT Stephen P. Schneider, Donald R. Kramer, Douglas L. Sarkkinen Kramer Gehlen and Associates, Inc.
Abstract A wide-flange girder connection to a concrete-filled steel tube column was recently designed for two low-rise building structures. Preliminary cost estimates indicated that this system was more economical than the more traditional structural steel column counterpart. A methodology to compute strength, stiffness and joint equilibrium is presented. Finally, some differences and limitations of the current U.S. design specifications are discussed.
1. Introduction Concrete-filled steel tube (CFT) columns combine the advantages of a ductile system, generally associated with steel structures, with the stiffness of concrete components. The advantages of the concrete-filled steel tube column over other composite systems includes: the steel tube provides formwork for the concrete, the concrete prolongs local buckling of the steel tube wall, the tube prohibits excessive concrete spalling, and composite columns add significant stiffness to a frame compared to more traditional steel frame construction. While many advantages exist, the use of CFTs in building construction has been limited due to, in part, a lack of construction experience and to the complexity of connection detailing. Consequently, a joint was needed that could utilize the favorable strength and stiffness characteristics of the concrete-filled tube column and yet be constructible. This paper summarizes a steel girder to concrete-filled steel tube (CFT) connection detail that has been designed for several recent projects constructed in Vancouver, WA., U.S.A. Similar connections have exhibited significant inelastic cyclic behavior and the detail discussed in this paper has shown to be fairly economical and constructible. The connection has been designed to accommodate the needed tolerances resulting from the
1270
rolling process, fabrication and construction. Circular CFTs were used because of their favorable ductility characteristics relative to the square tube, and were more accommodating when the structural frames were not oriented along orthogonal axes. The design of this connection is discussed along with the relevant requirements from the applicable U.S. design codes. A design methodology is presented, which consists of the flexural strength, stiffness and equilibrium at the joint. Results suggest that the moment depended on the assumptions used to determine strength. However, stiffness controls the design of many structural systems using moment-resisting connections. Flexural stiffness was shown to be highly variable depending on the method of computation. Finally, a reasonable evaluation of joint equilibrium was needed to ensure proper inelastic behavior of the structural system. These issues were critical in obtaining a safe and economical CFT joint design.
2. Basis of Connection Figure 1 shows the results from two of the six circular CFT connections tested by Schneider, et. al. (1998). Only circular tubes were studied since this connection tends to be more difficult compared to the square tube counterpart. The Type I connection was a connection that was attached to the skin of the steel tube only. This connection was favored by many of the practitioners on the advisory panel for this research project since it appeared to be the easiest to construct. Effectively, the flanges and the web were welded to the skin of the tube, and the through thickness shear of the tube wall controlled the distribution of flange force, or the flared geometry of the flange plate, to the tube wall. The Type II connection continued the girder section through the concretefilled steel tube. An opening was cut in the steel tube to allow the girder to pass through the core. Each connection tested consisted of a 356 mm diameter pipe with a 6.4 mm wall thickness, and a W14x38 for the girder. The yield strength of the pipe and the girder was 320 MPa, with an approximate concrete strength of 35 MPa. In all cases in this test program, assembly of the connection was to be done in the fabrication shop. This was primarily to control the quality of all welded joints. A stubout of the connection would be attached to the tube column and shipped to the construction site. The field splice would be made to the end of the connection stub-out of the connection. As the construction of the structural system progressed, the tube would be filled with concrete. Clearly, a connection like Type I provides the least amount of interference with the placement of the concrete infill. However, a connection like Type II may introduce significant difficulty in getting good consolidation of the concrete in the tube for lifts over several floors. As demonstrated by the normalized moment-rotation behavior shown in Fig. 1, the connection that continued through the CFT exhibited far superior behavior relative to the exterior-only Type I connection. For the Type I connection, the steel tube experienced high local distortions in the connected region. Fracture initiated in the connection stub at approximately 1.25% total rotation, and propagated into the tube wall by 2.75% rotation.
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This tearing propagate from the tips of the flange toward the web. Only one flange fractured, resulting in an unsymmetric M-θ behavior and a pinching of the hysteretic curves. Results of connection Type II exhibited quite stable inelastic behavior. Local flange buckling was observed at approximately 2.75% total rotation, and the web buckling was observed at about 3.0% total rotation. Deterioration of the inelastic characteristics were observed after the onset of local web buckling. Failure of the connection was caused by fracture of the beam flange in the connection stub region. This flange tearing eventually propagated into the web. Although the flexural strength Top & bottom Ty p.
Top & bottom. Each side.
Each side Ty p.
Each side Ty p.
Plate to match flange & web thickness
Section to match girder
Type II: Continuous Girder Connection
1.0 0.5 0.0 -0.5 -1.0 -1.5
Normalized Moment M / Mpp)) Normalized Moment( (M/M
1.5
Type I: Simple Welded Connection
-6.0
-3.0
0.0
3.0
6.0 -6.0
Connection Rotation ( % )
-3.0
0.0
3.0
Connection Rotation ( % )
Figure 1. Moment-Rotation Behavior of Tested CFT Connections.
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6.0
decreased approximately 30% from peak value, the hysteretic behavior remained stable even at large rotations. No crushing of the concrete was observed, and there was no apparent signs of local distress on the tube wall. These results clearly indicate that connections used in moment-resisting steel frame using CFT columns should utilize the continuous connection-type if the system is subjected to large seismic demands.
3. Connection Design A schematic of the connection recently designed for two moment-resisting systems using CFT columns is shown in Fig. 2. Both buildings were two stories: The first floor used a composite concrete slab on a steel girder framing system and the roof used a corrugated metal deck with open web joists. Although one building had an orthogonal layout for the lateral-load resisting frames, the second building had a highly irregular layout. Thus, connection design to a square tube would have been impractical in at least the second case. Circular CFTs were used for both buildings in lieu of the more traditional steel wide-flange columns because the preliminary cost estimates were that CFTs could be as much as 20% more economical. The basic premise of the connection in Fig. 2 was similar to the continuous girder test specimen, however, it was modified to accommodate construction tolerances. Primarily, the steel tube was slotted so that the steel girder could be placed in from above. The convenience of this was that girders can span over many of the CFT columns minimizing the number of field connections for the girder. The field splice for the girder can be located away from the column-girder joint, eliminating the critical flange welds that would otherwise be needed for moment-resisting steel frame connections. Further, the girder splice can be a bolted, end plate connection thereby minimizing the number of complete-joint penetration field welds.
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Slot Tube to Width of the Girder Flange. Ea. Side
Bent Closure Pl Typ.
Flange Holes for the Consolidation of the Concrete Infill
Figure 2. Continuous Girder CFT Joint. The slot in the tube provided other advantages in frame construction. Allowing for the tolerances needed for U.S. construction practices may preclude the use of some connections that have otherwise exhibited favorable experimental behavior. This may be due to a complex field assembly, or a detail that requires a tighter tolerance than may otherwise be possible. With the slotted steel tube connection the girders can be connected without significantly racking the frame. Further, the girder can be slightly out of alignment in plan, or in elevation, without introducing significant internal misalignment stresses in the girder or the columns. Finally, leveling of the girders can be made by leveling nuts applied to the girder at the bottom of the slot. This could be done by slightly over-cutting the base of the slot in the shop to ensure ease of construction. Experience during the construction of the first low-rise building in Vancouver, WA. suggested that the steel tube for the next level should be erected before the girder connection is fully welded. The connection of the upper steel tube must have a complete-joint penetration groove weld with a backing bar attached to the inside of the joint. Once the frame girders and columns were in place the joint of each CFT connection was completed. The vertical welds along the girder depth are critical. A bent plate welded to the girder web, spanning full depth between the girder flanges, must be used as a closure plate. This was either welded to the steel tube wall directly, or a
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filler plate was welded between the steel tube and the closure plate. Closure plates may or may not be needed between the bottom girder flange and the tube, but a closure will be needed above the top flange. Finally, the concrete can be placed in the steel tube. As shown in the detail, holes were drilled in the girder flange to allow good consolidation of the concrete around the girder flanges in the core of the steel tube. One drawback of this particular connection was that each column lift extended over only one floor. Thus, a complete-joint penetration weld was made for each column at each level. This was adequate for the two story buildings, but the slotted tube column might be impractical for buildings with several floors. In these cases, it was considered that a tube column could be used that could extend over several floors per lift. At the intermediate floors, a slot could be cut in the tube to accept a girder stub-out assembled in the shop. The girder could be only partially assembled so that girders and the frame could be aligned without introducing significant internal stresses. However, frame geometry would dictate whether a single- or multi-story lift would be more economical, since many more girder connections may be required in the multi-story lift compared to the number of column connections required in the single-story lift. Regardless, it was considered that the same basic connection could be used for either condition.
4. Design Issues The design of connections like this in the U.S. can be controlled by either the concrete code ACI-318 (1999) or by the steel code AISC (1994). Each specification results in slightly different design requirements. On some issues, like flexural stiffness, the code differences can make a significant impact on the design and analysis of the structural system. The following is the methodology used for design of this connection, and a discussion of some of the limitations from the available research. 4.1. Flexural Strength Since the current U.S. code is strength-based, the flexural strength of the structural elements was a primary consideration. The strength prediction of a wide-flange girder has evolved over many years and is therefore fairly well prescribed. However, the two available specifications differ slightly in the assumptions used to compute the flexuralstrength, axial-load interaction surface of the CFT column. In general, the concrete code (ACI) applied the same basic assumptions used for reinforced concrete sections to the composite element. The interaction surface was obtained by varying the curvature through the cross-section from full compression to full tension. Compatibility was enforced by the plane section assumption, and the compressive strain was maintained at 0.003 mm/mm. The compressive strength of the concrete was obtained by the Whitney rectangular stress block. Tension on the concrete section was ignored. The strength provided by the steel tube depended on the strain through the cross-section. Tube stress was computed as the strain times the elastic modulus, but was limited by the yield stress. Axial capacity of the cross-section for the
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imposed curvature was computed by the summation of stresses through the crosssection. The flexural strength of the cross-section was computed by the summation of the first moment of stresses. The major difference between the concrete code and the steel code was the assumption of curvature at full strength. Since the steel code (AISC/LRFD [1994]) is strength based, the axial-load, moment interaction surface was obtained by assuming a fully plastic cross-section. This was equivalent to an infinite curvature about the plastic neutral axis. A schematic of a stress distribution acceptable to the AISC/LRFD is shown in Fig. 3. This indicates that the tube wall on either side of the plastic neutral axis was at yield. The portion of the concrete in compression was then determined by the rectangular stress block assumptions. The strength of the CFT column was determined by both methods. In general the strength computed using the ACI assumptions produced less flexural capacity than the strength predicted by the ultimate strength calculations. As the interaction surface approached full tension or compression, the two methods converged on the same solution. The strength must be scaled by the appropriate resistance factors to produce an interaction surface to be used in design. A comparison in the strength from the two methods is shown in Fig. 4 (compression is shown as positive). These values were for 406 mm diameter steel tube pipes with 6.35 mm wall thickness, which was typical for the building designs. AISC described each quadrant of the strength interaction surface using a bilinear relation. The transition occurred at 30% of the axial capacity of the particular quadrant of the failure surface. To demonstrate the approximation of the AISC method, the factored strength surface was computed for the location of the plastic neutral axis at every location through the cross-section. As shown by this figure, several regions within
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PNA
=
=
Plastic Neutral Axis
AREA of CONCRETE in COMPRESSION
MOMENT STEEL STRESS
CONCRETE STRESS
Figure 3. Stress Distribution in CFT Column at Ultimate Strength. the interaction surface resulted in large differences between the two specifications. Also shown in Fig. 4 is the axial load moment demand for the CFT columns for one of the building designs. Since the building was only two stories, the axial load in the columns was relatively small. In general, the capacity of the CFT columns far exceeded the demand. General philosophy in the design of the CFT column is that the steel tube provides the longitudinal reinforcement and the confinement of the concrete core. However, the steel tube may be unable to resist the compression and the confinement of the concrete core simultaneously. Confinement of the core induces hoop, or tensile, stresses in the tube,
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while trying to resist compression due to flexure. Thus, it is possible that the tube resists primarily the confinement forces. Figure 4 illustrates the effect of ignoring the 6,000
Ultimate Strength
Axial Capacity ( kN )
4,000
2,000
0.0
AISC/LRFD
Ultimate Strength No Compression in Steel Tube
ACI 100
200
300
400
CFT Column Demand
500
600
-2,000
-4,000
Flexural Capacity ( kN-m )
Figure 4. Axial Load – Moment Interaction Used for CFT Design. compression in the steel tube. As shown, this impacts the compression and flexural capacities of the CFT column, but not the tensile strength. The curve shows the impact of losing the compression capacity of the steel, while the concrete strength remained the same. It is likely that the concrete strength might increase due to the confinement. Thus, some additional axial load and moment might be achieved by an increase in concrete strength due to the added confinement. 4.2. Joint Equilibrium To achieve an adequate seismic design, the strength of the joint must be considered. For the frames designed in Vancouver, WA. the hinging girder type of structural system was used. While it was easy to proportion the sizes of the CFT column and girder at the joint to provide the proper strength ratio, the joint must be able to sustain this load. Equilibrium of the joint is shown in Fig. 5. The moment in the joint must balance the moment induced by the girders, which in turn must be transferred to the CFT column. Two components were needed to resist the joint moment: The bearing strength between the flange of the steel girder and the concrete core, and the tension in the steel tube. The contact area between the steel girder and the compressive strength of the concrete core determined bearing strength. It was assumed
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that girder rotation occurred about the centroid of the CFT column. Locally, the strength of the concrete was considered to be approximately 20% higher than the cylinder strength because of the confinement in the core. Further, depending on the diameter of the concrete-filled steel tube and the wide-flange girder width, the upper MCT T
MBL
MBR T=Tension in Steel Tube
MCB
Figure 5. Equilibrium at the Joint. flange could also be considered for bearing strength. Finally, the remaining moment must be transferred to the steel tube. This will dictate the amount of shear transfer needed between the closure plates and the steel tube wall. This equilibrium was needed to induce the moment distribution in the cross-section as shown in Fig. 3. 4.3. Flexural Stiffness While the ability to predict the flexural strength of the CFT column is critical, the size of these elements was still controlled by flexural stiffness. Although both building systems were only two stories, they were both controlled by drift. It was found that the flexural stiffness of the CFT columns were responsible for 30% to 40% of the drift. Flexural stiffness of the girder accounted for almost the entire remaining portion of drift. Flexural stiffness varied significantly between the concrete and the steel codes. Flexural stiffness computed by ACI was EICFT = 1.223 EIS, where IS is the moment of inertia of the steel tube only. The stiffness predicted by the AISC/LRFD was EICFT = 1.903 EIS, which results in a 56% difference. For comparison, the flexural stiffness computed using a transformed section analysis was EICFT = 1.933 EIS. Further, flexural stiffness
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was 1.696 EIS when 70% of the core stiffness was used due to the cracked section modulus of the concrete. Because of the differences between the two code values, the transformed section method assuming a cracked moment of inertia of the concrete core seemed to be the most reasonable approximation.
5. Concluding Remarks This paper discussed an economical connection for a steel girder to a concrete-filled steel tube (CFT) column that has been designed for two recent building projects near Vancouver, WA. The anticipated behavior during a seismic event, and some critical issues in the design of the connection were also presented. Some comments regarding this joint behavior and design are worth noting: 1.
A girder connection that continues through the core of the CFT column will clearly have the potential to sustain a large seismic event. The continuous connection detail shown in this paper has proven to be reasonably economical and constructible relative to the wide-flange column frame.
2.
The flexural capacity computed by the ultimate strength method, as allowed by the AISC steel specification, resulted in more capacity than provided by the ACI concrete specification. This was a combination of the assumptions used in the analysis and the resistance factors imposed on the design.
3.
The computed flexural stiffness was shown to vary as much as 60% for the column sizes investigated for these building designs. A stiffness consistent with transformed properties of composite materials, and utilizing the limits of cracked moment of inertia were found to provide a reasonable value.
4.
Research is needed to identify true behavior of the CFT column regarding the strain demand on the compression side of the column in flexure, the compression capacity of the concrete core, the distribution of stresses and equilibrium of the joint and the flexural stiffness. Verification on the accuracy of the axial load, moment interaction surface is also needed. While reasonable assumptions can be made, these assumptions should be verified with test data.
6. References American Concrete Institute. (1999). ACI318-99. Building Code Requirements for Structural Concrete and Commentary. 1st Printing. ACI. Farmington Hills, MI. American Institute of Steel Construction. (1994). Manual of Steel Construction. Load & Resistance Factor. 2nd Edition. AISC. Chicago, IL. Schneider, S. P. and Y. M. Alostaz. (1998). “Experimental Behavior of Connections to Concrete-Filled Steel Tubes.” Journal of Constructional Steel Research, pp. 321-352.
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FRICTION SLIPPING BEHAVIOR BETWEEN CONCRETE AND STEEL -AIMING THE DEVELOPMENT OF BOLTED FRICTIONSLIPPING JOINT Tomokazu Yoshioka, Masamichi Ohkubo Kyushu Institute of Design, Japan
Abstract The authors are developing the connecting seismic shear walls to the surrounding structural frame through the bolted friction-slipping joints that function as energy dissipation dampers during an earthquake. This friction-slipping joint is composed of a steel plate, concrete plate, and the bolts to joint both together. This paper presents the outline of the dynamic loading tests to investigate the friction coefficient of the joint during slipping, changing displacement amplitude, loading velocity, concrete compression strength, thickness of concrete plate and the initial tension given into the bolts. And this paper also presents a simplified equation to predict the friction-slipping behavior of the joint.
1. Introduction In order to use a building continuously after a great earthquake, it is desirable to keep the earthquake response of the building into the elastic range. The concept called damage control design has been proposed as one of the seismic design methodology to archive such the strategy. In the building designed through the concept, seismic dampers as adjuncts are often applied to the main structure to dissipate earthquake vibration energy, and it is expected that the earthquake response displacement of the building is consequently minimized. The authors are developing the seismic shear wall installed into the structural frame through the bolted friction-slipping joints that function as energy dissipation dampers during an earthquake. At the joint, the surfaces between the steel plate attached to the structural frame and the reinforced concrete walls are rigidity tightened by steel bolts in general. However, slipping with a constant friction is allowed between the jointing surfaces, if the joint is subjected to the force that exceeds the friction force provided by the bolts. The concept of the shear wall system is illustrated in Fig.1. This joint system can dissipate the induced earthquake energy during slipping. In addition, the lateral
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FRICTIO N -SLIPPIN G JO IN TS
BEAM
C LEAR A N C E C LEA R AN CE LATER AL FO RCE
REIN FO RCED CO N CRETE W A LLS SLIP FRIC TION JO IN TS N OT ALLO W ED SLIPPIN G H Y STERESIS LO O P
B EA M CO LU M N
COLUM N
Figure 1: Concept of Shear Wall System force transmitted to the shear wall through the joint can be controlled by the setting adequately friction force due to the tightened bolt tension, so that the installed reinforced concrete wall can be prevented from earthquake damage as well. In this paper, the dynamic loading tests focussed on the friction-slipping joint were conducted to get the fundamental information regarding the slipping characteristics between the steel plate and concrete surface tightened by the bolts. And a simplified equation to predict the friction coefficient during slipping is presented on the basis of the statistical analysis for the test results.
2. Specimens Fig.2 shows the overall view of the assembled joint model specimen given in this test. The same two concrete blocks, which correspond a part of the concrete wall at the friction-slipping joint shown in Fig.1, sandwich a steel plate and the two concrete blocks and a steel plate are tightened together through a 19mm diameter high-tension steel bolt. In the loading test, the concrete blocks were rigidly fixed to the reaction steel frame and the sandwiched steel plate was loaded with a servo-actuator. To make the slipping displacement possible, the 26mm wide and 100mm long slot was provided in the steel plate as shown in Fig.3. Two slots are provided in the steel plate to use the same plate twice turning reversely and both side slots are applied to the one loading test. A double surfaces’ friction that consisted of two concrete plates and one steel plate was adopted in this test. However, another double surfaces’ friction technique such as the combination of two steel plates and one concrete plate can be actually considered.
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600
19mm DIA.BOLT FRICTION-SLIPPING SURFACES
26
100
250
100
REACTION
26
REACTION BLOCKS
REACTIONS
16
STEEL PLATE LOADING REACTION CONCRETE PLATES
Figure 3: Steel Plate
REACTION BLOCKS
THICKNESS=200/100
SLOT
SLIPPING DIRECTION
LOADING STEEL PLATE
CONCRETE PLATE
Figure 2: Assembled Joint Model
200
FRICTION-SLIPPING SURFACE
180
Figure 4: Concrete Block
Table 1: Summary of Testing Condition Series
Bolt Thickness fc Number of Tension (*1) (*2) Specimen (kN) (mm) (MPa)
Maximum Cyclic Velocity Amplitude Patterns (cm/s) (mm)
CS1 56.8 40 4 CS2 51.6 80 200 CS3 56.8 1 4 120 CS4 35.9 CS5 40 100 57.0 4 CS61 90 1 200 51.6 CS62 60 *1：thickness of concrete block,*2:concrete compression strength
1 3 2 1
The size of the steel plate is 250mm in width, 600mm in length and 16mm in thickness as shown in Fig.3. The steel plate is a mild steel of the Grade 400MPa tensile strength. The mill scale covered on the surface of the steel plate wasn’t eliminated in the tests. The size of the concrete block, which corresponds to the friction surface, is 180mm x 200mm rectangle as shown in Fig.4. The friction surface of the concrete block was provided with the condition after removing plywood. However, the tow corners of the concrete block intersected to the slipping axis were removed with about 10mm width to prevent stumbling. In the experiments, six test series were planned to compare the differences of the loading amplitude (40mm and 80mm), the loading velocity (4cm/sec and 1cm/sec), the concrete compression strength (50MPa and 30MPa), the concrete thickness
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Table 2: Detail of Cyclic Patterns Cyclic Pattern No.1 Cyclic Pattern No.2 Cyclic Pattern No.2
Amplitude (mm) Frequency (Hz) Num. of Cycs. Amplitude (mm) Frequency (Hz) Num. of Cycs. Amplitude (mm) Frequency (Hz) Num. of Cycs.
10 2 1 10 0.5 1 10 2 1
20 1 1 20 0.25 1 20 1 1
→ → → → → → 40 0.5 1
40 0.5 10 40 0.125 10 80 0.25 5
→ → → → → → 40 0.5 1
20 1 1 20 0.25 1 20 1 1
10 2 1 10 0.5 1 10 2 1
(200mm and 100mm) and the initial tension given into the bolt (60kN, 90kN and 120kN). Table 1 summarizes the entire scheme. For the CS1 to CS5 series four specimens were prepared under the same testing condition, while for the CS61 and CS62 only one specimen was prepared
3. Testing setup The load that enforced slipping at the joint surfaces was applied to the sandwiched steel plate by a 200kN servo actuator while the concrete blocks were fixed to the steel reaction frame as shown in Fig.2. Three different cyclic patterns were planed to make the time history of the enforced displacement. Table 2 shows the detail of the cyclic patterns that are arranged by the amplitude, the frequency and the number of cycles with a sinusoidal wave. The friction force, the relative slipping displacement between the steel plate and the concrete blocks and the bolt tension were measured. The intervals of the data sampling were set to 6 milliseconds, which was the maximum speed of the measuring equipment, for CS1, CS2, CS4 and CS6, 7 milliseconds for CS3, and 22 milliseconds for CS2.
4. Test Results Fig.5 shows the relations between the friction coefficient and the slipping displacement obtained by the experiments of CS1-1 and CS3-1. Here, the friction coefficient is that the load applied to the steel plate was divided by the tension force, which was introduced into the steel bolt before loading, considering the number of friction surfaces. Fig.6 shows the relations between the friction coefficient and the total slipping displacement in the specimens CS1-1 and CS3-1. Here, the total slipping displacement is the summation of slipping displacement experienced by the time from the beginning of the test. Both the specimens, which are the first one of specimens in the standard CS1 series and the CS3 series with the lower velocity than the standard series respectively, represent the common friction slipping characteristics to all the tests. In Fig.6, one characteristic behavior is observed regarding the relations between
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FRICTION COEFFICIENT
1.0
CS1-1:V=4cm/sec
CS3-1:V=1cm/sec
0.5
0.0
-0.5
-1.0 -25 -20 -15 -10 -5 0 5 10 15 20 SLIPPING DISPLACEMENT (mm)
25
-25 -20 -15 -10 -5 0 5 10 15 20 SLIPPING DISPLACEMENT (mm)
25
Figure 5: Friction Coefficient and Slipping Displacement Relations FRICTION COEFFICIENT
1.0
CS3-1:V=1cm/sec
CS1-1:V=4cm/sec
0.8 0.6 0.4 0.2 0.0 0
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
00
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
Figure 6: Friction Coefficient and Total Slipping Displacement Relations the friction coefficient and the total slipping displacement. It is that if an envelope curve is drawn on the relations between the friction coefficient and the total slipping displacement, the curve can be represent by two lines which consist of the first characteristic that the peak value of friction coefficients increases gradually as the total slipping displacement increases and the second characteristic that the peak value of the friction coefficients is almost stable after the total slip displacement reached a certain amount. This first characteristic is observed in all the tests although they were under the different testing conditions. However, the second one was not observed in only the CS5 series in which the thin of concrete blocks were used. In the cycle, while the stable friction slipping is kept, the relation between the friction coefficient and the slipping displacement approximately shows a rigid-plastic pattern as shown in Fig.5.
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5. Influence of Various Testing Conditions to the Friction Coefficients In order to actually apply the concept of bolted friction-slipping joints to the structural design of a building, the variation and the stability regarding friction coefficient FRICTION COEFFICIENT
1.0
(a) MAXIMUM AMPLITUDE
(b)T.S.D.=100mm
(c)T.S.D.=800mm
0.8 0.6 0.4
CS1(40mm) CS2(80mm)
0.2
CS1
CS2
CS1
CS2
0.0 0
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
00
20 40 60 20 40 60 80 20 AMPLITUDE (mm) AMPLITUDE (mm)
Figure 7: Influence of Slipping Amplitude (a)CS1
(b)CS2
SLIPPING WEAR SCARS
Figure 8: Conditions of Slipping Wear Scar during the slipping should be investigated under the various different conditions. However, it is difficult to discuss the friction coefficient by adopting the concept of tribology, because the friction-wear mechanism that occurred on the joint surfaces between steel and concrete are extremely complex. Therefore, several series of experiments under the various conditions were carried out, and the influences of the testing conditions to the friction-slipping behavior are investigated here. Firstly, we discuss the influence of the slipping amplitude comparing the result of the CS1 and CS2 series whose maximum amplitudes in the cyclic loading were 40 mm and 80 mm, respectively. Fig.7 shows the friction coefficients obtained from both CS1 and CS2. Here, the values of the friction coefficient plotted in these figures are represented at the time when the slipping displacement goes across the zero axis in each half cycle. As seen in Fig.7 (a), the friction coefficients in the CS1 series are generally higher than those in the CS2 series. According to Fig.7 (b), the difference between both the series is approximately 18 percents regarding the average friction coefficient in the range where the friction coefficient increases as the total slipping displacement increases. The
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coefficient of variation is approximately the same 10 percents in both the series. According to Fig.7(c), the difference of the friction coefficient between both the series is approximately 23 percents in the range where the friction-slipping behavior has stabilized, and it is little larger than those in Fig.7 (b). Fig. 8 shows the conditions FRICTION COEFFICIENT
1.0
(a) SLIPPING VELOCITY
(b) CONCRETE STRENGTH
0.8 0.6 0.4
CS1(56.8MPa) CS4(35.9MPa)
CS1(4cm/sec) CS3(1cm/sec)
0.2 0.0 0
FRICTION COEFFICIENT
1.0
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
00
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
(d) BOLT TENSION
(c) CONCRETE THICKNESS
0.8 0.6 0.4
CS1(N=120kN) CS61(N=90kN) CS62(N=60kN)
CS1(200mm) CS5(100mm)
0.2 0.0 0
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
00
200 400 600 800 1000 TOTAL SLIPPING DISPLACEMENT (mm)
Figure 9: Influence of Several Testing Conditions of the slipping wear scars observed on the surfaces of the steel plates after the testing. The slipping wear scar of the CS1 widely distributed along the slot, while the scars in the CS2 concentrated only in the diagonal corner areas on the plate. This difference of the scar distribution between both the series may cause the difference of friction coefficient. However, the reason why the difference of displacement amplitude causes the difference of the scars distribution is not cleared up in the tests. Secondary, in order to investigate the influence of other testing conditions, the comparisons of the friction coefficients between the CS1 and the other series are shown in Fig. 9(a) through (d). As seen in Fig. 9(a) and (b), the approximately same trends were observed among the three series of CS1, CS3, and CS4, regarding the relations between the friction coefficients and the total slipping displacement. This indicates that the loading velocity and the concrete compression strength little influence to the friction coefficient. In the comparison of the CS1 and CS5 series which identify except for the concrete block thickness, however, it was observed that the friction coefficients in the CS5 using thinner concrete blocks slightly decrease in the slipping after about 400mm of
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the total slipping displacement as shown in Fig.9(c). The decreasing of the friction coefficient wasn’t caused by the applicable decreasing of the bolt tension. Finally, the friction coefficients of the CS1 series, CS61 and CS62 were compared to investigate the influence of the initial bolt tension. As seen in Fig.9 (d), the friction coefficients in the range of the stable slipping of the CS61 and CS62 whose initial bolt tensions were 60kN and 90kN were smaller than those of the CS1 series with the higher 120kN bolt tension. The behaviors of the friction coefficient of the CS61 and CS62 resembled those of the CS2 shown in Fig.7, and the slipping wear scar distributions on the steel surface observed in the CS61 and CS62 also resembled those of the CS2 series shown in Fig.8. Therefore, smaller friction coefficients obtained in the CS61 and CS62 may be caused by the narrow contact area on the friction surfaces as mentioned before. However, the reason why the difference of the initial bolt tension caused the smaller contact area on the friction surfaces is not cleared up in the tests.
6. Equations to Predict the Friction Coefficient The variation of the friction coefficients during slipping was at maximum some 20 percents, according to the test results based on the various testing conditions. This suggests that if the differences of the slipping amplitude, the loading velocity, the concrete compression strength, the concrete plate thickness and the initial bolt tension are within the scope of the examined conditions, the friction coefficient during slipping seems to be little influenced by those conditions. In this paper, assumed that the variation and the decreasing behavior of the friction coefficient are so small that they can be ignored, the equations to predict the relations between the friction coefficient and the slipping displacement is obtained on the basis of the all test results. Equation (1) and (2) represent two characteristics that were observed in the range of the friction coefficient increasing and the range of the stable friction slipping. 0mm <= TSD <= 180 mm:
FC = 0.69 -1.25x10-5(TSD-180)2
180mm < TSD <=1000mm: FC = 0.69
(1) (2)
where FC = predicted friction coefficient TSD = total slipping displacement Equation (1) was derived by a regression analysis, which adopted a secondary polynomial model, by using all the friction coefficients measured at each end of a half cycle until 200mm of the total slipping displacement. We set the maximum friction coefficient during the stable slipping that was defined in equation (2). Table 3 shows the average friction coefficient and the standard deviation at each total
Table 3: Average and Standard Deviation of Friction Coefficient Start
1Cyc. 2Cyc. 3Cyc. 4Cyc. 5Cyc. 6Cyc. 7Cyc. 8Cyc. 9Cyc. 10Cyc. 11Cyc. 12Cyc. 13Cyc. 14Cyc.
T.S.D.
0 23 67 153 239 325 411 497 583 668 753 838 925 967 988 Ave. 0.36 0.38 0.54 0.65 0.68 0.69 0.70 0.70 0.70 0.69 0.69 0.69 0.69 0.69 0.68 S.D. 0.035 0.084 0.069 0.072 0.085 0.076 0.077 0.078 0.077 0.083 0.075 0.080 0.076 0.082 0.084
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Expriment
0.5 0.0
-0.5
FRICTION COEFFICIENT
FRICTION COEFFICIENT
1.0
1.0
Assumption
0.5 0.0
-0.5
-1.0
-1.0
-25 -20 -15 -10 -5 0 5 10 15 20 25 SLIPPING DISPLACEMENT (mm)
-25 -20 -15 -10 -5 0 5 10 15 20 25 SLIPPING DISPLACEMENT (mm)
Figure 10: Comparison of Hysteresis Loops 1.25
140
1.25
140
(a)
100 80 60 40 20
CS1
CS2
CS3
CS4
CS5
CS6
1.00
(b)
120
0.80
TEST RESULT Ar(mm)
120 TEST RESULT Ar(mm)
1.00
0.80
100 80 60 40 20
0
CS1
CS2
CS3
CS4
CS5
CS6
0 0
20
40
60
80
100 120 140
0
PREDICTED VALUE Ap(mm)
20
40
60
80
100 120 140
PREDICTED VALUE Ap(mm)
MAX. FRICTION COEFFICIENT
Figure 11: Comparison of Hysteresis Loop Areas 1.0
Upper Limit (=average plus 2 x S.D.)
0.8
0.6 CS1 CS3 CS5
0.4
Average of M.F.C. Obtained from Results in CS1, 3,4 and 5
CS2 CS4 CS6
0.2 0
200 400 600 800 TOTAL SLIPPING DISPLACEMENT (mm)
1000
Figure 12: Variation of Maximum Friction Coefficient
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slipping displacement that were based on the data observed at the first slipping and the end of slipping in each cycle in the total of twenty-two specimens. The average friction coefficients obtained after 4th cycle are equal to the value of equation (2) approximately. Fig. 10 shows the comparison between the hysteresis loops of the relations between the friction coefficient and slipping displacement obtained from the experiment of CS1-3 and those predicted by Equation (1) and (2). Both the hysteresis loops approximately match. Fig.11 shows the comparison of the loop’s area obtained from all the experiments and predicted by the equations, which area corresponds to the energy dissipation due to each cyclic friction slipping. Making the hysteresis loops by using Equation (1) and (2), the behavior of rigid-plastic pattern for the relations between friction coefficient and slipping displacement was assumed. As seen in Fig.11 (a), the proposed equations estimate approximately good hysteresis loop areas. The average and standard deviation regarding the ratio of the experiments to the predicted loops were 0.99 and 0.12, respectively. In addition, the comparison between the loop areas of the experiment and the equations subtracted 2 x S.D. is shown in Fig.11 (b). Here, the value of standard deviation S.D. was assumed to be equal to 0.085 which corresponds to the maximum standard deviation shown in Table 3. As seen in Fig.11 (b), the proposed equations that subtracted 2 x S.D. approximately estimated the lower limit for the test results. Finally, we discuss the maximum friction coefficient of the bolted friction-slipping joint. Fig.12 shows the maximum friction coefficients in every cycle obtained from all the test results. The average and the standard deviation of the maximum friction coefficients throughout the overall slipping, which are the sixteen values obtained from the results of CS1, CS3, CS4 and CS5 series, are 0.83 and 0.026, respectively. The maximum friction coefficient plus the two times of standard deviation equals to 0.88 and the value which estimates a upper limit of the test results is shown by a chained line in Fig.12.
7. Conclusion We presented the equations that represented the relations between friction-coefficient and slipping displacement for the bolted friction-slipping joint composed by concrete and steel plates. The equations are derived on the basis of the dynamic loading tests and the data analysis that considered the influences of the maximum slipping amplitude, the loading velocity, the concrete compression strength, the thickness of concrete plate and the initial bolt tension and the equations well predicted the friction-slipping behavior.
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AN EXPERIMENTAL STUDY ON THE CONNECTION JOINTS BETWEEN STEEL GIRDER AND REINFORCED CONCRETE COLUMN WITH VARIOUS TYPES OF EMBEDDED LOAD TRANSFERRING PLATES Nobuyoshi Ando, Isao Nishimura, Koichi Kamo Department of Architecture, Musashi Institute of Technology, Japan
Abstract This paper discusses the load bearing mechanism of the connection joins between reinforced concrete columns and steel girders. The discussion is based on the experimental results and data that have been obtained from six pieces of specimens. Because of the complexity of the bearing mechanism in the vicinity of the connection joints, the authors selected one experimental parameter in common for all of the specimens: the steel girder is arranged to penetrate into the joint core. Additional reinforcing steel parts are necessary to be placed inside of the panel zone so that the bending moment of the steel girder should be transferred to the columns by way of the connection joint. These reinforcing parts are the key parameters for this experimental study: 1 Band Plate, 2 Face Bearing Plate, and 3 Steel Web Plate. Attention is paid to the load bearing strength, stiffness, deformation capacity, and ductility factor associated with the panel zone. The experimentally obtained and clarified roles of those plates are stated qualitatively at the end of the paper.
1. Scope of the study There have been proposed various types of connection joints between reinforced concrete column and steel girder [3,4,5,6]. Because of the complex load transferring mechanism in the vicinity of the panel zone, there have been proposed a wide variety of formations for the reinforcing parts surrounding the connection joint. The illustrated in Figure 1 is the typical load bearing mechanism, which necessitates the following three reinforcing items; Band Plate, Face Bearing Plate, and Steel Web Plate. The expected role of Band Plate is enhancing the confine effect of concrete material at the end of column and transferring the reaction shear induced at the connection joint. On the other hand, Face Bearing Plate is supposed to transfer the reaction shear at the end of girder as well as to confine the concrete inside of the panel zone. Steel Web Plate has a rather subordinate contribution to increase the panel zone ductility after shear crack is induced at the panel zone. If the confinement of the panel zone is secured by the arrangement of both Face Bearing Plate and Band Plate, we could expect that the panel zone shear strength be mainly due to the
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concrete material shear strength. What this paper tries to clarify is the minimum requirements for those reinforcing plates which make it possible to transfer the full plastic moments induced at the ends of columns to the connected girders.
2. Specimens Illustrated in Figure 1 are the typical reinforcing formations adopted as the main parameters for the series of specimens. The key issue is the load transferring capacity or the shear strength of the panel zone. We wish to identify the shear strength and the ductility of the panel zone clearly from those of adjacent members. If the concrete column’s reinforcing bars got yielded during the static test loading, the displacement due to the column’s plastic moment rotation would be the main source for the total displacement, which should be avoided. Hence, attention is paid to the relative strength of the concrete columns to the shear strength of the panel zone. Obviously the full plastic moment of the steel girder should be high enough to avoid girder’s plastic deformation. The perspectives of all the specimens are shown in Figure 2. A-series specimens have the identical Band Plate and Face Bearing Plate in common.
A: Band Plates for transferring RC Column’s shear force B: Face Bearing Plates for transferring Steel Girder’s shear force C: Steel Web Plates for transferring Panes Zone’s shear force to the adjacent members
Figure 1 Load bearing mechanism and reinforcing plates embedded in the panel zone Table 1 Material Strength obtained from Steel Tensile Tests and Concrete Cylinder Test Thickness Yielding N/mm2 Tensile N/mm2 [mm] A-series B-series A-series B-series 9 286.1 423.6 Joint S.W.P Cover P. 20 or 28 252.6 259.6 409.5 425.7 F.B.P. 9 286.1 306.7 423.6 439.8 B.P. 6 286.1 306.7 423.6 439.8 Concrete [35.9] [18.6] RC 392.4 392.1 571.1 593.8 Column Bar Hoop 560.5 542 16 250.7 269.2 406.2 441.1 Steel Web 16 250.7 269.2 406.2 441.1 Girder Flange (*) RC Column's results are from compression tests.
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Figure 2 Perspectives of Reinforcing Plates for Specimens
Figure 3 Details of Reinforcing Plates for Specimens
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Figure 4 Cross Section of RC Column
Steel Web Plate is the only parameter for A-series specimens. Concrete Strength of A-series is 1.5 times as much as that of Bseries. (See Table 1.) B-2 has neither Band Plate nor Steel Web Plate, while B-1 has only Band Plate. Comparing A-4 with B-1, we can observe how concrete strength effects on the panel zone shear strength. There are six specimens in all for this experiment. They are all shown in Figure 3, where dimensions and rein-forcing plates are indicated. The tensile tests of the steel materials as well as concrete cylinder compression tests are all given in Table 1.
3. Loading set up and measuring instruments The set up for the loading and measuring instruments is shown in Figure 5. We wish to separate the shear deformation of the connection joint from other displacements such as the plastic deformation of the column or the elastic displacement due to the steel girder. Hence, the shear angle at the panel zone is measured by a set of two linear displacement sensors, which is shown in Figure 6. At the same time, we also detect the absolute rotation of the connection joint so that we can clearly separate the panel zone shear rotation from the concrete column’s bending rotation. The comparison between the overall rotational displacement and the panel zone shear rotation clarifies the fact that where the damage is concentrated.
Steel Girder : H-300x150x16x16 (SS400)
Figure 5 Loading and Measuring Instruments
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Figure 6 Displacement Sensors for Shear Strain and Volumetric Strain
4. Shear strain and volumetric strain of the panel zone The total tilting angle of steel girder, or R of the specimen girder, is plotted versus the actuator’s reaction force P in Figure 8, where the whole experimental results with respect to each specimen is shown for comparison. The comprehensive lateral displacement is divided into three elements, steel girder’s elastic displacement, panel zone shear rotation, and the RC column’s rotation at the face end of the joint. They are all illustrated in Figure 7. The strain tensor E at the panel zone is given by (1) and the strains e is obtained by multiplying the unit vector along with the displacement sensors. (See Equation (2).) εx Strain tensor: E = 1γ 2
1 γ 2 ε y
(1)
Strain in the direction of {u}: e = {u}t E{u}
(2)
Hence, strain e1 and e 2 in Figure 8 are measured, and then evaluated by 1 1 1 − 1 γ γ εx 1 1 2 2 2 e = − 2 (3) 2 1 1 1 2 2 ε y γ ε y 2 2 2 Hence, the volumetric strain ε and the shear strain γ are obtained by substituting (3) into (4) and (5), which are shown in Figure 11 and 10, respectively. (See Figure 8.) ε = ε x + ε y = e1 + e 2 (4) 1 e1 = 2
1 ε x 2 1 γ 2
γ = e1 − e 2 (5) The whole lateral displacement divided by height h is the total tilting rotation R, which is plotted versus lateral load P in Figure 9. The residue rotational angle, or R-γ, is supposed to be the summation of the elastic deformation angle of the steel girder and the moment rotation of the RC column. (See Figure 7 and 12.) 1 − 2 {u2 } = 1 2
1
y {u } = 2 1 1 2
x
Figure 7 Notations for Deformation Angles
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Figure 8 Strain in {u 1 } and {u 2 }directions
25 20 15 10 5 0 -5 -10 -15 -20 -25
P (t )
R (×10−3 rad )
-60 25 20 15 10 5 0 -5 -10 -15 -20 -25
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-20
0
20
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P (t )
60
B-2
R (×10−3 rad )
-60
-40
-20
0
20
40
60
Figure 9 Rotation R (=θ +γ +δ /h, See Figure 7 for notations.) versus Lateral Load P
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25 20 15 10 5 0 -5 -10 -15 -20 -25
P (t )
γ (×10 −3 rad )
-60 25 20 15 10 5 0 -5 -10 -15 -20 -25
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-40
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-60
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Figure 10 Shear Strain γ versus Lateral Load P
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0
P (t )
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A-2
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A-4
ε (× 10 −3 rad )
-40
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B-2
0
Figure 11 Volumetric Strain ε versus Lateral Load P
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P (t )
25 20 P(t ) 15 10 5 0 -5 -10 -15 -20 ε (× 10−3 rad ) -25 -60 -40 -20
B-1
-20
A-2
ε (× 10 −3 rad )
-60
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-60
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-60
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-60 25 20 15 10 5 0 -5 -10 -15 -20 -25
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-40
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Figure 12 Residue Rotation R-γ versus Lateral Load P
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P (t )
-60 25 20 15 10 5 0 -5 -10 -15 -20 -25
A-2
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5. Summary of experiment By comparing specimen B-1 and B2, especially by reviewing Figure 12, it would be safe to say that Band Plate has a vital effect on preventing the concrete column from cracking around the main reinforcing bars, which might be the major damage. Specimen B-2, which has no Band Plate, suffered from this type of failure. The shear angle γ and the volumetric strain ε are successfully separated by the method explained in this paper. Therefore, it was made possible to evaluate the advantage of Steel Web Plate by comparing Figure 10 and 11. Various types of Steel Web Plates are examined. As is shown in Figure11, the stiffness expected from those reinforcing plate’s influences on the volumetric strain. (See A-series specimens.) It is, however, not clear how much Steel Web Plates improve the comprehensive load-deformation performance. Yet, as the shear strength of the panel zone increases because of concrete high compressive strength, it will be necessary to secure the shear strength of the panel zone by means of Steel Web Plate. (See Figure 12 for A-4.) Judging from Figure 12, most of the specimens, except A-4 and B-2, remained elastic as far as RC columns and steel girders are concerned. Hence, we would deduce that the damage is concentrated on the panel zone. The maximum strength of any specimens of Aseries is around 1.5 times as much as that of specimen B-series. Hence, the major factor that influences the panel zone strength is the concrete material’s compressive strength. It is also noted from Figure 10 that the load-displacement curve has a slip character, which is a typical phenomenon associated with concrete failure due to shear damage. Further study will be necessary for qualitatively identifying how the weak-beam design frame will work with the connection joints reinforced by the load transferring plates.
References [1]. ACI Committee 318,”Building code requirements for reinforced concrete,” Report No. ACI 318-89, American Concrete Institute, Detroit, 1989 [2]. ACI-ASCE Committee 352,”Recommendations for design of beam column joints in monolithic reinforced concrete structures,” Journal of ACI, 82(3), pp.266-283, 1985 [3]. Nishiyama, I., Hasegawa, T., Yamanouch, H.,”Strength and deformation capacity of reinforced concrete column to steel beam joint panels,” Kenchiku Kenkyusho, No.71, Sept., Building Research Institute, Ministry of Construction of Japan, 1990 [4]. Sheikh, T.M., Deierlein, G.G., Yura, J.A., Jirsa, J.O.,”Moment connections between steel beams and concrete columns,” PMFSEL Report No.87-4, Univ., of Texas, Austin, 1987 [5]. Wakabayashi, M.,”A historical study of research on composite construction in Japan,” Composite construction in steel and concrete, C.D.Buckner and I. M. Viest, eds., ASCE, New York, N.Y., pp.400-427, 1988 [6]. Nishimura, Y., Minami, K.,”Stress transfer from steel beams to reinforced concrete columns,” Proceedings of Mixed Structures Including New Materials, IABSE, Zurich, Switzerland, pp.389-394, 1990
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LOW-CYCLE FATIGUE BEHAVIOUR OF PULL-PUSH SPECIMENS WITH HEADED STUD SHEAR CONNECTORS Silvano Erlicher, Oreste S. Bursi and Riccardo Zandonini Department of Mechanical and Structural Engineering, University of Trento, Italy.
Abstract Two series of pull-push specimens with 16 mm and 22 mm diameter headed stud shear connectors were built and tested as part of a general investigation on seismic design of steel-concrete composite beams with full and partial shear connection. In order to assess the shear connector performances from a seismic and damage standpoint, pull-push specimens have been exposed to series of variable, random and constant reversed slips. Main results are commented upon and evaluated in terms of yielding and maximum shear strength capacity as well as ultimate slip ductility. A comparison between experimental and prediction strengths derived by relevant design code provisions provides an estimate of their accuracy. Finally, a low-cycle fatigue damage model is investigated to establish damage limit domains for headed studs.
1. Introduction The earthquake resistant design of steel-concrete composite structures is still hindered by inadequate design code provisions. As a matter of fact, the part of Eurocode 8 (EC8) dealing with steel-concrete composite systems still appears as an informative Annex owing to lack of data [1]. Hence, extensive experimental and numerical research into the seismic resistance of composite members and structures under simulated-earthquake conditions is under way [2]. On the North-American side, a major step taken in recent years was the development of the provisions for the seismic design of composite structures [3]. With regard to composite beams of special moment frames, these provisions require both proper welding of shear connectors and additional connectors beyond those required in AISC LRFD [4] for dissipative zones. Nonetheless, there are several situations in which the required composite action between the steel beam and the concrete deck is rather low [5] and, thereby, full shear connection is needless. Eurocode 4 (EC4) [6] and AISC specifications [4] permit partial shear connection where the interface slip between the steel beam and the concrete deck cannot be ignored. In these
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conditions, the connector ability to exhibit ductility and dissipate energy depends mainly on its capability to withstand low-cycle fatigue during the seismic event. Thereby, if members embodying composite dissipative zones need to be designed, a better understanding of the cyclic behaviour of shear connection is required. The analysis of the low-cycle fatigue behaviour of shear connectors requires the availability of data for connectors loaded cyclically to failure. The vast majority of available useful data, however, is for connectors loaded monotonically. As far as the experimental analysis of push-type specimens exposed to cyclic loading is concerned, few exceptions are the recent works of Astaneh et al. [7] and Aribert et al. [8]. The study presented in this paper extends the recent research work conducted on 16 mm diameter headed stud shear connectors by Bursi and Gramola [9] to the cyclic behaviour and analysis of 22 mm headed stud shear connectors. Thereby, experimental data relevant to pull-push specimens subjected to monotonic, variable and random reversed displacements are evaluated with regard to their seismic performance in terms of strength and slip ductility. Moreover, a comparison between experimental and predicted strengths based on EC4 [6] and AISC specifications [4] provides some design indications. Finally, an energy-based fatigue model is calibrated on experimental data to establish damage limit domains for headed stud connectors. As a result, low statistical correlation among the experimental data has been found. 2. Experimental investigation The investigation focused on the determination of the seismic performance of headed stud shear connectors. To comply with the connector ductility requirements suggested for buildings in the EC4 specifications [6], connectors with 16 and 22 mm diameter and with an overall length after welding not less than 4 times the shank diameter have been considered. Thereby, eighteen elemental push-type specimens divided into two series Table 1. Nomenclature and test procedures of specimens with 16 mm shear connectors (Series I)
Table 2. Nomenclature and test procedures of specimens with 22 mm shear connectors (Series II)
Specimen
Test protocol
Specimen
Test protocol
NPM-01 NPM-02 NPC-01 NPC-02
Monotonic Monotonic ECCS ECCS
NPC-03 NPC-04
ATC (10 ey+) ECCS type
NPC-05
ATC (40 ey+)
RPM-01 RPM-02 RPC-01 RPC-02 RPC-03 RPC-04 RPC-05 RPC-06 RPC-07 RPC-08 RPC-09
Monotonic Monotonic ECCS ATC (3 ey+) ATC (6 ey+) ATC (9 ey+) ATC type ATC type ATC type Random Random
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were fabricated. The nomenclature that identifies the specimens is reported in Column 1 of Tables 1 and 2, whilst the relevant geometrical characteristics are depicted in Figs. 1 and 2, respectively. Both geometrical and mechanical characteristics of Series I specimens are similar to those of the companion steel-concrete composite beams exposed to cyclic and pseudodynamic loading [10]. In detail, shear studs are placed in two rows with large spacing as illustrated in Figs. 1 and 2, to allow stud shear loads within the concrete slabs to be redistributed. The reinforcement consists of a mesh of φ 12 whilst transverse rebars are designed against slab longitudinal splitting. TRW Nelson studs have a shank diameter of 16 mm and a mean height of 102 mm in Series I whilst Series II comprises Nelson studs with a shank diameter of 22 mm and a mean height of 126 mm. By using a TRW Nelson welding system a mean welded height of 4.5 mm has been obtained. The mechanical properties of concrete and shear studs are listed in Table 3. Specimens of all series were monotonically (push regime) and cyclically (pull-push regime) loaded in a quasi-static fashion, by means of a series of representative slip histories. Due to the random nature of seismic loading, several test protocols comprised between the extremes of constant-amplitude and random-amplitude slip reversals were applied to the specimens: i) the so-called Complete Testing Procedure proposed by the ECCS [11]; ii) the Cumulative Damage Testing Program suggested by the ATC [12]; iii) test procedures characterized by large slip reversals superimposed upon constant amplitude slips; iv) test protocols endowed with slip reversals of random amplitude. The first type of procedure is adopted to acquire data relevant to the maximum shear strength, the ultimate slip ductility, etc. Conversely, the second type of procedure provides the basis for developing fatigue-life relationships. The test program is described in Column 2 of the Tables 1 and 2, respectively. It comprises two classical monotonic tests to develop the backbone force-slip envelope for each specimen response. As a matter of fact, some seismic damage models use strength and deformation quantities derived from monotonic tests to normalize and/or formulate damage expressions. In addition, a slip elastic limit ey+ and the corresponding yield shear strength Py+ were determined as illustrated in Fig. 3. The ECCS test protocol [11], applied to the NPC-01 and RPC-01 specimens and depicted in Fig. 4, is characterized by sets of equi-amplitude slip (1+k)ey+, (k = 0,...,n). This sequence would provide a convenient benchmark against which to compare specimen performances subjected to variable amplitude testing. The ATC test protocol [12] with a set of equi-amplitude constant slips at 10ey+ is applied to the NPC-03 specimen and is illustrated in Fig. 5. This test protocol has been applied to the specimens NPC-05, RPC-02, RPC-03 and RPC-04 with equi-amplitude slip at 40ey+, 3ey+, 6ey+ and 9ey+ , respectively, and provides the basis for developing fatigue-life relationships. Table 3. Material properties of push-type specimens Series
Displacement test procedure
I II
Mon. & cyclic Mon. & cyclic
fcm (Mpa) 32.6 41.9
Concrete fctm Ecm (Mpa) (Mpa) 3.1 3.6
30379 32986
Shear stud fy fu (Mpa) (Mpa) 414 324
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528 457
Figure 1: Geometrical characteristics of Series I specimens
Figure 2: Geometrical characteristics of Series II specimens 40
P
(Py+,ey+) (Pp ,ep )
ECCS, 1986
30
(Pmax+,emax+)
20
+ +
Kh+
10
Ke,r+
e/ey
(Pu+ ,eu+ )
0
-10
(Pe+,ee+)
Envelope Trilinear approx. Bilinear approx.
Ke+
-20 -30 -40
e CYCLE NUMBER
Figure 3: Bi- and trilinear fits of a shear force-slip envelope
Figure 4: ECCS test protocol with constant and variable cycles 10
15
ATC (1992)
8
RANDOM
6
10
4 2
e/ey
e/ey
5 0
0 -2
-5
-4 -10
-6 -8
-15
-10
CYCLE NUMBER
CYCLE NUMBER
Figure 5: ATC test protocol with constant amplitude cycles
Figure 6: Test protocol with random amplitude cycles
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Moreover, additional procedures were conceived to analyze the slip sequence effects on cumulative damage. In detail, the test protocols applied to the RPC-05, RPC-06 and RPC-07 specimens are characterized by large slip reversals reproducing seismic pulses superimposed upon constant amplitude slips. Finally, the last two protocols applied to the specimens RPC-08 and RPC-09 were tracked from pseudo-dynamic tests on composite substructures exposed to the N69W component of the 1952 Taft earthquake [10]. In detail, the procedure applied to the RPC-09 specimen, depicted in Fig. 6, traces over slips from composite substructures with full shear connection. As a matter of fact, an amplified slip peak level greater than 6ey+ brings the specimens of Series II to collapse. This type of sequence provides a benchmark against which to compare random amplitude testing.
3. Main results and code comparison For brevity, hereinafter only the most significant results are commented upon. As far as the Series I is concerned, the monotonic shear force-slip (P – e) response of the NPM-02 specimen is depicted in Fig. 7. The observed inelastic behaviour is governed by stud yielding and concrete cracking. The specimen collapse was governed by local concrete crushing. With regard to the corresponding cyclic behaviour, the response of the NPC-02 specimen is plotted in the same figure. In this test, both stiffness and strength of stud connectors reduce at all stages owing to stud cyclic yielding and fatigue as well as to propagation and coalescence of micro-cracks in concrete. However, failure was governed by local concrete crushing. As far as Series II is concerned, the shear force-slip response relevant both to the RPM01 and the RPC-01 specimen are plotted in Fig. 8. The inelastic behaviour and failure are governed by stud shearing. With regard to the cyclic response, the RPC-01 specimen exhibits both stiffness and strength reduction owing to shear yielding and low-cycle fatigue in the studs. Reversed displacement cycles cause a limited reduction of the shear strength owing to the high concrete strength (see Column 3 of Table 3) whilst the ultimate slip reduction is evident. Due to the relatively high value of concrete strength collapse is governed by low-cycle fatigue of studs. Moreover, the pinching phenomena are evident, and the plateau corresponding to the minimum reloading force can be observed in the Figs. 7 and 8. The amount of the plateau may be related to the friction between concrete slab and steel flange. To extend our knowledge on stud connector seismic performances, they are compared from a cyclic standpoint. Thereby, a conventional elastic limit state characterized by the displacement ey+ and the corresponding force Py+ can be defined on the first part of each skeleton curve as schematically illustrated in Fig. 3. To determine these values the trilinear approximation of each curve, is determined on the basis of best-fitting and of the equivalence of the dissipated energy between the actual non-linear response and the idealized trilinear approximation up to (emax+ , Pmax+). Then, the linear elastic approximation with slope Ke+ and the linear strain-hardening approximation with slope Kh+ define the coordinates (ey+ , Py+). Imposing the condition P+ = Py+ = Pu+ the ultimate slip capacity eu+ can be identified. Thereby, the stud seismic performances can be
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evaluated also by means of the ultimate slip ductility factor eu+/ey+. The Columns 4 and 5 of Table 4 allow the slip reduction exhibited by the specimens subjected to cyclic loading with respect to those exposed to monotonic loading to be quantified. The minimum ductility ratio (eu+/ey+)NPC-02/(eu+/ey+)NPM-02 is about 55.4 per cent if ATC [12] tests at equi-constant amplitude and the ECCS [11] test protocol with unloading are disregarded. From the Columns 6 and 7 of the same table, the maximum shear strength reduction can be assessed. The strength ratio Pmax,NPC-02+/Pmax,NPM-02 reaches 71.8 per cent according to Column 7 of Table 4. At present, design codes do not predict the stud shear strength of connectors under cyclic loading and therefore, it is worthwhile to quantify their accuracy in such conditions. To verify the capabilities of headed stud strength provisions calibrated on monotonic loading, stud strength calculations according to EC4 [6] and AISC [4] are applied to the specimens under exam. These values have been evaluated with and without partial safety factors γ or reduction factors φ, respectively, using measured rather than nominal material properties. Predictions for individual connectors are indicated in Fig. 9 for Series I specimens. In the same figure, the experimental strength values Pmax+ are indicated too. It can be observed that codes predict correctly the failure mode, viz. concrete cracking and crushing. However, owing to reversed slip effects predicted strength values are non-conservative under cyclic loading. More specifically, test and predicted strength values draw the conclusion that the design resistance of headed stud shear connectors in dissipative zones can be obtained from the design resistance provided by EC4 [6] applying a concrete penalty factor equal to 0.75. This value agrees with the reduction factor proposed in the draft of the Eurocode 8 [1] regarding specific rules for steel-concrete composite buildings [13]. Conversely, a reduction factor of 0.55 is suggested for the AISC specifications [4], to achieve the same safety level of EC4 [6]. As far as slip is concerned, the slip capacity of the specimens NPC-01 and NPC-02 subjected to the ECCS test protocol [11] has been examined. Slip values collected in Table 4 bring to the conclusion that the minimum cyclic slip capacity is at least half of the slip capacity, i.e. 6 mm, required from EC4 [6] for ductile connectors. Similar conclusions can be drawn for Series II specimens with regard to strength (see Fig. 10) and cyclic slip capacity.
4. Seismic damage assessment Several of the pull-push specimens subjected to cyclic loading failed owing to low-cycle fatigue, viz. a damage process which results from a limited number of excursion well into the inelastic range. Therefore, a damage assessment of test results was conducted to provide a new quantitative evaluation strategy to the demand versus capacity. More specifically, additional limit states associated with low-cycle fatigue, viz. damage control (Damage index Di << 1) and low-cycle fatigue failure (Di = 1) can be defined, and the damageability of components can be predicted by means of non-linear dynamic computational analyses. In view of a damage model validation, it is deemed to be necessary to define failure, viz. to evaluate the cycle number Nf that entails collapse.
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160
80
120
REACTION FORCE (kN)
REACTION FORCE (kN)
PUSH 60 40 20 0 -20 -40 NPM-02 NPC-02
-60 PULL -80 -16
-12
-8
-4
0
4
8
80 40 0
PUSH PULL
-40 -80 RPM-01 RPC-01
-120
12
-160 -16
16
-12
-8
-4
4
120
12
16
LRFD (φ = 1)
100
LRFD (φ = 0.85)
90
EC4 (γυ = 1)
80 70
EC4 (γυ = 1.25)
60 50
SHEAR STRENGTH (kN)
180
Cyclic Monotonic
110
LRFD (φ = 1)
170 160
LRFD ( φ= 0.85)
150 140
EC4 (γ υ = 1)
130 120
EC4 (γυ = 1.25)
110 100
Cyclic Monotonic
90
40 20
25
30
35
40
45
50
80 20
55
25
30
f 'c , fck (MPa)
35
40
45
50
55
f 'c , fck (MPa)
Figure 9: Connector maximum strengths and code predictions of Series I specimens
Figure 10: Connector maximum strengths and code predictions of Series II specimens
4.0
2.5
NPC-04 Cyclic
NPC-02 NPC-03 2.5
NPC-01
2.0 -1.76
0.5 0.0
RPC-01 RPC-04 RPC-06
RPC-07 1.5
RPC-09
RPM-01
RPC-05
-1.13
NPM-02
1.5 1.0
Cyclic
RPC-03
2.0
NPC-05
E h / Py eu,m
3.0
Monotonic
RPC-02
Monotonic
3.5
Eh / Py eu,m
8
Figure 8: Monotonic shear force vs. controlled slip and hysteresis loops of Series II specimens
Figure 7: Monotonic shear force vs. controlled slip and hysteresis loops of Series I specimens SHEAR STRENGTH (kN)
0
SLIP (mm)
SLIP (mm)
1.0
Di = 1.0 R 2 = 0.57 0.2
0.4
0.6
0.8
RPM-02
Di = 1.0 R 2 = 0.57
NPM-01 1.0
1.2
1.4
0.5 0.0
1.6
0.4
0.6
0.8
1.0
eu / eu,m
eu / eu,m
Figure 11: Damage limit domain of Series I specimens
0.2
Figure 12: Damage limit domain of Series II specimens
1309
1.2
Table 4. Connector shear force-slip response parameters of Series I specimens Specimen NPM-01 NPM-02 NPC-01 NPC-02 NPC-03 NPC-04 NPC-05
Ke (kN/mm) 405.2 431.3 1106.6 803.6 534.2 1106.2 234.4
+
ey (mm) 0.1 0.1 0.03 0.04 0.01 0.03 0.17
+
eu (mm) 9.9 14.7 3.2 3.7 1 3.2 4
+
+
eu /ey
101.6 153.3 125.9 84.9 85.5 109.5 23.8
+
Py (kN) 39.5 41.3 28.3 34.6 6.3 32.6 39.4
+
Pmax (kN) 69.3 68.7 48.7 49.3 47.4 53.9 58.5
Due to the large uncertainty in the failure definition, different criteria have been adopted in this study. However, for the sake of brevity only two of them are discussed hereinafter. Firstly, Calado and Castiglioni [14] propose the use of the ratio ηf / η0 ≤ α with α = 0.5. This quantity is defined as the ratio ηf between the absorbed energy at the last cycle before failure and the energy that might be absorbed in the same cycle if the component would exhibit an elastic-perfectly-plastic behaviour over the same ratio η0, with reference to the first cycle in the inelastic range. Moreover, the criterion of Chai et al. [15] has been adopted. It relies on the design assumption that failure happens when the deteriorated resistance P+ approaches the plastic failure resistance Pu+ = Py+ depicted in Fig. 3. All the above-mentioned criteria have been applied to the specimens under investigation. With regard to the response provided by the ECCS procedure [11], a cycle number Nf of about 50 for Series I and of about 15 for Series II was estimated, respectively. Once failure is defined, it is appropriate to associate the final state of the specimen under cyclic loading to a unique point of an equivalent monotonic response. More specifically, it is deemed to be necessary the definition of a damage indicator, viz. a state variable that enables a one-to-one correspondence from any damaged state caused by cyclic loading to a unique point of a monotonic specimen response. In these conditions, the safety assessment is straightforward being unique the distance from failure. More specifically, a damage index Di is introduced, viz. a normalized damage indicator such that zero corresponds to the virgin state and one to the achievement of collapse, in agreement with the assumed failure criterion. Different choices relevant to damage indicators are available. Anew for brevity, only the damage model proposed by Chai et al. [15] and derived from the widely used model of Park and Ang [16] is discussed. In detail, this model takes into account the energy absorbed by the component during a monotonic loading process, labelled Ehm, and only the surplus of cumulative energy (Eh – Ehm) is considered significant to damage, Eh being the absorbed total energy. In these conditions, the damage index reads
Di =
eM β + eum
*
(E h − E hm )
(1)
Py eum
1310
in which eM defines the maximum slip reached by the component so far; eum is the maximum slip under monotonic loading, i.e. a measure of the maximum deformation capacity and β* an empirical factor evaluated on experimental basis. The application of the damage model expressed by Eq. (1) with Di = 1 to Series I specimens entails the damage limit domain illustrated in Fig. 11 with a slope of –1.76, an intercept equal to 3.34, Py = 323.2 kN, eum = 12.3 mm and a determination (correlation) coefficient R2 = 0.57. The application of the same model to Series II is illustrated in Fig. 12. In detail, a slope of –1.13, an intercept equal to 2.24, Py = 467.8 kN, eum = 10.2 mm and a determination coefficient R2 = 0.57 has been obtained. The slopes of the damage limit domains are rather different both for Series I and II whilst the coefficient R2 is small in both cases. The limited values of R2 show that a damage analysis is not easily applicable to steel-concrete shear connectors. Therefore, the definition of a damage model based on a simple linear combination of energy and of displacement, as in Eq. (1), should be improved. Moreover, the damage model should be strongly related to the evolution both of strength and of stiffness, in order to trace the shear connection response through its whole range.
5. Conclusions Test results relevant to two series of pull-push specimens embodying headed stud shear connectors have been presented in this paper. These results were derived from specimens subjected to series of monotonic, variable and constant equi-amplitude slips. Then, they were re-evaluated and compared in terms of global parameters such as yield shear strength, maximum strength as well as slip ductility factors. Some considerations about pinching phenomena were reported. Test results of Series I and Series II point out that connector slip ductility is enhanced if the cyclic behaviour is governed by concrete cracking and crushing. Moreover, a comparison between experimental and predicted shear strength values provided by relevant code provisions indicates that design specifications calibrated upon monotonic loading overestimate actual stud shear strength. Thereby, strength penalty factors are required whilst an assessment of maximum cyclic slip is possible. Furthermore, the damage index proposed by Chai et al. [15] has been applied to pull-push specimens, showing that its application to the composite specimens could be satisfactory only for design. Further analyses are currently underway to develop an improved damage model, related to suitable stiffness and strength degradation rules over the full range of the shear connector response.
Acknowledgements This research project is sponsored by grants from the Italian Ministry of the University and Scientific and Technological Research (M.U.R.S.T.) for which the authors are grateful. However, opinions expressed in this paper are those of the writers, and do not necessarily reflect the views of the sponsoring agency.
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References 1. 2.
3. 4. 5.
6. 7.
8.
9.
10.
11. 12. 13.
14.
15. 16.
CEN, 'ENV 1998-1-3, Eurocode 8 - Design provisions for earthquake resistance of structures - Part 1-3: Specific rules for various materials and elements', 1998. Plumier, A., 'European research and code developments on seismic design of composite steel concrete structures', Paper 1147 Twelve World Conf. Earth. Eng. A., 2000. American Institute of Steel Construction, 'Seismic provisions for structural steel buildings', AISC, Chicago, IL, 1997. American Institute for Steel Construction, 'Load and Resistance Factor Design Specifications for Structural Steel Building', 1. AISC, Chicago, IL, 1993. Civjan, S.A., Engelhardt, M.D. and Gross, J.L., 'Experimental program and proposed design method for the retrofit of steel moment connections', Paper 257 in Twelve World Conf. on Earthquake Eng., Auckland, 2000. CEN, 'ENV 1994-1-1, Eurocode 4 - Design of composite steel and concrete structures - Part 1-1: General rules and rules for buildings', 1994. Astaneh-Asl, A., McMullin, K.M., Fenves, G.L. and Fukuzava, E., 'Innovative semi-rigid steel frames for control of the seismic response of buildings', Report UCB/EERC-93/03, 1993. Aribert, J.M. and Lachal, A., 'Comportement de connecteurs acier-beton sous chargement cyclique repete en vue du dimensionnement parasismique des connexions', Proc. of 5th National Colloquium AFPS, Cachan, October 1999, 19-21, 479-488. Bursi, O.S. and Gramola, G., 'Behaviour of headed shear connectors under lowcycle high amplitude displacements', Materials and Structures, RILEM, 32, 290297, 1999. Bursi, O. S., and Gramola, G., 'Behaviour of composite substructures with full and partial shear connection under quasi-static cyclic and pseudo-dynamic displacements', Materials and Structures, RILEM, 33, 154-163, 2000. ECCS, 'Recommended testing procedures for assessing the behaviour of structural steel elements under cyclic loads', No. 45, Technical Committee 13, 1986. Applied Technology Council, 'Guidelines for cyclic testing of components of steel structures', 24, 1992. ICONS Topic 4 Extended Group, A., 'Draft of a 6 to Eurocode 8, Part 1.3. Specific rules for steel concrete composite buildings', ICONS Project Report, University of Liege, 1998. Calado, L. and Castiglioni, C.A. , 'Steel beam-to-column connections under low cycle fatigue: experimental and numerical research', 11th WCCE, Acapulco, Paper No. 1227, 1996. Chai, Y. H., Romstad, K. M., and Bird, S. M. ,'Energy-based linear damage model for high-intensity seismic loading', J. Struct. Engrg., ASCE, 121(5), 857-864, 1995. Park, Y. J, and Ang, A. H.-S., 'Mechanistic seismic damage model for reinforced concrete' J. Struct. Engrg., ASCE, 111(4), 722-739, 1985.
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STATIC TESTS ON VARIOUS TYPES OF SHEAR CONNECTORS FOR COMPOSITE STRUCTURES Hans (J.) C. Galjaard* and Joost C. Walraven** *Van Hattum en Blankevoort/Volker Stevin Construction Europe, The Netherlands **Delft University of Technology, Division of Concrete Structures, The Netherlands
Abstract The results and interpretations of push-out tests on shear connector devices for steelconcrete composite structures/bridges carried out in the Stevin laboratory are presented. The devices under investigation are headed studs, perfobondstrips, oscillating perfobondstrips, waveform strips and T-connectors. The oscillating-perfobondstrip, waveform strip and T-connector have specially been developed for this research project. Different concrete grades and types are used, like ordinary concrete, lightweight concrete, high strength concrete and lightweight high strength concrete, with and without steel fibres. The tests are done as specified in EuroCode 4 for standard push-out test. Large differences in ductility and strength between the various connector devices and concrete types have been observed. Sometimes unexpected behaviour occurred during testing, like brittle splitting failure in case of the (oscillating) perfobondstrip in normal concrete. A direct comparison for a specific shear connector device in combination with a certain concrete grade/type is possible. Although the number of samples in a test series is limited, it is still realistic to draw conclusions with respect to their strength/ductility based on EuroCode 4.
1. Introduction Application of high strength (lightweight) concrete could be useful for bridge decks, not only because of its enhanced strength, but moreover because of its improved endurance in a harsh environment. The design code for steel-concrete composite bridges EuroCode 4-2 [1] is however limited to concrete grades up to a strength of C50/60 (3.1.1(2)). This discourages the use of these materials for the decks of steel-concrete bridges. In steelconcrete composite bridges headed studs are often applied as an economic shear connection device. A major drawback is that the strength for concrete grades higher than C30/37 is governed by the strength of the steel cross section of the stud. Hence higher
1313
concrete grades will not be utilised by this connector device. Another drawback is the impossibility to automate the welding of headed studs. A prime objective of this research project is therefore the development of new shear connection devices with less disadvantages. For the purpose of comparison, and to investigate their behaviour in high strength (lightweight) concrete, existing shear connection devices like the headed stud and the perfobondstrip have been included in the research project.
2. Connector devices New connector devices were proposed, from which the three most promising devices have been selected based on economics, feasibility and diversity. The devices tested, including the ‘old’ headed-stud and perfobondstrip, are: - Headed studs φ 19 mm and a length of 125 mm, see Fig. 1. - Continuous perfobondstrip with a height of 100 mm, a thickness of 12 mm and 5 holes φ 50 mm, Fig. 1: Headed studs φ19 mm see Fig. 2. A continuous strip was selected because it is better weldable, using standard shop welding equipment, than a discontinuous one. Two fillet welds of 7 mm have been used to weld in on the HE-section. - Oscillating perfobondstrip with a height of 100 mm, a thickness of 8 mm, 5 holes φ 50 mm, and bend in 1.5 wave with an amplitude of 110 mm, see Fig. 3. It is believed that the curved form will Fig. 2: Continuous perfobondstrip give a better force transfer between steel and concrete compared with a straight connector. It is however recognised that welding might be difficult using present automated weld equipment. The strip is welded to the HE-shape with two fillet welds of 5 mm. - Waveform strip with a width of 50 mm, a thickness of 6 mm and bend in 2 waves with ampli- Fig. 3: Oscillating perfobondstrip tude 110 mm, see Fig. 4. The idea was to use point weld equipment for the production. Equipment with sufficient capacity is however very scarce, and it is doubtful whether the connector could be successfully welded in this way. For the tests it was welded to the HE-shape with propwelds φ25 mm. Fig. 4: Waveform strip
1314
-
T-connector: a section with a length of 300 mm of a standard T-shape 120 welded to the HE shape with two fillet welds of 6 mm, see Fig. 5. This connector evolved from the observation by Oguejiofor [2] that a large part of the bearing capacity of a perfobondstrip was the result of the direct bearing of the concrete at the front end of the (discontinuous) perfobondstrip. Therefore a T- Fig. 5: T-connector shape, which has a larger contact area than a single strip, and because of its shape will prevent vertical separation between HE-shape and concrete, seemed a good alternative. The main objective of this project is to get information about the behaviour of the ‘connection’ between steel and concrete. Other kinds of failure also had to be excluded. This resulted in a, sometimes, vast amount of splitting/shear reinforcement, see Fig. 7, and welds of the perfobondstrip, oscillating perfobondstrip and T-connector purposely made stronger than the connector itself.
3. Experimental set-up Three modifications have been made to the standard push-out test as described in chapter 10 of EuroCode 4 [1]: ‘Design assisted by testing’: - The test-specimens have been placed on a sliding support made of a greased Teflon plate between two stainless steel plates. These support conditions are similar to those used by Mainstone and Menzies [3], and are considered to give conservative results compared to the fixed supports of EuroCode 4. - For some connector devices concrete panels of 150 mm thick are too thin, and plates of 200 mm thick have been used. In particular for all tests with the (oscillating) perfobondstrip and for the later series with the Tconnector because of spalling problems with the first series. - For some tests the standard HE 260B section would not have sufficient capacity, and was replaced by a HE 240M section. Preliminary calculations for the capacity of the connector devices learned that the combination of (oscillating) perfobondstrip and high strength concrete could have a failure load of nearly 4000 kN. A special closed testing frame with an ultimate capacity of 5000 kN was developed for Fig. 6: Test set-up these tests, see Fig. 6. The longitudinal displacement between the concrete panels and the steel section was measured by LVDT’s with a range of 20 mm. The transverse separation between steel section and concrete panels was measured by LVDT’s with a range
1315
of 2, 3 and 5 mm respectively. The elongation at the outside of the concrete panels was measured by LVDT’s with a range of 2 mm. All data has been collected at an interval of 0.01 mm longitudinal displacement. The specimens have been tested in a deformation controlled way until failure or the maximum possible deformation of approximately 45 mm. For the test specimens certain combinations of connector device and concrete grade are used. The concrete grades vary from an ordinary C30/37 to high strength concrete C70/85. Lightweight concrete is included in the series as normal strength LC30/37 and high strength LC62/75. Concrete was used with and without added steel fibres giving a total of 8 possible concrete grades/compositions. The mix designs used are presented in Table 1. This table also shows the number of tests executed for a certain combination. Table 1: Concrete mixes used [kg/m3], averaged strengths [MPa], and number of tests Mix C30/37 C70/85 LC30/37 LC62/75 C30/37 C70/85 LC30/37 LC62/75 + fibres + fibres + fibres + fibres Portland cement/ Blast-furnace cement Microsilica slurry Water Sand 0-4 mm Gravel 4-16 mm Lytag 4-8 mm+ Lytag 6-12.5 mm+ Liapor F10+ Dramix RC 80/60 Average cube strength [MPa] Average splitting tensile strength [MPa] Headed-studs Perfobondstrip Oscillating perfobondstrip Waveform strip T-connector * Broken gravel
320/0
238/237
320/0
192 787 1044 -
50 125 797 974* -
160 751 249 464 -
41.1
99.2
2.90
238/237
320/0
238/237
50 124 192 797 787 1044 633 80BN Strength
50 124 797 974* 60BP
160 751 249 464 80BN
50 124 797 633 60BP
46.8
82.5
35.7
107.9
36.9
87.2
6.11
3.23
5.48
2.68
7.16
3.07
7.47
3 2
2 2
2 2
2 2
2 2
2 2
2
2
2
-
-
-
-
-
-
2 2 2 + 100% saturated
238/237
320/0
Number of tests 2 2 2 2 2
2
2 2 2 BN Type BN BP Type BP
Splitting or shear failure of the concrete panels had to be avoided, sometimes resulting in heavy reinforcement, see Fig. 7. All reinforcement is standard grade S500. The type of reinforcement provided is listed in Table 2.
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Table 2: Type of reinforcement per test-specimen Concrete grade C30/37 C70/85 LC30/37 LC62/75 C30/37 C70/85 LC30/37 LC62/75 + fibres + fibres + fibres + fibres 1 1 1 1 1 1 1 1 3 5 3 5 3 5 3 5
Headed-studs Perfobondstrip Oscillating 4 8 4 8 4 perfobondstrip Waveform strip 1 T-connector 2 6 7 6 7 Type: 1 2 x 5 φ10 BF and 2 x 4 stirrups φ10 BF per panel 2 2 x 5 φ16 BF and 2 x 4 stirrups φ10 BF per plate (for panel of 150 mm) 3 2 x 5 φ16 BF and 2 x 4 stirrups φ10 BF per plate (for panel of 200 mm) 4 2 x 5 φ20 BF and 2 x 4 stirrups φ10 BF per panel 5 2 x 5 φ25 BF and 4 x 10 mm anchor-plate and 10 hairpins and 2 x 4 stirrups φ10 BF per panel 6 2 x 5 φ25 BF and 2 x 10 mm anchor-plate and 2 x 4 stirrups φ10 BF per panel 7 2 x 5 φ12 BF and 2 x 4 stirrups φ10 BF per panel 8 2 x 5 φ25 BF and 4 x 10 mm anchor-plate and 10 hairpins and 2 x 4 stirrups φ10 BF per panel BF Fig. 7: Reinforcement perfobondstrip in : Both Faces
high strength concrete
4. Test results The differences between the various connector-devices with respect to ultimate load, ultimate displacement and general behaviour are considerable. An overview of the maximum loads and the accompanying displacements for these loads is given in Table 3. Only 2 tests per test specimen have been carried out. The results of these tests can nevertheless be regarded as a good indication for the behaviour of the connector device since the differences found between these 2 tests, and especially for the pre-peak behaviour, are generally very small. The graphs in this section always show the minimum force at a certain displacement for the 2 test-specimens investigated. The discussion of the results will be subdivided into two parts: 1 A comparison of the behaviour of the connector devices for a particular concrete type. 2 A comparison of the characteristic strength and ductility according to EuroCode 4. Due to its rather disappointing behaviour the waveform-strip is only included in the graphs for C30/37, and is not discussed any further.
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Table 3: Maximum load [kN]/displacement at maximum load [mm] per test
Headedstuds
Concrete grade C30/37 + C70/85 + LC30/37 LC62/75 + LC30/37 LC62/75 fibres fibres + fibres fibres
C30/37
C70/85
961/5.6 901/6.7 904/5.4
1015/4.6 818/6.2 1032/3.2 888/11.7
1001/5.3 1024/5.7
3209/11.0 1219/3.0 3151/10.2 1077/2.2
2556/6.2 1419/3.0 3269/11.0 1227/8.9 3001/15.2 2474/6.4 1500/3.6 3264/11.2 1285/8.4 3088/13.4
3787/4.6 1962/1.7 3918/5.7 1907/1.7
3334/4.7 2443/3.6 3424/2.2 2232/3.4
Perfobond1512/1.6 fobond1454/2.0 strip Oscillating 2193/2.2 perfobond2164/2.4 strip Waveform 510/3.8 strip 445/1.8 T1468/12.9 connector 1406/9.7
-
-
-
878/5.4 900/6.2
-
2006/11.3 1491/16.3 2111/15.2 1740/14.1 2084/12.9 1476/19.5 2077/13.9 1711/11.0
1035/3.3 891/11.3 1081/6.7 1068/5.4 811/6.5 974/2.9
-
-
-
-
-
-
-
-
-
4.1 Comparison of connector devices for a particular concrete type The comparisons of connector devices for a particular concrete type are shown in the Figs. 8 and 9 for all concrete types without fibres and for C30/37 with fibres. The dotted lines in these figures show the characteristic capacity obtained according to the testing procedure of EuroCode 4. The following conclusions can be drawn per concrete type: - The behaviour of the (oscillating) perfobondstrip is a bit disappointing for concrete C30/37 without fibres compared to, for instance, headed studs. This mainly has to do with the fast drop of the load capacity after the peak caused by splitting of the concrete panels in the plane of the bottom reinforcement (running through the holes in the perfobondstrip). It is not directly possible to conclude that the (oscillating) perfobondstrip should not be applied for C30/37; the splitting failure mode may have been induced by the (sliding) support conditions, what could be too conservative. The capacity of the perfobondstrip, and especially the oscillating-perfobondstrip, is larger than that of the headed studs. Both strips hardly deformed during testing, and could have been reused. An expected vertical splitting crack parallel to the longitudinal direction of the strip was not observed. Although this crack was observed for the T-connector it there seemed quite innocent compared to the spalling of the concrete cover of the bottom part of the T-connector during testing. This spalling however hardly effected the behaviour of the T-connector, which performed very well compared to headed studs. The T-connector equals the capacity of the perfobondstrip, but has a much larger ductility. The graph also reveals the rather disappointing behaviour of the waveform strip. - Concrete type C30/37 is the only mix where all connectors have been tested in combination with fibres (except the waveform connector. Fig. 8b. clearly reveals the effects which fibres have on the behaviour of T-connector and perfobondstrip, and especially the oscillating perfobondstrip; a significant greater ductility is obtained.
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All connectors show a better 2500 C30/37 without fibres ductility for LC30/37 comOscillating-perfobondstrip 2000 pared to C30/37 without fibres, but it is especially re- 1500 Perfobondstrip markable to notice the difT-connector ference in behaviour of the 1000 Headed studs oscillating-perfobondstrip. Waveform strip 500 This despite that LC30/37 is regarded to be a more brittle 0 0 10 20 30 40 material than C30/37. The Tdisplacement [mm] connector still behaves very well with respect to strength 2500 C30/37 with fibres and ductility. Oscillating-perfobondstrip 2000 The graphs for LC62/75 T-connector reveal that there is a signifi- 1500 Perfobondstrip cant increase in strength and Headed studs ductility of the (oscillating) 1000 perfobondstrip, and some in500 crease for the T-connector, 0 compared to LC30/37. They 0 10 20 30 40 all behave much better than displacement [mm] headed studs, and could very 2500 LC30/37 without fibres well be applied in combina2000 tion with LC62/75. For the Oscillating-perfobondstrip T-connector the concrete is 1500 no longer decisive, but the T-connector Perfobondstrip strength of the connector it- 1000 Headed studs self. 500 The graphs for C70/85 in Fig. 9 immediately reveal 0 0 10 20 30 40 the possibilities of the (oscildisplacement [mm] lating) perfobondstrip. They both have a much higher 4000 LC62/75 without fibres strength combined with a Oscillating-perfobondstrip much better ductility. High 3000 Perfobondstrip strength concrete really could use the potential of 2000 T-connector these connectors. The Headed studs strength of the T-connector 1000 is comparable to that of 0 LC62/75. For all connectors 0 10 20 30 40 displacement [mm] the strength of the concrete is no longer decisive, but the Fig. 8: Comparison of connector devices for a particular concrete type (Dotted line = cap. acc. EC4) force [kN]
-
-
force [kN]
force [kN]
force [kN]
-
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strength of the connector itself.
4000 Oscillating-perfobondstrip
force [kN]
3000
4.2 Strength and ductility according to EuroCode 4
C70/85 without fibres
Perfobondstrip
2000 T-connector
Headed studs The procedure for the determi- 1000 nation of the characteristic resis0 tance and slip capacity of con0 10 20 30 40 nector devices based on pushdisplacement [mm] out tests is given in section 10.2.5 of ENV 1994-1-1 (Euro- Fig.9: Comparison of connector devices for a particular concrete type Code 4-1) [1]. The characteristic resistance PRk should be taken as the minimum failure load of 3 tests reduced by 10%. Results for PRk for the connector devices investigated based on Table 3 can be found in Table 4. The slip capacity of a connector should be taken as the maximum slip measured at the characteristic load level, as shown in Fig. 10. The characteristic slip capacity δuk should be taken as the minimum test value of δu reduced by 10%. Conservatively not the maximum slip is measured for individual connector devices, but for the bottom limit of the curves of a particular connector device as shown in Figs 8 and 9. The calculated values for δuk are shown Fig. 10: Determination of characteristic in Table 4 and Fig. 11. resistance and slip capacity connecSection 6.1.2(3)(b) of ENV 1994-1-1 tor according EC 4-1 states that connector devices with a characteristic slip of not less than 6 mm have the same deformation capacity as headed studs. Headed studs of sufficient length in turn may be regarded to be ductile connectors. Examination of Table 4 learns that a lot of connectors, even headed studs, do not fulfil this requirement. It should however be noted that this ductility is only required when ideal plastic behaviour of the shear connection in the structure is considered. This is generally not the case for bridge structures where a number of shear connector devices discussed in this article could be well applied. Fig. 11 shows that there is an increase in capacity for all connector devices for higher cube strengths. This increase in cube strength is most beneficial for the (oscillating) perfobondstrip. It should however be remarked that the failure modes for the Tconnector and the (oscillating) perfobondstrip are different for lower and higher concrete strengths; the connectors device itself becomes governing for the higher concrete strengths. The capacity of the T-connector could easily be increased by providing a
1320
4000
Cube strength Characteristic strength (EC 4)
3000
Oscillating-perfobondstrip
Frk [kN]
Perfobondstrip 2000
T-connector 1000
Headed studs 0 0
20
40 60 80 Cube strength [Mpa]
100
120
100
120
50
Cube strength - Ductility (EC 4) 40
δu [mm]
longer connector, what is less easy for the (oscillating) perfobondstrip. The increase in strength for headed studs looks like a contradiction to the general accepted idea that the steel strength of the studs is governing from concrete grade C30/37 and up, and that the concrete strength therefore should have no effect. Due to the increase in Youngs-modulus of the concrete, and hence the increase in the bedding stiffness of the stud, the failure mode of the studs changes from a combined tension and shear failure to a pure shear failure mode. As a result the tensile force in the stud will reduce, and leave more capacity for the shear mode of failure.
T-connector
30
20
Oscillating-perfobondstrip
10
Perfobondstrip Headed studs
0 0
20
40 60 80 Cube strength [Mpa]
Fig. 11: Strength and ductility according to EC 4 Table 4: Strength and ductility according to EuroCode 4 Concrete grade C30/37 C70/85 LC30/37 LC62/75 C30/37 C70/85 LC30/37 LC62/75 +fibres +fibres +fibres +fibres Headed-studs PRk [kN] 814 907 732 901 790 930 730 877 (8) 3.4 4.9 4.4 4.6 3.0 5.4 3.1 δuk[mm] 5.0 Perfobondstrip PRk [kN] 1305 2836 969 2227 1277 2936 1104 2696 (2) 9.4 2.9 5.7 2.9 7.9 16.4 10.5 δuk[mm] 0.8 Oscillating PRk [kN] 1947 3409 1716 2976 2008 perfobondstrip δuk[mm] 1.9 6.5 2.7 4.6 7.6 Waveform strip PRk [kN] 400 (2) δuk[mm] 1.8 T-connector PRk [kN] 1266 1805 1314 1870 1537 (2) 38.8 16.4 37.8 δuk[mm] 16.1 15.8 (number of connectors per test-specimen)
For headed-studs and the T-connector there is some decrease in ductility for higher concrete strengths, whilst there is some increase for the (oscillating) perfobondstrip. Despite
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the decrease in ductility of the T-connector this device still is the most ductile connector for higher concrete strengths.
5. Conclusions The following general conclusions can be drawn with respect to the connector devices and concrete mixes investigated: - A failure mechanism not known from literature was observed for the (oscillating) perfobondstrip in concrete C30/37, LC30/37 and LC75/80 without fibres. - The addition of steel fibres had a very beneficial effect on the behaviour of the connection in general. The only exception are the headed studs where the behaviour of the steel limited the strength. - The connection in high strength concrete, which was expected to be very brittle, behaved in a very ductile way. The observation that the concrete panels did not split, and that the steel connector device had to deliver most of the deformations, seems an explanation for this ductility. - The behaviour of the T-connector is very promising, but there may be questions about its behaviour under dynamic loads. It actually has a very small bearing area on the concrete. Subsequently the stresses in the concrete must be very high, and local crushing of the concrete may occur. This in particular could cause a degradation of the connection under a dynamic load. This has to be further investigated. - Lightweight aggregate concrete often seemed to behave in a little bit more ductile way when compared to normal weight concrete, especially in the post-peak stage.
6. References 1 EuroCode 4: ENV 1994-2:1997, Design of composite steel and concrete structures – Part 2: Composite bridges (1997), European Committee for Standardisation (CEN) 2 Oguejiofor E.C. and Hosain M.U. (1994). A parametric study of perfobond rib shear connectors. Can. J. Civ. Eng. 21, 614-624 3 Mainstone R.J. and Menzies J.B. (1967). Shear connectors in steel-concrete composite beams for bridges – 1: Static and fatigue tests on push-out specimens. Concrete 1:9, 291-302
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STRUCTURAL MONITORING OF HYBRID SPECIMENS AT EARLY AGE USING FIBRE OPTIC SENSORS Branko Glisic , Daniele Inaudi SMARTEC SA, Switzerland
Abstract Hybrid structures, notably bridges, consisting of steel girders and concrete decks, are designed to exploit in the best way the mechanical properties of both materials. In order to guarantee safe, durable and low-cost service of such structures, a long-term quality and a robust connection between steel and concrete must be guaranteed. Even if experience in construction, maintenance and exploitation of these structures is large, a good and long-lived connection remains a challenging point in their realisation. This is mainly due to the initial incompatibility in the dimensional behaviour of two materials: early and very early age deformations of concrete (thermal expansion and total shrinkage) generate stresses in both materials even before service and imperils their good interaction. With the intention of a better understanding and an accurate numerical modelling of the steel-concrete connection in hybrid structures, measurements are indispensable and, in particular the deformation evolution in both materials during the early and very early age of concrete. In this paper we present examples of this type of measurements, the monitoring of the total dimensional evolution of hybrid elements, the determination of hardening time of concrete and structural monolithisation and, indirectly, the determination of concrete’s Young modulus evolution. An approach to concrete delamination detection is also assessed. All these parameters are evaluated using fibre optic sensors directly embedded in the fresh concrete or attached to steel elements. Their high accuracy, long-term stability and especially their ability to measure early and very early deformation of concrete are essential for monitoring of mentioned parameters.
1. Introduction Hydration is a complex physico-chemical exothermal process. During hydration, the water-cement suspension transforms to hardened cement paste; strength and stiffness of
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concrete increase; a considerable amount of heat is discharged; and early age deformation occurs. The deformation due to hydration is caused by hydration heating and cooling and by material transition to hardened cement paste (autogenous deformation). In case of hybrid structures, the early age deformation is restrained by steel elements. Therefore, residual tensile and compressive stresses are generated. Residual tensile stresses, generated before the tensile strength of concrete is fully developed, provoke early age cracking. Recent studies and research (e.g. [1, 2]) have shown that early age cracking of concrete can significantly increase the vulnerability of structures to noxious environmental influences. The cracks form "open doors" to the infiltration and penetration of noxious substances such as chlorides and sulphate water. These substances attack the concrete and rebars, and damage the structure, thereby reducing its long-term capacity and durability. Figure 1 [1] shows the influence of early age cracking on durability for a hybrid oldconcrete new-concrete structure. We assume that a similar law is valid in case of a new concrete – steel structure. Even small gains in concrete performance during very early age, have a consequence of extending considerably the life span of the structure. How does one evaluate the risk of the early age cracking? Generally there are two approaches, numerical simulation and monitoring. Numerical simulations are very complicated because of the problem complexity. They may be successful [1], only after calibration provided by measurements (notably of concrete parameters as Young modulus, strength, creep ratio etc.). Data collected by early age monitoring therefore represents a unique source of information for understanding the real structural behaviour. Performance Early age damage
Initial
Damage Propagation
Residual Capacity gained during early age
Minimal admitted level of capacity
Gained extension of life
Age
Durability of structure (life span)
Figure 1: Influence of early age damage on the durability of an hybrid structure [1] It is recommended to start deformation monitoring of hybrid structures from the moment of concrete pouring. In this way, the whole history of deformation is collected. This includes the very early age deformation, which is generated while the concrete is still not
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hardened. For this purpose, it is necessary to carry out the monitoring with sensor systems that are capable of such measurements.
2. SOFO monitoring system The deformation monitoring system named SOFO (French acronym of "Surveillance d'Ouvrage par Fibres Optiques" - "Monitoring of Structures by Optical Fibers") has been developed at the Stress Analysis Laboratory of the Swiss Federal Institute of Technology (IMAC-EPFL) [3]. It is based on fibre optic technology and is capable of monitoring micrometer deformations over measurement bases up to a few meters. It is particularly adapted to measure civil structures built with civil engineering materials such as concrete, steel and timber. Since 1993 it has been successfully applied to the monitoring of different types of structures such as bridges, tunnels and piles. Performance data are presented in more details in [3] and [4]. SOFO Standard Sensors can be applied externally, attached to the surface of the structure, but also, and more importantly, they can be applied internally, embedded in fresh concrete. Installation of sensors before the pouring of concrete is a required condition for deformation monitoring at very early age. A second obligatory condition is a good transfer of deformation from concrete to the sensor, which is guaranteed by the low stiffness of the sensor [4]. A typical application of the SOFO system to a civil structure is presented in Figure 2. Independent System Structure
Optical Cable
Sensors
Intermediate Connection Boxes Channel Switch
Central Connection Box
SOFO User's PC
Figure 2: Concept of the SOFO monitoring system
3. Early and very early age deformation of concrete The period which begins with pouring and finishes when all thermal processes in concrete are finished is considered here as the early age of concrete. It consists of the dormant period and the period of intense heat release, until the concrete temperature is balanced with the environment temperature. The duration of the early age varies from a couple of days to several weeks depending on the thermal properties of the concrete
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components, the heat production potential of cement, the additives, the environmental conditions (temperature and relative humidity), the cure (thermoisolation) and geometry of the concrete element (massive and thick elements need more time to cool than thin elements). The period included in the early age, during which the concrete is still not hardened, is conventionally called the very early age. The duration of the very early age is between several hours and one day depending mainly on the rate of hydration, concrete composition (notably the water-cement ratio) and curing conditions. Since the processes of solidification and hardening of concrete are continuous, it is difficult to precisely define the end of the very early age. American standards propose the setting time of concrete [5]. In this paper, the end of the very early age of concrete is conventionally called the hardening time of concrete [4]. The early age deformation of concrete is provoked by internal and external causes that have mechanical, thermal or hydraulic origins [6]. The sources of the early age deformation are presented in Table 1. Table 1: Origins of the early age deformation Mechanical Internal
-
External
Load
Thermal actions Hydration heat Ambient temperature variation, natural or artificial
Hydraulic actions Hydration hydraulic processes Ambient humidity variation, natural or artificial
The six following forms of the early age deformation are distinguished [4, 6]: • • • • • •
Plastic shrinkage, εp Autogenous shrinkage, εa Drying shrinkage and swelling, εh Carbonatation shrinkage, εcar Thermal deformation (expansion and contraction), εt , εt,e Load and creep deformation, εs and εϕ.
Some of them often appear simultaneously. In this case, their sum represents the total deformation. The total deformation of concrete at early age depends of different factors, such as concrete composition, curing, loads etc. It is always composed of at least two different types of deformation. In Figure 3, periods and possible simultaneous apparition of different types of early age deformation are represented. An example of total early and very early age deformation measured on a concrete element (see Figure 4) using SOFO Standard Sensor is represented in Figure 5. During monitoring, the concrete element was thermally and hydro isolated. Two components of deformation are dominant: thermal and autogenous deformation, but their action was restrained by the workform and friction with the steel beam.
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Early age
Internal influences
Dormant period
Very early age Period of intense hydration
Period of slow hydration
εa εcar
εt εa εca
External ε εt,e εp influences t,e εs εc 0.125
0.5 1
εt,e εh εs εϕ 2
4
8
16 32
Time [Day]
Figure 3: Periods of apparition of different types of deformations
4. Early age deformation measurement on steel - concrete specimens In this section we demonstrate how the early age monitoring helps to understand real behaviour of the structure. The aim of test is to compare two concretes with approximately equal mixtures but with different initial temperatures. 800x140
Concrete
F2
P6
160x10 SOFO Sensors in specimens P6 and F2
Steel
6x800
300x20 Dimensions in mm
Figure 4: Cross-section of the specimens P5, P6 and F2 The hybrid steel-concrete specimens, called P6 and F2, are analysed. Both specimens are mixed with 350 kg/m3 of the cement CEM I 52.5, the water cement ratio is of 0.48, granulate with maximal diameter of 32 mm, and 1.2% of plasticiser. The most important difference between these two concretes is the initial temperature: Concrete for the specimen P6 is refrigerated to 5°C using liquid nitrogen. Both specimens are cured in the
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same conditions after the pouring. Each specimen has the same length of 8.4 m, and identical dimensions of the cross section. The specimens are equipped with thermocouples and Standard Sensors. The sensor emplacement and the cross-section are presented in Figure 4. Both sensors are presented in the same figure only in order to facilitate the comparison. In the longitudinal direction the sensor are centred in the middle of the specimens' spans. The monitored deformations of both specimens are presented in Figure 5. Initial, maximal and final (71 hour after the pouring) temperatures of specimens are presented in Table 2. The difference between the very early age behaviour of the specimens is noticeable in Figure 5. The difference between the initial and the final temperature is approximately equal for both specimens (29.5°C for specimen P6 and 26.2°C for specimen F2). However, the thermal expansion of specimen P6 is higher by 75%. Moreover, the maximum in expansion of specimen P6 is achieved 8 hours later than for specimen F2. This difference in behaviour of specimens is the consequence of their different initial temperature: the hydration process of refrigerated concrete was slowed down due to low temperature, therefore the period of intense heating was long, and since in this period the thermal expansion coefficient (TEC) of concrete is elevated, the thermal expansion of concrete is higher than in the case of non-refrigerated concrete. Expansion
Contraction
St. & Dorm. period
Deformation [µε]
200 150 100 50
P6 F2
13 µε 89 µε
0
Contraction
Expan.
-50 0
10
20
24 h
30
40
50
60
70
Time [h] Figure 5: Behaviour of two different concretes cured in the same conditions Table 2. Initial, maximal and final temperatures of specimens P6 and F2 Specimen Initial temperature P6 6.2 F2 26.1 * 71 hour after the pouring
Maximal temperature 35.7 52.3
Final temperature* 26.7 33.1
If we suppose that a monitoring systems using external sensor was applied on the concrete 24 hours after the poring, then after 71 hours it would register a significantly
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smaller difference between total specimen deformations (13 µε instead 102 µε, see encircled area in Figure 5). The error obtained using such a way of monitoring is very high and it does not allow to understand the different behaviour between the specimens.
5. Hardening time of concrete and monolithisation of hybrid structures In the case of hybrid structures, the very early age deformation is partially restrained by the interaction with the steel element. Due to the dominant viscous behaviour of concrete at this stage, there are no important stresses generated by the interaction. During concrete hydration both materials deform, the concrete due to hydration, and the steel due to heat transferred from the concrete. Before hardening, the deformations of the new concrete and of the steel element are generally different since the mechanical interaction between them is weak, the new concrete is viscous and the thermal expansion coefficients are different [4,7]. With ageing, the concrete hardens, the interaction with steel element starts and their deformations become more and more interdependent. Furthermore, at the interface, the difference of deformations converges to a constant value. When this constant value is established, both materials deform equally. This means that a good interaction between them is created, and this is possible only if the concrete is hardened. Therefore, in the case of hybrid structures, the moment when the deformations of both materials (concrete and steel) at the interface begin to be equal is proposed as the hardening time of concrete [4]. The following example illustrates the determination of the hardening time in case of the specimen F1, which contains the same concrete and has the same length as the specimen F2. The cross-section of the specimen and the placement of the sensors are presented in Figure 6.
A-A B5
800x140
A-A
B3
16
Concrete
160x10
112
Sensors in specimen F1 6x800 Steel
B3 12
B5
200x15
30 2010
Dimensions in mm
42 8 20 30
Figure 6: Cross-section and sensors placement of specimen F1 The sensors B3 and B5 have been positioned 720 mm from the end of the specimen. The sensor B3 is attached to iron corners welded to the steel (see Figure 6). In this way it
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measures the deformation of the steel support. The sensor B5 is embedded into the concrete in order to measure its very early age deformation. The measurements of both sensors and their difference are presented in Figure 7. The hardening time is successfully determined using the difference between the measured deformations. The difference between measured deformations is presented in more details in Figure 8. 175
125 100 75
B3 (Steel) B5 (Concrete)
50
B3-B5 (Difference)
25
~8h30
Deformation [µε]
150
0 -25 -50 -75 0:00:00
6:00:00
12:00:00 18:00:00 24:00:00 30:00:00 36:00:00 42:00:00 48:00:00
Age [Hours] Figure 7: The (very) early age deformation of the specimen F1 and new concrete hardening time identification 10 5
Deformation [µε]
0 -5 -10
~8h30 Hardening time
-15 -20 -25 -30 -35 -40 -45
-44 µε
-50 0:00:00
6:00:00
12:00:00 18:00:00 24:00:00 30:00:00 36:00:00 42:00:00 48:00:00
Age [Hours] Figure 8: The difference between deformations of steel and concrete and concrete hardening time identification
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After the hardening time, the concrete and the steel deform at the interface in the same manner, meaning that both materials are well bonded and begin to behave as a monolithic structural element. Consequently, the hardening time presents also the time of monolithisation of the structure. In different numerical approaches, which include the analysis of structural behaviour at early age, the question of the time to start the analysis is very delicate. Before the hardening of concrete, the stresses generated in concrete are not so important, since the concrete is still plastic, and the restrained or imposed deformation is relaxed. That’s why we propose the hardening time of concrete as a starting time for numerical modellings of concrete.
6. Further research - Approach to delamination detection and evolution of Young modulus of concrete In this section, two approaches are proposed for further research. The first concerns the detection of delamination and the second evolution of Young modulus of concrete. The pair of sensors installed as shown in Figure 6 could be used to detect possible delaminations of concrete. If the structure behaves as a monolithic body, the deformations of both sensors are supposed to be equal. Since the sensors have a long gage length (0.2 to 6m), cracking of concrete without delamination will not affect significantly the difference between measurements performed by sensors. If a delamination appears, concrete and steel do not bond completely so their behaviour is more independent, and the absolute value of the difference between the measurements will significantly increase. This increase in the absolute value of the difference between the measurements will indicate the delamination. Using standard SOFO sensors embedded into the concrete of hybrid structures, could also allow the evolution of the Young modulus of concrete. For this purpose simultaneous deformation and temperature monitoring of the steel element is required. Since the mechanical behaviour of the steel is known, data obtained from its monitoring will allow the determination of the evolution of the bonding forces between the steel and concrete. Finally, by correlating the stresses obtained from bonding forces and deformation measured by the embedded standard sensor, it could be possible to retrieve evolution of relation strain – stress, e.g. the evolution of the Young modulus. This approach is very delicate since, at the early age, the thermal expansion coefficient of concrete is variable, and the creep can be significant. However some initial results obtained using this method showed good agreement with numerical modelling [8].
7. Conclusions An aspect of early and very early age monitoring of concrete in the case of hybrid, steel concrete specimens is presented, as well as its benefit for a better understanding the real structural behaviour. For this purpose a unique long-gage fibre optic monitoring system, allowing such measurements, is applied. The permanent monitoring of deformations using Standard SOFO Sensors, starting immediately after pouring, provides accurate
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measurements that help to enlarge and improve the knowledge of the real behaviour of concrete at early and very early age Diagrams that demonstrate early and very early age deformations of hybrid specimens cured in laboratory conditions were presented in this paper. Four characteristic periods are distinguished in the diagrams: the dormant period, the stabilisation period, the thermal expansion period and the contraction period. The alteration of TEC during the very early age is confirmed by the tests. Different behaviour of two identical concretes with different initial temperatures has proven this important characteristic of concrete at very early age. High difference between final thermal expansion deformations would not be determined accurately using traditional monitoring systems. A definition of the hardening time and an original approach for its determination are presented in this paper. The method is applicable to hybrid structures and was laboratory tested and validated.
Acknowledgements The work presented in this paper is performed in the ISS and IMAC laboratories of EPFL (Swiss Federal Institute of Technology, Lausanne, Switzerland). The authors of this paper would like to thank Dr. Jean-Marc Ducret from Ferward SA, Dr. Miguel Navarro Gomez and Mr. Alexandre Blanc from ICOM-EPFL for their help, advise and generosity during the realisation of the tests, Dr. Olivier Bernard from MCS-EPFL for advise concerning research on concrete at very early age and Mr. Raymond Délez from IMAC-EPFL whose help and mechanical knowledge was imperative.
References 1. Bernard O., "Comportement à long terme des éléments de structures formés de bétons d'âges différents", Ph.D. Thesis N° 2283, EPFL, Lausanne, Switzerland, 2000 2. “Thermal Cracking in Concrete at Early Age”, RILEM International Symposium, Munich, Germany, 1994 3. Inaudi D., “Fiber Optic Sensor Network for the Monitoring of Civil Structures”, Ph.D. Thesis N° 1612, EPFL, Lausanne, Switzerland,1997 4. Glisic B., “Fibre optic sensors and behaviour in concrete at early age”, Ph.D. Thesis N° 2283, EPFL, Lausanne, Switzerland, 2000 5. ASTM 04.02, US Norms 6. Aïtcin P.-C., Neville A., Acker P., "Les différents types de retrait du béton", Bulletin des laboratoires des Ponts et Chaussées, Vol. 215, pp 41-51, LCPC, Paris, 1998 7. Laplante P., Boulay C., "Evolution du coefficient de dilatation thermique du béton en fonction de sa maturité aux tout premiers âges", Materials and Structures, Vol.27, pp. 596-605, 1994 8. Ducret J.-M., "Etude du comportement réel des ponts mixtes et modélisation pour le dimensionnement", Ph.D. Thesis N° 1738, EPFL, Lausanne, Switzerland, 1997
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DEVELOPMENT OF INNOVATIVE COMPOSITE SYSTEM – BETWEEN STEEL AND CONCRETE MEMBERS Koji Kitagawa*, Hiroshi Watanabe*, Yoshihiro Tachibana*, Hirokazu Hiragi** and Akimitsu Kurita*** * Bridge Structure Division, Kawada Industries, Inc., Japan ** Department of Civil Engineering, Setsunan University, Japan *** Department of Civil Engineering, Osaka Institute of Technology, Japan
Abstract The authors have developed an innovative composite system between steel and concrete members combining the headed stud shear connectors and epoxy resin mortar. This system is called Post Rigid System (hereinafter, abbreviated to PR System), where the system have the behaviors of non- and full composite action under construction and in service, respectively. By using the PR System in steel-concrete composite structures, therefore, the introduction of prestressing force only into the concrete member can be done effectively. To confirm the applicability of PR System, fundamental tests were carried out. The resin mortar consist of epoxy resin and silica sands. It is possible to control the hardening time of resin mortar subject to a constructional plan of structure. To eliminate the composite action between steel and concrete, the shank of each stud is wrapped by the resin mortar-A and also the attaching surface of steel girder against the concrete member is plastered by resin mortar-B. The stud shear connector used in the PR System is named Post Rigid Stud (hereinafter, abbreviated to PR Stud). The concept of the PR System, various test results of resin mortar and PR Studs, also an application example for an actual bridge are presented and discussed in this paper.
1. Introduction In the past, no structural system that changes with the progress in the time from non- to full composite system has been developed. The fact of such structure system is called PR System. If this kind of PR System (Figure 1) is possible, the tensile stress that occurs during drying shrinkage in concrete restrained by steel members can be mitigated, and prestressing can be applied to concrete without restraint of steel members because the PR System is non-composite during prestressing and is composite when live load is applied later. The PR System will therefore extend the versatility of composite structures. We have developed a new type of stud called PR Stud (Photo 1) as a shear connector, and used Time-setting resin mortar-A and -B to realize the PR System, which is flexible
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for a while but becomes rigid at the serviceability state. In advance of the development of the PR Stud, testing and development were conducted on both of resin mortars, which plays an important role in the PR System, as to compressive strength and Young's modulus after hardening as well as viscosity and adhesive strength before the hardening. This paper also describes the construction work of Shiratori-bridge, which is the first bridge adopted the PR System. After hardening
State of resin
Non-composite
Headed stud shear connector
Full composite
Resin mortar-A for shear connectors
Under construction
Before hardening Initial
In service
Setting time of hardening
Figure 1. Behavior of the PR System
Time
Resin mortar-B for steel plates Photo 1. Details of PR Stud
2. Outline and required performance of the PR System In the PR System, as shown in Photo 1, Time-setting resin mortar-A is plastered to a steel plate surface that will later face concrete and resin mortar-B is also wrapped around each connector. Each resin mortar is cold-setting epoxy resin whose hardening time in practical use can be adjusted between 1 ~ 12 months by changing the amount of hardener, as confirmed through mix design tests. These gelatinous resin mortars before hardening permit the relative movement between steel plate and concrete, but resin mortar-A and -B do not permit the movement after hardening because of those increased compressive and adhesive strength. The PR Stud is a shear connector consisting of a headed stud shear connector whose shank is wrapped up with Time-setting resin mortar-A. Two-thirds of the total length of the stud from its welding reinforcement of base is wrapped in the resin mortar-A to provide resistance against pull-out force at the stud head, and the resin thickness is selected by the required amount of relative slip. The requirements and remarks on each resin mortar and the PR Stud are described below.
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2.1. Viscosity of resin mortars There are constructional requirements on both of resin mortars before hardening. The resin mortar-B should have a low viscosity so that it can be plastered by using a roller, and the resin mortar-A it should have a high viscosity so that it will not sag. 2.2. Compressive strength and Young’s modulus of resin mortars After hardening, both of resin mortars should be over compressive strength of the concrete, and resin mortar-B should be the Young's modulus of the degree which PR Stud behaves equivalent to ordinary studs. 2.3. Bond strength of resin mortar-B They are required that the bond strength of the resin mortar-B is very low before hardening, and that it is high after hardening. 2.4. Resistance of the PR Stud As shown in Figure 1, the PR Stud must have a low resistance against horizontal shear for a while after construction, but have shear resistance equivalent to that of ordinary studs after the hardening of the resin mortar-A.
3. Characteristic tests on Time-setting resin mortars The viscosity of each resin before hardening was adjusted by changing the amount of filler as described in 2.1, and low-viscosity resin-B for steel plates and high-viscosity resin-A for connectors were formulated. Silica sand was added to each resin to prepare Time-setting resin mortar, which was then subjected to compression and adhesion tests to select a mix proportion of resin mortars having characteristics suited for the PR System as described in 2.2 and 2.3. 3.1. Young's modulus and strength after hardening The test results are shown in Table 1. The values of Young's modulus and Poisson's ratio were obtained by the secant method for a compressive stress of 10 N/mm2 expected to occur in the serviceability state of resin surrounded by concrete. In the compression test, the compressive strength of the resins, more than 100 N/mm2, in any case far exceeds that of the concrete, but is nearly constant regardless of the content of silica sand. In addition, greater values of Young's modulus (close to the values specified in 2.2) were obtained at silica sand contents of 80% and 30% for the resins for connectors and steel plates, respectively. Resin mortars with these silica sand contents were used for the verification tests that followed. 3.2. Adhesive strength before and after hardening The test results are shown in Table 2. Adhesive strength before hardening is low and nearly constant regardless of displacement, and it after hardening is great (the
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requirement described in 2.3). The adhesive strength of the resin before hardening is expected to be lower at higher temperatures. Table 1. Results of a compression test
Compressive Young's Poisson's strength ratio modulus Resin mortar type Resin : Silica sand fr' (N/mm2) Er (N/mm2) µ Weight
Resin mortar-A for shear connectors Resin mortar-B for steel plates
1
:
0.0
103
0.68 ×104
0.37
1
:
0.8
134
1.53 ×104
0.32
4
0.38 0.35
1
:
0.8
130
0.41 ×10
1
:
0.3
131
0.65 ×104
Table 2. Result of an adhesion test (at an air temperature of 5 deg C)
Surface treatment
Average bond strength tr' (N/mm2)
Time-setting Before hardening resin mortar After hardening
Remarks
0.09
Cohesion of resin
5.03
Concrete failure
4. Push-out shear test of the PR Stud A push-out shear tests were carried out to confirm that restraining force of PR Studs before the hardening of resin mortars is low for the horizontal shearing force and that it has the shear resistance which is equivalent to ordinary studs, after the hardening of the resin mortars (the requirement described in 2.4). 4.1. Test specimen and method Three specimens were prepared for each of the five different specimen types to investigate the change of slip behavior and shear resistance in the push-out test before and after the hardening of resin mortars. An ordinary headed stud was used in type 1 to make a comparison with the PR Stud. Types 2 and 3 respectively correspond to before and after the hardening of the resin mortars having silica sand, with which the PR Stud was wrapped up the resin mortar-A; as mentioned in section 3.1, the Young's modulus of its mortar-A after hardening was about half that of the concrete. Types 4 and 5 respectively correspond to before and after the hardening of the resin mortars containing no silica sand; they were intended to investigate the effect of Young's modulus on the slip characteristic of the resin mortars.
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An H-shaped steel beam in the push-out specimen was split into two parts at web plate, which were positioned in the perpendicular condition weld PR Stud and connected with bolts after the casting and curing of concrete (Figure 2). The width of wrapping by resin mortar-A was set to 70 mm against pull-out force at the stud heads and the thickness of wrapping was set to 8 mm so that the amount of slip before the hardening, characteristic of the PR Stud, could be investigated. As for the surface treatment of steel plates in contact with concrete, resin mortar-B was plastered to a thickness of 1.5 mm, like in practical cases, in specimen types 2 and 4 (tested before the hardening of resin mortar), while wax was applied to the steel plates in types 1, 3, and 5 to investigate the shear characteristic provided only by the studs.
Load cell
ϕ19
Direction of loading
ϕ35
The strength of concrete was suppressed to about 30 N/mm2, comparable to values in actual bridges. Details of studs
70 110
Direction of concrete casting
160
Resin mortar (type 2 and 4) Waxed (type 1, 3 and 5)
500
2x 80
=1
60
50
0
Direction of concrete casting
PR Stud (type 2, 3, 4 and 5) Ordinary headed stud (type 1) Displacement meter
Figure 2. Push-over shear test specimen and arrangement Concrete failure plane
Stud failure plane
a) Concrete failure
b) Stud failure Figure 3. State of failure
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4.2. Test results The results of the static push-out shear test by increment cyclic method are shown in Table 3.
Specime n type
Type 1
1 2 3
Table 3. Result of a static push-out shear test Shear Slip constants for different State of Type of Material strength relative slip studs properties Qmax 0.2 0.5 1.0 2.5 5.0 failure (kN/stud mm mm mm mm mm 140 778 235 205 192 169 Stud
Ordinary fc'=28.9 headed stud Ec=23750
113 596 234 219 186 164
111 345 207 169 147 121 Concrete
Type 4
Type 3
Type 2
Avg.
Type 5
Stud
122 573 225 198 175 PR Stud 1 132 56 27 20 18 (with silica fc'=28.9 2 109 48 29 23 23 sand) Ec=23750 3 131 94 38 22 21 before Avg. hardening frd'=115.0 124 66 31 22 21 PR Stud Erd=15750 1 136 346 224 195 172 (with silica 2 118 457 223 176 117 frs'=101.0 sand) 3 134 603 282 218 181 Ers=6200 after Avg. hardening 129 469 243 196 157 PR Stud 1 135 48 25 19 17 (without fc'=33.3 2 137 88 33 21 19 silica sand) Ec=35200 3 110 74 28 19 19 before Avg. hardening frd'=103.0 127 70 29 20 18 PR Stud Erd=6800 1 117 171 106 76 87 (without 2 120 191 164 103 86 silica sand) frs'=130.0 3 119 223 141 116 113 Ers=4100 after Avg. hardening 119 195 137 98 95 fc' : Compressive strength of concrete Ec' : Young's modulus of concrete frd' : Compressive strength of resin mortar-A for connectors Erd' : Young's modulus of resin mortar-A for connectors frs' : Compressive strength of resin mortar-B for steel palates Ers' : Young's modulus of resin mortar-B for steel palates
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151 19 Concrete 21 Concrete 21 Concrete 20 161
Stud
104 Concrete 142
Stud
136 23 Concrete 19 Concrete 18 Concrete 20 99
Stud
108
Stud
118
Stud
108
Shearing force Q (kN/stud)
150 100 50 0 0
5
10 15 Relative slip δ (mm)
20
a) Type 1: ordinary stud
Shearing force Q (kN/stud)
150
Type 3
100 50 Type 2
0 0
5
10 15 Relative slip δ (mm)
20
b) Type 2 and 3: PR Stud (resin mortar with silica sand)
Shearing force Q (kN/stud)
150 Type 5 100 50 Type 4 0 0
5
10 15 Relative slip δ (mm)
20
c) Type 4 and 5: PR Stud (resin mortar without silica sand) Figure 4. Relationship between shearing force and relative slip
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The slope of the unloading line from the point of load Qa at relative slip δa to the point of load 0 at relative slip δb is defined as slip constant K at δa.
Q (kN)
Qa
0
δb δ (mm)
δa
K(δa) =
Qa δa – δb
Here, δa – δb is the amount of elastic recovery slippage.
Figure 5. Calculation of the slip constant 4.2.1. Maximum shear strength (Qmax) Table 3 indicates that in the cases of the ordinary stud and the PR Stud after the hardening, the ultimate state of failure is mostly the breaking of the base part of the stud, and in the case of the PR Stud before the hardening, the ultimate state of failure is the shear failure of concrete (Figure 3). Nevertheless, the average Qmax values are nearly the same at types 1 ~ 5. From this case, the PR Stud has shear strength comparable to that of an ordinary stud both before and after the hardening of resin mortars. 4.2.2. Slippage property Figure 4 indicates that the slippage property of the PR Stud changes drastically before and after the hardening of resin mortars in specimen of types 2 ~ 5. The shear force of the PR Stud before the hardening remained nearly constant as relative slip increased up to 5 ~ 8 mm, which corresponds to the wrapping thickness of the resin mortar-A (8 mm). This implies that the amount of slip at a constant shear force can increase up to the wrapping thickness of resin mortar-A. The PR Stud after the hardening of the resin mortar-A in type 3 showed shear resistance similar to that of the ordinary stud. The type 5 resin, containing no silica sand, was found to be more flexible than the ordinary stud because of its low Young's modulus after the hardening. 4.2.3. Slip constant, K Figure 5 shows how to calculate the slip constant, K. The slope of each unloading line in Figure 4 was calculated as a slip constant for the corresponding relative slip and was listed in Table 3. Types 3 and 1 resulted in nearly the same slip constants for any relative slip; this means the elastic recovery slip of the PR Stud after the hardening of the resin mortar having silica sand is almost the same as that of the ordinary stud. The slip constants of types 2 and 4 are about one-tenth of those of types 1 and 3; this means the PR Stud before the hardening of the resin mortar-A wrapping around the base part of the stud results in greater relative slip compared to the ordinary stud or the PR Stud after the hardening of the resin mortar, but exhibits excellent elastic recovery slip. 4.2.4. Summary of the push-out shear test The test results indicate that the PR Stud wrapped up with the resin mortar-A with silica is suited for the PR System (the requirement described in 2.4).
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5. Construction of Shiratori-bridge As one application example of PR System, it is non-composite, when the prestress is introduced by prestressed concrete steel, and the structure as composite structure is mentioned in service. The advantage of this PR System is that the loss of prestress due to the adhesion and friction of steel members can be minimized, and concrete and steel members can function efficiently as a result. Shiratori-bridge was designed and constructed based on the PR System concept as a connecting bridge in a golf course. Side view 17900
50 350
350 50
Cross section 3600
Main beam cross section 100 240 100
400 140
400
1000
2400
PR Stud 756
756
Resin Mortar Prestressing cable
1000
140
Prestressing cable
340
Figure 6. General drawing of Shiratori-bridge Table 4. Bridge specifications Bridge type Bridge length Bridge width Angle of skew Plane Pavement Floor slab Steel member Concrete
Pedestrian bridge 18.700 m 4.400 m 90.0 ° R= ∞ Asphalt (30 mm thick) Precast RC slab (140 mm SM400 Floor slab : σck=30 N/mm2 Web : σck=30 N/mm2
Table 5. Construction steps 1. Steel beam manufacturing 2. Resin mortar application 3. Concrete placement 4. Concrete curing 5. Tensioning of prestressing cable 6. Resin mortar curing 7. PRS beam (SC Beam) erection 8. Floor slab construction 9. Bridge deck construction
5.1. Specification of Shiratori-bridge Shiratori-bridge is designed for sidewalk live load and golf carts, a general drawing is given in Figure 6, the specifications are shown in Table 4, and construction steps are
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shown Table 5. The two main beams are PRS beams (named SC beams) in which steel beams are combined with prestressed web concrete by means of PR Studs and Timesetting resin mortar-B for steel plates. Precast concrete was used for the floor slab for the sake of reducing the construction period. The interface of the slab and the beams are combined through ordinary studs to form a composite beam system. While this was the first case to construct a PR System bridge, a sufficient cross section was adopted for the steel beams to ensure safety even without the web concrete. 5.2. Introduction of prestress to the PR System When the prestress is introduced to concrete in a conventional composite system, resistance caused by steel members needs to be taken into consideration. Even though only the concrete needs to be prestressed, the required input of prestress tends to increase due to this resistance. As a result, arrangement of prestressing cables may become difficult. In the PR System, however, concrete can be prestressed efficiently with little resistance from steel members, which are not well combined with the concrete before the hardening of resin mortars.
6. Summary In this paper, the basic concept of the PR System was first explained, and Time-setting resin mortars and PR Studs were tested to verify the practicability of the PR System (the requirement described in 2.1, 2.2, 2.3 and 2.4). We have reported on the construction of Shiratori-bridge as an example of a practical bridge by PR System. Because the PR System can be widely applied to various areas and structures, the effect of replacing a conventional structure with a PR System needs to be investigated on a case-by-case basis to identify the effective construction methods and the extent of application. The viscosity and hardening with the progress in the time of the Time-setting resin mortars used in the present study vary with temperature, and the slip constant before the hardening and the maximum sustainable shear depend on the stud diameter and the range wrapped by resin mortar-A. Such aspects require further investigation.
7. References [1] M.Sudo, H.Hiragi, A.Kurita, H.Watanabe, Y.Tachibana, and K.Kitagawa: Physical property tests on Time-setting resin mortar used for composite systems, The 55th Annual Conference of Japan Society of Civil Engineers (I), September 2000 (in Japanese). [2] K.Kitagawa, H.Hiragi, H.Watanabe, Y.Tachibana, and Y.Ushijima: Push-over shear test on Post Rigid (PR) Studs, The 55th Annual Conference of Japan Society of Civil Engineers (I), September 2000 (in Japanese). [3] Y.Tachibana, H.Hiragi, H.Watanabe, and K.Kitagawa: Outline of Shiratori-bridge, a Post Rigid System (PR System) bridge, The 55th Annual Conference of Japan Society of Civil Engineers (I), September 2000 (in Japanese).
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AN EXPERIMENTAL STUDY ON THE BOND-SLIP RELATIONSHIP BETWEEN THE CONCRETE AND STEEL WITH STUD Katsuyuki Konno*, Ahmed Farghaly** and Tamon Ueda** * Hokkaido Institute of Technology, Japan ** Hokkaido University, Japan
Abstract Beam type specimens where studs are used as shear connector are prepared to investigate constitutive relations. Parameters are stud height, compressive strength of concrete, stud spacing and steel plate thickness. The influences of these parameters are investigated in this study. The influence of the stud height is evaluated quantitatively and the influences of compressive strength of concrete, stud spacing and steel plate thickness are evaluated qualitatively.
1. Introduction Practical application of steel-concrete sandwich structure is getting more popular because of its high strength and easy construction. One of likely application is slab. However, capacity of sandwich slab, such as punching shear capacity, cannot be predicted with reasonable accuracy1). This is because load-carrying mechanism of sandwich slab has not been clarified yet. One of key issues for the clarification is constitutive relation for shear connector. In this study constitutive relation, transferred force-relative slip relationship, of stud shear connector is experimentally studied. There are studies on constitutive relations for stud. However, they are for studs in composite beam where stud is attached on flange plate of steel beam2). In sandwich structures steel plate on which shear connector is attached is externally attached to core concrete. This implies that steel plate in sandwich structure is more easily deformed in out-plane direction than flange plate in composite beam. Therefore, constitutive relations in sandwich structure are expected to be different from those in composite beam.
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2. Details of specimens Eight specimens were prepared for this experiment as shown in Table 1. Beam type of specimens was prepared as shown in Fig.1. No shear reinforcement was provided. The left side of the specimen in Fig.1 is tested side in which four studs were welded, while the right side was strengthened by arranging more studs. Headed studs that have 13mm diameter were welded to the steel plate. Material properties of the stud and steel plates are shown in Table 2. Parameters are stud height, compressive strength of concrete, stud spacing in longitudinal direction and steel plate thickness. Table 1 Specification of specimens fsy bt b S Ds hs ts r fc’ (N/mm2) (N/mm2) (mm) (mm) (mm) (mm) (mm) (mm) (mm) S-1 21.5 306 200 400 200 13 100 9 50 S-2 47.1 306 200 400 150 13 100 9 50 S-3 47.1 306 200 400 200 13 100 9 50 S-4 45.5 306 200 400 250 13 100 9 50 S-5 32.1 306 200 400 200 13 50 9 50 S-6 32.1 306 200 400 200 13 100 9 50 S-7 32.1 306 200 400 200 13 150 9 50 S-8 20.4 292 200 400 200 13 100 12 50 fc’ :compressive strength of concrete , fsy :yielding stress of steel plate , bt :spacing of stud in transverse direction , b :width of beam , S :spacing of stud in longitudinal direction , Ds :diameter of stud , hs :height of stud , ts :thickness of steel plate , r :width of loading plate Specimen
Table 2 Material properties of stud and steel plate Young’s modulus (GPa) 196 169 174 175
Material Stud Steel plate (6mm thickness) Steel plate (9mm thickness) Steel plate (12mm thickness)
Yielding stress (MPa) 378 255 306 291
1000 Displacement transducer
Artificial crack
400
Displacement transducer A
Displacement transducer
Displacement transducer B
Unit:mm Stud 2 Stud 4 Stud 1 Stud 3
Figure 1 Shape of specimen
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Poisson’s ratio 0.30 0.30 0.28 0.29
3. Experimental setup The deflection at the center of specimen stud was measured by displacement transducer B in Fig.1. The relative displacement between concrete and steel plate at the end : strain gage of the beam was measured by displacement transducer A in Fig.1. Strain gages were mounted on the steel plate (see Chapter 4) and studs (see Fig.2). The slip and the transferred force at studs were calculated by the strains of steel plate. Curvatures of Figure 2 Location of strain gages for stud studs were calculated by the strains of studs. The stud of 50mm height had 6 strain gages. The studs of 100mm height and 150mm height had 8 strain gages. The preliminary test of a specimen indicated that load decreased immediately after the crack had occurred at the center of the specimen. In order to prevent this immediate decrease in load, an artificial crack at the center of the span was introduced for the rest of the specimens.
4. Results of experiment 4.1 Transferred force and relative displacement at stud Figure 3(a) shows strain gages that were attached on the upper and lower surface of the steel plate to estimate the transferred shear force. Strain distribution in cross section d1 is shown in Fig.3(b) as an example. Strain at each location is an average of the upper and lower gages. Tensile force in cross section d1 was calculated by the hatched area (see Fig.3(b)) multiplied by the thickness and Young’s modulus of steel plate. Tensile force in cross section d2 was also calculated by the same procedure. The transferred force at stud 4 was assumed as difference between those two tensile forces. The load level of Fig.3(b) does not correspond to that of Fig.4(b). The slip δ was calculated by Eq.(1).
δ = δ 0 − ∫ ε dl
(1)
δ0 is relative displacement between concrete and steel plate at the end of the beam as shown in Fig.4(a). Figure 4(b) is strain distribution of the steel plate along the longitudinal direction obtained by the strain gages as shown in Fig.4(a). The relative displacement for stud 4 is obtained by taking integration of strain as shown by the hatched area in Fig.4(b). Four transferred force-relative slip relationships were obtained
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from four studs in one specimen. The average of the four transferred force-relative slip relationships is used to represent the experimental results of each specimen.
C L
d
c
3
1
3500
Strain(×10-6 )
Stud 2
4
Specimen Ｓ－ ７ Cross section ｄ２
3000 2500 2000 1500 1000 500 0 0
:strain gage
d1 d2
c1 c2
100
200
300
400
500
Distance from the side of specimen (mm)
Steel plate
(a) Top view of steel plate
(b) Strain distribution
Figure 3 Calculation of transferred force CL Steel plate
stud 3
stud 1 180 0
0
200
400
600
Top view
160 0
stud 2
800
140 0
1000 (mm)
:strain gage
Strain (×10 -6 )
stud 4
120 0 100 0 8 00 6 00
Location of stud
4 00 2 00 0 -20 0 0
200
400
600
800
1 00 0
-40 0
Concrete
Distance form center (mm)
Steel plate
(b) Strain distribution l
0
Side view
(a) Measurement Figure 4 Calculation of relative slip Figure 5 shows the transferred force-relative slip relationship of specimens S-1 and S-8. Points A and B in Fig.5 correspond to points A’ and B’ in Fig.6 which indicates the transferred force-curvature relationships. The stiffness of specimen S-8 suddenly starts to decrease at point A in Fig.5 at which the curvature suddenly start to increase as shown
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Transferred force (kN)
in Fig.6 (a). This fact implies that the relative displacement calculated by Eq.(1) is caused by deformation of the stud rather than that of the surrounding concrete.
-0.2
45 40 35 30 25 A 20(58.8kN) 15 ← 10 5 0 -5 0
B (68.3kN) →
ts= 9mm ts= 12mm Assumed line of (ts= 9mm)
0.2
0.4
0.6
0.8
180
180
160
160
140
140
120
120
80mm 60mm 40mm 20mm
100 80 60 40
Load （ｋ N）
Load (kN）
Slip (mm) Figure 5 Transferred force-relative slip relationship (parameter of steel plate thickness)
100
← A' 58.8kN
80 60 40
20
20
0
0
-20 -0.001 0
← B' 68.3kN
80mm 60mm 40mm 20mm
0.001 0.002 0.003
-20 -0.00025 0.00075 0.00175 0.00275
Curvature （ｒ ａｄ）
Curvature （ｒ ａｄ）
(b) Case of ts=9mm (a) Case of ts=12mm Figure 6 Curvature of stud (parameter of steel plate thickness) 4.2 Stud height Figure 7 shows transferred force-relative slip relationships of specimens S-5, S-6 and S7. The transferred force and relative slip relationship of specimen S-6 is close to that of specimen S-7. Curvatures of the stud were calculated by the strain gages attached on the stud and shown in Fig.8. Locations of the strain gages from the bottom of the studs are
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denoted in the legend. The curvatures of portions at height equal to or lower than 60mm become larger with increasing load, however the curvature of portion at height equal to or higher than 80mm is almost zero. Those behaviors indicate that the effective height of stud below which the stud is deformed exists. It was assumed that 70mm is the effective height of stud. Namely if a stud is higher than 70mm, its performance is almost same as a stud with 70mm height. It was also assumed that when a stud is lower than 70mm, its rigidity in the transferred force-relative slip relationship is proportional to height of the stud. The broken line in Fig.7 is the transferred force-relative slip relationship of specimen S-5 multiplied by 70/50 that is ratio of the assumed effective height to the stud height of specimen S-5. The broken line is close to the curves of specimens S-6 and S-7.
Transferred force (kN)
120 100 80 60 hs= 50mm
40
hs= 100mm hs= 150mm
20
70/50×(hs= 50mm)
0 -0.2
0
0.2
0.4
0.6
0.8
1
Slip （ mm)
200
150
150
100 50
36m m 24m m 12m m
0 -0.002 0 0.002 -50 Curvature (rad)
250 200
100
80m m 60m m 40m m 20m m
50 0
0.004
-0.001
0
0.001
-50 Curvature (rad)
0.002
Load （kN）
200
Load (kN)
Load (kN)
Figure 7 Transferred force-relative slip relationship (parameter of stud height)
150 100 50
120m m 90m m 60m m 30m m
0 -0.001 0 0.001 0.002 -50 Curvature (rad)
(b) hs=100mm (c) hs=150mm (a) hs=50mm Figure 8 Curvature of stud (parameter of stud height)
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Transferred force (kN)
4.3 Other factors Figure 9 shows the transferred force-relative slip relationship of specimens S-1, S-3 and S-6. The higher compressive strength of concrete has higher stiffness. It was observed that the difference in stiffness was greater than the difference in the compressive strength (transferred force ratio for the same relative displacement is greater than the compressive strength ratio).
-0.1
180 160 140 120 100 80 60 40 20 0 -20
fc'= 21.5MPa fc'= 47.1MPa fc'= 30.1MPa
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Slip (mm)
Figure 9 Transferred force-relative slip relationship (parameter of compressive strength)
Transferred force （ kN)
Figure 10 shows transferred force-relative slip relationship of specimens S-2, S-3 and S4. The transferred shear force was largest in the case of 200mm stud spacing. From the figure any clear effect of stud spacing in longitudinal direction cannot be seen. Variation in the transferred force–relative displacement relationships might be due to experimental scatter.
-0.1
180 160 140 120 100 80 60 40 20 0
s= 250mm s= 200mm s= 150mm 0
0.1
0.2
0.3
0.4
0.5
0.6
Slip （ｍｍ）
Figure 10 Transferred force-relative slip relationship (parameter of steel plate thickness)
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Figure 5 shows the transferred force-relative slip relationship of specimens S-1 and S-8. Specimen S-1 shows lower stiffness for lower transferred force and higher stiffness for higher transferred shear force, however the difference is not so significant between two specimens. Generally there was a rather large scatter among the observed transferred shear forcerelative displacement relationships, so that the effects of factors could not be seen clearly. Further experimental study is necessary.
5. Conclusions 1) It was considered that relative displacement at stud was induced by deformation of stud itself rather than that of its surrounding concrete. 2) It was clarified that there is an effective height of stud, which was around 70 mm, for shear transfer. Stiffness of the transferred force-relative slip relationship might be proportional to stud height when stud height is lower than the effective height. 3) It was observed that concrete compressive strength increases significantly stiffness of transferred force-relative displacement of stud. 4) Effects of other parameters considered in this study, stud spacing in longitudinal direction (loading direction) and thickness of base steel plate could not be seen clearly probably due to experimental scatter. Further experimental study is necessary.
6. References 1.
Takahashi,R., Ueda,T., Sato,Y., Konno,K. and Farghaly, A., ‘ Study on punching shear falure mechanism of open-sandwich slab with finite element method’, Proceedings of the 4th symposium on research and application of hybrid constructions, Nagoya, November, 1999 (Japan Society of Civil Engineering, Tokyo, 1999) 43-46. 2. Tajima,J, Machida,A, and Ohtomo,T, ‘Behavior of stud connector in joints between steel member and reinforced concrete member’, Proceedings of symposium on research and application of composite constructions, Tokyo, September, 1986(Japan Society of Civil Engineering, Tokyo, 1999)137-144.
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THE BEHAVIOR OF BEAM-TO-BOX COLUMN CONNECTION OF CFT WITH AIR CAVITY Lee, Myung-Jae*, Choi, Moon-Sik**, Kim, Jin-Ho*** and Jun, Sang-Woo**** *Dept. of Architectural Eng., Chung-Ang Univ., Korea **Dept. of Architectural Eng. Dan-Kuk Univ., Korea ***RIST, Korea ****RIST, Korea
Abstract The objective of this study is to investigate the structural behavior of beam-to-column connection of CFT(Concrete Filled Tube) when air cavity exists under the diaphragm of CFT members. CFT can be expected the confined effect between steel tube and infilled concrete if only the concrete is filled perfectly without air cavity. The rectangular hollow section members are used for steel tubing of CFT member in this study. The short column tests and the beam-to-column connection test with air cavity are carried out. The ratio of air cavity with respected to the infilled concrete area is also discussed about the strength and the deformation of connection by using of CFT. It is seen that the influence of air cavity about CFT is not severe within admissible range.
1. Introduction CFT(Concrete Filled Tube) columns have better structural performance compared with hollow tubular columns. The confined effect of CFT is well known from the test results. The width-to-thickness ratio of hollow tubular members is restricted respectively to use it for structural elements. The encasement of concrete can prevent steel parts from occurring local buckling in case of CFT. Infilled concrete can take a share in large axial forces of columns in case of high rise buildings. But it must be careful that air cavity occurs in the tube when concrete is not perfectly filled. There were some short column test about CFT with air cavity by another researchers, but the test of beam-to-column connection is seldom in the case of the CFT connection with air cavity. The objective of this study is to investigate the behavior of short columns and the structural behavior of beam-to-column connection of CFT when air cavity occurs under the diaphragm. The rectangular hollow section members are used for steel tube of CFT member. The parameters of the test for this study are the ratio of axial force and the ratio of air cavity with respect to the infilled area of concrete. The
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influences of those parameters are investigated from the test results. The ratio of air cavity with respected to the infilled area of concrete is also discussed about the strength and the deformation of connection by using of CFT.
2. Short Column Test with Air Cavity 2.1 Material properties of tubes and H-shaped section steel Two types of rectangular tube and one type of H-shaped section steel were used for specimens which are for short column test and beam-to-column connection test. The results of tension test are shown in Table 1. It was ascertained that their material properties satisfied Korean Standards (KS) as SS400 class steel. 2.2 Specimens with air cavity Six short columns with air cavity were tested to investigate the influence of strength and deformation. -250×250×6 is used for rectangular hollow section members. The configuration of specimens is shown in Figure 1. They have penetration type diaphragms with thickness 9mm and circular hole to fill concrete continuously. The ratio of air cavity varies from 0% to 75%, and it means the ratio of air cavity area with respected to the infilled area of concrete. The location of air cavity and the circular holes to fill concrete are shown in Figure 2. Soft styrene with 5mm thickness was used for artificial air cavity. The infilled concrete with 24 MPa compressive strength was used. 2.3 Short column test results Figure 3 shows the short column test setup. Test machine with 9800kN capacity was used. Maximum loads of short columns are shown in Table 2. Specimen RF-20 and specimen RF-20M are different in the diameter of circular hole. The ratios of strength in case of air cavity with respected to that without air cavity also shown in this table. Figure 4 shows the load-displacement relationships of short columns. CFT short columns have better structural performance compared with hollow tubular columns such as specimen RH-0 as shown in this figure. It can be seen from Figure 4 that the maximum strengths of all specimens are higher than the superposition strength of tube and concrete. The difference of initial stiffness can not be found even though in case of the ratio of air cavity of 50%. The initial stiffness changes in case of the ratio of air cavity of 75% compared with another cases. Table 1 : The results of tension test Yield strength Maximum (MPa) strength (MPa) 403 484 -250×250×6 288 459 -500×500×12 296 427 H-582×300×12×17
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Yield ratio Elongation (%) 0.83 0.63 0.69
33 42 46
Table 2 : The results of short column test with air cavity Diameter Ratio of Maximum Specimen Tube of hole air cavity load (kN) (mm) (%) RH-0 0 1089 RF-0 0 3736 128 RF-20 20 3559 -250×250×6 RF-20M 100 20 3550 RF-50 50 3197 128 RF-75 75 3003
Figure 1 : Configuration of specimens
Figure 2 : Location of air cavity
Figure 3 : Short column test setup
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Case of air cavity/ Case of no air cavity 1.00 0.95 0.95 0.86 0.80
The regression curves about air cavity of CFT was suggested as follows in Ref. 5.
(c N
c N0
)n + (α 100)n = 1
(1)
where, cN
= N max − s A⋅s σ y
c N0 =c A ⋅ σ B
N max : Maximum strength from test s c
A : Section area of steel tube A : Section area of concrete
sσ y
: Yield stress of steel
σ B : Compressive strength of concrete α : The ratio of air cavity (%) Test results are compared with Eq.(1) in Figure 5. The strengths of each specimen are presented in nondimension with their axial forces in this figure.
3. Beam-to-Column Connection test 3.1 Specimen with air cavity Five subassemblage specimens were tested to investigate the structural behavior. Their geometrical configurations are shown in Figure 6. The story height is 3600mm and span length is 5600mm. The steel section of column was fabricated by partial-penetration welding at every corner seam. Cross section of columns are 500mm square and shear span length is 1509mm. Distance from loading point of the beam to the column face is 2550mm. The beam-to-column connections were reinforced by two horizontal diaphragms with circular hole.
The parameters of specimen are the ratio of axial force, the ratio of air cavity. The specimens of BSM-00 and BSM-02 in Table 3 do not have air cavity. The specimens of BSM-02-10, BSM-02-20 and BSM-02-30 in Table 3 have 10%, 20% and 30% air cavity respectively. Soft styrene with 5mm thickness was also used for artificial air cavity as like as short columns. All the specimens except BSM-00 were tested in the condition of axial force ratio of 0.2. 3.2 The Results of Beam-to-Column Connection Test Three sets of loading system were used for test. Monotonic loading applied to each specimens assuming lateral loading condition. The configuration of beam-to-column connection specimen is shown in Figure 6. Dial gauges and wire strain gauges were used to measure displacements and strains.
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4500 4000 3500
Load (kN)
3000 2500
prediction load
2000
R H -0
1500
R F-0 R F-20 R F-20M R F-50
1000 500
m axim um load
R F-75
0 0
5
10
15
20
25
30
35
40
A xialD isplacem ent (m m )
Figure 4 : Load-Displacement relationships of rectangular CFT short columns
1 .0
cN / cNo
0 .8 0 .6 0 .4 E q .(1 ) (n = 2 ) E q .(1 ) (n = 1 .5 ) C FT
0 .2 0 .0 0
20
40
60
80
100
R a tio o f a ir c a vity (% )
Figure 5 : Relationships between CFT strength and air cavity
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2940kN Actuator
980kN Actuator
1509
980kN Actuator
D9
D7
D2
1509
D6 D4
D8
12
207 30
H-582x300x12x17 D3 ¡ à -500x500x13
500
D5
D1 500 Reinforced diaphragm detail
2800
2800
Figure 6 : Setup of beam-to-column connection specimen Table 3 : The results of beam-to column connection test Ratio of air H-shaped Specimen Tube cavity section steel identification (%) BSM-00 0 BSM-02 0 BSM-02-10 -500×500×12 H-582×300×12×17 10 BSM-02-20 20 BSM-02-30 30
Ratio of axial force 0.0 0.2 0.2 0.2 0.2
Maximum Maximum story shear story drift force (kN) (rad) 900 737 778 738 734
0.51 0.20 0.18 0.13 0.14
The results of beam-to-column connection test are listed in Table 3. The relationships of story shear force and story drift of each specimen are shown in Figure 7 and Figure 8. Qpb and Qyb mean equivalent plastic shear force and equivalent yielding shear force of beam respectively. Qcp and Qyc mean equivalent plastic shear force and equivalent yielding shear force of CFT column respectively. The structural behavior of BSM-00 specimen, which do not have air cavity and do not loaded axially, is shown in Figure 7(a). Maximum strength occurred in the point of welding crack of the flange of H-shaped beam. Local buckling happened in case of BSM-02 specimen but the behavior continued until the fracture of flange. The loading test was stopped in case of BSM-02-10 specimen when the flange fractured. The specimens of BSM-02-20 and BSM-02-30 showed very unstable behavior after the fracture of flange.
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1200 1000 800
800
Q yc
600 Q pb Q yb
400
Q pc Q yc
1000
Q c (kN)
Q c (kN)
1200
Crack of Fracture w elding of flange Q pc
Local buckling
600 Q pb Q yb
400 200
200
0 0.0
0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R t (rad)
0.1
(a) BSM-00
Fracture of flange
Q c (kN)
Q c (kN)
800
Q pb Q yb
400 200
0.1
0.2 0.3 R t (rad)
0.4
600 Q pb Q yb
400
0 0.0
0.5
0.1
0.2 0.3 R t (rad)
(d) BSM-02-20
1200
Q c (kN)
Fracture of flange
200
(c) BSM-02-10
800
Q pc Q yc
Fracture of flange Local buckling
600
Q pb Q yb
400 200 0 0.0
0.5
Q pc Q yc
1000
600
1000
0.4
1200
Q pc Q yc
800
0 0.0
0.2 0.3 R t (rad)
(b)BSM-02
1200 1000
Fracture of flange
0.1
0.2 0.3 R t (rad)
0.4
0.5
(e) BSM-02-30 Figure 7 : Story shear force–Story drift of BSM specimen
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0.4
0.5
1200 Q pc(N /N y=0 .2 )
Qyc(N/Ny=0.2)
1000
Q pc(N /N y=0 .0 )
Q c (kN) .
800 Qyc(N/Ny=0.0) 600 Qpb Qyb
400
BS M- 00 BS M- 02 BS M- 02- 10 BS M- 02- 20 BS M- 02- 30
200 0 0.0
0.2
0.4
0.6
0.8
R t (rad)
Figure 8 : Story shear force – Story drift of specimens according to air cavity It is seen in Figure 7 and Figure 8 that the connection strengths of all specimens are higher than the equivalent plastic shear force of H-shaped section beam although the crack of welding part or the fracture of flange occurred in all specimens. N/Ny in Figure 8 means the ratio of axial force. The deformation capacity of specimens with air cavity, that are BSM-02-10, BSM-02-20 and BSM-02-30, is lower than that of BSM-02 specimen, but it is thought that the tendency is not so severe. The difference of the quantity of air cavity is not seen from this test results. Almost same structural behaviors of specimens with air cavity were shown in the strength and the deformation as like as Figure 7. The influence of air cavity is not clear within the ratio of air cavity of 30% compared with the test result of BSM-02 specimen.
4. Conclusions The air cavity of CFT was investigated through the short column test and beam-tocolumn connection subassemblages test. Concluding remarks could be obtained as follows; (1) The difference of initial stiffness can not be found even though in case of the ratio of air cavity 50% from short column test results. (2) The strength of CFT columns depends on the ratio of air cavity, but the strengths of all specimens are higher than the superposition strength of tube and concrete.
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(3) The influence of air cavity is not clear from the beam-to-column connection subassemblages test within the ratio of air cavity 30%. (4) However the welding part of flange was fractured in all specimens with air cavity in case of axial loading and the deformation capacity of CFT can not be expected from test results.
5. References 1. 2. 3. 4. 5.
Korean Society of Steel Construction, ‘Recommendations for Design and Construction of Concrete Filled Steel Tubular Structures’, 2001 (in Korean) Matsui, C. et. al., ‘Concrete Filled Steel Tubes A Comparison of International Codes and Practices’, ASCCS, 1997 Architectural Institute of Japan, ‘Standard for Structural Calculation of Steel Reinforced Concrete Structures’, 1987 (in Japanese) Architectural Institute of Japan, ‘Recommendations for Design and Construction of Concrete Filled Steel Tubular Structures’, 1997 (in Japanese) Kosugi, et al, ‘A Experimental Study on Filling Up of CFT Columns (Stub Column Test)’, the proceedings of anniversary meeting of AIJ, 1989 (in Japanese)
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SHEET REINFORCEMENT O. Matthaei*, H.-P. Andrä**, Nguyen Viet Tue*** *Matthaei und Schotte Ingenieure, Consulting Engineers, Stuttgart, Germany **Leonhardt, Andrä und Partner, Consulting Engineers, Stuttgart, Germany ***König, Heunisch und Partner, Consulting Engineers, Frankfurt, Germany
Abstract Especially in case of shear or punching-shear failures the connection of concrete and steel elements influence the global behaviour of failure loads. In reinforced concrete structures, to exploit the material properties, shear elements are essential to connect the tension zone with the compression zone to increase the bending and shear capacity. Instead of using shear hooks or dowels a new shear and punching shear reinforcement working with concrete dowels will be presented. The local failure mechanism of concrete dowels to prevent the shear failure in flat slabs will be explained.
1. Introduction The most standards to design flat slabs with shear reinforcement in case of punching shear action have been developed out of the models from beams. Significant differences between stress results and stress combinations of continuous beams or slabs haven’t been considered. The major different is the direction and redistribution of stresses. In continuous beams, bending moment and shear stresses act in the same direction, in slabs independent from each other and for slabs which are supported on surrounded holes even orthogonal. Reinforced concrete slabs approach in case of increasing the crack widths to hole supported slabs. Therefore the division of effects of bending moment and shear force, especially the internal forces near interior-column don’t allow a comparison between shear behaviour in beams and in flat slabs. In some design standards, where no consideration of the „real“ physical behaviour of slabs is used, the lack is tried to compensate with safety factors.
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In order to find a „near“ physical model for the punching shear behaviour we define: Punching shear failure is the burst of a concentric stamp of cone out of the plate, where the internal forces next to the column are comparable to slabs, which are, supported circuit the column, with a hole in the middle. The resistance only depend on the normal to the cone surface activated tensile strength of concrete.
2. Failure mechanism and mode of action of shear reinforcement Failure mechanism often means rotation of plate sectors around the column side, figure 1.
Figure 1: Rotation of Plate sectors In case of this failure mechanism one or more circlet cracks opened wedge-shaped. This means by using shear reinforcement that steel elements at the close range to the column have less strain and therefore less stress than the elements at the outer perimeter, figure 2.
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Figure 2: “theoretical” strain in shear reinforcement according to the opened wedge-shaped Compared to test results, stresses in shear reinforcement generally appear like in figure 3. Finally you will come to the conclusion that the expected cracks and failure mechanism should be wrong.
Figure 3: stresses and strains in shear reinforcement according to measured results in tests
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In analogy with failure mode and measured results you must come to the conclusion that the shear reinforcement is working like a suspension through the separated shapes, not only to increase the shear capacity also to connect the compression zone with the tensile zone, which is essential for the bending capacity, figure 4.
Figure 4: circuit supported slab round column Shear reinforcement in the inner perimeter have to carry in comparison to outer perimeters more loads. These forces are supported next to the column, so due to this tensile forces in the compression zone will appear next to the column especially during increasing the loads up to the failure load. Thereby with this theoretical model, the measured strains in shear reinforcement are comparable with the crack-width observed in several tests.
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Figure 5: radial bending in the zone close to the column, observed and measured crack-width Close to the column the thickness of the separated plate is not enough to anchor single hooks. These elements will broke and won’t further work as proper shear elements to prevent the punching shear failure, figure 6. In figure 7 the classical stud-rail is able to fulfil this, cause of the rail, which is penetrating into the column.
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Figure 6: anchorage problem of single hooks in the inner perimeter
Figure 7: prevention of anchorage problems by using of stud-rails The isolation of the direction of action from bending and shear forces enable other possibilities to increase the punching shear resistance by the use of steel cellar inside the plate, i.e. like the “Geilinger Kragen” or the “Tobler Walm”. Herein the shear forces were carried radial to “steel column head” and not like in the classical strut and tie model.
Figure 8: steel column head
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3. Sheet reinforcement As a consequence to the observed mechanism of failure mode the authors suggest thin vertical sheet metals, called „sheet reinforcement“, arranged round the column, between the top and bottom reinforcement, figure 9.
3 2 1
1 2 3
Figure 9: Perfobond Sheet Reinforcement
These sheets will carry the shear forces out of the concrete, by concrete-dowels, and will carry them to the column. These holes are preventing a possible cut off into sectors due to the sheets. The shear reinforcement is extremely thin, only about 3mm thick. A stability problem won’t exist cause of the covered and surrounded concrete. To prevent a drop down failure in case of dynamic loads like in case of earthquakes the sheet will envelope the bending reinforcement of the column. Once the shear forces are in the sheet the internal loads can easily be redistributed, up to the minimal punching shear cone in the failure state. According to the steel column head an isolate direction of action of bending and shear is possible, figure 10.
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Figure 10: Perfobond Sheet Reinforcement in circuit supported slab round column With this kind of shear reinforcement a punching shear failure can easily be prevented. The failure mechanism will be in analogy to the yield-line theory, figure 11.
Figure 11: failure mechanism forced to sheet reinforcement according to yield line theory
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4. Conclusion From the characteristics of the punching shear failure in comparison to “simple” shear fracture the different mode of operation in case of different reinforcements is explained. As a consequence to the observed mechanism of failure mode the authors suggest thin vertical sheet metals, called „sheet reinforcement“, as a new shear reinforcement, working in analogy to the perfobond. To the true model of action at this time tests and a Non-linear FE-Analysis is in progress.
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COMPOSITE GIRDERS OF REDUCED HEIGHT Ulrike Kuhlmann, Jürgen Fries, Andreas Rieg Institute of Structural Design, University of Stuttgart
Abstract Composite girders with reduced height and slim-floor girders are an attractive and economical alternative to normal reinforced concrete beams and slabs. Due to the shallow height of these section types their structural behaviour differs decisively from normal composite beams. As a consequence the common design philosophy for normal composite beams leads to uneconomical safe side assumptions for the ultimate carrying capacity and to far too large calculated deformation values for the serviceability limit state. The results of investigations on a slim-floor hat section are presented and some specific problems of these composite section types are discussed. The design method of common composite beams have to be modified for composite girders with reduced height and especially the contribution of the concrete section to the structural behaviour of composite girders with reduced height is relevant.
1. Introduction Economical and architectural advantages have led to new forms of composite cross sections which consist of a reinforced concrete slab connected to a steel girder that only slightly exceeds the slab thickness (see Figure 1.1 a)). Innovative sections even include the steel section within the slab (see Figure 1.1 b)). Especially for the latter, named slimfloor sections, a rapid and promising development has taken place. transverse reinforcement
transverse reinforcement
headed studs
headed studs steel I-profile
profiled steel sheets or filigree floor elements
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UPE-profile welded bottom flange
Figure 1.1: a) Composite section with reduced height, b) Slim-floor section In comparison to common reinforced concrete slabs and beams composite girders of reduced height show significant advantages [2], [3]: - They have a high load resistance and flexural stiffness. - The reduced depth allows a better exploitation of the building height or even extra floors. a)
-
b) Due to the high degree of prefabrication of the steelwork they are easily and quickly erected. Standard fasteners may be used for installation. The dead load per floor is reduced.
The hat section shown in Figure 1.1 b) has been chosen for further investigations because of the following reasons: - The plane bottom view allows a free architectural design and may be used as final room enclosure. - Headed studs can be applied to realise a systematical composite action. - Transverse to the slim-floor girder spanning slabs may act continuously. - By welding of the steel hat section precamber can easily be attained. For the slim-floor hat section intensive investigations as well experimentally as numerically have been undertaken. They led to design guides for practical usage [3], [12] but also revealed some specific problems.
2. Definition of composite girders with reduced height For normal composite sections an external moment is balanced by a pair of internal normal forces only completed by the bending resistance of the steel section. The bending resistance of the concrete slab is usually negligible. In contrary due to their geometrical properties composite girders with reduced height lie between composite beams and pure reinforced concrete beams. Their concrete bending resistance and flexural stiffness are of importance. Neglecting this influence e. g. by usage of the common calculation methods developed for normal composite sections leads to an uneconomical safe side estimation of the ultimate carrying capacity and to unrealistic high calculated deformation values in the serviceability limit state. To distinct composite sections with normal height and reduced height the following criteria may be applied: a) Ratio of the flexural stiffness of the concrete to the overall flexural stiffness Ic,0/Ii,0 > 0,1 b) Appearance of cracks due to bending in the concrete chord in serviceability
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Figure 2.1 a) shows the distinction of composite beams of reduced and normal height in dependence of the slab thickness hc. Two lines separate the ranges of composite girders with normal height and composite girders with reduced height. Line 1 represents the borderline between composite sections in cracked and uncracked condition in serviceability limit state. Line 2 gives composite sections characterised by a ratio of the flexural stiffness of the concrete chord to the overall flexural stiffness Ic,0 / Ii,0 = 0,1. In HEA
possible span lb [m] 25
1000
normal height
normal height
8 00
20
reduced height 6 00
15
reduced height
4 00 2 00
10
1
hc
1
2
HEA
slab thickness hc [cm]
0 16
20
24
28
lb
5
slab thickness hc [cm]
0
32
2
16
20
24
28
32
Figure 2.1 b) the possible simple beam spans lb corresponding to the cross sections shown in Figure 2.1 a) for the ultimate limit state are given. The possible spans range up to 10 ÷ 20 m. So composite girders with reduced height have a wide field of application. a) b) Figure 2.1: Distinction of composite girders with reduced height (concrete C30/37, steel S 355, live load p = 3,5 kN/m²). Line 1: cracks in concrete chord, line 2: Ic,0/Ii,0 = 0,1 But also the even more slender slim-floor girders with the hat section show a range of application [1], [3] which forms an attractive alternative to usual reinforced concrete beams underneath the slab, see Figure 2.2.
span of slab ls [m]
p = 3,5 kN/m² span of slim-floor girders lb [m] C 30/37 4 5 6 7 8 9 10 4 5 6 7 8 9 10
transverse reinforcement
headed studs
UPE-profile welded bottom flange profiled steel sheets or filigree floor elements
simple beam continuos beam
Figure 2.2: Slim-floor beams composed of channel profile welded to a steel plate
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3. Structural behaviour of composite girders with reduced height and slim-floor girders 3.1.
Behaviour in ultimate limit state
3.1.1. Moment resistance For composite girders with reduced height the distribution of the internal moments and forces differs decisively from the behaviour of normal composite beams (see Table 3.1). Whereas for normal composite beams almost the whole external moment is balanced by a pair of internal forces and the internal concrete and steel moment are of the order of only 5 %, for composite girders with reduced height the contribution of the concrete moment Mc to the overall load resistance reaches up to 30 % provided a common degree of partial shear connection of η ≥ 0,7. There are two main reasons for this increase of the concrete moment: First the concrete chord of composite girders with reduced height has a higher reinforcement ratio than normal composite girders due to crack-width limitation (see paragraph 3.2.2) and a possible fire protection reinforcement. Additionally the lever arm of this reinforcement is comparably large to the shallow overall height of the composite girder. Table 3.1:
Internal forces and moments of composite girders with reduced height
Internal moments ULS SLS
normal height slim-floor normal height slim-floor
Mc
Ma
MV = Na * ast
5% 30 % 5% 30 %
5% 5% 30 % 10 %
90 % 65 % 65 % 60 %
The concrete moment does not only contribute to the moment resistance of the composite section but also reduces the amount of necessary shear connectors because the concrete moment acts just in the concrete member. 3.1.2. Influence of the structural system of the slab In the case of slim-floor girders the effects of the continuous slab must be taken into account: The support moment of the continuous slab at the slim-floor beam is balanced by a pair of forces (see Figure 3.1 a)), tension in the upper slab reinforcement and pressure at the lower part of the steel section. Additionally the supporting of the slab on the lower flange of the steel section causes a transverse moment in the lower steel flange (see Figure 3.1 b)).
a) Support moment of the slab
b) Supporting of the slab on the lower flange
Figure 3.1: Effects of the continuous slab on the steel section of the slim-floor girder
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Both effects may be considered by reducing the effective cross section of the steel section in the structural analysis of the composite girder [1], [2], [3]. 3.1.3. Shear force resistance In contrast to normal composite beams the shear force of the concrete chord of composite sections with reduced height should not be neglected. The shear force of the concrete chord reaches up to 140 % of the shear force of the steel section [1], [12]. But to take advantage of the shear resistance of the concrete the concrete chord must be supported directly so that the shear force of the concrete chord is transferred straight to the support. It is recommended to perform the check of the shear force resistance in three steps so that the higher steps are only used if first is proved to be insufficient [1]: 1. The shear force shall be transferred by the resistance of the steel section only. 2. Additionally the shear resistance of the concrete chord without shear reinforcement may be taken into account. 3. The shear resistance of the concrete chord is increased by shear reinforcement. 3.1.4. Shear connection between steel and concrete In case of slim-floor girders the connection between concrete and steel is located in the lower region of the concrete section. According to Becker [6] the load bearing capacity of headed studs decreases down to 90 % of the normal value because of the presence of transverse tension. However in tests performed at the University of Stuttgart this influence of the location of the shear connection on the load bearing capacity of the headed studs could not be observed [1].
3.1.5. Fire resistance In the case of composite girders with reduced height similar to conventional composite sections the required fire resistance periods are normally achieved by common preventive measures against fire, e. g. fire protection casing. For slim-floor sections often sufficient fire resistance can be attained by arranging of fire protection reinforcement, fire resistance periods up to R120 are possible. Therefore these girders feature a high economy. In corporation with Salzgitter AG, Peine, Germany design tables for the slim-floor hat section shown in Figure 1.1 b) for diverse fire protection periods have been carried out [3]. 3.2.
Behaviour in serviceability limit state
3.2.1. General The flexural stiffness Ic,0 of the concrete chord of composite girders with reduced height normally amounts about 30 ÷ 60 % of the total flexural stiffness Ii,0 of the composite girder and therefore should not be neglected. The high bending moments in the concrete chord result cracking of the concrete already in the serviceability limit state (see Figure 3.2). The theory of elasticity is not valid anymore. The assumptions of the common
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elastic calculation methods are not fulfilled. In contrast to normal composite beams, whose concrete chord is fully under compression and therefore uncracked (see Figure hc ha
hc ε
ε
ha
3.2), elastic calculation methods need modification when being applied to composite girders with reduced height in serviceability limit state. a) normal height – concrete under pressure b) reduced height – cracks in concrete Figure 3.2: Composite beams with conventional sections in serviceability limit state The different distribution of the internal forces and moments of normal composite beams and composite girders with reduced height in serviceability limit state shows Table 3.1. To prevent the formation of wide cracks in composite girders with reduced height a longitudinal bottom reinforcement has to be added to the concrete section. The calculation of deflections of composite girders with reduced height with the common elastic calculation methods often leads to unrealistic high deflection values. In order to meet the requirements of serviceability a steel section is chosen that is bigger than for the ultimate limit state [1], [3]. In these cases the check of serviceability determines the design of the cross section and the high load resistance of these composite sections cannot be fully exploited. 3.2.2. Reinforced concrete chord In order to calculate the flexural stiffness of composite girders with reduced height and of slim-floor girders more realistically and to take advantage of the economy of these types of sections it is important to consider the contribution of the reinforced concrete chord [1], [2]. The additionally crack width limiting reinforcement and a possible fire resistance reinforcement highly increase the stiffness of the composite section. This influence becomes more significant with decreasing depth of the composite section, because the relative lever arm of the reinforcement increases. For the determination of a realistic stiffness the non-linear structural behaviour of the concrete chord in cracked condition has to be considered. In the case of a rigid shear connection this can be dealt with moment-curvature relationships for the whole composite section [1], [4] and in the case of a ductile shear connection with momentaxial-force-curvature relationships for the concrete section [1]. In the serviceability limit state for positive moments the influence of tension-stiffening on the flexural stiffness of composite girders with reduced height may be neglected [2],
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[4]. Tension-stiffening can be considered as an additional tension force which for a constant curvature causes an additional moment Mcm in the section. If the initial flexural stiffness of the composite section is high, such as for composite girders in serviceability, M Mcm high initial stiffness low initial stiffness
Mcm κ this only effects a slight increase of the flexural stiffness (see Figure 3.3). If the initial flexural stiffness is low, e. g. for composite girders with a yielding steel section, the increase of the flexural stiffness becomes more significant. Figure 3.3: Influence of tension-stiffening depending on the flexural stiffness As in the serviceability limit state the steel section of composite girders with reduced height remains elastical the increase of the stiffness due to tension-stiffening cannot be taken advantage of in building practice [1], [2], [4]. 3.2.3. Long-term behaviour of the concrete The long-term behaviour of the concrete caused by creep and shrinkage has to be considered in the cracked condition, too. Normally the distribution of the shrinkage strains εcs over the depth of the concrete chord is assumed to be constant. However in cracked regions of the concrete the stress resulting of shrinkage may be neglected. Thus in the design of ordinary reinforced concrete structures a triangular distribution of the shrinkage strains is considered (see Figure 3.4) [2], [4]. If this assumption is applied to composite girders with reduced height the calculated shrinkage deflections can be reduced up to 20 ÷ 50 %. εcs,∞ (a)
εcs,∞ (b)
Figure 3.4: Shrinkage of composite girders with reduced height. (a) composite girders with normal height, (b) recommendation for composite girders with reduced height. The time-dependent deflections resulting of creep and shrinkage of the concrete as well as the deflections resulting of imposed live loads and temperature stress cannot be influenced by precamber. If division walls cannot follow this deflections without damage a composite section with a higher stiffness or division walls which are not liable to settlement have to be chosen. Both measures reduce the economy of the system.
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3.2.4. Effective width of the concrete chord The effective width beff of the concrete chord takes the non-linear stress distribution in transverse direction into account. Whereas the influence of the effective width on the load bearing capacity is little, the flexural stiffness in the serviceability limit state is decisively concerned. The design rules of Eurocode 4, part 1-1 [9] only consider the parameters span length and support conditions. The load level is not taken into account. So in the serviceability limit state and the ultimate limit state the same values are applied. The effective width of the concrete chord for bending significantly exceeds the value for axial forces. It can even reach the existing width of the concrete chord in the case that the concrete chord is line-supported over the whole width. As in the common elastic calculation methods the concrete moment is neglected, this influence is not taken into account. First investigations indicate that as a consequence the flexural stiffness Ii,0 of composite sections with reduced height increases up to 30 ÷ 100 %. Further on the formation of cracks in the concrete causes a redistribution of the concrete stresses near the steel section to more outside lying regions of the concrete chord and the effective width increases, too. In the case of partial shear connection this increase rises higher because the contribution of the flexural stiffness of the concrete chord to the overall flexural stiffness becomes more important. Shrinkage of the concrete is restrained by the steel section. Because of the shear lag of the concrete chord this restraint decreases with increasing distance from the steel section [1], [4]. This may be considered by a fictitious width beff,s of the concrete chord. Neither in Eurocode 4 [9] nor in the known literature this fictitious width beff,s of the concrete chord is specified. So in design practice often the width beff,s for shrinkage is taken equal to the existing width of the concrete chord. That leads to unrealistically high calculated shrinkage deflections especially in the case of composite girders with reduced height. First investigations indicated that by the use of a more realistic width beff,s the calculated total deflection of composite girders with reduced height may be reduced to 20 ÷ 40 %. At the moment investigations concerning the effective width of concrete chords of composite girders with reduced height at the Institute of Structural Design, University of Stuttgart intend to specify the effective width of the concrete chord more precisely. The aim is that by a more realistic deformation check in many cases the verification for serviceability limit state can be fulfilled. 3.2.5. Shear connection between steel and concrete In case of partial shear connection the deflection of composite girders exceeds the one with full shear connection, because the slip between the steel and concrete reduces the composite action. In Eurocode 4, part 1-1 [9], 5.2.2 (6) this effect is taken into account by the following increasing factor δ/δc: δ δ = 1 + α ⋅ (1 − η) ⋅ a − 1 δc δc
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With
δa δc η α
deflection if only the flexural stiffness of the steel section is considered deflection of the composite girder with full shear connection degree of partial shear connection factor to consider the production process
In the case of composite girders with reduced height and slim-floor sections the increasing factor δ/δc according to Eurcode 4 results up to five and more [1], [2]. This leads to unrealistically high calculated deflection values and an uneconomical safe side design. In the French standard DAN [11] additionally the influence of the span of the beam on the increasing factor δ/δc is taken into account. For common degrees of partial shear connection of η ≥ 0,6 the increasing factor δ/δc is lower than 2. Also Dabaon determined the increasing factor δ/δc experimentally to less than 2 [5]. Further on an additional reason leads to the recommendation not to use the design rules of Eurocode 4 [9] concerning the increasing factor δ/δc [1]: Due to the partial shear connection the restraint of the steel section against shrinkage is lower than for full shear connection. If there is no shear connection at all the concrete chord shortens and slips on the steel section. Thus for partial shear connection the increasing factor of the shrinkage deflection lies between 1, for full shear connection, and 0, without shear connection. The calculation according to Eurocode 4, part 1-1 leads to a mechanical wrong deflection and an increasing factor δ/δc more than one [1], [2]. We recommend to consider the influence of a partial shear connection on the deflection of composite girders by the following modified flexural stiffness Ii of the composite girders [1], [12]: I i = α g ⋅ I i ,elastic = α c ⋅ I c,elastic + α a ⋅ I a ,elastic + α St ⋅ (Si ,elastic ⋅ a St ) [cm4] With
αg, αc, αa, αst reducing factors of the flexural stiffness of the composite, the concrete and the steel section as well as the static moment flexural stiffness of the composite section for full shear Ii,elastic connection according to the elastic theory effective flexural stiffness of the composite section with partial Ii shear connection Ic,elastic, Ia,elastic elastic flexural stiffness of the concrete and the steel section static moment of the composite section Si,elastic lever arm between steel and concrete ast
The global reduction factor αg can be estimated to 0,55 ÷ 0,65 for short term loading and to 0,15 ÷ 0,35 for long term loading [1], [12]. The reduction factors αc and αSt interact and depend on the degree of partial shear connection, the amount and position of the reinforcement, the time dependent behaviour of the concrete, etc [1], [12].
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4. Acknowledgement The authors gratefully acknowledge the financial support of their research by Arbeitsgemeinschaft industrieller Forschungsvereinigungen „Otto von Guericke“ e.V. AiF and Salzgitter AG, Peine.
5. Conclusions In this paper the different behaviour of composite girders with reduced height and slimfloor girders compared to normal composite beams are discussed and a distinction between these two girder typs is proposed. It is shown, that for the treated composite sections especially the contribution of the internal concrete moment to the load bearing capacity and the stiffness of the concrete section is of importance and for a realistic calculation and economic design should not be neglected. Composite girders offer the chance of combining the advantages of both materials to receive a common section which is as fire resistant as a concrete slab as quickly erected as a steel girder with similar easy means of connecting girders and columns and shows a higher stiffness and resistance than both. But to achieve this design and calculation must reflect the true behaviour of the section which for composite girders with reduced height lies between that of a normal composite girder and a pure concrete girder.
References [1] Kuhlmann, U., Fries, J.: Optimierung der Bemessung von deckengleichen Verbundträgern in Hutform, AiF research project, Institute of Structural Design, University of Stuttgart, Germany, 2001 [2] Kuhlmann, U., Fries, J.: Slim-Floor Deckenträger mit Hutprofil, Fachseminar und Workshop, Verbundbau 2, FH München und Bauen mit Stahl e.V. München, 1998 [3] Kuhlmann, U., Fries, J., Leukart, M.: Bemessung von Flachdecken mit Hutprofil, Stahlbaukalender 2000, Verlag Ernst & Sohn, 2000 [4] Rieg, A.: Kriechen und Schwinden bei Verbundträgern mit niedriger Bauhöhe, Diplomarbeit, Institute of Structural Design, University of Stuttgart, Germany, 1998 [5] Dabaon, M.: Beitrag zur teilweisen Verdübelung bei Verbundträgern, Dissertation, Institute of Steel, Timber and Mixed Building Technology, University of Innsbruck, Austria, 1993 [6] Becker, J.: Beitrag zur Auslegung der Verdübelung von Verbundträgern des Hochbaus unter ruhender und nichtruhender Belastung, Dissertation, Fachgebiet Stahlbau, University of Kaiserslautern, 1997 [7] Michl, T.: Gebrauchstauglichkeitsuntersuchungen beim Millenium Tower, Stahlbau 68 (1999), issue 8, page 631-640 [8] Kuhlmann, U., Kürschner, K.: Ausgewählte Trägeranschlüsse im Verbundbau, Stahlbaukalender 2001, Verlag Ernst & Sohn, 2001
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[9] Eurocode 4, Design of composite steel and concrete structures, Part 1-1: General rules and rules for buildings, ENV 1994-1-1, 1992 [10] Eurocode 3, Design of steel structures; Part 1.1: General rules and rules for buildings, ENV 1993-1-1, 1992 [11] Norme expérmentale AFNOR P22-391, Document d’Application National de la France pour ENV 1994, Partie 1-1 (DAN), 1994 [12] Fries, J.: Zum Tragverhalten von Flachdecken mit Hutprofil im positiven Momentenbereich, Dissertation, Institute of Structural Design, University of Stuttgart, Germany, 2001, in preparation
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INNOVATIVE DEVELOPMENT OF LIGHT STEEL COMPOSITES IN BUILDINGS R.M. Lawson*, S.O. Popo-Ola*+, D. N. Varley$ The Steel Construction Institute, Ascot, United Kingdom + Department of Civil Engineering, Imperial College of Science,Technology & Medicine $ Terrapin International Limited, United Kingdom *
Abstract Light steel construction comprises cold formed steel sections of typically 1.2 to 3.2 mm thickness. Composite construction is well established using hot rolled steel sections, but this paper explores the applications of light steel construction acting compositely with in-situ concrete or heavy duty boarding materials. A composite beam system is described which uses profiled strip or ‘top-hat’ shear connectors attached by pins to double C sections. A full-scale load test demonstrates its load resistance and stiffness for a 9m beam span. A complete building system may be envisaged which uses C and Z sections acting as permanent formwork to in-situ concrete. Walls may be constructed from two skins of vertically orientated decking which possess high compression and shear resistance, as demonstrated by a series of load tests. Flooring and walling materials can improve the stiffness of light steel floor joists and wall panels, and the results of various serviceability tests are presented which demonstrate the increase in stiffness that can be achieved. A full-scale test on a 2 storey building constructed using light steel framing shows that the masonry cladding can have an important effect on the shear resistance and stiffness of the building.
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1. Introduction Composite construction is well established in modern building practice(1,2). The main components are a steel framework, steel decking, shear connectors, and in-situ concrete with mesh reinforcement. The benefits of composite construction are: speed of construction due to rapid erection of the steel framework, economy in use of materials, robustness to damage, and good performance in service The same principles can be extended to other forms of steel construction. Light steel framing comprises galvanized cold formed steel sections of C or Z or similar forms of 1.2 to 3.2 mm thickness. Steel decking is often used as a flooring element with floor boarding, or acting with in-situ concrete to form a composite slab. Composite action can be achieved in various ways, but as yet no design methods exist for the composite design of light steel frames or floors, other than conventional composite slabs designed to BS 5950 Part 4(3). This paper reviews the various opportunities for, and applications of composite construction using light steel frames and components, and presents the available test results that demonstrate the degree of composite action that can be achieved. The forms of construction reviewed in this paper are: • • • • •
composite beams using double-C sections with steel decking and in-situ concrete, and strip shear connectors attached by powder actuated pins. composite frames using C and Z sections with steel decking and in-situ concrete in which the framework acts as permanent formwork. steel decking orientated vertically acting with in-situ concrete to form a doubleskin composite wall. heavy duty flooring acting compositely with light steel floor joists to improve the stiffness of the floor. heavy duty walling acting compositely with light steel wall panels to improve the diaphragm action of the wall.
In modern composite construction, the steel framing elements are erected first and provide a stable structure which is capable of supporting construction loads. The composite action that is developed later with the concrete or other material serves to provide resistance to imposed loads, and importantly, to improve the stiffness of the construction. Often serviceability criteria dominate in modern design and therefore control of deflections and vibration response are as important as load resistance. More slender construction can be achieved by composite action, which leads to benefits in terms of floor-floor zones. Good robustness and seismic resistance are also achieved by these composite systems.
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2. Composite Light Steel Beams Composite light steel beams use double C sections rather than hot rolled steel I beams, but the general form of construction is similar to conventional composite construction. Importantly, welded shear connectors cannot be used for the relatively thin steel used in light steel construction, and therefore it has been necessary to develop alternative forms of shear connectors using powder actuated, or pneumatically driven pins. These shear connectors use ‘top hat’ or profiled strip steel elements which are fixed by 2, 3 or 4 pins per deck rib. The precise form of these shear connectors is not so important because of the relatively low force that is transferred locally to the concrete. However, the ‘top hat’ or profiled shape is designed to support the mesh reinforcement and help to provide crack control at the supports. The two forms of shear connector are illustrated in Figure 1.
Figure 1: Typical light steel composite beam using profiled strip shear connectors
The general principles of composite design using light steel sections are: •
the light steel beams are designed elastically to support the loads acting during construction. Single temporary props may also be used to control deflections at this stage.
•
the composite light steel beams are designed plastically to support the loads acting at the ultimate limit state. Plastic design is possible because the steel section acts entirely in tension.
•
the minimum degree of shear connections should observe the requirements of EC4 or BS 5950 Part 3. This is justified if the shear connectors achieve the ‘ductility’ requirements of EC4, corresponding to 6 mm minimum deformation at their design resistance.
Push-out tests have been carried out to establish the load-slip relationship of the profiled strip shear connectors using 2 powder-actuated pins per deck rib(4). The test shear resistance per pin is approximately 13 kN for a base steel thickness of 2.4 mm. Failure occurs by rotation of the pin and eventually by pull out of the pin at a deformation of over 6 mm.
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2.1. Tests on Light Steel Composite Beams Terrapin Limited wished to extend the spanning capabilities of their 425 mm double C sections, and have developed a ‘top hat’ shear connector for use in composite applications. A full-scale beam test was devised to demonstrate the degree of composite action that can be achieved. The configuration of this test is illustrated in Figure 2. The beam span was 9.3m and the slab span was 2.4m. The steel thickness was 3 mm, and the steel grade was nominally S280 (280 N/mm2 yield strength).
Figure 2:
Configuration of test on light steel composite beam
The ‘top hat’ shear connectors were attached separately to each C section using 2 pins per rib, and mesh reinforcement was placed on top. The total slab depth was 110 mm using normal weight concrete placed on PMF CF 46 decking. The beam was propped during and after the concreting operation until the concrete had reached its design strength. Loading was applied by pallets of plasterboard each weighing approximately 18.0 kN. Because of the practicalities of this form of loading, the load-deflection performance is not exactly linear. An acceptance test was first carried out at the design imposed load of 6.7 kN/m2, and the permanent deflection on unloading was less than 1 mm. Later, the design factored load of 9.3 kN/m2 was applied, corresponding to a moment of 226 kNm, which is 109% more than the elastic moment resistance of the steel sections. The maximum slip recorded at this load was 9.8 mm. The load-displacement graph is shown in Figure 3. The maximum displacement was 49 mm (span/190), and the permanent deflection on unloading was 24 mm.
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A load of 3.4 kN/m2 was then re-applied and maintained for 30 days. This load was considered to be representative of the maximum long-term or permanent load that might be experienced in a typical building. The creep deflection was less than 1 mm after this duration of loading(5). 400
Applied Load
P, (kN)
350 300 250 Failure Load = 336 kN Max mid-span defl. = 68mm
200 150
Strength Load = 259 kN Mid-span defl. = 50mm
100
End-support, failure load Mid-span, strength load
50
Mid-span, failure load
0 0
10
20
30
40
50
60
70
80
Vertical deflection (mm)
Figure 3: Load-deflection curve for beam test Finally, the test load was increased to failure which occurred at 12.7 kN/m2. Just prior to this point, the maximum displacement was 68 mm (span/132). The maximum moment was 312 kNm, which is 188% more than the elastic moment resistance of the beam. Based on the measured yield strength of the steel, the degree of shear connection was 84%. Beam failure occurred by longitudinal shear due to rotation of the pins. This mode of failure also provoked local buckling of the top flange due to local compression and the lack of restraint between the ribs of the composite slab. Local buckling did not occur prior to this point. Back-analysis of the composite beams showed that the plastic composite resistance of the beam could be developed. The comparison between the test and back-analysed bending resistances and stiffnesses are presented in Table 1. The natural frequency of the unloaded composite beam was also measured at 8 Hz, which when reduced for the other permanent loads would give a ‘design’ value of approximately 6.5 Hz. This natural frequency is satisfactory for almost all building applications.
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Table 1:
Results of composite beam test using ‘top hat’ shear connectors. Parameter Measured Calculated Design property property property Steel bending resistance 149 kNm 108 kNm Composite bending resistance 312 kNm 308 kNm Steel second moment of area 9,034 cm4 Composite second moment of area 34,570 cm4
2.2. Design Tables for Light Steel Composite Beams The load-span characteristics of light steel composite beams using double C sections may be determined from conventional composite theory to BS 5950 Part 3 or EC4. The design criteria are: • bending resistance of the steel section at the construction stage (using elastic properties). • bending resistance of the composite section, taking account of partial shear connection. • imposed load deflection (based on elastic composite properties). • total deflection including the construction stage and imposed load deflections. • minimum natural frequency (> 4 Hz). Load-span tables for typical unpropped and propped beams are presented in Table 2. The design of unpropped beams is generally limited by total deflection, and the design of propped beams is limited by bending resistance of the composite section. Table 2:
Load-span table for unpropped and propped beams
IMPOSED LOAD kN/m2 DESIGNATION Matrex-Channel 425 x 90 x 2.4 425 x 90 x 2.5 425 x 90 x 2.6 425 x 90 x 2.7 425 x 90 x 2.8 425 x 90 x 2.9 426 x 90 x 3.0 428 x 90 x 3.1 430 x 90 x 3.2
LE m 8.4 8.5 8.7 8.9 9.0 9.2 9.3 9.4 9.5
Unpropped 2.5 δE δS mm mm a 9 29 a 10 29 a 10 31 a 11 31 a 11 33 a 12 34 a 12 35 g 13 35 g 13 36
Ν 14 14 15 15 15 16 16 16 16
LP m 9.9 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8
c c d d d d d d d
Propped 2.5 δP δS mm mm 16 14 16 14 17 15 18 16 19 16 19 17 20 18 21 18 21 19
Ν 17 17 17 17 18 18 18 18 18
By comparison, the spanning capabilities of the equivalent non-composite beams would be only 60% of these spans, which demonstrates clearly the benefit of composite action.
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Importantly, the increase in stiffness of the composite section is over 5 times that of the steel section. The first practical application of this form of construction was in the extension to British Steel’s Training Centre at Ashorne Hill, Warwickshire as shown on Figure 4. In this project, the beam spans ranged from 8 to 10m. Wider ‘top hat’ sections were used, but the same general principles of design apply.
Figure 4:
Application of light steel composite construction using ‘top-hat’ shear connectors
3. Light Steel Composite Frames There are various examples worldwide of the use of cold-formed sections or decking to provide the formwork to in-situ concrete frames. A system of slim floor construction developed in France is illustrated in Figure 5. In this form of construction, the Z sections used as secondary beams span between the primary slim floor beams. The depth and spacing of the secondary beams can be selected to match the slab depth and span requirements of the construction.
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Figure 5: Slim floor beam using composite Z sections as secondary beams
Figure 6: Finnish system of light steel composite construction
In Finland, the steel company Rautaruukki have developed a wide ribbed U section which acts compositely with the in-situ concrete placed in it. The U section is propped approximately every 3m at the construction stage. The system also incorporates composite concrete-filled hollow sections with special ‘saddles’ on which the U section beam is supported. No fire protection is required, if additional bar reinforcement is placed in the in-situ concrete, as in a conventional T beam. This construction system is illustrated in Figure 6. In Australia, profiled decking is used to provide permanent formwork to the sides and soffit of deep beams and large columns. The disadvantage of the system is that secondary frames are required to support the decking and to resist concrete pressures. A cross-section is shown in Figure 7. In New Zealand and Canada, C and Z sections have been combined to form primary and secondary beams, and as complete frameworks which support in-situ concrete. These composite frames achieve excellent seismic resistance by confining the in-situ concrete under repeated loading and by enhancing the bending resistance of the connections.
Figure 7: Profiled sheeting used as permanent formwork to deep beams and columns
Figure 8: Light steel framework as permanent formwork to in-situ concrete
An extension of this system to incorporate double-skin shear walls is presented in Figure 8. The edge beams are formed by C and Z sections. C sections within the wall support the top and bottom of the decking.
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4. Composite Walls Composite walls use two skins of vertically orientated decking, usually of re-entrant form, with in-situ concrete between them. Ties placed at approximately 1.0m apart vertically resist the concrete pressures during construction. Tests on composite walls of various width and deck configurations have been carried out at the University of Strathclyde. Because of the difficulty in achieving shear transfer at the top of the wall, the composite wall is structurally more efficient when it is relatively slender, so that its composite properties are utilized in resisting buckling at mid-height. The advantages of composite walls are therefore: • • • • •
Slender wall construction can be achieved. Permanent formwork requires no external support. Internal ties resist the concrete pressure. Acts as a shear wall to eliminate bracing. Attachments can be made easily.
Various forms of composite walls using deck profiles are shown in Figure 9.
Inter-locking wall units
Composite walls using re-entrant steel decking
Composite walls using trapezoidal steel decking
Figure 9:
Different forms of composite walls using decking and interlocking units
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5. Light Steel Flooring Light steel floor joists are widely used in housing and in low-rise building construction for spans of 3 to 5m. They comprise C sections of 150 to 250 mm depth and 1.2 to 2.4 mm thickness which are placed 400 to 600 mm apart. Floor boarding attached to the joists improves their stiffness considerably, but until recently, no test data existed to quantify this effect. Furthermore, multiple layers of board and plasterboard, and suspended ceilings are often used to increase the acoustic insulation of the floors, and these additional layers can have a considerable beneficial effect on stiffness. Similarly, profiled decking may be used as part of a composite flooring system in which boarding is fixed by frequent pins or screws. This system has been shown to provide a very stiff construction, which improves the lateral transfer of loads across the decking.
6. Diaphragm action of wall panels Light steel framing uses storey high wall panels which are either unbraced or braced depending on whether they provide shear resistance to wind loads applied to the building. Bracing may be in the form of integral bracing members within the thickness of the wall panels or as external flats attached to the face of the panel. Internally, plasterboard is attached directly to the wall panels, and provides a stiffening effect, which is dependent on the frequency of fixings, on the rigidity of the plasterboard and the presence of openings.
References 1. 2. 3. 4.
5.
British Standards Institution, BS 5950: Part 3.1 Code of practice for design in composite construction, BSI, 1991 Eurocode 4: ENV 1994-1-1: British Standards Institution, BS 5950: Part 4 Code of practice for design of composite slabs profiled steel sheeting. BSI, 1992 Popo-Ola, S. O. and Lawson, R. M Push-out Tests with Matrex Bolted Channel Connector & Fibre Reinforced Concrete, The Steel Construction Institute, Report No. RT-794 submitted to Terrapin International Limited. February 2000. Popo-Ola, S. O. and Lawson, R. M Full-scale Test on Matrex Composite Floor System using Top-hat Strip Connectors fastened with Hilti X-EDNK22 pins. The Steel Construction Institute, Report No. RT-704 submitted to Terrapin International Limited. July 1998.
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INTENTIONAL AND UNINTENTIONAL SHEAR CONNECTIONS IN SHALLOW FLOOR COMPOSITE STRUCTURES Matti V. Leskelä University of OULU, Structural Engineering Laboratory, FINLAND
Abstract Developments in shallow floor structures over the last ten years have produced systems in which composite behaviour is frequently encountered due to various bond interfaces between concrete and steel components. Depending on the types of structural elements used in the floor, this composite action may be defined as either intentional or unintentional. Both forms have an influence on structural behaviour and on design decisions, and this paper discusses the important features to bear in mind when considering composite interaction, its rating in the serviceability state and possible deterioration when entering the plastic behaviour and ultimate limit states. A special case in shallow floor construction is the integration of hollow core slabs with beams, and these problems are also discussed. The phenomena observed are explained on the basis of the general flexural theory of composite structures and numerical studies carried out by the finite element method. An overview of development during the last ten years is given.
1. Introduction One of the basic ideas of employing steel beams integrated within the depth of a concrete slab is that the concrete should provide natural fire protection for the steel member. A number of steel profiles, both open and boxed sections, and three main types of decking are available. For fast erection of the floor, propping of the beams and slabs is avoided as far as possible, which implies that the steel members should be capable of carrying the entire weight of the decking. 1.1 Composite interaction Composite interaction in ordinary composite beams is always intentional and is ensured by a mechanical connection. A designer who is used to dealing with shear connections of this kind may feel that composite behaviour in a shallow floor construction is
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complicated. It may perhaps be understood that the connection is distributed over a number of locations, but it may not be clear how the interaction between the material components works. The problem becomes easier when it is realized that there is a general principle according to which two members connected to each other continuously in one interface form a composite system independent of the location of the connection interface (see [1, 3]). Thus, it is only the overall properties of a multiply interfaced connection that are of interest, and not their distribution within the cross-section. Due to the limited depth of shallow floors, it is not possible to employ stud shear connectors effectively, and designs with no mechanical connections between the decking slab and the beam have been implemented. In the most conservative approach, composite interaction is omitted in the resistance design, referring to a lack of mechanical connection. Composite interaction will occur at least in the serviceability state, and the phenomena induced have sometimes been referred to as ‘unintentional composite effects’ [2], as the assumptions made by the designer cannot change the real physical behaviour of the system. The effects are highly variable: in the serviceability state the bond connections are rigid and composite interaction is highly effective, whereas in the plastic range of behaviour only limited use can be made of the initially rigid bond shear connections. 1.2 Steel sections and types of decking Various open asymmetric sections are common in countries with rolled section production and welded boxed and built-up sections are typical of Scandinavian countries. Three main types of the decking may be recognized in shallow floors, (1) hollow core slabs, (2) deep decking composite slabs and (3) concrete composite slabs with prestressed planks [1]. The general term ‘solid type’ may be used for (2) and (3). Hollow core slabs provide for fast, efficient erection of the floor, and fresh concrete is required only for grouting the joints and possibly filling the beam section. Precast decking elements form a good working platform as soon as they have been assembled, and no propping is required even in long spans. Deep decking composite slabs differ in the depth and form of their profile, and these variations influence the spans that can be employed without propping. Slabs with prefabricated planks do not differ in principle from uniform solid slabs, and their connection to the beam is similar to that used with deep decking composite slabs. More weight is involved, however, so that these systems are mostly used in heavy-duty floors where high eigenfrequencies are required.
2. Connection characteristics Good connection characteristics in any composite beam are ones that provide high initial stiffness and enough ductility in the connection to enable the system to maintain the compressive stress resultant of the concrete flange as high as possible during plastic straining. Unfortunately grouted joints do not meet the ductility requirement, although
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the initial stiffness of the joint is high. A general form of the load-slip relationship for a connection is presented in Figure 1, where the parameters Fsmax and δs1 influence the effective bending stiffness of the composite system and the residual force Fsmin correlates with the degree of shear connection when applying the partial connection theory of shallow floor beams [4]. Connection force Fs Fsmax
Fsmin δ s1
Connection slip δ s
Figure 1: Load-slip curve of a connection When Fsmin is considerably smaller than Fsmax, the effective design strength of the connection cannot be assumed to be high, as slips δs >> δs1 normally occur in the plastic state of stresses. The connection forces first reach their maximum in the sections where the vertical shear forces of the beam are highest. Consequently, the first unloading in the connection and the maximum slips occur in the same regions, i.e. the supports. What gradually happens in such connections may be described as the ‘zip-flyer effect’, and this influences the plastic bending resistance obtained in the beam. 2.1 Beams integrated with hollow core slabs Hollow core slabs are the most common decking elements used in Scandinavia, and the initial aim when developing new shallow floor beams in the early 1990’s was to exploit the upper hull of the voided decking elements as the compression flange of the composite beam. Thus connections arranged between the beam and the slab elements were intentional from the very beginning, even though not all the consequences of the interaction were understood until full-scale flooring tests and their associated research had been carried out [5, 6]. It was observed in the tests that the failure of the hollow core units often occurred before the onset of yielding in the beam section, and it was not possible to develop full plasticity in the beam without the slabs collapsing. Fortunately the failure loads on the decking are high enough to make a reasonable design of floor possible, provided that special rules are followed and the phenomena involved are taken into account [5, 6 and 7].
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Several explanations have been presented for the reduced vertical shear resistance of hollow core slabs, but the composite interaction maintained by the joints on the sides of the beam covers the overall behaviour well and is also observed in connection with other types of slab. Shallow floors are normally erected without propping the beams, and only a live load will activate composite action in them. Initially, the joints on the sides of the beam are not cracked and their stiffness is high, and consequently the bending stiffness of the composite system is at its highest. The load path between the compressive force of the concrete flange (= upper hull of the hollow core units), Nc, and the tensile force of the beam, Nt, goes directly from the hulls to the top of the beam (interface i1 in Figure 2), i.e. in the most efficient way. The shear forces in the connection can be evaluated by applying the full interaction theory of composite beams. As the load increases, horizontally extending vertical cracks develop, starting from where the shear force on the beam is highest. Cracking reduces the stiffness of interface i1 and redistribution of the connection forces follows. At the same time, the load path changes to go through the depth of the slab to the bottom flange of the beam, where the connection is still effective (interface i3 in Figure 2), and the webs of the slab units (interface i2 in Figure 2) take on the role of maintaining a shear connection between the hulls of the decking.
i1
N c
i2
N
t
i3
Horizontal shear
Figure 2: Connection interfaces and load paths in case of hollow core decking If no major slipping occurs in the bottom connection, the horizontal shear forces in the web of the slab will increase more or less linearly and cause failure of the webs when their multi-directional failure condition is exceeded. Fsmin (Figure 1) varies depending on the properties of the bottom connection, but unloading of connection forces there will release horizontal shear forces from the webs of the slab. This is a favourable effect for the capacity of the slab, and it was also observed in the tests that the reduction in slab capacity is smallest in systems in which the slabs are supported on the beams with the weakest bond interfaces [5]. As the horizontal slip capacity between the hulls of the slab is quite limited, the webs can fail due to the ‘Vierendeel effect’(see right hand side of Figure 2), which becomes more prominent as the deflection of the beam increases [6].
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The sensitivity of hollow core units to a reduction in capacity varies depending on the type of the slab cross-section and its details [5, 7]. Other factors that affect the capacity arise from the characteristics of the connections, and it may be understood from Figure 2 that measures taken to keep the interfaces i1 intact will improve the capacity of slabs supported on beams. 2.2 Beams integrated with solid types of slab In principle, connections between the solid types of slab and steel beams do not differ from those of hollow core slabs, and interfaces i1 to i3 can be identified in the same way. Interface i2 can be ignored here, however, as it has been seen in tests that web failures are not possible in the slabs employed. The main difference between the types of slab is that in the solid types the cross-section of the slab in the direction of the beam follows the Bernoulli hypothesis of planes remaining plane during bending, which is not the case in voided sections. Considering the connections, there may be differences in the quality of the concrete work, e.g. depending on the site conditions, detailing, etc., and this may affect the role of individual interfaces. In asymmetric open sections good contact is easily obtained in the web surfaces, but there will be air trapped in the voids under the top flange, i.e. the only effective contact will be in the web. The behaviour of the system with increasing load is similar to that explained in the previous section, but there are no limitations with respect to the development of plasticity in the steel section. In deep decking composite slabs the depth of concrete above the sheet profile serves as the compression flange for the beam and its total area within the design width influences the load at which the bond resistance of the connection (Fsmax) is exceeded, while beyond that point it is the ratio Fsmin/Fsmax that defines how high an axial force can be maintained during slipping of the concrete. A partial connection theory of shallow floor beams [4] was developed for evaluating the bending resistance between Mpl.Rd (= maximum plastic resistance of the composite beam) and Mapl.Rd (= plastic resistance of the steel section alone). Information on the connection resistance is required in order to employ the method for design purposes.
3. Load-slip properties of various connections Interfaces i1 and i3 are of no interest separately, but when summed they form the connection that is used in the partial connection theory. There are a variety of possibilities for arranging a mechanical connection in shallow floor beams, but the bond and friction effects are always present and influence the behaviour. Initially it is the bond that governs any connection behaviour, and it is only after the bond resistance has been exceeded that other components can become active.
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The idea in the standard push-out test for shear connectors explained in Eurocode 4 [8] is that the steel joist is axially loaded with respect to the concrete parts of the specimen causing longitudinal shear in the connection interfaces. The same principle can be applied when comparing the connections in shallow floor structures experimentally. The question of the validity of such tests for indicating the real properties of the connection is frequently raised in discussions, but they are in any case useful for comparing different configurations. Push-out specimens cast in an upright position (Figure 3) contain better compacted concrete and the effective bond area is greater than in structures cast horizontally. Various connection characteristics are presented in Figure 4 as mean curves from pushout tests with an asymmetric I-section [4]. When the total bond area in the specimen is denoted as Ab and the bond area of the web as Ab,w, then Aw,b/Ab = 0.46. FRam
FRam
Slip transducer
Loading plate
F Tie
FTie
FTie
Concrete block
FTie
FRam
FTie
Figure 3: General principle for the push-out test employed for the shallow floor beam 3.1 Bond connections A considerable scatter has been observed in the bond strengths between steel and concrete in various tests, and the situation is evidently influenced by the properties of the concrete and the condition of the steel surface. In Eurocode 4 [8] the bond is considered only in the columns, and 0.4 MPa is given as the design strength for the interfaces of concrete filled tubes. This value can be used when evaluating the possibility of exceeding the bond strength in the serviceability limit state. As seen in Figure 4, these connections are not ductile, and the residual strength depends on the frictional effects involved. 3.2 Checkered interfaces Checkered steel surfaces provide a better adhesive bond with the concrete, but their ductility depends on how well the transverse separation of the concrete from the steel
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interface is prevented. This effect is referred to as lateral confinement in Figure 4, which is based on a previous report [4]. It should be pointed out that all the curves in this figure were obtained from specimens with identical dimensions and similar material properties. In some of the tests lateral confinement of the concrete was arranged by employing adjustable ties that prevent separation of the concrete from the web surface. The tightening was varied in order to observe the effect of the confinement. As seen in Figure 4, the prevention of transverse separation at checkered interfaces noticeably improves the resistance and produces a connection with excellent ductility. Checkered webs + bars through the web
1
Checkered webs with lateral confinement 0.75
Bars through the web 0.5
Checkered webs
0.25
Bond connection in plain web surfaces
0 0
2
4
6
8
10
Slip displacement, mm
Figure 4: Properties of various shear connections 3.3 Transverse bars through the web The behaviour of transverse ribbed bars (2 φ12 per specimen) was studied both in specimens with plain web surfaces and in specimens with checkered web surfaces. These tests were identified by the tags ‘Bars through the web’, and the bars were also seen work well in producing lateral confinement. The properties of the specimens make it possible to distinguish various component characteristics from the overall behaviour, on the assumption that these will appear to be superimposed. The characteristics of the bars were deducted by extracting the ‘Bond connection’ diagram from the ‘Bars through the web’ diagram, whereupon it became clear that the bars start taking up load only after the occurrence of a certain slip, which correlates with the looseness of the web holes. The maximum load in the bars is reached only after a total slip of 10 mm, which is not ideal for the stiffness of these connections. It should also be noted that the maximum load is related to nominal shear stress 0.8fsk in the bar rather than to fsk, which is the yield strength of the bar.
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3.4 Frictional effects Floors are two-way systems that are formally regarded as one-way structures by separating the behaviour of slabs and beams. When wishing to avoid excessive conservatism in the design of the shear connection, the frictional effects due to transverse bending in the slabs should be allowed for, as it is not reasonable to make complicated designs for the connections that may reduce the efficiency of the construction. Considering Figure 5, the resistance of the connection on one side of the steel member should be evaluated as the minimum of the two values vRd.1 and vRd.2: vRd.1 = vRd.mc + µAefsk/γs vRd.2 = 2.5AcvητRd + Aefsk/γs where vRd.1 is the resistance at the steel concrete interface, which follows the surface of the steel section, vRd.2 is the resistance at the vertical interface, through concrete slab [8] and vRd.mc ≥ 0 is the total resistance of the bond and mechanical connection. Ae is the area of the hogging reinforcement in the slab per unit length of the beam and µ is the coefficient of friction at the steel-concrete interface. The value vRd.mc for the bond connection should be evaluated on the basis of the residual strength available after slipping. Numerical evaluation indicates that vRd.1 will give the minimum result. A e, strength fsk /γs
Mslab
Fr Fj.
Fr Fj.
Ae
Mslab A cv
F r
Fr Beam section
µFj.
Elevation outside the steel beam
Figure 5: Influence of slab bending on the connection interfaces of the beam. The existence of the frictional effects µFj.⊥ cannot be verified in the beam tests, where no transverse bending is produced, but on the basis of the equilibrium of the internal forces, the maximum for Fj.⊥ is the plastic force Aefsk/γs in the reinforcement. It has been doubted, whether Fj.⊥ can develop unconditionally or not, but this argumentation can be rebutted by considering the following statements. (1) Frictional forces can be allowed for whenever there is a hogging reinforcement of the slab designed for the decking loads. The ultimate limit state of the floor beam follows from the same loading arrangement as for the hogging moment of the slab, i.e. the slabs are loaded on both sides of the beam by the maximum design load (dead weight + live load). If there is
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maximum load on one side of the beam only, this is not the determining case, as the intermediate beams are never designed for this kind of loading. (2) Verification of the connection resistance is required at the ends of the beam, where its deflection can never eliminate Fj.⊥. The shear spans in which µFj.⊥ is considered are defined in the same way as in the composite slabs to Eurocode 4.
4. Discussion Hollow core slabs were intuitively supported on beams even before 1990’s, but research into their real composite interaction with the beams was started only after the findings in the tests conducted in Finland [5]. Non-linear finite element analyses in connection with the tests have revealed the important role of the connection characteristics for the resistance of precast units. In fact, the brittle characteristics of a typical bond connection are favourable for the resistance of the slab units, although the performance of these connections should be improved in case of the solid types of slab [4]. It has become customary in Finland that a fictitious plastic bending resistance is evaluated for the beams that support hollow core slabs as well, omitting the concrete compression flanges outside the beam section. This procedure, originally proposed by Bode et al. [2], provides an estimate of the capacity more easier than does evaluation of the elastic bending resistance based on stress histories and use of composite cross-sectional properties. The flanges outside the beam section should always be taken into account when evaluating the deflections, however. This is important for defining the precamber correctly. Although it is not desirable to improve the resistance of the shear connection with hollow core slabs, this may be required in the case of the solid types of slab, for which there are no limitations on achieving the plastic bending resistance. The partial connection theory [4] developed on the basis of the principles presented in Eurocode 4 [8] implies that in slabs with greater solid depth more attention should be paid to shear connection, and mechanical connection should be considered. This conclusion can also be drawn from the beam tests. The general bending theory of shallow floor beams indicates that, to make a system composite, a shear connection is only required in one location in the depth of the section, provided that the associated components follow the Bernoulli hypothesis of planes remaining planes in bending. The same rule has also been observed to be valid in inelastic behaviour states when carrying out non-linear finite element analyses. The upper flange is the natural and only location for a connection in traditional composite beams in which the sectional parts appear to be stacked, but shallow floor beams do not normally have enough concrete above the top flange for headed stud connectors, and it should also be understood that bond connections to the upper surface of the top flange will not be efficient if there is nothing to prevent separation of the
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concrete from the interface. The web interfaces of the steel section are the most effective location for the connection, as transverse bending of the slab creates frictional effects against the web and the splitting effects in the concrete due to mechanical connection are best avoided between the flanges. Horizontally placed studs have been studied in Germany [9], and the resistance and ductility of such studs depend on the prevention of splitting. A connection based on longitudinal reinforcing bars of large diameter welded to the web has been proposed in a previous report [4], and the properties for this connection may readily be evaluated from the CEB Model Code [10]. When placed appropriately, the reinforcing bars may have a double function of serving as a fire reinforcement as well.
5. References 1.
2.
3.
4.
5. 6.
7. 8. 9.
10.
Leskelä, M.V., ‘Shallow Floor Integrated Beams - Research on the Composite Behaviour’, in ‘Theorie und Praxis im Konstruktiven Ingenieurbau’, Festschrift zu Ehren von Prof. Dr.-Ing. Helmut Bode, ibidem Verlag, Stuttgart, 2000 199212. Bode, H., Dorka, U.E., Stengel, J., Sedlacek, G. and Feldmann, M., ‘Composite Action in Slim Floor Systems’, in ‘Composite Construction in Steel and Concrete III’, Proceedings of an Engineering Foundation Conference, Irsee, Germany 1996, American Society of Civil Engineers, 1997 472-485. Leskelä, M.V., ‘Shallow Floor Beam Behaviour - General Theory’ in ‘VII Suomen Mekaniikkapäivät Tampereella 25. - 26.5.2000’, Nide 2, 2.kokouspäivän esitelmät. Pressus Oy. (Proceedings of the VII Finnish Mechanics Days, Vol. 2, prentations on the 2nd day), Tampere University of Technology, Engineering Mechanics, Tampere, Finland, 2000 489-498. Leskelä, M.V. and Hopia, J., ‘Steel Sections for Composite Shallow Floors’, Report RTL 0053E, University of Oulu, Structural Engineering Laboratory, March 2000, Oulu, Finland. Pajari, M., ‘Shear resistance of prestressed hollow core slabs on flexible supports’, VTT Publications 228, Espoo, Finland 1995. Leskelä, M.V. and Pajari, M., ‘Reduction of the Vertical Shear Resistance in Hollow Core Slabs when Supported on Beams’, in ‘Concrete 95, Conference Papers’, Volume One, CIA and FIP, Brisbane, Australia, 1995 559-568. ‘Special design considerations for precast prestressed hollow core floors. Guide to good practice prepared by fib Commission 6’, Sprint-Druck Stuttgart, 2000. ENV 1994-1-1, ‘Design of steel and concrete composite structures, Part 1-1: General rules and rules for buildings’, CEN 1992. Kuhlmann, U., Kürschner, K. and Breuninger U., ‘Zum Tragverhalten von liegenden Kopfbolzdübeln’, in ‘Theorie und Praxis im Konstruktiven Ingenieurbau’, Festschrift zu Ehren von Prof. Dr.-Ing. Helmut Bode, ibidem Verlag, Stuttgart, 2000 361-373. Comité Euro-International du Béton, ‘CEB-FIP Model Code 1990. Design Code’, Thomas Telford, Redwood Books, Trowbridge, Wiltshire, 1993.
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