VOL. 111, NO. 2 MARCH-APRIL 2014
ACI STRUCTURAL
J O U R N A L
A JOURNAL OF THE AMERICAN CONCRETE INSTITUTE
CONTENTS Board of Direction
ACI Structural Journal
President Anne M. Ellis
March-April 2014, V. 111, No. 2
Vice Presidents William E. Rushing Jr. Sharon L. Wood Directors Neal S. Anderson Khaled Awad Roger J. Becker Dean A. Browning Jeffrey W. Coleman Robert J. Frosch James R. Harris Cecil L. Jones Cary S. Kopczynski Steven H. Kosmatka Kevin A. MacDonald David M. Suchorski Past President Board Members James K. Wight Kenneth C. Hover Florian G. Barth Executive Vice President Ron Burg
Technical Activities Committee Ronald Janowiak, Chair Daniel W. Falconer, Staff Liaison JoAnn P. Browning Chiara F. Ferraris Catherine E. French Fred R. Goodwin Trey Hamilton Kevin A. MacDonald Antonio Nanni Jan Olek Michael M. Sprinkel Pericles C. Stivaros Andrew W. Taylor Eldon G. Tipping
Staff
Executive Vice President Ron Burg Engineering Managing Director Daniel W. Falconer Managing Editor Khaled Nahlawi
a journal of the american concrete institute an international technical society
235 Web Crushing Capacity of High-Strength Concrete Structural Walls: Experimental Study, by Rigoberto Burgueño, Xuejian Liu, and Eric M. Hines 247 Response of Precast Prestressed Concrete Circular Tanks Retaining Heated Liquids, by Michael J. Minehane and Brian D. O’Rourke 257 Bond Strength of Spliced Fiber-Reinforced Polymer Reinforcement, by Ali Cihan Pay, Erdem Canbay, and Robert J. Frosch 267 Flexural Behavior and Strength of Reinforced Concrete Beams with Multiple Transverse Openings, by Bengi Aykac, Sabahattin Aykac, Ilker Kalkan, Berk Dundar, and Husnu Can 279 Experimental Assessment of Inadequately Detailed Reinforced Concrete Wall Components, by Adane Gebreyohaness, Charles Clifton, John Butterworth, and Jason Ingham 291 Behavior of Epoxy-Injected Diagonally Cracked Full-Scale Reinforced Concrete Girders, by Matthew T. Smith, Daniel A. Howell, Mary Ann T. Triska, and Christopher Higgins 303 High-Performance Fiber-Reinforced Concrete Bridge Columns under Bidirectional Cyclic Loading, by Ady Aviram, Bozidar Stojadinovic, and Gustavo J. Parra-Montesinos 313 Analysis of Early-Age Thermal and Shrinkage Stresses in Reinforced Concrete Walls, by Barbara Klemczak and Agnieszka Knoppik-Wróbel 323 Effects of Casting Position and Bar Shape on Bond of Plain Bars, by Montserrat Sekulovic MacLean and Lisa R. Feldman 331 Performance of Glass Fiber-Reinforced Polymer-Doweled Jointed Plain Concrete Pavement under Static and Cyclic Loadings, by Brahim Benmokrane, Ehab A. Ahmed, Mathieu Montaigu, and Denis Thebeau 343 Nonlinear Static Analysis of Flat Slab Floors with Grid Model, by Dario Coronelli and Guglielmo Corti 353 Effect of Steel Stirrups on Shear Resistance Gain Due to Externally Bonded Fiber-Reinforced Polymer Strips and Sheets, by Amir Mofidi and Omar Chaallal 363 Punching of Reinforced Concrete Flat Slabs with Double-Headed Shear Reinforcement, by Maurício P. Ferreira, Guilherme S. Melo, Paul E. Regan, and Robert L. Vollum 375 Behavior of Concentrically Loaded Fiber-Reinforced Polymer Reinforced Concrete Columns with Varying Reinforcement Types and Ratios, by Hany Tobbi, Ahmed Sabry Farghaly, and Brahim Benmokrane
Staff Engineers Matthew R. Senecal Gregory M. Zeisler Jerzy Z. Zemajtis Publishing Services Manager Barry M. Bergin Editors Carl R. Bischof Kaitlyn Hinman Ashley Poirier Kelli R. Slayden Editorial Assistant Tiesha Elam
Contents cont. on next page
Discussion is welcomed for all materials published in this issue and will appear ten months from this journal’s date if the discussion is received within four months of the paper’s print publication. Discussion of material received after specified dates will be considered individually for publication or private response. ACI Standards published in ACI Journals for public comment have discussion due dates printed with the Standard. Annual index published online at http://concrete.org/Publications/ACIStructuralJournal. ACI Structural Journal Copyright © 2014 American Concrete Institute. Printed in the United States of America. The ACI Structural Journal (ISSN 0889-3241) is published bimonthly by the American Concrete Institute. Publication office: 38800 Country Club Drive, Farmington Hills, MI 48331. Periodicals postage paid at Farmington, MI, and at additional mailing offices. Subscription rates: $161 per year (U.S. and possessions), $170 (elsewhere), payable in advance. POSTMASTER: Send address changes to: ACI Structural Journal, 38800 Country Club Drive, Farmington Hills, MI 48331. Canadian GST: R 1226213149. Direct correspondence to 38800 Country Club Drive, Farmington Hills, MI 48331. Telephone: 248.848.3700. Website: http://www.concrete.org.
ACI Structural Journal/March-April 2014
233
387 Repair of Prestressed Concrete Beams with Damaged Steel Tendons Using Post-Tensioned Carbon Fiber-Reinforced Polymer Rods, by Clayton A. Burningham, Chris P. Pantelides, and Lawrence D. Reaveley 397 Study of Composite Behavior of Reinforcement and Concrete in Tension, by John P. Forth and Andrew W. Beeby 407 Flexural Capacity of Fiber-Reinforced Polymer Strengthened Unbonded Post-Tensioned Members, by Fatima El Meski and Mohamed Harajli 419 Size Effect on Strand Bond and Concrete Strains at Prestress Transfer, by José R. Martí-Vargas, Libardo A. Caro, and Pedro Serna-Ros 431 Proposed Minimum Steel Provisions for Prestressed and Nonprestressed Reinforced Sections, by Natassia R. Brenkus and H. R. Hamilton 441 Lateral Strain Model for Concrete under Compression, by Ali Khajeh Samani and Mario M. Attard 453 Discussion Cyclic Loading Test for Beam-Column Connection with Prefabricated Reinforcing Bar Details. Paper by Tae-Sung Eom, Jin-Aha Song, Hong-Gun Park, Hyoung-Seop Kim, and Chang-Nam Lee Shear Strength of Reinforced Concrete Walls for Seismic Design of Low-Rise Housing. Paper by Julian Carrillo and Sergio M. Alcocer Performance of AASHTO-Type Bridge Model Prestressed with Carbon FiberReinforced Polymer Reinforcement. Paper by Nabil Grace, Kenichi Ushijima, Vasant Matsagar, and Chenglin Wu
460
In ACI Materials Journal
462
Reviewers in 2013
MEETINGS 2014 MARCH 19-21—ICRI 2014 Spring Convention, Reno, NV, www.icri.org/Events/2014_ Spring/conv_home.asp 22—ASA Spring 2014 Committee Meetings, Reno, NV, www.shotcrete.org
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[email protected] ON COVER: 111-S23, p. 269, Fig. 3—Diagonal reinforcement spiraling around circular openings.
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Contributions to ACI Structural Journal The ACI Structural Journal is an open forum on concrete technology and papers related to this field are always welcome. All material submitted for possible publication must meet the requirements of the “American Concrete Institute Publication Policy” and “Author Guidelines and Submission Procedures.” Prospective authors should request a copy of the Policy and Guidelines from ACI or visit ACI’s website at www.concrete.org prior to submitting contributions. Papers reporting research must include a statement indicating the significance of the research. The Institute reserves the right to return, without review, contributions not meeting the requirements of the Publication Policy. All materials conforming to the Policy requirements will be reviewed for editorial quality and technical content, and every effort will be made to put all acceptable papers into the information channel. However, potentially good papers may be returned to authors when it is not possible to publish them in a reasonable time. Discussion All technical material appearing in the ACI Structural Journal may be discussed. If the deadline indicated on the contents page is observed, discussion can appear in the designated issue. Discussion should be complete and ready for publication, including finished, reproducible illustrations. Discussion must be confined to the scope of the paper and meet the ACI Publication Policy. Follow the style of the current issue. Be brief—1800 words of double spaced, typewritten copy, including illustrations and tables, is maximum. Count illustrations and tables as 300 words each and submit them on individual sheets. As an approximation, 1 page of text is about 300 words. Submit one original typescript on 8-1/2 x 11 plain white paper, use 1 in. margins, and include two good quality copies of the entire discussion. References should be complete. Do not repeat references cited in original paper; cite them by original number. Closures responding to a single discussion should not exceed 1800-word equivalents in length, and to multiple discussions, approximately one half of the combined lengths of all discussions. Closures are published together with the discussions. Discuss the paper, not some new or outside work on the same subject. Use references wherever possible instead of repeating available information. Discussion offered for publication should offer some benefit to the general reader. Discussion which does not meet this requirement will be returned or referred to the author for private reply. Send manuscripts to: http://mc.manuscriptcentral.com/aci Send discussions to:
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S04 Note: Paper 111-S04 of the January-February 2014 ACI Structural Journal has been reprinted herein with corrected figure art. Please reference the March-April 2014 version of this paper only.
Web Crushing Capacity of High-Strength Concrete Structural Walls: Experimental Study by Rigoberto Burgueño, Xuejian Liu, and Eric M. Hines This paper discusses the relationship between concrete strength and web crushing capacity based on results from large-scale tests of thin-webbed structural walls with confined boundary elements. Eight walls with concrete strengths ranging from 39 to 138 MPa (5.6 to 20 ksi) were tested to web crushing failure under cyclic and monotonic loading. These tests clearly demonstrated differences between elastic and inelastic web crushing behavior and their dependence on concrete strength. Walls with higher concrete strengths reached higher levels of displacement ductility due to an increase in web crushing capacity. Evidence with respect to monotonic tests showed that degradation of the diagonal compression struts from cyclic loading increases with concrete strength, thus limiting the inelastic deformation capacity gains. Thus, concrete compressive strength does not linearly increase web crushing strength as implied by rational web crushing models; rather, the relationship is nonlinear, with a decreasing limit as concrete strength increases. The ACI shear stress limit considerably underestimated the web crushing capacity of the walls. Test results and observations are reported with the intent of providing physical insight into the web crushing failure mechanism and the inherent limits of thin-webbed concrete members in shear.
possibility because they have observed deformed configurations in the inelastic range that could undermine the benefits of increased concrete strength. The work described herein represents an attempt to answer this question experimentally and thereby establish limits for the future analytical prediction of web crushing failures. This experimental program proceeded with the intention of testing the following two hypotheses: 1. Web crushing strength increases in proportion to fc′ as long as the struts are not damaged. Hence, transformation from an elastic web crushing failure to an inelastic web crushing failure can be achieved simply by increasing the concrete strength; and 2. Damage to struts caused by cyclic loading and inelastic deformations can limit web crushing strength independently of fc′. Hence, increases in fc′ may not lead to proportional increases in ductility capacity. The experimental program designed to test these two hypotheses consisted of two sets of four structural walls with a range of concrete strengths. One set of walls was tested cyclically, and the other set was tested monotonically.
Keywords: ductility; high strength; shear walls; web crushing.
RESEARCH SIGNIFICANCE Elastic and inelastic web crushing failures were consistently achieved in a series of large-scale structural wall tests designed to study the relationship between concrete compressive strength and web crushing strength of thinwebbed members. The results of these tests validate both the dependence of web crushing capacity on fc′ and the significant degradation of web crushing capacity experienced for a range of concrete strengths under cyclic loading in the inelastic range. Physical insight developed from observations and measurements of these tests provides a firm foundation for establishing the limits of thin-webbed reinforced concrete member design. Consistency of the test results indicates that it may be possible to design thin-webbed elements to experience significant inelastic deformations before failing in shear, opening up new possibilities for acceptable ductile failure modes of reinforced concrete members.
INTRODUCTION Over the past 50 years, web crushing capacity of reinforced concrete members has emerged as a primary design concern in three distinct contexts: gravity loading of thin-webbed beams in the 1960s,1-4 seismic loading of structural walls with confined boundary elements in the 1970s,5-9 and seismic loading of hollow bridge piers with confined corner elements in the 1990s.10-13 In each context, motivation to design lightweight members based on physical insight led to large-scale structural testing programs that discovered web crushing capacities significantly in excess of the average shear stress limits recommended by ACI-318.14 Researchers in charge of these testing programs have repeatedly emphasized the importance of understanding shear behavior in terms of diagonal tension and diagonal compression instead of average shear stresses. While diagonal compression demands depend on member geometry and reinforcement, diagonal compression capacities depend on the size and strength of the most heavily loaded struts. Previous research programs established consensus regarding the linear dependence of web crushing capacity on concrete compressive strength fc′ and web thickness. Limits on the value of fc′ itself, however, were not evaluated. Could the web crushing capacity of a 30 MPa wall be increased by a factor of four simply by increasing the concrete strength to 120 MPa? Seismic researchers have hesitated to endorse this ACI Structural Journal/March-April 2014
WEB CRUSHING SHEAR CAPACITY Work in the 1960s on thin-webbed girders established that properly reinforced concrete webs could resist diagonal compression loads in the elastic range almost equal ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. 2011-322.R2, doi:10.14359.51686515, was received May 23, 2013, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
235
Fig. 1—Elastic and inelastic shear web crushing: (a) definition of elastic and inelastic web crushing failure modes and critical regions in wall; (b) free body diagrams used for assessing flexure-shear web crushing capacity of structural wall with confined boundary elements13; and (c) schematic of strut degradation due to cyclic loading. to the compressive strength of concrete itself, resulting in average shear stresses an order of magnitude higher than the prevailing provisions.15 It was during this work that the term “web crushing” was conceived, and a case was made to consider diagonal compression capacity independently of average shear stresses. Work in the 1970s, 1980s, and early 1990s on structural walls with confined boundary elements under seismic loads emphasized the dependence of web crushing capacity on inelastic deformation and the realignment of cracks in the web crushing region, but recommended assessment of web crushing capacity in terms of average shear stresses.9,16 Among these works, the effect of concrete strength on web crushing capacity was witnessed through the tests by the Portland Cement Association (PCA)7,9 in the mid-1970s on walls with boundary elements. Wall B6 with a concrete compressive strength of 22 MPa (3165 psi) failed in web crushing at significantly lower deformation capacity than Wall B7 with a concrete compressive strength of 49 MPa (7155 psi). No further high-strength concrete (HSC) structural walls were tested, however. Work in the late 1990s and early 2000s on hollow bridge piers with confined corner elements clearly distinguished between elastic web crushing and inelastic web crushing, and tied the assessment of inelastic web crushing to the development of the plastic hinge region,12 emphasizing the interaction of inelastic flexure and shear behavior in this zone.13 The physically based method of assessment by Hines and Seible13 recognized the focus on principal stresses from the 1960s research, accounted for inelastic deformations, and allowed accurate assessment of cross sections with various relations between depth of web and depth of boundary elements. A review of the model is provided as follows; however, for a detailed description of the model, the reader should refer to Reference 13. The approach to web crushing capacity by Hines and Seible13 is based on the assessment of capacity and demand
236
on individual struts inside the plastic hinge region as it spreads up the height of a wall. As shown in Fig. 1(a), two distinct shear transfer mechanisms were identified for the plastic hinge region and the regions elsewhere. Elastic, or standard shear, struts are formed in the wall web in regions that have not experienced significant tensile strains along both the longitudinal (vertical) and transverse directions, leading to a parallel shear cracking pattern (at an angle θs). In other words, this region is stressed mainly under in-plane shear stress while the effect of elastic flexural strain is not significant. By comparison, plastic flexural strains force the struts inside the plastic hinge region to realign so that they all converge in the flexural compression toe. This can be understood by considering that the flexural crack at the base of the wall prohibits shear force transfer into the footing at any location except for the flexural compression toe, and that the struts should fan upward until they are able to carry the full elastic shear force. These fanning struts are considered as inelastic or flexure-shear struts. Based on the noted force transfer mechanisms, Hines and Seible13 proposed a web crushing capacity model through equilibrium analysis of the free body diagrams of isolated elastic (or standard) and inelastic (or flexure-shear) diagonal struts (Fig. 1(b)). Calculating the demand of forces on the elastic struts NDs and the compressive capacity NCs of these struts leads to the standard shear web crushing equation proposed by Oesterle et al.7 and Paulay and Priestley16
NCs ≤ kfc′sin θ s cos θ s N Ds
(1)
The inelastic struts in the plastic hinge region differ from their elastic counterparts both in demand and capacity. On the demand side, the inelastic struts are required to transfer inelastic shears at angles that are consistent with the spread ACI Structural Journal/March-April 2014
of plasticity Lpr. On the capacity side, these struts become narrower toward the compression toe from which they fan. Following Hines and Seible,13 the critical flexure shear crack angle θfs is calculated as A f jd v yv + f1t w s θ fs = tan −1 2 T − Tyav
(
)
jd −1 = tan L pr
(2)
Web crushing is then estimated to occur when the capacity NCfs of the critical strut (Eq. (3)) is equal to the demand NDfs on this strut (Eq. (4))
NCfs = kfc′t w Rdθ
N Dfs =
(3)
∆T − f1 st w sin θ fs cos θ fs
(4)
The related variables are determined from a moment-curvature analysis of the cross section and the strut geometry, as shown in Fig. 1(b). The concrete compressive strength softening factor k is calculated according to the modified compression field theory17 with a simplified approach for determining the principal tensile strain ε1. It should be noted that while the model has no explicit limit on fc′, its prediction quality for HSC is uncertain because the available test data for calibration of the model was from tests of normalstrength concrete (NSC) walls. ACI 318-1114 does not reflect the direct dependence of web crushing capacity on fc′, but rather defines the expression in Eq. (1) as 0.83√fc′ (MPa) (10√fc′ [psi]), although √fc′ is a quantity commonly related to concrete tensile strength and diagonal tension failures. A maximum value of 0.69 MPa (100 psi) is adopted by the code because of the lack of test data and practical experience with concrete strengths more than 69 MPa (10,000 psi). The proportional increase of web crushing capacity with fc′ implied by Eq. (3) indicates the potential of achieving a ductile force-displacement response in structural walls even if ultimately limited by web crushing. Figure 2 shows simulated force-displacement responses for structural walls with heavily reinforced boundary elements12 along with web crushing predictions. Curves for walls with concrete compressive strengths varying from 34 to 138 MPa (5 to 20 ksi) are shown. The web-crushing capacity envelopes after Hines and Seible13 and the ACI Code14 limits are also plotted. It can be seen that force-deformation response of the walls is only slightly affected by the increased concrete compressive strength. The Hines and Seible model, however, predict the web crushing capacity to increase dramatically with an increase of concrete strength. The ACI limit is clearly conservative and independent of the inelastic deformations in the wall. The Hines and Seible model implies that a 34 MPa (5 ksi) wall would fail by web crushing at the onset ACI Structural Journal/March-April 2014
Fig. 2—Analytical force-displacement response with web crushing capacity predictions. of yielding, while a 138 MPa (20 ksi) wall would fail in flexure. The model, however, assumes integrity of the struts, which are known to degrade with increase ductility demand and cyclic loading as schematically shown by the cracking pattern in Fig. 1(c). Nonetheless, the suggestion that web crushing strength can be directly and consistently related to concrete compressive strength is indicative of new possibilities for increasing shear capacities of thinned-webbed structural members with increased concrete strength. EXPERIMENTAL PROGRAM Test unit identification, geometry, and reinforcement details To verify the aforementioned hypotheses and establish rational performance levels on the inelastic web crushing limits for HSC structural walls, eight 1/5-scale cantilever structural walls with design concrete compressive strengths of 34, 69, 103, and 138 MPa (5, 10, 15, and 20 ksi) were tested under cyclic and monotonic loading.18 The walls had a barbell-type cross section with thin webs and heavily confined boundary elements, and were designed to induce a web crushing failure and not to represent a component from a prototype structure. The test unit cross sections with reinforcement details are shown in Fig. 3. The identification name for the walls starts with M, followed by two digits denoting the design concrete compressive strength in kip/in.2 (1 kip/in.2 [ksi] = 6.895 MPa) and then by a letter describing the loading protocol: C for cyclic and M for monotonic loading. For example, test unit M10C refers to the wall with a design concrete strength of 69 MPa (10 ksi) and subjected to cyclic loading. All walls had an effective length of 2540 mm (100 in.) for an aspect ratio (M/V) of 2.5. In all cases, the wall web was 508 mm (20 in.) deep and 76 mm (3 in.) thick. The boundary elements had a depth of 254 mm (10 in.). As shown in Fig. 3 and Table 1, the steel reinforcement was essentially the same for all walls, with a small variation in the longitudinal reinforcement of the boundary elements in Wall M15C and in the transverse reinforcement spacing for Walls M20C and M20M. The reinforcement ratios for the web and boundary elements of the test units are given in Table 2.
237
Table 1—Test unit steel reinforcement material properties and layout Test unit
M05C M05M
M10C M10M
M15C
M15M
M20C* M20M
Bar
Size
Spacing, mm
fy, MPa
fu, MPa
εsh
Esh, MPa
M1
M25
4 bars
524
—*
—
11,034
M2
M22
4 bars
448
672
0.0026
11,262
m
M10
127
445
692
0.0083
7759
T
M10
102
445
692
0.0083
7759
S
M10
76
459
703
0.0075
7759
M1
M25
4 bars
464
697
0.0096
8966
M2
M22
4 bars
448
672
0.0094
8966
m
M10
127
476
746
0.0060
8966
T
M10
102
476
746
0.0060
8966
S
M10
76
545
730
0.0050
7586
M
M19
12 bars
439
705
0.0078
8966
m
M10
127
481
759
0.0054
9655
T
M10
102
481
759
0.0054
9655
S
M10
102
503
756
0.0030
7931
M1
M25
4 bars
586
—
—
2759
M2
M22
4 bars
421
630
0.0093
8621
m
M10
127
478
748
0.0060
10,690
T
M10
102
478
748
0.0060
10,690
S
M10
76
510
656
0.0072
5517
M1
M25
4 bars
451
703
0.0054
9310
M2
M22
4 bars
446
699
0.0060
8966
m
M10
127
438
703
0.0043
8793
T
M10
*
76 , 102
438
703
0.0043
8793
S
M10
76
443
717
0.0037
8621
*
— is not displayed in response.
Note: 1 MPa = 0.145 ksi.
Table 2—Test unit steel reinforcement ratios Test unit
ρl
ρn
ρs
ρh
M15C
0.0528
0.0147
0.0357
0.0183
M20C and M20M
0.0556
0.0147
0.0237
0.0244
All others
0.0556
0.0147
0.0237
0.0244
Material properties The HSC for this research was attained with traditional mixture constituents following examples from commercially available mixtures.18 Compressive, tensile, and flexural strengths were assessed through standard testing, and the values at the day of testing for all walls are provided in Table 3. Table 1 lists the properties for the steel reinforcement with reference to the nomenclature noted in Fig. 3. The properties given in Table 1 are average values from three tensile tests on 457 mm (18 in.) long segments for each of the reinforcement bars.
238
Fig. 3—Test unit cross sections with reinforcement details (refer also to Table 3). Loading protocol The test setup (Fig. 4) was designed to load the walls in-plane as cantilevers. The walls were loaded monotonically and cyclically with constant axial load. The axial load for all test units was 579 kN (130 kip), corresponding to 0.10fc′Ag for a reference concrete strength of 34 MPa (5 ksi). Axial load was applied using hydraulic jacks and highstrength rods reacting against the top load stub through a spandrel beam. The horizontal load was applied with a servo-controlled actuator connected to a load stub at the top of the wall. Lateral stability was provided by a pair of parallel inclined tensioned chains on both sides of the wall. Cyclic and monotonic loading, respectively, were applied on two test units with the same design concrete strength to assess shear strength/stiffness degradation and inelastic web crushing limits under different loading histories. Cyclic tests were done according to an incrementally increasing fully reversed cyclic pattern. Four cycles (in quarter increments) were first applied in force control until the theoretical first yield force, Fy′, defined as the force at the onset of yield of the extreme longitudinal reinforcing bar in tension as obtained from a moment-curvature analysis. The top displacement at the theoretical first yield force, Δy′, determined by the average of the measured values from the positive and negative loading excursions, was used to define the experimental elastic bending stiffness, KE = Fy′/Δy′. The ideal yield displacement,19 Δy, corresponding to displacement ductility one (μΔ = 1), was determined using the experimental stiffness at first yield and the ideal yield force, Fy, by Δy = Fy/KE. The ideal yield force Fy was computed by means of a moment-curvature analysis and corresponded to the moment at the critical section at which either the extreme confined concrete fibers reached εc = 0.004 or the extreme steel fiber in tension reached εs = 0.015, whichever occurred first.19 The remainder of the test was conducted in displacement control with two cycles each at the system displaceACI Structural Journal/March-April 2014
Table 3—Test unit concrete material properties fc′, MPa
ft′, MPa
fr′, MPa
Test unit
Design fc′, MPa
x
σ
x
σ
x
σ
M05C
34
46.0
1.37
3.25
0.207
5.49
0.0897
M05M
34
38.9
1.23
3.55
0.0966
5.37
0.0551
M10C
69
56.4
1.86
4.50
0.331
6.57
0.221
M10M
69
84.0
1.37
5.54
0.490
7.33
0.669
M15C
103
102
1.01
5.70
0.441
9.01
0.559
M15M
103
111
4.99
6.17
0.910
0.935
1.08
M20C
138
131
3.01
6.19
0.400
11.5
0.359
M20M
138
115
2.55
5.96
0.172
10.2
0.593
Note: 1 MPa = 0.145 ksi.
Table 4—Force and displacement values at theoretical and ideal yield Test
M05C M05M M10C M10M M15C M15M M20C M20M
Fy′, kN
578
576
583
618
586
644
576
572
Δy′, mm
17.6
18.5
18.4
15.8
15.7
16.2
13.5
15.2
Fy, kN
842
836
723
745
731
816
809
803
Δy, mm
25.7
26.9
22.9
19.1
19.6
20.6
19.1
21.3
Note: 1 kN = 0.225 kip; 1 mm = 0.0394 in.
shear deformations were measured on two wall segments (one from the wall base to 1016 mm [40 in.] high, and the second one from the noted level to the wall top) with a pair of displacement transducers arranged in opposing diagonal directions on one wall face. Global displacement at the effective height of the wall (2540 mm [100 in.]) was measured with a string potentiometer. Further details of the instrumentation are reported elsewhere.18
Fig. 4—Test setup overview. ment ductility levels μΔ = 1, 1.5, 2, 3, 4, and 6, or until failure of the test unit. The monotonic tests were conducted by applying the lateral load in force control until Fy′, and then in displacement control until failure. The values of Fy′ and Δy that defined the loading protocol are listed in Table 4. Instrumentation The walls were instrumented to measure segmental flexural curvatures, shear deformations, and steel reinforcement strains. The layout of the external instrumentation is shown in Fig. 5. Flexural section curvatures were calculated using displacement transducers placed along the height of the column on both sides of the boundary elements. Average ACI Structural Journal/March-April 2014
OBSERVATIONS Common behavior Common behavior observed on all test units is described herein. No cracking was observed up to 0.25Fy′. At 0.5Fy′, flexural cracking in the boundary elements and diagonal shear cracking in the webs appeared. At 0.75Fy′, elastic shear cracking developed throughout the entire web. The HSC walls developed a denser pattern of flexural and shear cracks than the NSC walls. With increasing displacement ductility crack density increased and the active cracks became wider. Overall, shear crack spacing in the HSC walls was much smaller than for the NSC walls. Even though diagonal shear cracking under tension does not control the capacity of the walls, it defines the height and width of the struts, and thus affects the strut capacities. Strut capacity is also affected by crack width, which dictates shear slip behavior at the crack interface. Finally, relatively larger cover concrete spalling on the compression boundary element was observed on the HSC walls. Nonetheless, the heavily confined boundary elements had no problem resisting the compression force. 239
Fig. 5—External instrumentation layout (units in mm). (Note: 1 mm = 0.0394 in.) Damage patterns and failure mechanisms Peculiarities on damage pattern, web crushing failure, and ductility capacity are described herein individually. All walls failed in web crushing according to the experimental aim. Walls M05C and M10C failed on the first excursion to μΔ = 2, and web crushing occurred at μΔ = 1.8. In both walls, there was a sudden loss of strength upon failure of approximately 40%. Wall M15C performed in a ductile manner up to μΔ = 4, and failed in web crushing on the second excursion to ductility 4. This HSC wall had a gradual loss of strength upon failure, losing only approximately 8% of its strength compared with the load reached during the first cycle at ductility 4. Wall M20C performed in a ductile manner up to its failure by web crushing on the first excursion to μΔ = 6. Web crushing started to develop at a top displacement of 66 mm (2.6 in.), and the wall strength degraded by roughly 40% when the displacement reached the target displacement for ductility six. Wall M05M failed by elastic web crushing at μΔ = 2.3. Walls M10M, M15M, and M20M performed in a ductile manner up to web crushing failure at μΔ = 7, 6.5, and 9.2, respectively. The damage and failure patterns in the wall bottom third region (850 mm [33 in.]) for all test units are shown in Fig. 6. Test units with lower concrete compressive strength (M05C, M05M, and M10C) failed after only minor levels of inelastic response (Fig. 6(a) to (c)). Tensile cracking was minimal, and cracks fully closed upon load reversal. No crack realignment was observed and thus these walls were limited by standard, or elastic, web crushing. The failures were sudden and the crushing of the concrete struts occurred along the interface of the wall web and the compression boundary element, and instantly propagated along the wall height. The rest of the test units exhibited moderate to high ductile behavior before web crushing failure. Cracking was more extensive, and 240
crack spacing was much smaller. The fanning flexure-shear cracking pattern was formed within the plastic hinge region, with fairly flat cracks close to the bottom and much steeper cracks at the top. An example of this inelastic flexure-shear failure mode is shown in Fig. 6(d) for Wall M10M. Loading protocol had a large influence on damage and failure patterns. This can be seen by comparing the failure modes between the cyclic and monotonic tests for Walls M15 and M20 (Fig. 6(e) to (h)). The monotonically loaded units developed a denser crack pattern, with multiple branching and wedge-shaped struts. Conversely, the cyclic tested walls had wider spaced cracks and struts with a more uniform width. The uniform damage pattern from denser cracking in the monotonic tests allowed for more diagonal compression load paths in the wall web. The consistent loading also permitted the struts to remain integral, thus allowing these walls to sustain larger inelastic deformations. In constrast, the wider cracking pattern from cyclic loading led to larger crack misalignment and damage to the diagonal struts, which reduced deformation capacity. The cracking pattern due to cyclic loading is illustrated in Fig. 1(c) and shown in Fig. 7, which illustrates the degradation of inelastic struts for wall M20C upon reaching the second negative displacement target (second cycle) for μΔ = 4. Figure 7(a) is a view of the bottom region of the wall from which the fanning crack pattern inside the plastic zone can be discerned. The close-up view of the wall web in Fig. 7(b) shows the crisscross cracking pattern from the reversed loading cycles. Upon reloading, crack misalignment results from shear deformations due to yielding and bond-slip effects in the longitudinal and transverse web reinforcement. As cracks close for the compression load path to reestablish in the previously formed struts, the crack misalignment induces large local stresses due to shear friction and distortion of the struts. This causes the web cover concrete to lose its bond to the reinforcement and spall off, as seen in the lower left region of the wall web (Fig. 7(b)). The test units gradually lost their load-carrying capacity as a result of the diminished load transfer efficiency of the concrete struts. Web crushing in the cyclically loaded walls was observed to expand over a large area within the plastic hinge region, and crushing of the flexure-shear struts initiated in the center of the web and then extended to the edge of the compression boundary element (Fig. 6(e) and (g)). The noted differences between the cyclic and monotonic responses became more significant for higher values of concrete compressive strength. RESULTS Force-deformation response The hysteretic force-displacement response of the four walls under cyclic loading is shown in Fig. 8. Again, failure in all cases was due to web crushing. Recalling that the reinforcement details were essentially the same for all walls, the test results demonstrate that increased concrete compressive strength allowed the walls to considerably increase their inelastic deformation capacity by delaying shear failure. Web crushing was thus shifted from an essentially elastic level for Wall M05C, failing after completion of two cycles at μΔ = 1.5, to a highly stable ductile response for Wall M20C, failing after ACI Structural Journal/March-April 2014
Fig. 6—Damage and failure patterns in wall bottom third region (850 mm [33.5 in.]). sustaining two full cycles at μΔ = 4. Comparison of inelastic deformation capacity in terms of displacement ductility is adequate because the ideal yield displacement for all walls did not vary greatly, as shown in Table 4. The ductile behavior displayed by Walls M15C and M20C shows that these units preserved the high stiffness and lateral load-carrying capacity characteristic of structural walls, mostly provided by the web, while benefiting from the inelastic deformation capacity of column flexural hinges at the boundary elements. Finally, the energy dissipation capacity, as judged by the area of the hysteresis loops, is also notably increased solely due to the increase of the concrete compressive strength. Inelastic behavior characteristics According to Eq. (2) the length of the plastic hinge region Lpr is directly proportional to the angle of the flexural-shear cracking, and hence the force demand on the critical inelastic strut. The spread of plasticity can be taken as the length over which plastic curvatures exceed the yield curvature from an ACI Structural Journal/March-April 2014
idealized bilinear moment-curvature response.19 The curvature profiles of the M10 and M20 walls are shown in Fig. 9. For cyclic loaded test units that failed at low to medium ductility levels, the curvature distribution along the height was almost linear until failure. For monotonic loaded test units that failed at a high ductility level, the plastic rotation was mainly concentrated within 300 mm (12 in.) from the bottom of the wall. It can be seen, however, that the spread of plasticity is very similar at equal displacement ductility levels for both monotonic and cyclic loaded walls. The curvature distributions provide local-level evidence of the significant inelastic flexural deformations sustained by the walls. Furthermore, the observed fanning crack pattern (Fig. 6) and the essentially linear distribution of plastic curvatures along the plastic hinge region (with the linearity only disturbed by boundary effects at the footing) suggests that Eq. (4) can be used to assess the demand on the critical inelastic strut. Table 5 shows the separate contribution of flexure and shear effects to the displacement at the wall top for the cycli241
Fig. 7—Degradation of inelastic struts for M20C wall during ductility 4 cycling: (a) view of wall bottom third region (850 mm [33.5 in.]); and (b) close-up view of wall web.
Fig. 8—Hysteretic force-displacement response of cyclic tests. (Note: 1 MPa = 0.145 ksi; 1 mm = 0.0394 in.) cally tested units at the first positive peak of each ductility level. The flexure-induced displacement Δf at the top of the wall was calculated by adding the contribution of individual sectional rotations. The top wall displacement due to shear Δs was calculated by summing the shear deformations measured on the two wall segments (Fig. 5). From the data in Table 5 it can be confirmed that the shear displacements are linearly related to the flexural displacements.12 For the eight tested walls,18 the average ratio of shear to flexural displacements was 0.23, with a standard deviation of 0.04. Figure 10 shows the average shear stress versus shear strain hysteretic response of Wall M20C in the bottom and top wall segments. The shear deformations were mainly concentrated in the bottom wall segment (1016 mm [40 in.] from the base), which is where the plastic hinge region develops. It can be seen that the average shear stresses considerably exceeded the ACI limits. This observation applies to all walls because they had similar levels of lateral load resistance. To provide further insight and quantitative information on the performance of the tested walls, Fig. 11 provides a brief overview of average strain demands at mid-depth on the wall 242
web. Shown in Fig. 11(c) are longitudinal strain profiles for the M20 walls, which have a linear variation along the height (with disturbance near the footing). The strains were calculated using the displacement transducers along both sides of the boundary elements (Fig. 5). The profiles are consistent with the moment gradient on the wall. It can be further observed that the strain profiles for both M20 walls are essentially the same at equal displacement ductility demands. This was consistent for the other three wall sets, supporting the evidence of equal flexural demands on monotonic and cyclic tests. Principal strains in the wall web were estimated from consideration of a whole wall segment (web and boundary elements) through Mohr’s circle with the measured longitudinal strains, the measured average shear strains (Fig. 5), and neglecting the transverse strains (due to the presence of the heavily reinforced boundary elements). Principal strain values calculated this way at the web mid-depth are shown in Fig. 11(b) against displacement ductility for all walls. Except for some deviations for the M05 walls, the average principal strains were equal for all walls at the same displacement ductility level.
ACI Structural Journal/March-April 2014
Fig. 9—Average curvature strain profiles for: (a) M10 walls; and (b) M20 walls.
Fig. 10—Average shear stress-strain response of: (a) bottom; and (b) top segments of Wall M20C. Monotonic versus cyclic loading A comparison of the force-displacement envelopes of the cyclic and monotonic tests is shown in Fig. 12. It is clear that higher fc′ resulted in higher inelastic deformation capacity. The force-deformation response of the walls, up to their respective deformation limit, is considered to have been essentially the same, with minor differences due to: a) variations in fc′; b) longitudinal reinforcement differences for Wall M15C (Fig. 3); c) earlier spalling in the compression toe for Wall M20C; and d) reduction of the effective concrete compressive strength due to more severe cracking for the cyclically loaded walls. The increase in deformation capacity, however, was not directly proportional to fc′, particularly for the cyclic loaded walls. The monotonic and cyclic deformation capacities of the M05 walls were essentially the same (Fig. 12(a)). The response was similar because both walls failed close to the elastic range, and only minimal cycling was done on Wall M05C. The responses of the other walls show that while increased concrete strength leads to larger deformation capacity, cyclic loading curtails this improvement. The deformation capacity reduction of the cyclically tested walls is attributed to the damage of the flexure-shear struts from cyclic loading, which reduces their capacity to transfer load from the tension to the compression boundary element. This effect is best seen by observing the responses for the M15 walls in Fig. 12(c). The effect was not as clearly captured for the M10 walls (Fig. 12(b)) because fc′ for M10C was lower than that for M10M. Nonetheless, given the response of Wall M15C, it can be expected that if fc′ for Wall M10C had been closer to the design target, its deformation capacity would have been increased, and the cyclic and monotonic envelopes would have been similar to those obtained for the M15 walls. Comparison of the M20 wall response envelopes indicates a ACI Structural Journal/March-April 2014
Table 5—Flexure and shear components of wall top displacement at first positive peak of each ductility level Ductility μΔ = 1.0 μΔ = 1.5 μΔ = 2.0 μΔ = 3.0 μΔ = 4
Displacement
M05C
M10C
M15C
M20C
Δf, mm
18.5
18.0
14.5
14.5
Δs, mm
5.08
6.10
3.53
3.30
Δf, mm
28.4
27.7
22.6
23.1
Δs, mm
7.62
7.87
4.83
4.57
Δf, mm
—
—
30.5
30.7
Δs, mm
—
—
6.60
6.60
Δf, mm
—
—
47.0
47.0
Δs, mm
—
—
9.40
9.91
Δf, mm
—
—
62.5
62.0
Δs, mm
—
—
13.2
15.5
Note: 1 mm = 0.0394 in.
significant effect of cyclic loading on the deformation limit of Wall M20C despite the larger concrete strength in M20C compared with that in M20M. It is thus hypothesized that the reduced deformation capacity in the cyclically tested HSC walls is due to the negative convergence of an increased stress intensity field at crack misalignment and a reduced cracking bridge zone from the higher strength concrete. This can be understood upon considering that HSC experiences dramatic strength degradation in the postpeak response, and the effect of further strength increase is not appreciable. For structural walls, the later effect would indicate a curtailing effect on the increased inelastic deformation gains on web crushing capacity for increasing values of fc′. The reduced gain in deformation capacity of Wall M20C compared with that of Wall M15C would seem to indicate 243
Fig. 11—Overview of average strain demands on wall webs: (a) longitudinal strain profiles in M20 walls; and (b) principal strains versus ductility. that increased concrete strength does not lead to additional deformation capacity beyond a certain point. Wall M20C, however, failed after completion of two cycles at μΔ = 4, while M15C failed during the first loading branch of the second cycle at μΔ = 4. Evaluation of the dissipated hysteretic energy (area inside the hysteresis loop) shows that all walls provided essentially the same level of specific energy dissipation for a given displacement ductility level.18 This can be qualitatively seen by observing the hysteretic responses in Fig. 8. Because the walls had the same reinforcement details, this is to be expected. Thus, the increased shear capacity of the HSC walls improved their hysteretic energy dissipation capability. Based on this evaluation, Wall M20C had 27% higher energy dissipation capacity than Wall M15C.18 The sum of the dissipated energy for all ductility levels shows that increased concrete strength increased the inelastic energy dissipation capacity of the walls by delaying web crushing failure. Considering the strut resistance mechanism proposed by Hines and Seible13 (Fig. 1(b)), the similitude in principal strain values (Fig. 11(b)) indicates that the force demand in the walls at equal displacement ductility levels was the same. It is clear, however, that the walls had different deformation and web crushing capacities. The difference is then attributed to the concrete strength (as reflected in Eq. (3)) and the loading pattern. This was explored by estimating the concrete softening factor k using experimentally derived values for Lpr and the shear force at web crushing failure. Equation (1) was used for Walls M05C, M05M, and M10C because they are considered to have failed by elastic web
244
crushing, while the rest of the walls, which failed by inelastic web crushing, followed Eq. (3). Figure 13(a) plots the calculated values of k versus normalized shear distortions in the plastic hinge region. The maximum (condition before web crushing) average shear distortion within the plastic hinge region, γm, was normalized by the strain at peak stress in compression εco′, which was estimated from the model by Tasemir et al.20 The figure also shows the concrete strength reduction factor relation proposed by Collins21 in terms of shear strains, which is essentially the constitutive model for cracked concrete in compression in the modified compression field theory (MCFT). This relation has been shown to relate well to test data in which the compression stresses act along uniform parallel struts across the section,9 or elastic shear. Results from this program, however, deviate from the noted model in interesting ways. The data in Fig. 13(a) shows how the monotonic and cyclic tests follow different degradation trends for the softening factor k, with lower values and a faster decay with increasing shear distortion for the cyclic walls. The experimental k values are plotted against concrete strength in Fig. 13(b), where again the data is clearly segregated in terms of the loading protocol. The cyclic and monotonic wall data was fitted with exponential functions only for the purpose of illustrating the data trends. It can be seen that the M05 data points are close to each other because both failed in elastic web crushing. For increasing concrete strengths, the softening factor decays faster for the cyclic walls. It is of interest to note that the softening factor (and thus, the inelastic web crushing capacity) is affected both by the cyclic loading and the increase in concrete strength, or, stated differently, cyclic loading had an increased detrimental effect on the effective capacity of the shear resisting struts with increasing concrete compressive strength. Web crushing capacity models Table 6 compares the web crushing capacities with different predictive models. It can be noted that ACI shear provisions considerably underestimate the web crushing strength. At the same time, the prediction quality of the model by Hines and Seible13 on the cyclic tests deteriorates with increasing concrete strength. Thus, the experimental program revealed that rational web crushing models like the one by Hines and Seible need further considerations to be applicable to HSC structural walls. A modified version of the Hines and Seible model, as well as the finite element implementation of the MCFT in modeling the behavior of the HSC walls was proposed by Liu,22 and will be reported in a future paper by the authors. CONCLUSIONS Eight cantilever walls were tested with design concrete compressive strengths of 34, 69, 103, and 138 MPa (5, 10, 15, and 20 ksi) under cyclic and monotonic loading to study the effects of HSC and damage accumulation on the inelastic web-crushing capacity of structural walls. The following conclusions are offered specifically referring to structural walls with well-confined boundary elements: 1. The experiments clearly demonstrated the differences between elastic and inelastic web crushing behavior and their dependence on concrete compressive strength;
ACI Structural Journal/March-April 2014
Fig. 12—Comparison of force-displacement envelopes for cyclic and monotonic tests: (a) M05; (b) M10; (c) M15; and (d) M20. (Note: 1 kN = 0.225 kip; 1 mm = 0.0394 in.; 1 ksi = 6.895 MPa.)
Fig. 13—Average compression softening factor k versus: (a) normalized maximum shear distortion in plastic region; and (b) concrete compressive strength. Table 6—Comparison of web crushing capacities with models ACI 31814
Experiment
Hines and Seible13
Test unit
Δu, mm
Fu, kN
Δu, mm
Fu, kN
Difference, %
Δu, mm
Fu, kN
Difference, %
M05C
45.0
803
8.64
342
–81
48.5
821
8
M05M
45.0
855
8.13
322
–82
26.9
725
–40
M10C
42.7
751
8.38
387
–80
64.3
751
51
M10M
130
900
9.91
478
–92
101
853
–22
M15C
78.7
819
10.2
497
–87
128
889
62
M15M
133
934
11.7
542
–91
160
966
20
M20C
76.5
815
14.0
589
–82
M20M
189
923
13.2
553
–93
Flexure 196
992
3
Notes: 1 kN = 0.225 kip; 1 mm = 0.0394 in.
2. Increase in concrete compressive strength enhances the ductility and hysteretic energy capacity of structural walls by preventing web crushing shear failures; 3. Web crushing strength increases in proportion to fc′ as long as struts remain undamaged. Hence, transformation from an elastic web crushing failure to an inelastic web crushing failure can be achieved simply by increasing the concrete strength; 4. Damage to struts caused by cyclic loading and inelastic deformations limits web crushing strength independently of fc′. ACI Structural Journal/March-April 2014
While this conclusion may be generally well recognized for walls limited by both elastic and inelastic web crushing, experimental evidence from this research, based on corresponding monotonic and cyclic tests, showed that degradation from cyclic loading increases with increasing concrete strength; 5. Concrete compressive strength does not linearly increase web crushing strength as implied by rational web crushing models; rather, the relationship is nonlinear, with a decreasing limit as concrete strength increases. This obser245
vation is not well-described by current web crushing models. Therefore, it is advised that these models consider the limits demonstrated by the reported tests when considering HSC to improve the web crushing performance of walls; 6. The web crushing capacity of structural walls with well-confined boundary elements was found to be well in excess of levels acceptable in current practice for a wide range of concrete compressive strengths; and 7. Rational assessment of web crushing limits can open up new possibilities for acceptable ductile failure modes on reinforced concrete structural walls. AUTHOR BIOS
ACI member Rigoberto Burgueño is an Associate Professor of structural engineering and Director of the Civil Infrastructure Laboratory at Michigan State University, East Lansing, MI. He received his BS, MS, and PhD from the University of California, San Diego, La Jolla, CA. He is a member of ACI Committees 341, Earthquake-Resistant Concrete Bridges, and 440, Fiber-Reinforced Polymer Reinforcement. His research interests include nano-engineered structural materials, composite materials and structures, multi-scale modeling, and seismic performance of reinforced concrete structures. ACI member Xuejian Liu is a former Graduate Research Assistant at Michigan State University, where he received his PhD in civil engineering. He is a member of Joint ACI-ASCE Committee 445, Shear and Torsion. His research interests include the seismic behavior of reinforced concrete structures and fiber-reinforced concrete. ACI member Eric M. Hines is a Principal at LeMessurier Consultants, Inc., Cambridge, MA, and is a Professor of Practice at Tufts University, Medford, MA. He received his PhD in structural engineering from the University of California, San Diego. He is a member of ACI Committee 341, Earthquake-Resistant Concrete Bridges. His research interests include the seismic performance of low-ductility structural systems in moderate seismic regions and inelastic behavior of reinforced concrete structures.
Av dθ Esh Fu Fy Fy′ f1 fc′ fu fy fyv jd k Lpr NCfs NCs NDfs NDs R S T Tyav tw Δu Δy ΔT ε1 εsh φy μΔ θfs θs ρh ρl ρn ρs
246
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
NOTATION
area of transverse steel at given level incremental angle for calculating critical strut area elastic modulus at onset of strain hardening shear force at ultimate ideal yield shear force first yield shear force principal tensile stress unconfined concrete compressive cylinder strength ultimate steel stress steel yield stress transverse steel yield stress distance between flexural tension and compression force resultants concrete compression strength softening factor plastic hinge region length flexure-shear strut compression capacity standard shear strut compression capacity flexure-shear strut compression demand standard shear strut compression demand radius for critical compression strut fan transverse reinforcement vertical spacing flexural tensile force resultant effective average flexural tensile yield force resultant structural wall thickness test unit flexural top displacement ideal yield lateral displacement incremental tensile flexural force principal tensile strain steel strain at onset of strain hardening ideal yield curvature displacement ductility flexure-shear crack angle measured from longitudinal axis shear crack angle measured from longitudinal axis structural wall transverse reinforcement ratio boundary element longitudinal reinforcement ratio structural wall longitudinal reinforcement ratio boundary element transverse reinforcement ratio
ACKNOWLEDGMENTS
The research described in this paper was carried out under funding from the National Science Foundation under Grant No. CMS-0530634. The authors thank the staff and students of MSU’s Civil Infrastructure Laboratory, where the reported work was conducted.
REFERENCES
1. Leonhardt, F., and Walther, R., “The Stuttgart Shear Tests 1961,” Transaction No. 111, Cement and Concrete Association, London, UK, 1961, 134 pp. 2. Mattock, A. H., and Kaar, P., “Precast-Prestressed Concrete Bridges, 4, Shear Tests of Continuous Girders,” Journal, Portland Cement Association Research and Development Labs, V. 3, No. 1, Jan. 1961, pp. 19-46. 3. Robinson, J. R., “Essais a l’effort trenchant de pouters a ame mince en béton armé,” Annales des Ponts et Chaussées, Mar.-Apr. 1961, pp. 226-255. 4. Placas, A., and Reagan, P. E., “Shear Failure of Reinforced Concrete Beams,” ACI Journal, V. 68, No. 10, Oct. 1971, pp. 763-773. 5. Wang, T. Y.; Bertero, V. V.; and Popov, E. P., “Hysteretic Behavior of Reinforced Concrete Framed Walls,” Earthquake Engineering Research Center Report 75/23, University of California, Berkeley, Berkeley, CA, Dec. 1975, 367 pp. 6. Oesterle, R. G.; Fiorato, A. E.; Johal, L. S.; Carpenter, J. E.; Russell, H. G.; and Corley, W. G., “Earthquake Resistant Structural Walls—Tests of Isolated Walls,” NSF Report GI-43880, Portland Cement Association, Skokie, IL, 1976, 315 pp. 7. Oesterle, R. G.; Ariztizabal-Ochoa, J. D.; Fiorato, A. E.; Russell, H. G.; and Corley, W. G., “Earthquake Resistant Structural Walls—Tests of Isolated Walls, Phase II,” NSF Report ENV77-15333, Portland Cement Association, Skokie, IL, 1979, 331 pp. 8. Vallenas, J. M.; Bertero, V. V.; and Popov, E. P., “Hysteretic Behavior of Reinforced Concrete Structural Walls,” Earthquake Engineering Research Center Report 79/20, University of California, Berkeley, Berkeley, CA, 1979, 234 pp. 9. Oesterle, R. G.; Fiorato, A. E.; and Corley, W. G., “Web Crushing of Reinforced Concrete Structural Walls,” ACI Journal, V. 81, No. 3, May-June 1984, pp. 231-241. 10. Hines, E. M.; Seible, F.; and Priestley, M. J. N., “Seismic Performance of Hollow Rectangular Reinforced Concrete Piers with Highly-Confined Corner Elements—Phase I: Flexural Tests, and Phase II: Shear Tests,” Structural Systems Research Project Report 1999/15, University of California, San Diego, La Jolla, CA, 1999, 266 pp. 11. Hines, E. M.; Dazio, A.; and Seible, F., “Seismic Performance of Hollow Rectangular Reinforced Concrete Piers with Highly-Confined Corner Elements—Phase III: Web Crushing Tests,” Structural Systems Research Project Report 2001/27, University of California, San Diego, La Jolla, CA, 2001, 239 pp. 12. Hines, E. M.; Restrepo, J. I.; and Seible, F., “Force-Displacement Characterization of Well Confined Bridge Piers,” ACI Structural Journal, V. 101, No. 4, July-Aug. 2004, pp. 537-548. 13. Hines, E. M., and Seible, F., “Web Crushing of Hollow Rectangular Bridge Piers,” ACI Structural Journal, V. 101, No. 4, July-Aug. 2004, pp. 569-579. 14. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp. 15. ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-63),” American Concrete Institute, Farmington Hills, MI, 1963, 144 pp. 16. Paulay, T., and Priestley, M. J. N., Seismic Design of Reinforced Concrete and Masonry Buildings, Wiley Interscience, New York, 1992, 768 pp. 17. Vecchio, F. J., and Collins, M. P., “The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal, V. 83, No. 2, Mar.-Apr. 1986, pp. 219-231. 18. Liu, X.; Burgueño, R.; Egleston, E.; and Hines, E. M., “Inelastic Web Crushing Performance Limits of High-Strength-Concrete Structural Wall— Single wall Test Program,” Report No. CEE-RR–2009/03, Michigan State University, East Lansing, MI, 2009, 281 pp. 19. Priestley, M. J. N.; Seible, F.; and Calvi, G. M., Seismic Design and Retrofit of Bridges, John Wiley & Sons, Inc., New York, 1996, 686 pp. 20. Liu, X., “Inelastic Web Crushing Performance Limits of HighStrength-Concrete Structural Walls,” PhD dissertation, Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, 2010, 215 pp. 21. Tasdemir, M. A.; Tasdemir, C.; Akyuz, S.; Jefferson, A. D.; Lydon, F. D.; and Barr, B. I. G., “Evaluation of Strains at Peak Stresses in Concrete: A Three-Phase Composite Model Approach,” Cement and Concrete Composites, V. 20, 1998, pp. 301-318. 22. Collins, M. P., “Toward a Rational Theory for RC Members in Shear,” Proceedings, ASCE, V. 104, No. ST4, Apr. 1978, pp. 649-666.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S21
Response of Precast Prestressed Concrete Circular Tanks Retaining Heated Liquids by Michael J. Minehane and Brian D. O’Rourke The present study investigated the influence of heated water storage, upward to 95°C (171°F), on precast prestressed concrete circular tanks. Modern design standards for concrete liquidretaining structures require that thermal effects be considered for the serviceability limit state and the ultimate limit state when deemed significant. Most recognized standards, however, do not provide guidance for the analysis of such effects. Research in this area is also limited and almost exclusively concerned with ambient thermal conditions, with a maximum temperature change of 30°C (54°F) in any instance. A finite element study incorporating thermomechanical coupling investigated the magnitude of stresses associated with thermal storage. A linear eigenvalue analysis examined the ultimate limit state of buckling for restrained tank walls due to the thermallyinduced combined axial compression and bending. Consequent design implications were established and recommendations made for accommodating thermal loading. Keywords: buckling; elevated temperature; finite element analysis; material properties; prestressed concrete; reservoirs; thermal loading; thermal storage.
INTRODUCTION The significance of thermal effects on concrete reservoir walls for ambient conditions is long established. An early study by Priestley1 determined that temperature gradients of 30°C (54°F) through the wall thickness can exist in warm climates when the effects of solar radiation are considered. Priestley1 demonstrated that the resulting tensile stresses were large enough to overcome the residual compression, and cracking would inevitably occur. Ghali and Elliott2 developed closed-form solutions for the thermal analysis of elastic tank walls with varying base restraint and that are free at the top. Through numerical examples, it was shown that a gradient of 30°C (54°F) through the wall thickness was sufficient to cause cracking. This supported Priestley’s1 proposal that the design should be based on a serviceability criterion of limiting crack widths rather than a limiting tensile stress. Although modern design standards require that thermal effects are considered for the serviceability limit state, few provide guidance for the analysis of such effects. Pioneering design codes with regard to this are NZS 31063 and AS 3735,4 which provide design tables, originally derived by Priestley,1 to calculate hoop forces and vertical moments for tank walls free at the top and either free-sliding, pinned, or fixed at the base. The studies reviewed were exclusively applicable to tank walls free at the top. As thermal storage tanks require a roof, the associated radial restraint at the top of the wall alters the internal force distribution. Moreover, the magnitude of the internal forces resulting from the thermal expansion of ACI Structural Journal/March-April 2014
the tank walls will be shown to be prohibitive from a design perspective, unless provisions are made for radial displacement during service. RESEARCH SIGNIFICANCE This paper investigates the feasibility and implications of thermal storage using cylindrical concrete reservoirs, for which there is currently a paucity of information. The research has practical applications in the oil, gas, and nuclear containment industries, in addition to thermal storage for district heating and related schemes. Although particular reference is made throughout to precast prestressed concrete storage tanks, the research is also applicable to partially prestressed and reinforced concrete reservoirs. INFLUENCE OF ELEVATED TEMPERATURES ON MATERIAL PROPERTIES Mechanical properties EN 1992-1-2,5 EN 1992-3,6 and FIB Bulletin 55: Model Code 20107 each define the reductions in the mechanical properties of both the concrete and steel reinforcement for elevated temperatures. For the temperature range under consideration for the current study, the associated strength reductions are insignificant. It is reasonable to suggest that any minor reduction in the strength and stiffness of concrete may be discounted when the effect of long-term thermal exposure is considered. Mears8 tested concrete specimens subjected to a constant temperature of 65°C (149°F) for 5000 days and observed that the long-term exposure had, in fact, the effect of increasing the compressive strength and the modulus of elasticity of concrete. The same trend was also recorded by Komendant et al.,9 who tested concrete at 71°C (160°F) for 270 days, and Nasser and Lohtia,10 who tested concrete at 121°C (250°F) for 200 days. It would appear, however, that this trend is only valid for temperatures below 150°C (302°F), as long-term exposure to temperatures in excess of this resulted in a reduction in the mechanical properties of concrete.10,11 Creep Creep of concrete increases at higher temperatures. Extensive research has been carried out on the influence of temperature on concrete creep for structures used in nuclear ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-065, doi:10.14359.51686441, was received February 23, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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Fig. 1—Creep coefficient multipliers with increasing temperature. (Note: °F = 1.8°C + 32.) containment. It would appear from the literature that the use of a thermal scaling factor, or creep coefficient multiplier, is appropriate in accounting for temperature effects on creep. Figure 1 presents a comparison of creep coefficient multipliers from guidance provided by CEB 20812 and fib Bulletin 55: Model Code 20107 in addition to experimental studies carried out by Brown,13 Gross,14 and Nasser and Neville.15 For a temperature of 95°C (203°F), the creep coefficient multipliers range from approximately 1.95 to 2.45. An accurate evaluation of creep at elevated temperatures is difficult to attain, as creep is sensitive to the evaporable water in the mixture. Consequently, an accurate value of the moisture content is desirable if a precise assessment is to be made. The moisture content, particularly at elevated temperatures, is sensitive to the member thickness. The majority of the experimental results were developed for the walls of nuclear containment structures, which are generally members of wall thicknesses in the range of 1000 to 1500 mm (39 to 59 in.). Because the walls of precast prestressed storage tanks are much thinner—typically 150 to 250 mm (5.9 to 9.8 in.)—the walls would lose much more moisture comparably, which would suggest that a lower value of a creep coefficient multiplier may be more appropriate. The experimental results are generally based on uniaxial tests. As prestressed concrete circular tanks are subject to a multiaxial state of stress, a further reduction in the predicted creep strain would be appropriate, in line with the findings of Hannant16 and McDonald.17 Bond strength Numerous experimental studies conclusively reveal that the bond strength decreases with increasing temperature. This is primarily attributed to the differing coefficients of thermal expansion for steel and concrete. Figure 2 compares test results from studies by Harada et al.,18 Kagami et al.,19 248
Fig. 2—Residual bond strength ratio with increasing temperature. (Note: 1°F = 1.8°C + 32.) Haddad et al.,20 Chang and Tsai,21 Bažant and Kaplan,22 and Huang.23 A wide scatter in the residual bond strength ratios (ratio of bond strength of heated specimen to that of a specimen at ambient temperature) is observed. This is primarily due to the many variables involved, including concrete mixture, compressive strength, exposure duration, method of cooling, and bar size. Stress relaxation Owing to different coefficients of thermal expansion, steel expands relative to concrete with increasing temperature. Consequently, for pretensioned members, this will effectively increase the loss of prestress due to stress relaxation. fib Bulletin 55: Model Code 20107 quantifies the increase in loss due to stress relaxation with increasing temperature for a duration of 30 years (Fig. 3). The significance of high temperatures on the stress relaxation is evident, as a value of approximately 2.5% at ambient temperature increases to approximately 15.0% at 100°C (212°F). FINITE ELEMENT ANALYSIS Finite element analysis was carried out using commercial finite element software. The cylindrical structure was idealized using two-dimensional (2-D) axisymmetric models comprising quadrilateral solid field and continuum elements. The thermomechanical transient analysis incorporated a semicoupled procedure and was time-stepped according to predefined intervals. A semicoupled analysis involves running the thermal and structural analyses separately and is conducted when the thermal solution is not considerably affected by changes in geometry. The thermal analysis, which runs first, is governed by the quasi-harmonic transient heat conduction equation. The resulting temperature distribution for a given time step is subsequently fed to the structural analysis for the calculation of displacements ACI Structural Journal/March-April 2014
and consequent stresses and strains. A maximum element size of 0.3 m (0.98 ft) was established following a mesh convergence study. The material properties used throughout the finite element study are given in Table 1. Verification of modeling procedure The modeling procedure was verified with existing results in the literature from Priestley,1 Ghali and Elliott,2 and Vitharana and Priestley.24 In each case, the numerical examples considered a tank wall pinned at the base, free at the top, and subject to a 30°C (54°F) ambient temperature gradient. Figure 4 shows the finite element model for the comparison with Priestley1 for a tank of dimensions R = 15.1 m (49.5 ft), H = 7.2 m (23.6 ft), and t = 0.2 m (7.87 in.). As is evident from Fig. 5, good agreement for hoop forces and vertical bending moments was observed in each instance.
Idealization and boundary conditions To idealize a typical precast concrete tank incorporating a roof, the wall ends were restrained from radial displacement but free to rotate. The top of the wall was also free to displace vertically because the strain due to thermal expansion far exceeds that imposed by the self-weight of typical roof construction comprising precast flooring on a grid of columns. Figure 6 shows the mesh discretization for the axisymmetric models and displays a deformed contour of hoop forces obtained from the structural analysis. DESIGN IMPLICATIONS Limiting compressive stress For a tank restrained radially at its ends, the hoop force induced by thermal storage is compressive over the entire height of wall and is significant in magnitude. It is necessary to check the resulting compressive stress against limits provided in design standards and guidance. Table 2 presents compressive stress limits from standards and guidance, including EN 1992-1-1,25 BS 8007,26 PCI,27 and NZS 3106.3 The limits are expressed in terms of the concrete cylinder strength fck. The limit stipulated by BS 8007 is given in terms of the cube strength fcu, but an approximate conversion is made herein. Although compressive stresses exceeding those given in Table 2 may not lead to failure, nonlinearity associated with creep at higher stress-strength ratios would need to be taken into account. Table 1—Material properties used in finite element study
Fig. 3—Increase in stress relaxation with increasing temperature, after fib Bulletin 55: Model Code 2010.7 (Note: 1°F = 1.8°C + 32.)
Material property
Value
Modulus of elasticity, MPa (psi)
33,000 (4.78 × 106)
Poisson’s ratio
0.2
Coefficient of thermal expansion, /K (/F)
10 × 10–6 (5.55 × 106)
Thermal conductivity, W/mK (Btu.in/h.ft2°F)
1.5 (10.4)
Specific heat, J/kgK (Btu/lb°F)
900 (0.21)
Convective heat transfer coefficient, W/m2K (Btu/h ft.2°F)
8.33 (1.47)
Fig. 4—Deformed contour of stresses and associated internal force distribution for comparison with Priestley1 (in MPa). (Note: 1 MPa = 145 psi.) ACI Structural Journal/March-April 2014
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Figure 7 gives hoop compressive stresses for various temperatures for a tank with dimensions D = 30.4 m (99.7 ft), H = 7.0 m (23 ft), and t = 0.2 m (7.9 in.). A concrete cylinder strength of 40 MPa (5800 psi) and a modulus of elasticity of 33 GPa (4744 ksi) is assumed. These section dimensions and material properties are used for each numerical example Table 2—Limiting compressive stress at service from modern design standards/guidance Design standard/guidance
Limiting compressive stress at service
EN 1992-1-1
0.45fck
BS 8007
≈ 0.41fck (0.33fcu)
PCI
0.45fck
NZS 3106
0.40fck
presented in this study. As thermal storage tanks commonly incorporate external insulation, the resulting temperature distribution involves predominantly a constant temperature across the concrete section with a small temperature differential. As such, for simplicity, the small differential that may be present is ignored herein. Figure 7 shows that an average temperature of approximately 50°C (90°F) across the concrete section produces localized hoop compressive stresses at the wall ends that exceed each of the limits given in Table 2. Circumferential post-tensioning As the thermally induced hoop forces over the wall height are compressive, the circumferential post-tensioning requirements remain unchanged. The hoop tension arising from hydrostatic loading when the liquid is not heated is the
Fig. 5—Verification of modeling procedure with Priestley,1 Ghali and Elliott,2 and Vitharana and Priestley.24 (Note: 1 m = 3.28 ft; 1 MPa = 145 psi; 1 kN/m = 5.71 kip/in.; 1 kNm/m = 0.225 kip-ft/ft.)
Fig. 6—Finite element model showing deformed contour of hoop stresses (in MPa). (Note: 1 MPa = 145 psi.) 250
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Fig. 8—Compressive hoop forces with increasing temperature. (Note: 1 kN/m = 5.71 kip/in.; 1°F = 1.8°C + 32.) Fig. 7—Compressive hoop stresses with increasing temperature. (Note: 1 MPa = 145 psi; 1°F = 1.8°C + 32.) critical loading condition that the circumferential post-tensioning is designed to cater for. Figure 8 includes the tensile force distribution resulting from hydrostatic loading derived using the beam-on-elastic foundation analogy. Vertical prestressing The vertical bending moment distribution arising from hydrostatic and thermally induced loading is given in Fig. 9. To establish an approximate upper limit on the vertical moments, a cracking moment was calculated from the following equation
I M cr = ( ft + fmax ) t / 2
(1)
where I is the second moment of area; t is the wall thickness; ft is the concrete tensile strength; and fmax is the concentric precompression stress required to eliminate tensile stresses while also satisfying maximum compressive stress limits at the extreme fiber. Figure 10 applies the cracking moment to the previously derived vertical bending moments. The moments represent total moments, that is, the hydrostatic moments subtracted from the thermally induced moments, because the two loadings are coexistent. It is apparent that an average temperature across the concrete section of approximately 40 to 50°C (72 to 90°F) produces vertical moments that exceed the cracking moment. This temperature limit is approximately consistent with that for the compressive stress requirement.
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Fig. 9—Vertical bending moments with increasing temperature. (Note: 1 kNm/m = 0.225 kip-ft/ft; 1°F = 1.8°C + 32). Influence of creep on thermal response The magnitude of strain-induced effects such as thermal, creep, and shrinkage stresses at a given time is directly proportional to the concrete modulus of elasticity at that time. As such, realistic values of the modulus of elasticity 251
Fig. 10—Total vertical moments with increasing temperature. (Note: 1 kNm/m = 0.225 kip-ft/ft; 1°F = 1.8°C + 32.) are desirable if an accurate evaluation is to be made of the structural response. A common approach employed by modern design standards involves the use of an age-adjusted modulus of elasticity that includes a creep component. Figure 11 shows the influence of creep on the concrete modulus of elasticity using the age-adjusted or effective modulus of elasticity defined in EN 1992-1-125 as follows Ec ,eff =
Ecm 1 + f ( ∞, to )
(2)
Inputs to the EN 1992-1-125 creep model were concrete modulus of elasticity = 33 GPa (4744 ksi); wall thickness t = 200 mm (7.87 in.); relative humidity = 80%; concrete compressive cylinder strength = 40 MPa (5800 psi); age at loading = 28 days; normal cement class. Figure 11 also includes a thermally adjusted effective modulus of elasticity using a creep coefficient multiplier of 1.5. Influence of cracking on the thermal response Estimating thermal stresses based on elastic section properties is only valid for uncracked sections, as is the case for prestressed tanks where decompression is satisfied. For reinforced concrete or partially prestressed tank walls, cracking has the effect of considerably relaxing the thermal response. NZS 31063 and AS 37354 account for this using load-reduction factors that allow for the reduced section stiffness that accompanies cracking. The factors include
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Fig. 11—Influence of creep on concrete modulus of elasticity in accordance with EN 1992-1-1.25 (Note: 1 GPa = 143.7 ksi.) tension-stiffening effects and, depending on the wall thickness and reinforcement ratio, can result in load-reduction factors exceeding 0.5. An experimental study by Vitharana et al.28 investigated the moment-curvature response of reinforced concrete wall elements subject to applied and thermal loading. The study concluded that the ACI 31829 Branson formulation and the CEB-FIP MC7830 formulation provided upper and lower bounds, respectively, for the experimentally observed moment-curvature responses. Vitharana et al.28 also proposed a modified Branson equation that showed good agreement with test results for wall elements subject to a simultaneous axial force and flexural moment. BUCKLING ANALYSIS It has been established that thermal loading subjects restrained tank walls to significant combined axial compression and bending. Because precast prestressed concrete tanks are essentially shell structures, buckling stability should to be addressed. For relatively stiff structures, linear eigenvalue buckling analysis is a technique that can be applied to approximate the maximum load that can be sustained prior to structural instability or collapse. The underlying assumptions of a linear eigenvalue buckling analysis are that the linear stiffness matrix remains unchanged prior to buckling and the stress stiffness matrix is a multiple of its initial value. Accordingly, provided the prebuckling displacements have an insignificant influence on the structural response, the technique can be used effectively to predict the load at which a structure becomes unstable. ACI Structural Journal/March-April 2014
Fig. 12—Buckled shape of cylindrical shell restrained at its ends and subject to thermally induced combined axial compression and bending. Commercial finite element software was used to carry out the linear eigenvalue buckling analysis. The three-dimensional (3-D) models comprised thick shell elements. The thermally induced compressive hoop forces and vertical bending moments, derived from the axisymmetric modeling, were simulated using a combination of internal stress-strain loading and externally applied radial pressure loading. The applied loading includes a partial safety factor of 1.55 for persistent thermal actions in accordance with EN 199031 and EN 1991-1-5.32 For plate or shell structures, it is prudent to include an initial geometric imperfection, as the buckling load is often sensitive to any deviation from the true geometry. Bradshaw33 made efforts to measure concrete cylindrical shells in the field and concluded that imperfections were observed to be as large as the shell thickness. Therefore, for the current study, an initial geometric imperfection of the order of magnitude of the shell thickness was adopted and was represented as out-of-roundness. The mode of buckling obtained from the finite element analysis is given in Fig. 12, with the same mode observed for all tank sizes. The buckled shape displays the characteristic sinusoidal buckle waves consistent with Koiter’s34 classical linearized shell buckling theory. The mode shape is sinusoidal both axially and circumferentially. Figure 13 presents the eigenvalues extracted from the finite element study for various average temperatures and H2/Dt ratios. The eigenvalues, l, are ratios of the buckling load to the applied load. An eigenvalue equal to unity indicates that structural instability or buckling has occurred. The lowest eigenvalue extracted from the buckling analysis was 2.52. Thus, the ultimate limit state of buckling was not reached for the temperature range considered. FREE-SLIDING CONDITION Theoretically, for a free-sliding condition, an average temperature across the concrete section does not induce any additional stresses. For a gradient experienced across the wall thickness, however, associated hoop and vertical bending stresses develop. Figure 14 is an example for a freesliding wall subject to a temperature distribution resulting from the storage of heated liquids. The inside and outside temperatures are taken as 95 and 80°C (171 and 144°F), ACI Structural Journal/March-April 2014
Fig. 13—Eigenvalues from finite element linear buckling analysis. (Note: 1°F = 1.8°C + 32.) respectively. This arrangement is slightly conservative, as the use of sufficient external insulation would generally result in a temperature difference between the inside and outside faces of less than 10°C (18°F). Comparing the results observed in Fig. 14 with those in Fig. 8 and 9, it is evident that the magnitude and significance of the internal forces are far less for a free-sliding wall. A noteworthy observation is the hoop tension developed over the majority of the wall height which, although not excessive in magnitude, would need to be summed to the hydrostatic hoop tension when calculating circumferential posttensioning requirements. CONCLUSIONS AND RECOMMENDATIONS The following conclusions and recommendations may be drawn from the current study:
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Brian D. O’Rourke is a Lecturer and Researcher in the Department of Civil, Structural and Environmental Engineering at Cork Institute of Technology. His research interests include structural behavior and materials technology. He is a Chartered Engineer and member of Engineers Ireland.
NOTATION
D = diameter Ec,eff = effective or age-adjusted concrete modulus of elasticity Ecm = secant concrete modulus of elasticity fck = concrete compressive cylinder strength fcu = concrete compressive cube strength fmax = maximum concentric precompression stress required to eliminate tensile stresses ft = concrete tensile strength H = wall height I = second moment of area Mcr = cracking moment R = radius T = wall thickness x = height from base of wall f(∞,t0) = final creep coefficient l = eigenvalue
REFERENCES
Fig. 14—Internal forces resulting from thermal storage for a free-sliding wall. (Note: 1 kNm/m = 0.225 kip-ft/ft; 1 kN/m = 5.71 kip/in.) 1. For the most part, the temperature under consideration for the present study does not have a significant adverse effect on the material properties. The most important factors that require consideration are creep of the concrete, bond strength, and stress relaxation for pretensioned and nonpretensioned reinforcement. Where material properties form inputs for analysis and design, any associated reduction should be accounted for, particularly if unfavorable. 2. For a tank wall restrained radially at its ends, the internal forces resulting from the storage of heated liquids have been shown to be significant. As such, a temperature exceeding approximately 50°C (90°F) across the concrete section appears to be prohibitive based on compressive stress limits and vertical prestressing constraints. Consequently, it is recommended that internal insulation be provided to prevent temperatures from exceeding this. 3. A linear eigenvalue buckling analysis has revealed that the ultimate limit state of buckling for a wall with restrained ends was not reached for the temperature range considered. A minimum eigenvalue of 2.52 was observed. 4. Where provisions are made for radial displacements at the wall ends during service, the 95°C (171°F) maximum temperature does not induce excessive stresses. Complications may arise, however, surrounding possible leakage at the joints. Accordingly, it is recommended that a polymer liner be included, thereby eliminating concerns regarding liquid-tightness. AUTHOR BIOS
ACI member Michael J. Minehane is a Structural Design Engineer at RPS Group Ltd., Cork, Republic of Ireland. He received his BEng and MEng from Cork Institute of Technology, Republic of Ireland, in 2010 and 2011, respectively. His research interests include prestressed concrete, strutand-tie modeling, and finite element analysis.
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1. Priestley, M. J., “Ambient Thermal Stresses in Circular Prestressed Concrete Tanks,” ACI Journal, V. 73, No. 10, Oct. 1976, pp. 553-560. 2. Ghali, E., and Elliott, E., “Serviceability of Circular Prestressed Concrete Tanks,” ACI Structural Journal, V. 89, No. 3, May-June 1992, pp. 345-355. 3. NZS 3106, “Code of Practice for Concrete Structures for Retaining Liquid,” Standards Association of New Zealand, 2009, 83 pp. 4. AS 3735, “Concrete Structures for Retaining Liquids—Commentary (Supplement to AS 3735-2001),” Standards Australia, 2001, 65pp. 5. EN 1992-1-2, “General Rules—Structural Fire Design,” Brussels, Belgium, 2004. 6. EN 1992-3, “Design of Concrete Structures, Part 3: Liquid Retaining and Containment Structures,” Brussels, Belgium, 2006. 7. Fédération Internationale du Béton (fib), “Model Code 2010: Volume 1 First Complete Draft,” fib Bulletin 55, Lausanne, Switzerland, 2010, 317 pp. 8. Mears, A. P., “Long Term Tests on the Effect of Moderate Heating on the Compressive Strength and Dynamic Modulus of Elasticity of Concrete,” Concrete for Nuclear Reactors, SP-34, C. E. Kesler, ed., American Concrete Institute, Farmington Hills, MI, 1972, pp. 355-375. 9. Komendant, J.; Nicolayeff, V.; Polivka, M.; and Pirtz, D., “Effect of Temperature, Stress Level, and Age at Loading on Creep of Sealed Concrete,” Douglas McHenry International Symposium on Concrete and Concrete Structures, SP-55, B. Bresler, ed., American Concrete Institute, Farmington Hills, MI, 1978, pp. 55-81. 10. Nasser, K. W., and Lohtia, R. P., “Mass Concrete Properties at High Temperatures,” ACI Journal, V. 68, No. 3, Mar. 1971, pp. 180-186. 11. Carette, G. G., and Malhotra, V. M., “Performance of Dolostone and Limestone Concretes at Sustained High Temperatures,” Temperature Effects on Concrete (ASTM STP 858), T. R. Naik, ed., ASTM International, West Conshohocken, PA, 1985, pp. 38-67. 12. Comité Euro-International du Béton (CEB), “Fire Design of Concrete Structures: in Accordance with CEB/FIP Model Code 90,” Bulletin D’Information 21, Lausanne, Switzerland, 1991, 120 pp. 13. Brown, R. D., “Properties of Concrete in Reactor Vessels,” Conference on Prestressed Concrete Pressure Vessels, Westminster, Mar. 1968, Paper 13, pp. 131-151. 14. Gross, H., “High-Temperature Creep of Concrete,” Nuclear Engineering and Design, V. 32, No. 1, Apr. 1975, pp. 129-147. 15. Nasser, K. W., and Neville, A. M., “Creep of Concrete at Elevated Temperatures,” ACI Journal, V. 62, No. 12, Dec. 1965, pp. 1567-1579. 16. Hannant, D. J., “Strain Behaviour of Concrete Up to 95°C under Compressive Stresses,” Conference on Prestressed Concrete Pressure Vessels, Westminster, Mar. 1968, pp. 177-192. 17. McDonald, J. E., “Creep of Concrete under Various Temperature, Moisture and Loading Conditions,” Douglas McHenry International Symposium on Concrete and Concrete Structures, SP-55, B. Bresler, ed., American Concrete Institute, Farmington Hills, MI, 1978, pp. 31-53. 18. Harada, T.; Takeda, J.; Yamane, S.; and Furumura, F., “Elasticity and Thermal Properties of Concrete Subjected to Elevated Temperatures,” Concrete for Nuclear Reactors, SP-34, C. E. Kesler, ed., American Concrete Institute, Farmington Hills, MI, 1972, pp. 377-406.
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19. Kagami, H.; Okuno, T.; and Yamane, S., “Properties of Concrete Exposed to Sustained Elevated Temperatures,” Third International Conference on Structural Mechanics in Reactor Technology, Paper H1/5, London, UK, 1975, pp. 1-10. 20. Haddad, R. J.; Al-Saleh, R. J.; and Al-Akhras, N. M., “Effect of Elevated Temperature on Bond between Steel Reinforcement and Fibre Reinforced Concrete,” Fire Safety Journal, V. 43, 2008, pp. 334-343. 21. Chiang, C., and Tsai, C., “Time-Temperature Analysis of Bond Strength of a Rebar after Fire Exposure,” Cement and Concrete Research, V. 33, 2003, pp. 1651-1654. 22. Bažant, Z. P., and Kaplan, M. F., Concrete at High Temperature: Material Properties and Mathematical Models, Longman Group Limited, England, 1996, 424 pp. 23. Huang, Z., “Modeling the Bond between Concrete and Reinforcing Steel in a Fire,” Engineering Structures, V. 32, 2010, pp. 3660-3669. 24. Vitharana, N. D., and Priestley, M. J., “Significance of Temperature-Induced Loadings on Concrete Cylindrical Reservoir Walls,” ACI Structural Journal, V. 96, No. 5, July-Aug. 1999, pp. 737-749. 25. EN 1992-1-1, “Design of Concrete Structures, Part 1: General Rules and Rules for Buildings,” Brussels, Belgium, 2004.
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26. BS 8007, “Code of Practice for Design of Concrete Structures for Retaining Aqueous Liquids,” BSI, London, UK, 1987. 27. PCI Committee on Precast Prestressed Concrete Storage Tanks, “Recommended Practice for Precast Prestressed Concrete Storage Tanks,” PCI Journal, V. 32, No. 4, 1987, pp. 80-125. 28. Vitharana, N. D.; Priestley, M. J.; and Dean, J. A., “Behaviour of Reinforced Concrete Reservoir Wall Elements under Applied and Thermally-Induced Loadings,” ACI Structural Journal, V. 95, No. 3, May-June 1998, pp. 238-248. 29. ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-89) and Commentary,” American Concrete Institute, Farmington Hills, MI, 1989, 353 pp. 30. Comité Euro-International du Béton/Fédération Internationale du Béton, “Model Code for Concrete Structures,” third edition, Paris, 1978, 348 pp. 31. EN 1990, “Basis of Structural Design,” Brussels, Belgium, 2005. 32. EN 1991-1-5, “Actions on Structures—Part 1-5: General Actions— Thermal Actions,” Brussels, Belgium, 2008. 33. Bradshaw, R. R., “Some Aspects of Concrete Shell Buckling,” ACI Journal, V. 60, No. 3, Mar. 1963, pp. 313-328. 34. Koiter, W. T., “On the Stability of Elastic Equilibrium,” PhD thesis, Technological University of Delft, the Netherlands, 1945.
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ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S22
Bond Strength of Spliced Fiber-Reinforced Polymer Reinforcement by Ali Cihan Pay, Erdem Canbay, and Robert J. Frosch To provide increased insight regarding the bond behavior of fiber-reinforced polymer (FRP) bars, 41 glass FRP, carbon FRP, and steel reinforced concrete beams with unconfined tension lap splices were tested. The test results are analyzed to evaluate the influence of splice length, surface deformation, modulus of elasticity, axial rigidity, and bar casting position on bond strength. Furthermore, the test results are compared with the current design expression recommended by ACI Committee 440 to evaluate its applicability. This comparison clearly indicates that the current design expression is inadequate, and that a new design equation is needed. More importantly, however, this research sheds light on the importance of the axial rigidity of the reinforcement on bond strength. Test results demonstrate that bond strength is linearly related to the axial rigidity of the reinforcement. This finding has future implications regarding the development of improved design expressions and allowing for an improved understanding of bond strength. Keywords: bond strength; development length; fiber-reinforced polymer (FRP) reinforcement; reinforced concrete; splice length.
INTRODUCTION Fiber-reinforced polymer (FRP) reinforcement can provide an alternative solution for structures susceptible to corrosion and where low electric conductivity or magnetic transparency is required. FRP bars, however, are anisotropic, have different physical and mechanical properties than that of steel reinforcement, and remain linear-elastic until failure. The modulus of elasticity of glass and aramid FRP bars are approximately one-fifth that of steel. Although carbon FRP (CFRP) bars have a higher modulus than glass FRP (GFRP) bars, their modulus is approximately two-thirds that of steel reinforcing bars. Consequently, design procedures used for steel reinforced members are not necessarily applicable for FRP reinforced structures. Because the physical and mechanical properties of FRP bars are different from those of steel reinforcement, especially the surface deformation and the modulus of elasticity of the reinforcement, the bond behavior of FRP reinforced concrete specimens is expected to be quite different than that of steel reinforced specimens. An early study on the first generation of FRP reinforcement by Fish (1992) made this fact apparent. The difference in bond strength on modern FRP reinforcement is clearly evident from the tests completed by Mosley et al. (2008), which found that glass (GFRP) and aramid (AFRP) bars achieved approximately 50% of the stress developed by steel reinforcement for the same bar size and splice length. Based on these tests, among others, provisions for the development and splices of FRP reinforcement were developed (Wambeke and Shield 2006) ACI Structural Journal/March-April 2014
and incorporated into ACI 440.1R-06 (ACI Committee 440 2006). While 240 specimens were included in the study by Wambeke and Shield, the majority of the tests had relatively short development lengths, with l/db less than 30, and only 20 splice tests (14 confined splices by Tighiouart et al. [1999] and six unconfined splices by Mosley et al. [2008]) were included. Splice tests are the preferred test method for the determination of development lengths, but only a few were available at the time. Splice tests are preferred because they provide a “realistic stress-state in the vicinity of the bars” (ACI Committee 408 2003). It is for this reason that they are used as the basis of the ACI 318-11 (ACI Committee 318 2011) development length expressions. While knowledge regarding the bond strength of FRP reinforcement is developing, there is a scarcity of data available from splice tests, particularly unconfined splices that are commonly used in FRP applications. In addition, a number of questions that were highlighted by Mosley et al. (2008) remain unanswered. In particular, the study recommended evaluating the effect of longer splice lengths for FRP reinforcement, as the maximum splice investigated was 18 in. (457 mm) for a No. 5 (15.9 mm) bar (l/db = 28.8). The previous research indicated that bond strength is proportional to the square root of the development length, but it is not clear if this trend continues as the development length increases. Furthermore, as only No. 5 bars were tested, it is not clear if the findings are appropriate for other bar sizes. This study also found that the surface deformation of the FRP does not significantly affect bond strength. Different deformations are now available that can shed further light on this subject. Finally, the study found that bond strength is related to the modulus of elasticity of the reinforcement based on tests of steel (E = 29,000 ksi [200 GPa]), GFRP (E ≈ 5500 ksi [37.9 GPa]), and AFRP (E ≈ 6800 ksi [46.8 GPa]). Carbon fiber bars are now available with E that falls between that of steel and GFRP (E ≈ 20,000 ksi [138 GPa]), which may provide additional understanding regarding this behavior. RESEARCH SIGNIFICANCE The objective of this research study is to provide additional experimental data from splice tests to improve understanding of the bond strength between FRP reinforcement and concrete. Of particular interest is the influence of a ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-069.R1, doi:10.14359.51686519, was received June 19, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
257
Table 1—Specimen details
Fig. 1—Typical test specimen.
Fig. 2—Cross section detail at splice region. number of variables, including splice length, bar size, reinforcement modulus of elasticity, and reinforcement deformation type. A secondary objective is to evaluate the applicability of current design expressions for the bond strength of FRP reinforcement to determine if the current expressions can be reliably used for extended splice lengths and bar sizes considering the limited range for which the expressions were developed. SPECIMEN DESIGN Five series of beams were tested to evaluate the bond strength. The specimens were designed to provide a systematic evaluation of the primary variables and were reinforced with either GFRP, CFRP, or steel bars. Both No. 5 and 8 (15.9 and 25.4 mm) bars were also considered, with the exception of carbon bars, for which No. 8 bars were not available. Splice lengths were considered from 12 in. (305 mm) up to 54 in. (1372 mm). A typical test specimen is illustrated in Fig. 1, while dimensions for each specimen are provided in Table 1. Cross-sectional details of the specimens are shown in Fig. 2. All beams were rectangular in cross section, with a total depth of 16 in. (406 mm). Specimens were designed with a clear spacing of 1 in. (25.4 mm) between the bars located in the splice region and with a 1.5 in. (38.1 mm) side and top clear cover. This limitation represents the minimum clear spacing and minimum clear cover allowed by ACI 318-11. Three reinforcing bars were spliced at the center of the constant moment region of the beam. The width of the specimens was controlled by the minimum cover and spacing limitations and the size of the reinforcement; therefore, the width of specimens was 8.75 in. (222 mm) for the specimens reinforced with No. 5 (15.9 mm) bars, and 11 in. (279 mm) 258
LS, in. (mm)
L, ft (m)
LV, ft (m)
LM, ft (m)
12, 18, 24 (305, 457, 610)
13.5 (4.11)
3 (0.91)
6 (1.83)
36 (914)
18 (5.49)
3.75 (1.14)
9 (2.74)
54 (1372)
18 (5.49)
3.75 (1.14)
8.5 (2.59)
for the specimens reinforced with No. 8 (25.4 mm) bars. Concrete cover and spacing of the reinforcing bars were maintained constant throughout the experimental program, and no transverse reinforcement was provided in the constant moment region. Two No. 3 (9.53 mm) longitudinal steel bars were provided in the compression side of the beam to prevent collapse at failure. In addition, the shear spans were reinforced with No. 3 (9.53 mm) steel stirrups to prevent shear failure before bond failure. In addition to the primary variables, several other variables were considered. While previous tests clearly indicate that the modulus of elasticity is a primary parameter, it is not clear if this is solely due to the modulus E or due to the axial rigidity AE of the reinforcement. Therefore, a specimen was designed where the E of the reinforcement remains the same using the same reinforcement material, but the cross-sectional area A is reduced. To maintain the same surface area and deformation pattern, a hollow bar was used to reduce A. In addition, top and bottom-cast specimens were constructed to evaluate the influence of the casting position and allow for linkage between top and bottom-cast results. In the top-cast position, the specimens qualify as “top bar” if more than 12 in. (305 mm) of fresh concrete is cast below the reinforcement. In total, the experimental program consisted of 41 reinforced concrete beam specimens. Details of the specimens are summarized in Table 2. A four-part notation system is used to identify the specimens. The specimens were identified first by the descriptive label B (bond) followed by the reinforcement type (Tables 3 and 4), the bar size, and finally by the splice length. For example, B-HC-5-12 stands for a bond test with No. 5 (15.9 mm) CFRP bars spliced at 12 in. (305 mm). Bottom-cast specimens were identified by adding the notation “b” to the splice length. MATERIALS FRP reinforcement FRP reinforcement included glass bars (No. 5 and 8 [15.9 and 25.4 mm]) and carbon bars (No. 5 [15.9 mm]) with different surface deformations. Three types of bar surfaces were considered to evaluate the effect of varying surface deformations, including: 1) sand coating; 2) wrapped indentations and sand coating; and 3) fabric texture. For glass bars, all three surface types were included. For carbon bars, only the sand coating and fabric texture surfaces were possible because the wrapped indentation significantly reduces the tensile strength of the bar, which makes this surface treatment impractical. A general view of the bar surfaces is shown in Fig. 3. As shown, the same surface type (sand coated and fabric texture) was obtained for both types of ACI Structural Journal/March-April 2014
Table 2—Specimen details and test results Series
I
II
III
IV
V
Bar size Ls, in. (mm) Casting position Test age, days Ptest, kip (kN) ftest, ksi (MPa) μavg, psi (MPa)
Specimen
Bar type
Deformation
B-S1-8-18
Steel
Deformed
No. 8
18 (457)
Top
28
33.0 (147)
40.8 (281)
570 (3.93)
B-PG-8-18
Glass
Sand-coated
No. 8
18 (457)
Top
29
24.1 (107)
27.9 (192)
390 (2.69)
B-HG-8-18
Glass
Sand and wrapped
No. 8
18 (457)
Top
31
20.5 (91.2)
23.7 (163)
332 (2.29)
B-HG1-5-18
Glass
Sand and wrapped
No. 5
18 (457)
Top
32
14.2 (63.2)
40.7 (281)
357 (2.46)
B-HGO-5-18
Glass
Sand and wrapped
No. 5
18 (457)
Top
35
11.5 (51.2)
32.9 (227)
289 (1.99)
B-PG-5-18
Glass
Sand-coated
No. 5
18 (457)
Top
36
16.5 (73.4)
47.3 (326)
415 (2.86)
B-S1-5-18
Steel
Deformed
No. 5
18 (457)
Top
37
24.1 (107)
72.2 (498)
633 (4.36)
B-HC-5-18
Carbon
Fabric texture
No. 5
18 (457)
Top
38
19.9 (88.5)
58.8 (405)
515 (3.55)
B-HC-5-12
Carbon
Fabric texture
No. 5
12 (305)
Top
28
15.1 (67.2)
44.5 (307)
585 (4.03)
B-S1-8-36
Steel
Deformed
No. 8
36 (914)
Top
31
37.1 (165)
57.2 (394)
400 (2.76)
B-PG-8-36
Glass
Sand-coated
No. 8
36 (914)
Top
32
19.9 (88.5)
28.9 (199)
202 (1.39)
B-HG-8-36
Glass
Sand and wrapped
No. 8
36 (914)
Top
34
21.0 (93.4)
30.4 (210)
212 (1.46)
B-HG1-5-36
Glass
Sand and wrapped
No. 5
36 (914)
Top
35
12.4 (55.2)
44.3 (305)
194 (1.34)
B-HGO-5-36
Glass
Sand and wrapped
No. 5
36 (914)
Top
38
13.3 (59.2)
47.5 (328)
208 (1.43)
B-PG-5-36
Glass
Sand-coated
No. 5
36 (914)
Top
40
13.9 (61.8)
49.9 (344)
219 (1.51)
B-HC-5-36
Carbon
Fabric texture
No. 5
36 (914)
Top
42
22.9 (102)
84.6 (583)
371 (2.56)
B-S2-8-12
Steel
Hollow Deformed
No. 8
12 (305)
Top
133
18.1 (80.5)
29.7 (205)
465 (3.21)
B-S1-8-12
Steel
Deformed
No. 8
12 (305)
Top
130
21.9 (97.4)
27.3 (188)
571 (3.94)
B-PG-8-12
Glass
Sand-coated
No. 8
12 (305)
Top
104
17.1 (76.1)
20.0 (138)
418 (2.88)
B-HG-8-12
Glass
Sand and wrapped
No. 8
12 (305)
Top
106
14.0 (62.3)
16.3 (112)
341 (2.35)
B-S1-8-12b
Steel
Deformed
No. 8
12 (305)
Bottom
111
21.2 (94.3)
26.3 (181)
551 (3.80)
B-HG-8-12b
Glass
Sand and wrapped
No. 8
12 (305)
Bottom
124
14.5 (64.5)
16.9 (117)
354 (2.44)
B-PG-8-12b
Glass
Sand-coated
No. 8
12 (305)
Bottom
126
15.8 (70.3)
18.4 (127)
385 (2.65)
B-S2-5-24
Steel
Deformed
No. 5
24 (610)
Top
129
23.5 (105)
70.9* (489)
467 (3.22)
B-HC-5-24
Carbon
Fabric texture
No. 5
24 (610)
Top
132
21.9 (97.4)
64.7 (446)
426 (2.94)
B-PC-5-24
Carbon
Sand-coated
No. 5
24 (610)
Top
139
24.1 (107)
71.8 (495)
472 (3.25)
B-HG1-5-24
Glass
Sand and wrapped
No. 5
24 (610)
Top
142
13.6 (60.5)
39.0 (269)
256 (1.77)
B-HG2-5-24
Glass
Fabric texture
No. 5
24 (610)
Top
148
16.5 (73.4)
47.6 (328)
313 (2.16)
B-PG-5-24
Glass
Sand-coated
No. 5
24 (610)
Top
153
16.7 (74.3)
48.0 (331)
316 (2.18)
B-HG1-5-24b
Glass
Sand and wrapped
No. 5
24 (610)
Bottom
155
14.7 (65.4)
42.2 (291)
277 (1.91)
B-PG-5-24b
Glass
Sand-coated
No. 5
24 (610)
Bottom
161
17.7 (78.7)
50.8 (350)
334 (2.30)
B-HG1-5-12
Glass
Sand and wrapped
No. 5
12 (305)
Top
156
9.5 (42.3)
27.4 (189)
361 (2.49)
B-PG-5-12
Glass
Sand-coated
No. 5
12 (305)
Top
160
10.6 (47.2)
30.4 (210)
400 (2.76)
B-HG-8-24
Glass
Sand and wrapped
No. 8
24 (610)
Top
161
20.8 (92.5)
24.1 (166)
253 (1.74)
B-HG-8-54
Glass
Sand and wrapped
No. 8
54 (1372)
Top
175
22.8 (101)
33.0 (228)
154 (1.06)
B-HG1-5-54
Glass
Sand and wrapped
No. 5
54 (1372)
Top
177
14.1 (62.7)
50.4 (347)
148 (1.02)
B-PG-5-54
Glass
Sand-coated
No. 5
54 (1372)
Top
181
14.1 (62.7)
50.6 (349)
148 (1.02)
B-HC-5-54
Carbon
Fabric texture
No. 5
54 (1372)
Top
183
22.9 (102)
85.0 (586)
249 (1.72)
B-HG1-5-12b
Glass
Sand and wrapped
No. 5
12 (305)
Bottom
162
12.1 (53.8)
34.8 (240)
458 (3.16)
B-PG-5-12b
Glass
Sand-coated
No. 5
12 (305)
Bottom
164
13.6 (60.5)
39.0 (269)
514 (3.54)
Glass
Sand and wrapped
No. 8
24 (610)
Bottom
169
23.0 (102)
26.7 (184)
280 (1.93)
B-HG-8-24b Reinforcement yielded.
*
ACI Structural Journal/March-April 2014
259
Table 3—Mechanical properties of fiber-reinforced polymer bars Bar type
Producer
Producer 1 Glass
No. 5
Designation
Surface deformation
Er, ksi (GPa)
fu, ksi (MPa)
HGO
Sand and wrapped
5800 (40.0)
71 (490)
HG1
Sand and wrapped
6400 (44.1)
98 (676)
HG2
Fabric texture
7300 (50.3)
115 (793)
No. 8
HG
Sand and wrapped
5700 (39.3)
76 (524)
No. 5
PG
Sand
6400 (44.1)
89 (614)
No. 8
PG
Sand
6200 (42.7)
76 (524)
Producer 1
No. 5
HC
Fabric texture
18500 (127.6)
129 (889)
Producer 2
No. 5
PC
Sand
21700 (149.6)
—*
Producer 2
Carbon
Bar size
Coating of bar peeled at anchor at 100 ksi (689 MPa).
*
Table 4—Mechanical properties of steel bars Bar size No. 5
No. 8
Fig. 3—Carbon, glass FRP, and steel bars. FRP reinforcement (glass and carbon), allowing for evaluation of the influence of the material type independent of the surface deformation. Tensile tests on representative coupons were performed for each type of reinforcement to determine their mechanical properties. Coupons for FRP bars were tested considering the requirements of ACI 440.3R-04 (ACI Committee 440 2004). The measured modulus of elasticity and ultimate strength of the FRP bars are provided in Table 3. Two types of sand and wrapped bars were tested: HGO and HG1. The designation HGO represents older GFRP bars from the same manufacturer that were previously tested in the study by Mosley et al. (2008). Over time, the surface deformation on the bars has changed slightly; therefore, two different configurations of the same surface treatment were considered. In addition, these bars allow for comparison with the earlier study. Steel reinforcement Deformed steel reinforcement consisted of No. 5 and 8 (15.9 and 25.4 mm) bars, meeting ASTM A615 Grade 60. To evaluate the effect of axial rigidity, a No. 8 (25.4 mm) hollow reinforcing bar was constructed by drilling a 0.5 in. (12.7 mm) diameter hole through a 16 in. (406 mm) length of the deformed bar to reduce the cross-sectional area in the splice region, as shown in Fig. 3. Bars of each size were obtained from the same heat to ensure consistent reinforcement material properties in each phase. Table 4 presents the properties of the steel bars.
260
Designation
Bar type
fy, ksi (MPa)
fu, ksi (MPa)
S1
Deformed
75 (517)
95 (655)
S2
Deformed
60 (414)
100 (689)
S1
Deformed
76 (524)
97 (669)
S2
Hollow deformed
76 (524)
97 (669)
Concrete The same mixture proportion was used for all test series. The concrete used a coarse aggregate consisting of river gravel with a 0.75 in. (19 mm) maximum aggregate size. Batch weights and slump for each series are provided in Table 5. Concrete compressive and splitting tensile strengths were obtained from the average of three 6 x 12 in. (152 x 305 mm) cylinders, and are also provided in Table 5. Concrete material tests were timed with the testing program such that results were obtained on the first, middle, and last day of specimen testing for each series. The concrete strengths reported are the average over the days of testing for each test series. As noted in Table 2, which provides the concrete age on the day of testing, specimens in each series were tested within a fairly short timeframe. Therefore, the variation of concrete strengths from the average during the duration of testing was within 3% for each series. Across all series, concrete compressive strength varied from 4010 to 5470 psi (27.7 to 37.7 MPa), even though the same concrete mixture was ordered. CONSTRUCTION Specimens in each series were cast at the same time from the same batch of concrete. The concrete was placed in the forms in two layers, and each layer was vibrated using mechanical vibrators. The beams were screeded, and the surface was finished with a magnesium float. The beams were covered with wet burlap, and plastic sheets were placed on top of the burlap to prevent moisture loss before final set. For each series, cylinders were cast simultaneously with the beams. The cylinders were consolidated, cured, and stored in the same manner as the test specimens.
ACI Structural Journal/March-April 2014
Table 5—Concrete mixture and mechanical properties Material
Series I
Series II
Series III
Series IV
Series V
Cement Type I, lb/yd (kg/m )
425 (252)
430 (255)
429 (255)
430 (255)
428 (254)
Fine aggregate, lb/yd (kg/m )
1651 (980)
1591 (944)
1611 (956)
1550 (920)
1609 (955)
Coarse aggregate, lb/yd (kg/m )
1847 (1096)
1849 (1097)
1842 (1093)
1850 (1098)
1842 (1093)
Water, lb/yd3 (kg/m3)
163 (97)
145 (86)
196 (116)
240 (142)
184 (109)
Air, oz/yd3 (mL/m3)
1.1 (43)
1.1 (43)
0
0
0
Water reducer, oz/yd3 (mL/m3)
8.7 (336)
7.8 (302)
6.5 (251)
1.5 (58)
6.4 (247)
Slump, in. (mm)
4 (102)
5 (127)
5.5 (140)
3 (76)
4.5 (114)
fc′, psi (MPa)
5260 (36.3)
5470 (37.7)
4010 (27.7)
4640 (32.0)
4170 (28.8)
ft, psi (MPa)
590 (4.07)
520 (3.58)
380 (2.62)
440 (3.03)
430 (2.96)
Casting position
ftest, ksi (MPa)
Ratio, top/bottom
Top
30.4 (210)
Bottom
39.0 (269)
Top
27.4 (189)
Bottom
34.8 (240)
Top
48.0 (331)
Bottom
50.8 (350)
Top
39.0 (269)
Bottom
42.2 (291)
Top
20.0 (138)
Bottom
18.4 (127)
Top
16.3 (112)
Bottom
16.9 (117)
Top
27.3 (188)
Bottom
26.3 (181)
Top
24.1 (166)
Bottom
26.7 (184)
3
3
3
3
3
3
Table 6—Influence of casting position Bar size
Splice length
Bar type PG
12 in. (305 mm) HG1 No. 5 PG 24 in. (610 mm) HG1
PG 12 in. (305 mm)
HG
No. 8 S1 24 in. (610 mm)
HG
Average
TEST SETUP AND PROCEDURE Beams were placed on two supports, and two equal, concentrated loads were applied at the end of the cantilever with hydraulic rams, creating a constant moment region between the supports as shown in Fig. 1. The rams were connected to a single hydraulic hand pump to obtain equal pressure in each ram. Load was applied in 0.5 kip (2.22 kN) increments for the specimens with No. 5 (15.9 mm) bars, and 1 kip (4.45 kN) increments for the specimens with No. 8 (25.4 mm) bars. At each load stage, the crack pattern was mapped, and crack widths were measured on the beam top surface. Cracks were mapped and measured up to a critical load, beyond which it was considered unsafe to approach the beam. Displacements at the ends, supports, and midspan were monitored with displacement transducers, while loads were monitored using load cells. In Series I and II, three strain gauges were placed on the reinforcing bars at the ends of the splice region. Two were attached to the middle reinforcing ACI Structural Journal/March-April 2014
0.78
0.79
0.94
0.92
1.09
0.96
1.04
0.90 0.93
bars, and one was attached to the outer reinforcing bar. The strains measured with strain gauges and strains calculated based on flexural theory agreed well; therefore, no strain gauges were installed on the FRP reinforcing bars for the remaining series. Strain gauges, however, were installed on all steel reinforced specimens where there was a possibility of yielding the reinforcement. STRUCTURAL BEHAVIOR Specimens with the same beam width and shear span in a given series cracked at approximately the same load. The stiffness of the specimens was approximately the same up to the cracking load. Flexural cracks usually first occurred at the support or simultaneously at the support and in the constant moment region. As loading increased, further cracks formed within the constant moment region, shear span, and splice region. All specimens failed in a brittle side-splitting mode in the splice region. Two different types of side splitting were observed during failure. In the first type, the concrete 261
Fig. 4—Splitting failure. cover in the splice region exploded. In the second case, the failure was not explosive, and the cover remained intact with the reinforcement. Photographs captured at the time of failure that illustrate the failure types are shown in Fig. 4. The splitting plane observed after failure indicated that failure typically initiated from the splitting cracks present on the side face. No damage to the surface deformations was observed on any of the reinforcing bars. To further illustrate the response, the applied load versus end deflection curves for Series I are presented in Fig. 5. Behavior of the specimens can be described by three distinct stages. In the first stage, before flexural cracking, the load-deflection curves are linear and the slopes are approximately identical, indicating that before cracking, the stiffness of the specimens is primarily controlled by the concrete. All specimens in a given series cracked at approximately the same load, with slightly higher loads achieved for the stiffer bars. In the second stage, after flexural cracking, the slope reduces; however, the response remains essentially linear up to failure. In this stage, the flexural stiffness is a function of the modulus of elasticity and cross-sectional area of the bars. Bars with a lower modulus of elasticity resulted in a lower flexural stiffness. In general, beams reinforced with steel bars had the highest stiffness, followed by beams reinforced with CFRP bars, and then by GFRP bars. Beams reinforced with different types of GFRP bars have approximately the same stiffness due to their similar moduli of elasticity. In the final stage, all specimens failed suddenly by splitting of the concrete in the splice region. The same observations were made for the specimens tested in the other series (Series II to V). Load versus deflection plots for all specimens are presented in Pay (2005). In each series, among the specimens with the same cross-sectional dimensions and shear span length, steel reinforced specimens reached the highest load, followed by CFRP and then GFRP reinforced specimens. Specimens reinforced with GFRP deflected most, followed by CFRP and steel reinforced specimens. Based on observation, the modulus of elasticity of the reinforcing bar was directly proportional to the failure load, and inversely proportional to the deflection at the time of failure.
262
Fig. 5—Load-deflection curves of Series I specimens with No. 5 bars. BOND STRENGTH The maximum applied load Ptest at the ends of the cantilever (Fig. 1) and computed reinforcement stress reached at failure ftest for each specimen are provided in Table 2. The reinforcement stress at failure was calculated using both cracked section analysis and moment-curvature analysis. For moment-curvature analysis, the Hognestad stress-strain curve was used, and the tensile strength of the concrete was neglected. Values from both analyses were approximately the same; therefore, stresses from the crack section analysis are presented herein. The average bond stress μavg was calculated assuming that the tension force in the bar is resisted by a uniform distribution of stress along the surface of the splice. Nominal cross-sectional dimensions were used in all calculations. It should be noted that the steel reinforcement in Specimen B-S2-5-24 yielded before splitting failure; therefore, its results will not be considered in future analyses. The variables investigated in this study are evaluated in the following sections. To eliminate the effect of variations in the concrete strength, bar stresses and forces are presented normalized by the fourth root of the concrete compressive strength. As presented in ACI 408R-03 (ACI Committee 408 2003) and Canbay and Frosch (2005), the influence of the compressive strength on bond strength is best represented by the fourth root. Considering the differences in concrete compressive strength in this study, the square root tradi-
ACI Structural Journal/March-April 2014
Fig. 6—Effect of splice length on bond strength (No. 5 bars).
Fig. 7—Effect of splice length on bond strength (No. 8 bars).
tionally used to represent tensile strength would produce similar findings.
and wrapped bars for No. 5 (15.9 mm) glass bars can be seen in Fig. 6. For this bar size, the results of the sand-coated bars and the wrapped and sand-coated bars were similar, with the sand-coated bars reaching slightly higher bond stresses than the wrapped and sand-coated bars except for the 54 in. (1372 mm) splice specimens, which failed at approximately the same stress. In addition to these commercially available reinforcing bars, No. 5 (15.9 mm) fabric texture glass bars were specifically produced for this test program to evaluate the effect of the bar surface. This bar type was tested using a 24 in. (610 mm) splice (B-HG2-5-24) and reached a normalized stress of 45.9 ksi (316 MPa), which is essentially the same as that achieved with the companion sand-coated bar (46.3 ksi [319 MPa] for B-PG-5-24). Therefore, GFRP bars with a fabric surface texture that is considerably smoother were capable of reaching stresses as high as the sand-coated GFRP bar. In considering the No. 8 (25.4 mm) bar reinforced specimens (Fig. 7), the same trend is apparent where the sand-coated bars provided similar bond stresses to the sand and wrapped bars. Slightly higher bond stresses were developed with the sand-coated bars for the shorter splices, with approximately the same stress for the longer 36 in. (914 mm) splice. Overall, the sand-coated GFRP bars were observed to reach slightly higher stresses for the shorter splice lengths among the deformation types tested in the experimental program. Considering the minor differences in test results and the variations expected in bond tests, however, the variations in surface deformation produced little difference in bond strength.
Splice length The influence of splice length on bond strength was evaluated among specimens with the same bar size and surface type for splice lengths ranging from 12 to 54 in. (305 to 1372 mm), and is presented in Fig. 6 for the No. 5 (15.9 mm) specimens and Fig. 7 for the No. 8 (25.4 mm) specimens. Best-fit power trend lines are also provided to illustrate the trends of the data. As shown, bar stresses reached at failure increase as the splice length increases. The effectiveness of increasing the splice, however, decreases as the length increases, as evidenced by the decreasing slope. In addition, the slope of the curve, which indicates the strength gain provided by increasing the splice length, is different for each reinforcement type. The strength gain for the steel and carbon bars as the splice length increases is significantly greater than that for the glass bars. For example, doubling the splice length of the No. 5 (15.9 mm) glass bars from 18 to 36 in. (457 to 914 mm) increased the stress by only 6%, while the same increase in splice length for the carbon bars resulted in a 43% increase in bar stress. In previous studies, the influence of splice length for steel (Canbay and Frosch 2005) and short FRP splices (Mosley et al. 2008) was found to be proportional to the square root; therefore, increasing the splice length from 18 to 36 in. (457 to 914 mm) results in a 41% increase in bar stress. While the square root is reasonable for the carbon bars, it significantly overestimates the increase for the glass reinforcement, and is not appropriate. Based on these results, the effect of splice length on the ultimate stress reached by the reinforcement appears to be a function of the modulus of the elasticity of the reinforcement. The benefits of an increase in splice length decrease as the modulus of elasticity is decreased. As previously discussed, the bar stress at failure increases as the modulus of elasticity increases. Surface deformation Three types of surface deformations induced on GFRP bars were tested to evaluate the effect of surface deformation on splice strength. A comparison of sand-coated versus sand
ACI Structural Journal/March-April 2014
Modulus of elasticity The effect of the modulus of elasticity of the reinforcement was investigated among the specimens having the same surface deformation and bar size. Figure 8 shows the normalized bar stress versus modulus of elasticity for No. 5 (15.9 mm) bars with a 24 in. (610 mm) splice. Although two different surface deformations are considered, the data points follow a linear trend as the modulus of elasticity increases. Clearly, the modulus of elasticity of the reinforcement has a significant influence on the bond strength of the reinforcement, with bond strength increasing as the modulus increases.
263
Fig. 8—Effect of modulus of elasticity on bond strength. (Note: 1 in. = 25.4 mm.) Axial rigidity Axial rigidity of the bar is calculated by multiplying the nominal cross-sectional area of the bar A and the modulus of the elasticity of the reinforcement E. The effect of axial rigidity for No. 5 (15.9 mm) bars is illustrated in Fig. 9, where the normalized bar force at failure is plotted versus the axial rigidity AE for the various splice lengths. As shown, there is an approximately linear trend between axial rigidity and bar force. The effect of axial rigidity for No. 8 (25.4 mm) bars is shown in Fig. 10. Carbon bars were not available in this bar size to enable three points to be plotted across the horizontal axis; therefore, only two points are available for the 18 and 36 in. (457 and 914 mm) splice lengths. For the 12 in. (305 mm) splice, however, a specimen (B-S2-8-12) was constructed that contained the hollow deformed steel reinforcing bar in addition to a specimen containing the identical bar that was not hollowed out (B-S1-8-12). The bars in both specimens have the same modulus of elasticity, surface area, and deformation pattern. Due to the reduction in cross-sectional area, however, the axial rigidity was reduced. As shown in Fig. 10, the hollow steel bar reached a lower bar force than that of the solid bar, which indicates the importance of axial rigidity on splice strength. Furthermore, the influence of axial rigidity is shown to again be approximately linear. Considering these results, the axial rigidity of the reinforcement rather than the modulus of elasticity of the reinforcement alone is a primary factor influencing splice strength. Bar casting position Eight bottom-cast specimens were tested along with eight companion top-cast specimens to determine the effect of casting position on the behavior of specimens with lap-spliced reinforcement and provide connection of the results of the top bar specimens with the large body of test results that exist for bottom-cast lap-splice specimens. Based on the test results (Table 6), the bond strength of top-cast specimens is generally lower than that of the bottom-cast specimens, as expected. It should be noted, however, that the reinforcement in two of the top-cast specimens reached higher bar stresses than the companion bottom-cast specimens even though the slump of the concrete in the series in which they were cast (Series III) was the highest. Research by Ferguson and Thompson (1962), Jirsa et al. (1982), and 264
Fig. 9—Effect of axial rigidity on bond strength (No. 5 bars). (Note: 1 in. = 25.4 mm.)
Fig. 10—Effect of axial rigidity on bond strength (No. 8 bars). (Note: 1 in. = 25.4 mm.) DeVries et al. (2001) demonstrates that the influence of casting position on bond strength is primarily affected by concrete slump and bleeding; therefore, this behavior was unexpected. Furthermore, the steel reinforced specimens (No. 8 [25.4 mm] with 12 in. [305 mm] splice) produced essentially the same ratio as the companion FRP reinforced specimens. Regardless, in comparing the eight companion top and bottom-cast specimens, an average reduction in strength of 7% was observed. The most significant reduction (22%) was only observed for the No. 5 (15.9 mm) specimens with a 12 in. (305 mm) splice. As the splice length increased to 24 in. (610 mm), the ratio decreased resulting in only a 7% strength reduction. Interestingly, No. 8 (25.4 mm) specimens with a 12 in. (305 mm) splice produced essentially no difference in strength. Based on the tests conducted herein, the top-cast bar specimens produced only a minor reduction in strength. Therefore, the test results from the top-cast specimens can be compared directly with existing test data from bottom-cast test specimens. In the worst case, they will only be slightly conservative. DESIGN EVALUATION To evaluate the bond strength of the FRP reinforced specimens, the data was analyzed considering the current ACI 440.1R-06 design recommendation where the bar stress ffe can be computed according to Eq. (1). As noted, the term C/db should not be taken larger than 3.5. For the specimens ACI Structural Journal/March-April 2014
Fig. 11—Comparison of strength calculations of CFRP.
Fig. 12—Comparison No. 5 GFRP.
of
strength
calculations
of
Fig. 13—Comparison No. 8 GFRP.
of
strength
calculations
of
tested in the experimental program conducted herein, C/db is always less than 3.5, and this limit does not control. The test results of the FRP specimens were not evaluated with ACI 318-11 or ACI 408R-03 recommendations because these expressions were derived for specimens reinforced with steel deformed bars and, as previously discussed by Mosley et al. (2008), are not applicable f fe =
fc′ l C le C 13.6 e + ≤ 3.5 (1) + 340 where a db db db db
where C is the lesser of the cover to the center of the bar or one-half the center-to-center spacing of the bars being developed, in.; le is embedded length of reinforcing bar, in.; and α is the top bar modification factor (1.5 for reinforcement placed so that more than 12 in. [305 mm] of fresh concrete is cast below the development length or splice; 1.0 for other reinforcement). The calculated reinforcement stresses at failure were compared with the experimental results. The ratio of the experimental to calculated stresses for each reinforcement type is illustrated in Fig. 11 through 13. The equations were evaluated with and without the bar location factor. It should be noted that the bar location factor for FRP reinforcement is 1.5 according to ACI 440.1R-06, whereas a factor of 1.3 is currently used by ACI 318-11 and ACI 408R-03. The top bar factor of 1.5 was recommended in the work by Wambeke and Shield (2006) in considering a comparison of eight top bar tests relative to the bulk of the data (75 splitting failures in total). Unfortunately, no comparison tests were available to directly evaluate the top bar effect. Based on comparisons conducted in this research program for specimens with a depth of 16 in. (406 mm), the maximum top bar effect developed was 1.28, with an average of 1.08. Therefore, the 1.5 factor appears overly conservative. This difference in results may be explained considering that six of the eight top bar tests evaluated by Wambeke and Shield (2006) were from splice specimens, while the majority of the bottom bar data to which they were compared were from beam end and notched beam tests, which typically produce higher bond strengths. Therefore, the ratio resulting from this analysis ACI Structural Journal/March-April 2014
can be expected to be higher than from a direct comparison of splice results. In addition, as noted previously, identical specimens with the only variable being casting position were not available. Therefore, other parameters potentially influenced the comparison. As shown in Fig. 11, for the CFRP reinforced specimens, the ratio of the experimental to calculated stress ranges from 0.8 to 1.15 when the bar location factor is not considered. With the bar location factor, the equation provides conservative results, and ranges from 1.21 to 1.73. The conservatism decreases, however, as the splice length increases. While ACI 440.1R-06 does not indicate that Eq. (1) does not apply for carbon reinforcement, the expression was developed from the results of only GFRP bars. Although the ACI 440.1R-06 equation was derived from a database of GFRP bars, Fig. 12 and 13 illustrate that the equation provides unsafe results for the GFRP reinforced specimens in this investigation even with the inclusion of the bar location factor (α = 1.5). The unconservatism increases as the splice length increases from 12 to 54 in. (305 to 1372 mm). In the case of bottom-cast specimens, the experimental results are as low as 52% of the calculated values for the No. 8 (25.4 mm) bars. Based on comparisons of the experimental and calculated results, even with the 265
recommended bar location factor of 1.5, the ACI 440.1R-06 expression produces significantly unconservative results for the GFRP bar reinforced specimens tested in this experimental program. The level of unconservatism varies with the splice length, the reinforcement location (if location factor is included), bar size, and bar type. The ratio of experimental to calculated results is also observed to generally decrease as the splice length increases. CONCLUSIONS Based on the results of this research program, the following conclusions were made: 1. Bond strength is a function of the modulus of elasticity of the reinforcement. As the modulus of elasticity increases, the bond strength linearly increases; 2. Bond strength is a function of the axial rigidity AE of the reinforcement. As the axial rigidity increases, the bond strength linearly increases. This relationship suggests that development of a unified design approach for the development of reinforcement, regardless of reinforcement type, is possible; 3. Bond strength increases with increasing splice length; however, this relationship is nonlinear. While previous research on relatively short splices (Mosley et al. 2008) supported a square root relationship between bond strength and splice length for FRP reinforcement consistent with that observed for steel reinforcement (Canbay and Frosch 2005), the longer splice lengths tested indicate that this relationship is not constant, and depends on the modulus of elasticity of the reinforcement. For GFRP reinforcement, the relationship is significantly lower than the 0.5 power; 4. Bond strength is essentially independent of the surface deformation for the FRP reinforcement tested. While three significantly different deformation patterns were considered, similar bond strengths were developed. This finding supports earlier results (Mosley et al. 2008), and also provides support that a common design procedure can be used for a variety of FRP bar types. This finding, however, does not imply that surface deformation is not required. Tests were conducted by Pay (2005) using smooth bars. These bars failed at extremely low stresses in a pullout mode, and illustrate that some level of deformation is required; 5. Top bar cast specimens produced only slightly lower bond strengths (average 7% reduction) than bottom-cast specimens. The maximum reduction was 22%, which results in a maximum top bar factor of 1.28. In addition, similar factors were observed for steel and FRP reinforced specimens, indicating that a different factor is not needed for FRP reinforcement. Based on this research, the 1.5 factor recommended by ACI Committee 440 (2006) appears overly conservative. While this research suggests a lower factor, a top bar factor of 1.3 consistent with ACI 318-11 is recommended; and 6. The ACI 440.1R-06 equation for the development of reinforcement results in significantly unconservative results for the test results reported herein. For No. 5 (15.9 mm) bars, all results are unconservative if the top bar factor (α = 1.5) is not included. For the No. 8 (25.4 mm) bars, all results are unconservative regardless of whether the top bar factor
266
is included. These results clearly indicate that an improved design expression for FRP reinforcement is needed. AUTHOR BIOS
Ali Cihan Pay is a Structural Engineer at Enka Teknik, Istanbul, Turkey. He received his BS and MS from Middle East Technical University, Ankara, Turkey, and his PhD from Purdue University, West Lafayette, IN. Erdem Canbay is an Associate Professor of civil engineering at Middle East Technical University. He received his BS from Istanbul Technical University, Istanbul, Turkey, and his MS and PhD from Middle East Technical University. Robert J. Frosch, FACI, is a Professor of civil engineering and Associate Dean of the College of Engineering at Purdue University. He received his BSE from Tulane University, New Orleans, LA, and his MSE and PhD from the University of Texas at Austin, Austin, TX. He is a member of the ACI Board of Direction, is Chair of ACI Subcommittee 318-D, Flexure and Axial Loads (Structural Concrete Building Code), and is a member of ACI Committees 224, Cracking; and 318, Structural Concrete Building Code.
ACKNOWLEDGMENTS
This study was conducted at both the Karl H. Kettelhut Structural Engineering Laboratory and Bowen Laboratory for Large Scale Research at Purdue University, and was made possible under the sponsorship of the Indiana Department of Transportation (INDOT) and the Federal Highway Administration (FHWA) through the Joint Transportation Research Program (JTRP) Project No. SPR-2491. Their support is gratefully acknowledged. Thanks are extended to Hughes Brothers Inc. and Pultrall Inc. for providing the FRP reinforcing bars used in this experimental program.
REFERENCES
ACI Committee 318, 2011, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 503 pp. ACI Committee 408, 2003, “Bond and Development of Straight Reinforcing Bars in Tension (ACI 408R-03),” American Concrete Institute, Farmington Hills, MI, 49 pp. ACI Committee 440, 2004, “Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures (ACI 440.3R-04),” American Concrete Institute, Farmington Hills, MI, 40 pp. ACI Committee 440, 2006, “Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06),” American Concrete Institute, Farmington Hills, MI, 44 pp. ASTM A615/A615M-12, 2012, “Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 6 pp. Canbay, E., and Frosch, R. J., 2005, “Bond Strength of Lap-Spliced Bars,” ACI Structural Journal, V. 102, No. 4, July-Aug., pp. 605-614. DeVries, R. A.; Moehle, J. P.; and Hester, W., 1991, “Lap Splice Strength of Plain and Epoxy-Coated Reinforcements,” Report No. UCB/ SEMM-91/02, University of California, Berkeley, Berkeley, CA, 93 pp. Ferguson, P. M., and Thompson, J. N., 1962, “Development Length of High Strength Reinforcing Bars in Bond,” ACI Journal, V. 59, No. 7, July, pp. 887-922. Fish, K. E., 1992, “Development Length of Fiber-Composite Concrete Reinforcement,” master’s thesis, Iowa State University, Ames, IA, 129 pp. Jirsa, J. O.; Breen, J. E.; Luke, J. J.; and Hamad, B. S., 1982, “Effect of Casting Position on Bond,” International Conference on Bond in Concrete, Paisley College of Technology, Paisley, Scotland, pp. 300-307. Mosley, C. P.; Tureyen, A. K.; and Frosch, R. J., 2008, “Bond Strength of Nonmetallic Reinforcing Bars,” ACI Structural Journal, V. 105, No. 5, Sept.-Oct., pp. 634-642. Pay, A. C., 2005, “Bond Behavior of Unconfined Steel and Fiber Reinforced Polymer (FRP) Bar Splices in Concrete Beams,” doctoral dissertation, Purdue University, West Lafayette, IN, 321 pp. Tighiouart, B.; Benmokrane, B.; and Mukhopadhyaya, P., 1999, “Bond Strength of Glass FRP Rebar Splices in Beams Under Static Loading,” Construction and Building Materials, V. 13, No. 7, pp. 383-392. Wambeke, B., and Shield, C., 2006, “Development Length of Glass Fiber-Reinforced Polymer Bars in Concrete,” ACI Structural Journal, V. 103, No. 1, Jan.-Feb., pp. 11-17.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S23
Flexural Behavior and Strength of Reinforced Concrete Beams with Multiple Transverse Openings by Bengi Aykac, Sabahattin Aykac, Ilker Kalkan, Berk Dundar, and Husnu Can Reported are the results of experiments on 10 rectangular reinforced concrete (RC) beams with and without multiple web openings. The effects of opening geometry, the use of longitudinal stirrups in the posts between the openings, the use of diagonal reinforcement around openings, and the longitudinal reinforcement ratio on the flexural behavior of RC beams with openings were investigated. The stirrups in the posts were shown to have a significant contribution to the ductility of an RC beam with openings if no diagonal reinforcement is used. For the same reinforcement details, RC beams with circular openings were found to have higher load capacities and ductilities than beams with rectangular openings. The experiments indicated that the posts between the openings need to be prevented from undergoing shear failure to avoid Vierendeel truss action and allow a beam to develop its ductility and bending capacity. Keywords: diagonal reinforcement; plastic mechanism; reinforced concrete beam; shear failure; shear reinforcement; Vierendeel truss; web crushing failure; web opening.
INTRODUCTION Ducts and pipes associated with the mechanical, electrical, and sewer systems in a building are usually located underneath the floor beams, resulting in a considerable loss in the usable floor height. Passage of these ducts and pipes through web openings in floor beams offers an effective way to utilize the entire floor height, providing a more economic and compact design. Nevertheless, the presence of opening(s) in a reinforced concrete (RC) beam reduces its load-carrying capacity and increases its service-load deflections. The studies on concrete beams with transverse openings in the literature focused on providing these beams with strengths and rigidities comparable to their solid counterparts by proper reinforcement detailing. In this way, the negative effects of the stress concentrations around the openings could be eliminated, the load-carrying capacities increased, and the deflections decreased. Different types of services, including cooling and ventilation systems, power and sewer systems, and technology and communication services, need to be effectively located and distributed within structures. The presence of multiple openings in a beam is needed to accommodate several pipes and ducts related to various services. Steel beams with multiple web openings (cellular beams) are commonly used for this reason. In this study, the presence of multiple openings in RC beams was considered to improve the design of RC structures. In an extensive experimental study on continuous RC beams with a large rectangular opening, Mansur et al. (1991) established that the failure of these beams is generally related ACI Structural Journal/March-April 2014
to Vierendeel truss action. The deformations in a beam with an opening were shown to increase and the collapse load to decrease as the opening is moved to a more highly stressed portion of span. As the opening length and depth increase, Mansur et al. (1991) found that the Vierendeel action becomes more pronounced, and the decrease in the collapse load increases. Mansur et al. (1992) proposed that the deflections of an RC beam with a large rectangular opening can be approximately estimated by assigning reduced flexural and shear rigidities to the parts of containing the opening. Tan and Mansur (1996) proposed design guidelines for the strength and serviceability limit states of RC beams with large openings. Mansur (1998) identified different shear failure modes of RC beams with web openings and developed design equations. The tests carried out by Tan et al. (2001) on RC beams with circular openings indicated that the use of diagonal reinforcement offers an effective method in crack control. Mansur (1999) developed design equations for RC beams subject to torsion in addition to bending and shear. The equations correspond to the beam failure as a whole, termed as beam-type, and failure of the top and bottom chords separately, termed as frame-type. Mansur et al. (2006) concluded that flexural capacities of RC beams with large circular openings can be closely estimated using strut-and-tie models. Yang et al. (2006) investigated the strength and behavior of RC deep beams with web openings, and showed that the failure of a deep RC beam is caused by the diagonal cracks projecting from the corners of the opening. In all aforementioned studies, RC beams with one or two openings were considered. The failure in these beams is generally related to the shear because the openings are usually located in shear spans. In a recent experimental program (Dundar 2008; Egriboz 2008; Aykac and Yilmaz 2011), the influence of multiple openings in the span was investigated. The presence of multiple openings was assumed to provide a more efficient design by helping the stress concentrations around openings to be distributed to the entire beam length. Furthermore, the presence of openings in the central zone in addition to shear spans was assumed to shift the failure mode of the beam from brittle shear failure to ductile flexural failure. Attempts were made to prevent the brittle modes of shear failure (beam-type and frame-type), and the ductilities of the beams were increased ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. 2012-070.R2, doi:10.14359.51686442, was received October 20, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
267
Fig. 1—Reinforcement details of specimens without openings. (Note: 1 mm = 0.0394 in.) EXPERIMENTAL STUDY
Table 1—Test beams
Beam
Opening
Amount of longitudinal reinforcement
Stirrups in posts
Diagonal reinforcement
Concrete batch
RBn
No
Moderate
No
No
2
RBb
No
High
No
No
3
RRxn
Square
Moderate
No
Yes
1
RRxcn
Square
Moderate
Yes
Yes
1
RRxb
Square
High
No
Yes
2
RRxcb
Square
High
Yes
Yes
2
RCb
Circular
High
No
No
2
RCcb
Circular
High
Yes
No
2
RCxb
Circular
High
No
Yes
1
RCxcb
Circular
High
Yes
Yes
1
by proper detailing: short stirrups in the chords, and posts and full-depth stirrups next to openings. Furthermore, RC beams with different opening geometries were tested within the scope of the program to establish the geometry which affects the strength and ductility of an RC beam to a lesser extent. This paper reports 10 experiments carried out within the program. The influence of the use of diagonal reinforcement around the openings, the use of stirrups in the posts, and the opening geometry are the main test parameters. A comparison of the experimental results with the estimates from the theoretical methods yielded valuable conclusions. RESEARCH SIGNIFICANCE This study investigates the effects of different shear reinforcement schemes and the opening geometry on flexural behavior of RC beams with multiple transverse openings. RC beams with different longitudinal reinforcement ratios were tested, and different failure modes of RC beams with openings were investigated within the course of the study. The experimental results were compared with estimates from different theoretical formulations in the literature to provide background knowledge for establishing design rules for RC beams with multiple openings. The findings of the present study will also guide further studies in the field. 268
Test specimens A total of 10 rectangular RC beams, each 150 mm (5.9 in.) wide, 400 mm (15.7 in.) deep, and 4.0 m (13.1 ft) long, were tested. Four specimens had 200 x 200 mm (7.9 x 7.9 in.) square openings, and four specimens had Ø200 mm (Ø7.9 in.) circular openings. The reinforcement details of the beams are illustrated in Fig. 1 and 2. In terms of flexural reinforcement ratios, the beams denoted with letter “n” were moderately reinforced (tension reinforcement ratio rt = 0.0078), and the beams denoted with letter “b” were heavily reinforced (rt = 0.014). The letter “x” in the specimen names corresponds to the presence of Ø10 nonprestressed cables spiraling around openings (Fig. 3), and “c” corresponds to short stirrups in posts in longitudinal direction (Table 1). Material properties Table 2 tabulates the compressive strength of concrete of each specimen on the test day obtained from 150 x 300 mm (6 x 12 in.) cylinder tests. The mean values and standard deviations of these material tests are tabulated in Table 2 together with the number of material tests. The mean values and standard deviations of the yield and tensile strengths of the S420 reinforcing bars and the number of samples for each bar size are tabulated in Table 2. Test setup and procedure A 200 kN (45 kip) capacity steel frame was used for the tests. The load, applied by a hydraulic cylinder and measured by an electronic load cell, was equally distributed to four loading points by main and secondary spreader beams (Fig. 4). In this way, the simply supported beams were loaded at two points, each located at a distance of 300 mm (11.8 in.) from midspan, and two points, each located at a distance of 1200 mm (47.2 in.) from midspan. Six-point bending was adopted instead of four-point bending to more closely simulate the moment distribution in a beam subjected to uniform distributed loading, which is the most common loading condition in real practice. The midspan vertical deflection, the support settlements, and the distortions in ACI Structural Journal/March-April 2014
Table 2—Results of material tests Cylinder compressive strength, MPa (ksi)
Yield strength, MPa (ksi)
Tensile strength, MPa (ksi)
Material test
Mean
Standard deviation
RBn
26.8 (3.9)
3.8 (0.6)
2
—
—
—
—
—
—
RBb
33.9 (4.9)
2.8 (0.4)
4
—
—
—
—
—
—
RRxn
27.2 (3.9)
4.5 (0.6)
2
—
—
—
—
—
—
No. of tests
Mean
Standard deviation
No. of tests
Mean
Standard deviation
No. of tests
RRxcn
26.3 (3.8)
3.5 (0.5)
2
—
—
—
—
—
—
RRxb
27.9 (4.0)
1.4 (0.2)
2
—
—
—
—
—
—
RRxcb
24.8 (3.6)
5.8 (0.8)
2
—
—
—
—
—
—
RCb
27.8 (4.0)
2.7 (0.4)
2
—
—
—
—
—
—
RCcb
29.2 (4.2)
2.0 (0.3)
2
—
—
—
—
—
—
RCxb
28.3 (4.1)
3.6 (0.5)
2
—
—
—
—
—
—
RCxcb
26.1 (3.8)
6.1 (0.9)
2
—
—
—
—
—
—
Ø10 bars
—
—
—
476.0 (69.0)
10.2 (1.5)
6
695.7 (100.9)
6.8(1.0)
6
Ø12 bars
—
—
—
550.5 (79.8)
3.6 (0.5)
6
646.0 (93.7)
3.3 (0.5)
6
Fig. 2—Reinforcement details of specimens with openings. (Note: All dimensions in mm; 1 mm = 0.0394 in.) openings were measured with the help of linear variable displacement transducers (LVDTs). The load and deflection measurements were recorded by a data acquisition system. The beams were loaded up to failure, and the cracks were marked and the crack widths measured. FAILURE MODES AND THEORETICAL EQUATIONS Failure modes of reinforced concrete beams with openings Beam- and frame-type shear and web crushing failures are the three common types of shear failure in RC beams with openings. In beam-type failure (Fig. 5(a)), a single crack extending through the entire depth results in failure. This diagonal crack is assumed to pass through the center of opening. The frame-type shear failure (Fig. 5(b)) takes place when two distinct cracks form in the top and bottom chords, and one of the chords fails due to this cracking. Web
ACI Structural Journal/March-April 2014
Fig. 3—Diagonal reinforcement spiraling around circular openings. crushing failure (Fig. 5(c)) is caused by crushing of concrete between the diagonal cracks. Based on the plastic hinge method, RC beams with openings are prone to failure due to formation of a collapse mechanism that is composed of four plastic hinges. This type 269
Fig. 4—Test setup of present experimental program. of failure is denoted as Vierendeel truss action (Fig. 5(d)) because the beams behave similar to a Vierendeel panel. Vierendeel action causes an RC beam to fail at moments below its bending capacity. Preventing Vierendeel action and various forms of shear failure ensures that an RC beam with openings will reach its bending capacity and fail in a tension-controlled flexural mode due to crushing of concrete in the compression zone, which is denoted as flexural failure (Fig. 5(e)). In the present study, the plastic methods based on truss analogy (plasticity truss and strut-and-tie methods) were not used. In these methods, the load capacity of an RC beam is obtained from the axial capacities of different struts and ties, obtained from the reinforcement available in each truss member. RC beams with openings contain numerous Band D-regions, and these beams are modeled with a larger number of truss members compared with RC beams without openings, causing lengthy and tedious calculations. Theoretical equations used in analysis Shear strength and shear forces in chord members— Following the ACI approach (ACI Committee 318 2005), Mansur (1998) was able to develop the following formula for beam-type failure Vn = 0.17 ⋅ fc′ ⋅ b ⋅ ( d − do )
+
Av ⋅ f yv s
⋅ ( dv − do ) + Ad ⋅ f yd ⋅ sin a
(1)
where fc′ is the concrete strength; b is the beam width; d is the effective depth; do is the depth of opening; dv is the distance between the centroids of extreme tension and compression reinforcement layers; s is the stirrup spacing; Av is the area of stirrups; Ad is the cross-sectional area of the diagonal reinforcement within the failure surface; fyv and fyd are the yield strengths of the stirrups and diagonal reinforcement, respectively; and a is the angle of inclination of diagonal reinforcement. The Architectural Institute of Japan (1988) gives the following formula for the beam-type shear failure of RC beams with openings
270
Fig. 5—Failure modes of RC beams with multiple transverse openings. 0.092 ⋅ ku ⋅ k p ⋅ ( fc′ + 17.7) 1.61 ⋅ do ⋅ 1 − M h . 0 12 + ⋅ b ⋅ dv Vn = V ⋅d +0.846 ρw′ ⋅ f yv (2)
where h is the beam depth; ku is a size coefficient, varying from 0.72 to 1.0; kp (Eq. (3)) is a factor accounting for the reinforcement ratio; M and V are the bending moment and shear force at critical section, respectively; and rw′ (Eq. (4)) is the web reinforcement ratio within dv
100 ⋅ As k p = 0.82 ⋅ b ⋅ d
ρ′w =
0.23
(3)
Av + Ad (sin a + cos a ) b ⋅ dv
(4)
where As is the area of tension reinforcement. Mansur (1998) modified the maximum allowable shear force (Vu)max formula of ACI 318 (ACI Committee 318 2005) for RC beams with openings ACI Structural Journal/March-April 2014
Table 3—Analytical and experimental ultimate load values Ultimate load, kN (kip)
Beam
Failure mode
Test Pex
Todeschini et al. (1964) Pan
RBn
Beam-type flexural
163.8 (36.8)
164.7 (37.0)
160.5 (36.1)
0.99
1.02
59.4 (2.3)
RBb
Beam-type flexural
245.8 (55.2)
291.7 (65.6)
289.0 (65.0)
0.84
0.85
95.6 (3.8)
RRxn
Vierendeel truss
156.4 (35.2)
159.6 (35.9)
156.9 (35.3)
0.98
1.00
62.5 (2.5)
RRxcn
Beam-type flexural
169.3 (38.1)
159.6 (35.9)
156.9 (35.3)
1.06
1.08
62.5 (2.5)
RRxb
Vierendeel truss
232.2 (52.2)
288.8 (64.9)
286.8 (64.5)
0.80
0.81
94.2 (3.7)
RRxcb
Web crushing
255.1 (57.3)
288.8 (64.9)
286.8 (64.5)
0.88
0.89
94.2 (3.7)
RCb
Diagonal tension
269.3 (60.5)
288.8 (64.9)
286.8 (64.5)
0.93
0.94
94.2 (3.7)
RCcb
Beam-type flexural
272.3 (61.2)
288.8 (64.9)
286.8 (64.5)
0.94
0.95
94.2 (3.7)
RCxb
Beam-type flexural
278.5 (62.6)
289.3 (65.0)
287.2 (64.6)
0.96
0.97
93.3 (3.7)
RCxcb
Beam-type flexural
284.1 (63.9)
289.3 (65.0)
287.2 (64.6)
0.98
0.99
93.3 (3.7)
(Vu )max = 5 ⋅ 0.85 ⋅ 0.17 ⋅
fc′ ⋅ b ⋅ ( d − do )
(5)
For frame-type shear failure, Mansur (1998) suggested that the shear capacities of both chords should be checked against the shear forces calculated from the following equations, proposed by Nasser et al. (1967)
Vut (Vub ) = Vu ⋅
At ( Ab ) At + Ab
(6)
where At and Ab are areas of the top and bottom chords, respectively; Vu is the shear force in the section; and Vut and Vub are the shear forces at the top and bottom chords, respectively. Tan and Mansur (1996) suggested that the shear force in the section should be distributed to the chords in accordance to their flexural rigidities rather than their cross-sectional areas. Flexural modes of failure—The bottom and top chords in RC beams with openings are subjected to axial and shear forces and bending moments. Due to axial forces and moments in the chords, the liability of an RC beam to develop a failure mechanism composed of four hinges can be evaluated with the help of interaction diagrams as established by Tan and Mansur (1996) and Mansur and Tan (1999). Considering that the hinges at the top and bottom chords are subjected to compression and tension, respectively, and the differences in the directions of moments at different hinges, an interaction diagram is prepared for each hinge and checked against the forces and moments that develop in the hinges at service loads. Tan and Mansur (1996) proposed that the axial forces in the chords can be obtained from
ACI Committee 318 (2005) PACI Pex/Pan Pex/PACI Neutral axis depth, mm (in.)
Nb = − Nt =
Mm z
(7)
where Nt and Nb are the axial forces in the top and bottom chords, respectively; Mm is the bending moment at the section
ACI Structural Journal/March-April 2014
of hinging; and z is the distance between the centroids of the chords. ANALYSIS OF TEST RESULTS Failure modes, ultimate loads, ductilities, and rigidities of beams Both reference beams (RBn and RBb) underwent tension-controlled flexural failure (Fig. 6). In both beams, the load was preserved, while the cover concrete crushed and later dropped suddenly resulting in failure when the top bars buckled and concrete crushing initiated. In both beams, no considerable diagonal cracking took place in shear spans (Fig. 7(a)). Table 3 indicates that the experimental ultimate load of RBn was in close agreement with the values calculated from the rectangular stress block analysis of ACI 318-05 (ACI Committee 318 2005) PACI and from the Todeschini et al. (1964) stress-strain model Pan. The load capacity of RBb remained below the bending capacities calculated from both models. Furthermore, Table 4 indicates that the ultimate shear forces Vu in both beams at failure were smaller than their respective shear strength values Vn, implying that shear had no influence on failure. Table 5 tabulates the deformation ductility index (DDI) and rigidity values of the specimens. DDI is the ratio of a beam’s deflection at the instant when the applied load drops to 85% of the ultimate load to the deflection at yielding of tension reinforcement. DDI is an indicator of the deformability of a beam without a significant reduction in load. The rigidity values in the table correspond to the slope of the initial linear branch of the load-deflection curve. In RC beams, it is quite cumbersome to determine the slope of the moment-curvature diagram due to variation of the flexural stiffness along the span caused by the discrete flexural cracks. Therefore, slope of the load-deflection curve was adapted. Four different types of failure were observed in beams with openings. RRxn and RRxb failed due to the formation of plastic failure mechanism (Fig. 8(a) and (b)). In both RRxn and RRxb, two hinges formed at the ends of the top and bottom chords of the opening closest to the end 271
Fig. 6—Concrete crushing and buckling of compression bars in reference beams. support (Fig. 8(b)). The two beams differed in the locations of the remaining two hinges, which formed at the right ends of the top and bottom chords of the fourth opening in RRxn (Fig. 9(a)) and the fifth opening in RRxb (Fig. 9(c)). Unlike RC beams with one or two openings, the considerable distance between the hinging locations provided that the stresses in the mechanism were distributed to greater portions of the beam and the reversal of curvature took place over a longer length. The posts inside the failure mechanism were also observed to fail in shear (Fig. 8(b)), which was primarily related to the lack of stirrups in the posts. RRxn failed at an applied load close to its ultimate capacity (Table 3), implying that the failure of a moderately reinforced concrete beam with multiple openings due to formation of a mechanism does not result in significant reductions in its load capacity. The formation of mechanism caused greater reductions in the capacity of RRxb. Table 5 and Fig. 7(b) show that both RRxb and RRxn had ductile behaviors up to failure, with the DDI value of RRxb only 20% smaller than RBb, and the DDI of RRxn 40% smaller than RBn. The fact that RRxn and RRxb exhibited ductilities and load capacities comparable to their respective reference beams originated from two reasons. First, the diagonal reinforcement in the beams carried the shear loads in the posts even after the failure of the posts. Second, the significant longitudinal
272
distance between the hinges prevented the excessive stress concentrations around hinges. Figures 9(b) and (d) illustrate the linear approximations of the interaction diagrams of RRxn and RRxb, respectively. Because the top chords are subjected to compression and bending, the yield planes above the bending moment axis are composed of two linear segments, which intersect at the point corresponding to balance failure. The yield planes below the moment axis correspond to the bottom chords subjected to tension as well as bending. The points corresponding to the axial forces and moments at the hinges at failure are also shown in the diagrams. Both figures indicate that all of the points corresponding to the hinges remain inside the yield surfaces implying that no hinging was expected at failure. Nevertheless, the plastic hinging at locations shown in Fig. 9(a) and (c) and failure of RRxn and RRxb due to hinging might be induced by the excessive shear deformations in the posts causing additional stresses. RRxcn, RCcb, RCxb, and RCxcb failed in flexure after yielding of tension reinforcement (Fig. 8(c)). The final failure was caused by the crushing of cover and core concrete and buckling of compression bars. In these beams, the shear cracks initiated in the chords and posts at the beginning of loading did not widen and propagate in further stages of loading, and the flexural cracks at the central part of the beam controlled the behavior (Fig. 7(a)). Table 3 indicates that all of these beams failed at loads close to their respective bending capacities. RCcb, RCxb, and RCxcb exhibited greater ductilities than their reference beam RBb, with relative DDI values greater than unity, and had rigidities close to the rigidity of the reference (Table 5). The neutral axis depth values given in Table 3, calculated using the Todeschini et al. (1964) stress-strain model, indicate that the compression zone in each beam remained within the top chord up to failure and was not affected from the openings. RCb underwent frame-type shear failure (Fig. 8(d)) due to severe shear cracking in the chords of the opening closest to the left end (Fig. 7(a)). Despite the final failure being originated from shear, RCb exhibited a ductile flexural behavior up to failure, and the longitudinal reinforcing bars in the beam yielded before failure. This explains why the load capacity of the beam was only 7% smaller than its calculated capacity (Table 3), and its DDI value was almost equal to the DDI value of the reference beam (Table 5). Table 4 indicates that the nominal shear strengths of the chords were significantly smaller than the shear forces in the chords at failure. The use of short stirrups (Fig. 2) in the chords could not prevent the frame-type failure. Table 4 shows that RCcb was also liable to frame-type shear failure considering the significant discrepancies between the nominal shear strengths of the chords and the shear forces in the chords at failure. RCcb, however, failed in flexure, which can be attributed to the presence of stirrups in posts. RRxcb failed due to web crushing in the chords above and below the second opening (Fig. 7(a) and 8(e)). Due to this failure, RRxcb could not reach its bending capacity (Table 3), and had a limited ductility (Table 5). The failure of the beam was not a diagonal tension failure because both the chords and the beam had adequate shear strengths (Table 4). ACI Structural Journal/March-April 2014
Table 4—Shear force and shear strength values Beam-type failure
Frame-type failure Top chord
Vn, kN (kip)
Bottom chord
Beam
ACI
AIJ
Vu, kN (kip)
Vnt, kN (kip)
Vut, kN (kip)
Vnb, kN (kip)
Vub, kN (kip)
RBn
168.7 (37.9)
—
81.9 (20.6)
—
—
—
—
RBb
165.7 (37.2)
—
122.9 (27.6)
—
—
—
—
RRxn
242.8 (54.6)
141.9 (31.9)
78.2 (17.6)
86.8 (19.5)
39.1 (8.8)
86.8 (19.5)
39.1 (8.8)
RRxcn
242.8 (54.6)
141.9 (31.9)
84.7 (19.0)
86.8 (19.5)
42.3 (9.5)
86.8 (19.5)
42.3 (9.5)
RRxb
257.8 (58.0)
141.8 (31.9)
116.1 (26.1)
94.2 (21.2)
58.1 (13.1)
94.2 (21.2)
58.1 (13.1)
RRxcb
257.8 (58.0)
141.8 (31.9)
127.6 (28.7)
94.2 (21.2)
63.7 (14.3)
94.2 (21.2)
63.7 (14.3)
RCb
147.2 (33.1)
90.0 (20.2)
134.6 (30.2)
38.9 (8.7)
67.3 (15.1)
38.9 (8.7)
67.3 (15.1)
RCcb
147.2 (33.1)
90.0 (20.2)
136.2 (30.6)
38.9 (8.7)
68.1 (15.3)
38.9 (8.7)
68.1 (15.3)
RCxb
257.9 (58.0)
142.1 (31.9)
139.3 (31.3)
94.3 (21.2)
69.6 (15.6)
94.3 (21.2)
69.6 (15.6)
RCxcb
257.9 (58.0)
142.1 (31.9)
142.1 (31.9)
94.3 (21.2)
71.0 (16.0)
94.3 (21.2)
71.0 (16.0)
Fig. 7—(a) Cracking patterns of specimens at failure; and (b) load-deflection curves of specimens. Nevertheless, both the chords and the entire beam were subjected to shear forces above their maximum allowable shear forces calculated from Eq. (5), which caused crushing of concrete between the diagonals. Table 6 indicates that RRxb, RCb, RCcb, RCxb, and RCxcb were also prone to web crushing because the shear forces at failure exceeded the maximum allowable shear forces. None of these beams, ACI Structural Journal/March-April 2014
however, underwent web crushing failure. The maximum allowable shear is calculated from Eq. (5) by assuming that the depth of each chord is constant along its length, which is an over-conservative assumption for circular openings. In chords above and below circular openings, the chord depth increases from mid-length of the chord to sides. Therefore, the maximum shear force tolerable by a chord in an RC 273
Table 5—Ductilities and rigidities of beams Deformation ductility index (DDI) Beam
Absolute
Rigidity
Relative
Absolute, kN/mm (kip/in.)
Relative
RBn
17.8
1.00
10.12 (57.8)
1.00
RRxn
10.7
0.60
5.77 (32.9)
0.57
RRxcn
8.4
0.47
5.87 (33.5)
0.58
RBb
6.4
1.00
12.05 (68.8)
1.00
RRxb
5.6
0.88
8.86 (50.6)
0.74
RRxcb
1.0
0.16
8.62 (49.2)
0.72
RCb
6.1
0.95
8.87 (50.6)
0.74
RCcb
9.5
1.48
9.32 (53.2)
0.77
RCxb
7.8
1.22
10.80 (61.7)
0.90
RCxcb
8.1
1.27
11.03 (63.0)
0.92
ultimate load and rigidity values greater than those of RCcb, while the DDI value of RCcb exceeded the value of RCxcb. The rigidity and load capacity of an RC beam with openings can be increased by using diagonal steel if the posts are reinforced with stirrups, but the diagonal reinforcement does not contribute to the ductility in this case.
Fig. 8—Flexural and shear failure modes of specimens with openings. beam with circular openings is greater than the value from Eq. (5). This might be the reason that none of the specimens with circular openings failed in diagonal compression. Web crushing in the chords might have affected the failure of RRxb, which eventually failed due to Vierendeel action. Effect of diagonal reinforcement on beam behavior Figure 10 indicates the load-deflection curves of beams with and without diagonal reinforcement. The load-deflection curves indicate that the use of diagonal reinforcement in an RC beam increases its energy absorption capacity. The DDI, rigidity (Table 5), and ultimate load (Table 3) values of RCxb are higher than the values of RCb, implying that diagonal reinforcement contributes to the flexural behavior if no stirrups are used in the posts. RCxcb, on the other hand, had 274
Effect of stirrups in posts on beam behavior Figure 7(b) illustrates that the stirrups in the posts significantly contribute to the energy capacity if no diagonal reinforcement is used. The DDI value of RCcb (Table 5) is also considerably greater than the value of RCb, implying the significant contribution of the stirrups to the ductility in the absence of diagonal reinforcement. In beams with rectangular openings, it appears that the use of stirrups in the posts does not contribute to the ductility and energy capacity of the beam if the beam has diagonal reinforcement. The DDI values of RRxcn and RRxcb were considerably smaller than the values of RRxn and RRxb, respectively. In beams with circular openings and diagonal reinforcement, the stirrups in the posts have almost no contribution to the ductility. The DDI value of RCxcb is approximately equal to the value of RCxb. Table 3 indicates that, in all cases, the use of stirrups has a positive but minor effect on the load capacity. To summarize, the stirrups in the posts improve the behavior of a beam when the beam does not have diagonal reinforcement. In the presence of diagonal reinforcement, the stirrups in the posts have little or no contribution to the flexural performance. The use of stirrups in the posts in addition to diagonal reinforcement causes the posts to be too strong, shifting the failure to the chords. If the chords fail in brittle modes (Vierendeel truss action, diagonal tension, or compression), the beam exhibits limited ductility. Effect of opening geometry on beam behavior Figure 11 illustrates the load-deflection curves of beams with the same reinforcement details but with different opening geometries. Both plots indicate that RC beams with circular openings have much greater energy capacities than the beams with rectangular openings. The DDI and ACI Structural Journal/March-April 2014
Table 6—Adequacy of beams for shear Beam-type failure (entire section)
Frame-type failure (chord members)
Beam
(Vu)max, kN (kip)
Vu, kN (kip)
(Vut)max, kN (kip)
Vut, kN (kip)
RBn
248.0 (55.8)
81.9 (20.6)
—
—
RBb
235.3 (52.9)
122.9 (27.6)
—
—
RRxn
105.0 (23.6)
78.2 (17.6)
55.2 (12.4)
39.1 (8.8)
RRxcn
105.0 (23.6)
84.7 (19.0)
55.2 (12.4)
42.3 (9.5)
RRxb
106.4 (23.9)
116.1 (26.1)
54.8 (12.3)
58.1 (13.1)
RRxcb
106.4 (23.9)
127.6 (28.7)
54.8 (12.3)
63.7 (14.3)
RCb
106.4 (23.9)
134.6 (30.2)
54.8 (12.3)
67.3 (15.1)
RCcb
106.4 (23.9)
136.2 (30.6)
54.8 (12.3)
68.1 (15.3)
RCxb
107.1 (24.1)
139.3 (31.3)
55.2 (12.4)
69.6 (15.6)
RCxcb
107.1 (24.1)
142.1 (31.9)
55.2 (12.4)
71.0 (16.0)
rigidity values of RCxb and RCxcb are significantly higher than the values of RRxb and RRxcb, respectively (Table 5). Furthermore, the ultimate loads carried by RCxb and RCxcb considerably exceeded the ultimate loads of RRxb and RRxcb, respectively (Table 3). The less favorable behavior of RC beams with rectangular openings is mainly due to the stress concentrations in the corners. In beams with rectangular openings, the shear cracks in the posts were observed to project from these sharp corners (Fig. 12), and these cracks caused reductions in the rigidities and load capacities. Secondly, the smaller areas of the circular openings compared with the rectangular ones resulted in less reductions in the beam capacities. Although rectangular openings have more adverse effects on the beam behavior compared with circular openings, provision of rectangular openings in RC beams might be unavoidable, considering that the air-conditioning ducts in buildings are usually rectangular. RC beams with rectangular openings should be more carefully designed because they are more prone to Vierendeel action and shear failure of the chords. SUMMARY AND CONCLUSIONS Two reference beams, four RC beams with multiple circular, and four beams with multiple rectangular openings were tested to determine the flexural performance of RC beams with openings. Three of the beams had moderate amounts of flexural reinforcement, while the remaining beams were heavily reinforced. Each beam with openings had longitudinal bars and full-depth stirrups adjacent to openings and short stirrups in the chords. The longitudinal reinforcement ratio, opening geometry, and use of diagonal reinforcement and longitudinal stirrups in the posts were the main test parameters. The experiments and comparison with theoretical formulations yielded the following conclusions: • The use of diagonal reinforcement contributes to the ductility and load capacity if the posts are not reinforced with stirrups in longitudinal direction. Similarly, the
ACI Structural Journal/March-April 2014
Fig. 9—Hinging locations and interaction diagrams of Beams RRxn and RRxb. (Note: 1 kN = 0.225 kip; 1 kN.m = 0.738 kip-ft.)
•
•
•
stirrups in the posts increase the ductility and capacity of RC with openings in the absence of diagonal steel. The simultaneous use of diagonal reinforcement and stirrups in the posts has minor or no contribution to ductilities and load-carrying capacities of RC beams with openings. The presence of diagonal reinforcement and stirrups in the posts causes the posts to be overly strong, which leads to failure of the chords rather than the posts. For the same reinforcement details, RC beams with circular openings have higher ductilities and load capacities compared with the beams with rectangular openings. The experiments indicated that the stress concentrations at corners of rectangular openings result in cracking, which leads to the reductions in the flexural rigidities without exhibiting full ductility. In RC beams with multiple openings, the considerable distance between the hinging locations causes the stresses in the failure mechanism to be distributed to greater portions of the beam compared with the beams with one or two openings. Therefore, RC beams with multiple openings exhibit a more ductile behavior even if they fail due to Vierendeel action. The posts 275
Fig. 10—Contribution of diagonal reinforcement to beam ductility in presence and absence of stirrups in posts.
•
•
•
remaining inside the failure mechanism in Vierendeel action were observed to fail in shear. Diagonal reinforcement around the openings was found to carry the forces in the posts and prevent the complete failure of an RC beam, even after the failure of the posts. The large shear deformations in the posts were shown to cause Vierendeel action. The failure of an RC beam with openings due to Vierendeel action causes greater reductions in the load-carrying capacity as the longitudinal reinforcement ratio of the beam increases. The use of short stirrups in the chords is not an adequate measure for prevention of frame-type shear failure. The use of diagonal reinforcement and stirrups in the posts limits the extent of shear cracking in the chords, and prevents the frame-type shear failure. RC beams with openings are more liable to web crushing (diagonal compression) failure if the chords and beams have high amounts of shear reinforcement and small widths.
DESIGN RECOMMENDATIONS FOR REINFORCED CONCRETE BEAMS WITH WEB OPENINGS The experimental and analytical results obtained within the scope of the present study indicated that the load capaci276
Fig. 11—Contribution of circular opening geometry on beam ductility.
Fig. 12—Shear cracks projecting from corners of rectangular openings. ties and ductilities of RC beams with multiple openings can be increased by proper strengthening of the chords and posts. When the chords are weak in shear, an RC beam with openings is prone to diagonal tension or compression failures of the chords. The use of short stirrups proved to be effective for preventing frame-type shear failure. Furthermore, the chords should be designed to not exceed the maximum allowable shear force to prevent web crushing failure. RC beams with rectangular openings are more prone to different forms of shear failure compared with beams with circular ACI Structural Journal/March-April 2014
openings. Special attention should be given to shear design of beams with rectangular openings. The shear forces are distributed to the chords in accordance to their cross-sectional areas. The most efficient design is achieved when the openings are placed at mid-depth of the member. When the centers of openings are offset from mid-depth, one of the chords of each opening is weaker than the other, and is more vulnerable to different forms of shear failure. The presence of several openings proved to be effective in improving the behavior of a beam. Unlike RC beams with one or two openings, the stresses inside failure mechanism were observed to be distributed to greater portions of the beam. The posts inside the failure mechanism should be designed to resist the excessive deformations in the mechanism. The use of longitudinal stirrups in the posts or diagonal reinforcement was shown to effectively delay shear failure of the posts and increase the ductility and load capacity. The present experiments indicated that the use of longitudinal stirrups in the posts with a volumetric ratio of 0.016 provided an RC beam with circular openings with a load capacity and DDI 11 and 48% greater than its reference. Similarly, the use of diagonal reinforcement with a volumetric ratio of 0.017 resulted in an increase of 13 and 22% in the load capacity and DDI of an RC beam with circular openings compared with its reference. RC beams with rectangular openings reached load capacities close to their references in the presence of diagonal reinforcement, with a volumetric ratio of 0.013. Nevertheless, the DDI value of the moderately reinforced RC beam with rectangular openings remained approximately 40% of its reference in this case. It was found that the simultaneous use of longitudinal stirrups and diagonal steel causes the posts to be overly strong, causing the chords to fail before the posts. In the present study, the beams strengthened with both diagonal reinforcement and longitudinal stirrups in the posts exhibited ductilities more than 50% smaller than the beams with only diagonal reinforcement. AUTHOR BIOS
Bengi Aykac is a Lecturer in the Civil Engineering Department at Gazi University, Ankara, Turkey, where she received her BS, MS, and PhD. Her research interests include behavior of concrete beams strengthened by jacketing techniques, concrete beams strengthened with steel plates, and crack repair by epoxy injection. Sabahattin Aykac is an Assistant Professor in the Civil Engineering Department at Gazi University, where he received his BS, MS, and PhD in 1989, 1993, and 2000, respectively. His research interests include strengthening and repair of concrete beams, earthquake behavior of strengthened concrete beams, and concrete beams with openings. Ilker Kalkan is an Assistant Professor in the Department of Civil Engineering at Kirikkale University, Kirikkale, Turkey. He received his BS from Middle East Technical University, Ankara, Turkey, in 2004, and his MS and PhD from the Georgia Institute of Technology, Atlanta, GA, in 2006 and 2009, respectively. His research interests include structural stability, fiber-reinforced polymer concrete, and strengthening of concrete beams. Berk Dundar is a Civil Engineer at Aydiner Construction Company, Turkey. He received his BS from Dokuz Eylul University, Izmir, Turkey, in 2005, and his MS from Gazi University in 2008. His research interests include the behavior of concrete beams with openings. Husnu Can is a Professor in the Civil Engineering Department at Gazi University, Ankara, Turkey. He received his BS from Ankara Higher Tech-
ACI Structural Journal/March-April 2014
nology Institute in 1967; his MS from Tulane University, New Orleans, LA, in 1977; and his PhD from Ankara University, Ankara, Turkey, in 1983. His research interests include behavior of strengthened reinforced concrete beams under repetitive loading and the behavior of strengthened reinforced concrete columns.
ACKNOWLEDGMENTS
This paper represents a condensation of the thesis prepared at Gazi University, Ankara, Turkey, by B. Dundar under the supervision of H. Can and S. Aykac toward the degree of Master of Science.
Ab Ad At Av do dv
= = = = = =
fyd fyv z a
= = = =
r t
=
NOTATION
cross-sectional area of bottom chord cross-sectional area of diagonal reinforcement within failure plane cross-sectional area of top chord cross-sectional area of stirrups diameter of circular opening or depth of rectangular opening distance between centers of extreme tension and compression steel layers yield strength of diagonal reinforcement yield strength of stirrups distance between centroids of top and bottom chords angle of inclination of diagonal reinforcement with longitudinal beam axis tension reinforcement ratio
REFERENCES
ACI Committee 318, 2005, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary,” American Concrete Institute, Farmington Hills, MI, 430 pp. Architectural Institute of Japan (AIJ), 1988, “Standard for the Structural Calculation of Reinforced Concrete Structures,” Architectural Institute of Japan, Tokyo, Japan, 207 pp. Aykac, S., and Yilmaz, M. C., 2011, “Behaviour and Strength of RC Beams with Regular Triangular or Circular Web Openings,” Journal of Faculty of Engineering and Architecture of Gazi University, V. 26, No. 3, pp. 711-718. (in Turkish) Dundar, B., 2008, “Behaviour and Strength of Reinforced Concrete Beams with Regular Openings,” MSc thesis, Gazi University, Ankara, Turkey, pp. 16-22. (in Turkish) Egriboz, Y. E., 2008, “Behaviour and Strength of R/C Beams with Regular Rectangular or Circular Web Openings,” MSc thesis, Gazi University, Ankara, Turkey, pp. 27-35. (in Turkish) Mansur, M. A., 1998, “Effect of Openings on the Behaviour and Strength of R/C Beams in Shear,” Cement and Concrete Composites, V. 20, No. 6, pp. 477-486. Mansur, M. A., 1999, “Design of Reinforced Concrete Beams with Small Openings under Combined Loading,” ACI Structural Journal, V. 96, No. 5, Sept.-Oct., pp. 675-681. Mansur, M. A.; Huang, L. M.; Tan, K. H.; and Lee, S. L., 1992, “Deflections of Reinforced Concrete Beams with Web Openings,” ACI Structural Journal, V. 89, No. 4, July-Aug., pp. 391-397. Mansur, M. A.; Lee, Y. F.; Tan, K. H.; and Lee, S. L., 1991, “Tests on RC Continuous Beams with Openings,” Journal of Structural Engineering, ASCE, V. 117, No. 6, pp. 1593-1606. Mansur, M. A., and Tan, K. H., 1999, Concrete Beams with Openings: Analysis and Design, CRC Press, Boca Raton, FL, 224 pp. Mansur, M. A.; Tan, K. H.; and Weng, W., 2006, “Analysis of Concrete Beams with Circular Web Openings Using Strut-and-Tie Models,” Malaysian Journal of Civil Engineering, V. 18, No. 2, pp. 89-98. Nasser, K. W.; Acavalos, A.; and Daniel, H. R., 1967, “Behavior and Design of Large Openings in Reinforced Concrete Beams,” ACI Journal, V. 64, No. 1, Jan., pp. 25-33. Tan, K. H., and Mansur, M. A., 1996, “Design Procedure for Reinforced Concrete Beams with Large Web Openings,” ACI Structural Journal, V. 93, No. 4, July-Aug., pp. 404-411. Tan, K. H.; Mansur, M. A.; and Wei, W., 2001, “Design of Reinforced Concrete Beams with Circular Openings,” ACI Structural Journal, V. 98, No. 3, May-June, pp. 407-415. Todeschini, C. E.; Bianchini, A. C.; and Kesler, C. E., 1964, “Behavior of Concrete Columns Reinforced with High Strength Steels,” ACI Journal, V. 61, No. 6, June, pp. 701-716. Yang, K. H.; Eun, H. C.; and Chung, H. S., 2006, “The Influence of Web Openings on the Structural Behavior of Reinforced High-Strength Concrete Deep Beams,” Engineering Structures, V. 28, No. 13, pp. 1825-1834.
277
NOTES:
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S24
Experimental Assessment of Inadequately Detailed Reinforced Concrete Wall Components by Adane Gebreyohaness, Charles Clifton, John Butterworth, and Jason Ingham An experimental study undertaken to assess the seismic behavior of reinforced concrete (RC) walls constructed prior to the introduction of seismic design requirements in the New Zealand Standard Model Building By-law is presented. The geometric characteristics and material properties of the test specimens were replicated from those of an existing building. The primary test variables considered were wall thickness, magnitude of applied axial compressive load, and aspect ratio. In addition, the influence of the longitudinal reinforcing bar splices, which are positioned in locations that are not permitted by current design standards, on the seismic performance of the walls was investigated. The response of the test specimens was dominated by rocking, after yielding of the longitudinal reinforcing bars located adjacent to the boundaries of the walls occurred. The peak strength and the stiffness of the test specimens dropped rapidly and significantly after low-level drift cycles. Overall, the test specimens exhibited poor ductility and limited energy dissipation capacity. Provisions for required tension splice lengths of plain round bars in ASCE/SEI 41-06 were found to be excessively conservative. Keywords: existing buildings; lap splice; lightly reinforced; walls.
INTRODUCTION Reinforced concrete (RC) buildings constructed prior to the 1970s in New Zealand and other seismically active countries were not designed and detailed to undergo a ductile mode of failure.1,2 Poor performance of this class of buildings has been observed in earthquakes occurring in many countries around the world, such as Chile in 1985,3 Turkey in 1999,4 Chile in 2010,5 and New Zealand in 2011.6 During the recent 2010/2011 Canterbury (New Zealand) earthquake sequence, this class of buildings performed poorly and in some cases collapsed catastrophically. Christchurch City Council Building Safety Evaluation statistics indicate that 60% of the pre-1970 RC buildings in Christchurch were deemed suitable for restricted access only or were unsafe after the 6.3 magnitude Christchurch earthquake on February 22, 2011, which claimed 181 lives.7 The majority of the fatalities were attributed to the collapse of two RC buildings—the PGC building and the CTV building, which were constructed in 1963 and 1986, respectively.8 The PGC building had RC stair/lift core walls that had similar reinforcing bar configurations to the walls discussed herein, and the poor performance of the singly and lightly reinforced walls led to the collapse of the building.9 Previous research attention has primarily been directed toward the structural components of pre-1970 RC frame buildings, principally inadequately detailed columns and beam-column joints, owing to the clear seismic risk in this class of buildings that these structural components ACI Structural Journal/March-April 2014
pose. Although there have been a number of experimental studies10-13 where the seismic performance of existing walls was assessed, studies that evaluated the performance of lightly and singly reinforced walls with detailing similar to those found in the PGC building are limited. Test specimens considered in experimental studies reported in the literature were doubly reinforced,11-13 used higher longitudinal reinforcing bar ratios than those found in many older buildings,10-13 or used deformed bars instead of plain round bars.10,11,13 In addition, few of the test specimens investigated previously had spliced longitudinal reinforcement.12 Therefore, it was concluded that a study was necessary to assess the seismic performance of singly and lightly RC walls incorporating inadequate longitudinal bar splices. The experimental study presented herein was based on the walls of a case study building located in Wellington, New Zealand. This street corner building was constructed in 1928 before the publication of NZSS 95,14 which introduced seismic-resistant design requirements in New Zealand for the first time. The building has internal, one-way, moment-resisting, riveted steel frames and RC walls located at the perimeter as the lateral-force-resisting systems. The walls have limited openings on sides adjacent to neighboring buildings and have larger and more regular openings on the street frontages. The case study building was assessed15 in accordance with the nonlinear dynamic procedure detailed by ASCE/SEI,2,16 using a suite of seven earthquake records17 relevant to the seismicity of the building site, to determine the performance of the building during a likely earthquake. From the assessment, it was found that the capacity of the building will be exceeded in moderate level earthquakes, which were defined as being one-third as strong as the design level earthquakes relevant to the building site.18 The walls were identified to be the primary lateral-force-resisting components of the building, and those walls located at the street frontages were found to be the most critical walls of the building. To obtain an understanding of the seismic performance of walls similar to those found in the case study building, an experimental program was undertaken on replicas of typical segments of the most critical walls. The configuration of the reinforcing bars within the walls was determined from the original structural drawings and construction specifications of the case study building. The walls are ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-071.R2, doi:10.14359.51686520, was received August 13, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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singly reinforced with widely spaced plain round bars, and the quantity of longitudinal and transverse reinforcement within these walls is less than what is required by current standards19,20 to induce a ductile response. The longitudinal reinforcing bars are spliced just above the floor levels. The spliced reinforcing bars, which would be required by current design standards20 to be hooked, lack proper end anchorages. In addition, the splice lengths are too short according to current design standards19,20 to initiate yielding of spliced reinforcing bars before slip occurs. There is also a lack of transverse confinement reinforcement to contain concrete in compression zones and to prevent longitudinal reinforcing bars from buckling. Similar to the wall piers, the coupling beams of the case study building, which would typically receive diagonal reinforcement if constructed to current standards,21 are reinforced with longitudinal and transverse reinforcement to resist flexure and shear, respectively. RESEARCH SIGNIFICANCE Because RC buildings constructed before the 1970s comprise a considerable portion of vulnerable RC structures that pose significant seismic risk, as-built performance assessment and seismic retrofitting, preferably without loss of heritage attributes to the buildings, are crucial steps toward ensuring better performance in future earthquakes. Current recommendations2,3,16 for the assessment and improvement of existing RC walls are based on modern design codes, which address new walls and are not necessarily applicable to walls designed and constructed following outdated methods. The experimental study presented herein intends to contribute to a more realistic seismic performance assessment of existing nonconforming RC walls. EXPERIMENTAL PROGRAM Twelve full-scale wall components were constructed in-place and tested in the Civil Test Hall of the University of Auckland as part of a research program planned to assess the seismic performance of existing buildings in New Zealand. The test matrix is presented in Table 1. Description of test specimens The geometric characteristics and reinforcing bar configurations of the test specimens were determined based on the original structural drawings and construction specifications of the case study building. The walls in the bottom five stories of the case study building are 230 mm (9 in.) thick, and the walls in the upper four stories are 150 mm (6 in.) thick. Both types of walls are provided with a single layer of reinforcement consisting of 10 mm (3/8 in.) diameter plain round reinforcing bars placed at 305 mm (12 in.) centers spacing, in both the horizontal and vertical directions and located at the midthickness plane of the walls. In addition, two 12 mm (1/2 in.) diameter boundary bars are placed around all openings. The longitudinal bars are spliced just above the floor levels with splice lengths of 305 and 457 mm (12 and 18 in.) for the 10 and 12 mm (3/8 and 1/2 in.) diameter bars, respectively, with no transverse reinforcing bar enclosing the lap. In Fig. 1, the dimensions and reinforcing bar arrangements of the test specimens are presented. 280
Table 1—Test matrix Test specimen
lw, mm
h, mm
t, mm
M/Vlw
Compressive axial load, kN
WPS1
1300
1750
150
1.35
200
WPS2
1300
1750
230
1. 35
300
WPS3
1300
2400
150
0.92
0
WPS4
1300
2400
230
0.92
0
WPS5
1300
2400
150
0.92
0
WPS6
1300
2400
230
0.92
0
WPS7
1300
2400
150
0.92
200
WPS8
1300
2400
230
0.92
300
WPS9
1300
2400
150
0.92
200
WPS10
1300
2400
230
0.92
300
WSS1
1000
1600
150
0.8
0
WSS2
1000
1600
230
0.8
0
Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.
Ten of the test specimens (WPS1 to WPS10) were replicated wall piers and the remaining two test specimens (WSS1 and WSS2) were replicated coupling beams. Eight of the wall piers (WPS3 to WPS10) and both of the coupling beams had boundary reinforcement, as shown in Fig. 1. In four of the wall piers (WPS5 to WPS8), the longitudinal reinforcing bars were spliced near the base of the wall piers, whereas in the remaining test specimens, the longitudinal reinforcing bars were continuous and were anchored outside the wall piers. During construction of the test specimens, a concrete compressive strength of 21 MPa (3.0 ksi) was specified to reflect the average strength determined from core samples extracted from the case study building. In addition, Grade 300 (fy = 300 MPa [43.5 ksi]) plain reinforcing bars were planned to be used, as this grade is close to the strength of the nominal Grade 240/250 reinforcing bars used during the era of construction of the building. Some of the reinforcing bars used, however, were incorrectly supplied as Grade 500 (fy = 500 MPa [72.5 ksi]). This error was identified only after the testing program was completed. Generally, Grade 500 bars have a shorter yield plateau, rupture at lower strain levels, require longer development lengths, and are more likely to buckle than Grade 300 bars. However, reinforcement grade did not significantly affect the behavior of the test specimens, apart from the apparent influence on wall strength. Material properties of the test specimens are summarized in Table 2. Test setup and instrumentation The first two wall piers (WPS1 and WPS2) were tested as vertical cantilevers (refer to Fig. 2(a)), while the remaining eight wall piers (WPS3 to WPS10) and the coupling beams (WSS1 and WSS2) were subjected to double bending using a steel loading beam mounted on and anchored to the top RC blocks (refer to Fig. 2(b)). As shown in Fig. 2(c), the coupling beams were rotated and tested in a vertical orientation. The double bending loading condition was represenACI Structural Journal/March-April 2014
Fig. 1—Test specimen geometries and reinforcement details. ACI Structural Journal/March-April 2014
281
Table 2—Material properties Longitudinal and transverse reinforcement
Longitudinal reinforcement splices
Boundary reinforcement
Test specimen
fc′ MPa
Al, At, mm
fy, fyt, MPa
fult, MPa
ρl, %
ρt, %
Ab, mm
fy, MPa
fult, MPa
Splice
lb, φ10, mm
lb, φ12, mm
WPS1
18.4
φ10
530
667
0.20
0.18
—
—
—
No
—
—
WPS2
20.9
φ10
300
429
0.13
0.12
—
—
—
No
—
—
WPS3
19.6
φ10
351
488
0.20
0.17
4φ12
388
555
No
—
—
WPS4
16.2
φ10
351
488
0.13
0.11
4φ12
305
436
No
—
—
WPS5
29.4
φ10
348
487
0.20
0.17
4φ12
516
662
Yes
305
457
WPS6
24.8
φ10
348
487
0.13
0.11
4φ12
516
662
Yes
305
457
WPS7
21.3
φ10
344
456
0.20
0.17
4φ12
305
438
Yes
305
457
WPS8
22.5
φ10
344
456
0.13
0.11
4φ12
305
438
Yes
305
457
WPS9
20.2
φ10
490
631
0.20
0.17
4φ12
301
433
No
—
—
WPS10
19.3
φ10
490
631
0.13
0.11
4φ12
301
433
No
—
—
WSS1
18.7
φ10
351
472
0.21
0.20
4φ12
321
426
No
—
—
WSS2
21.4
φ10
351
472
0.14
0.13
4φ12
321
426
No
—
—
tative, as closely as possible, of the fixed-fixed sway support condition of wall components in multi-story buildings. Compressive axial load was applied to the wall piers using four high-strength bars that were positioned parallel to the wall centerline and anchored to the strong floor (refer to Fig. 2(a) and (b)). Typical test specimen instrumentation is shown schematically in Fig. 3. Load cells, denoted as LC1 to LC3, were employed to measure the magnitude of forces applied on the test specimens. The lateral displacement of the test specimens was measured using potentiometer TP1 and the readings were corrected to provide the horizontal displacement of the top of the test specimens. Portal gauges PG1-PG6, PG7-PG14, and PG15-PG24 were used to measure rocking, flexural, and shear deformations, respectively. Relative sliding displacements that could have occurred during the tests at the foundation block-specimen, specimen-top block, and strong floor foundation block interfaces were also monitored using portal gauges PG25, PG26, and PG27, respectively. Ten strain gauges per test specimen were attached to the transverse and longitudinal reinforcement. Strain gauges were glued at the midheight of the starter bars to four pairs of spliced bars (one on the starter bar and another one on the main bar) to monitor the performance of the splices located within four of the test specimens (WPS5 to WPS8). Testing procedure The test specimens were subjected to quasi-static cyclic loading, with the loading regime based on the ACI-recommended22 loading sequence for assessing the performance of new RC structural components. Potentiometer TP1 (refer to Fig. 3) was employed for the loading regime displacement control. OBSERVED RESPONSE The inelastic response of the test specimens was dominated by rocking (refer to Fig. 4). All of the test specimens 282
exhibited wide cracks localized at the bottom and at the top of the walls (refer to Fig. 5) accompanied by rupture of longitudinal reinforcement located adjacent to the wall boundaries. No significant flexural and shear deformations were observed or recorded within the body of the walls. The magnitude of the sliding deformations observed at the wall-foundation block interfaces was insignificant when compared to the magnitude of wall rocking deformations. No sliding took place at the wall-top block interfaces. There was visible slipping of the spliced bars along the provided splice length, especially during testing of those specimens that were not subjected to axial load. Fracturing of all of the continuous longitudinal bars was observed during testing, while none of the spliced bars were fractured. The test specimens that were subjected to double bending responded as intended, with crack development being anti-symmetric about the midheight of the walls at drift cycles of less than 1%. When the testing progressed to drift cycles of greater than 1%, the top sections of the test specimens underwent significantly larger rotations than did the bottom sections, as the top of the test specimens were not fully restrained against rotation. This support condition resulted in an upward shifting of the inflection point, which in turn led to larger bending moments being developed at the base of the walls, causing the cracks at the bottom of the walls to become wider and the cracks at the top of the walls to close up. During testing of WPS5 and WPS6, the cracks at the top of the walls became fully closed with the longitudinal reinforcement that had previously yielded in tension hidden in the cracks. Strain gauge readings indicated that the bars at those locations had already yielded in tension during early cycles of loading. At drifts of greater than 1%, damage was localized at the base of the walls and the walls were rocking on their foundation blocks. Significant spalling of concrete was observed at all wall corners of the thinner test specimens (WPS3, WPS5, WPS7, and WPS9) (refer to Fig. 5). The thicker test specimens ACI Structural Journal/March-April 2014
Fig. 3—Typical wall instrumentation.
Fig. 2—Test setup. having axial load (WPS2, WPS8, and WPS10) experienced relatively limited spalling that was located at the bottom wall corners only. Spalling of concrete during testing of the coupling beam specimens (WSS1 and WSS2) was limited to the top wall corners only. The spalling of concrete in the compression zones, which was later exacerbated by excessive compression at the wall toes as the displacement demand increased, was initiated by buckling of longitudinal reinforcement. Buckling of longitudinal reinforcement was observed during all tests except for those specimens subjected to no axial load and being 230 mm (9 in.) thick (WPS4 and WPS6). These two specimens also exhibited no spalling of concrete (refer to Fig. 5 for the response of WPS4). Reinforcement grade had no discernible influence on reinforcing bar buckling and concrete spalling.
ACI Structural Journal/March-April 2014
Fig. 4—Typical components of the lateral displacement of wall. RESULTS AND DISCUSSIONS The lateral-force-carrying capacity of the test specimens was limited by their flexural strength, with the experimentally obtained peak strengths and corresponding drift values presented in Table 3. The test specimens with continuous longitudinal reinforcing bars developed 99 to 108% of their calculated flexural strength and the test specimens with spliced longitudinal reinforcing bars developed 97 to 102% of their computed flexural strength. The calculated flexural strengths were determined following routine section analysis procedures and by considering all the reinforcement within the cross section of the test specimens to contribute to the strength. The calculations used experimentally determined reinforcing bar yield strengths and concrete compressive strengths. The strengths of the test specimens with 283
Fig. 5—Typical state of test specimens at end of test. lap-spliced longitudinal reinforcing bars were computed assuming that the splices would develop the yield strength of the spliced bars. The strength of the test specimens degraded quickly after low drift cycles, as shown in Fig. 6, due to rupture of the longitudinal reinforcing bars located adjacent to the wall boundaries. For test specimens subjected to applied axial compressive load, the lateral-force-carrying capacity of the test specimens was not completely lost after the longitudinal reinforcing bars had ruptured, due to the flexural strength attributable to the applied axial load. However, these test 284
specimens had to maintain their axial-load-carrying capacity to retain the residual strength to higher drift demands. For example, because of loss of axial-load-carrying capacity, WPS9 could not achieve the same level of ductility and residual strength as was exhibited by all other wall pier specimens. Slipping of the spliced bars along the provided splice length improved the performance of test specimens having spliced longitudinal bars, especially those specimens that were not subjected to compressive axial load (refer to Fig. 6).
ACI Structural Journal/March-April 2014
Table 3—Measured and calculated strengths of test specimens Test specimen
VTest, kN
Drift at VTest, %
Vn,SF*, kN
Vn,S†, kN
Vn,F‡, kN
VTest/Vn,SF
VTest/Vn,S
VTest/Vn,F
WPS1
162
0.96
616
395
151
0.26
0.41
1.07
WPS2
174
0.66
647
513
167
0.27
0.34
1.04
WPS3
159
0.43
404
389
147
0.39
0.41
1.08
WPS4
149
0.20
404
455
148
0.37
0.33
1.01
WPS5
199
0.35
536
424
195
0.37
0.47
1.02
WPS6
194
0.44
536
508
197
0.36
0.38
0.98
WPS7
231
0.36
662
391
233
0.35
0.59
0.99
WPS8
271
0.5
802
492
278
0.34
0.55
0.97
WPS9
260
0.36
740
478
259
0.35
0.54
1.00
WPS10
308
0.21
880
564
310
0.35
0.55
0.99
WSS1
160
0.09
361
320
149
0.44
0.50
1.07
WSS2
150
0.04
361
417
151
0.42
0.36
0.99
Average
0.36
0.45
1.02
Standard deviation
0.05
0.09
0.04
*
Nominal shear friction capacity according to ACI 318-11.
†
Nominal shear capacity according to ACI 318-11.
‡
Nominal flexural capacity according to ACI 318-11 and assuming splices would develop yield strength of spliced bars.
Note: 1 kN = 0.225 kip.
The boundary and distributed longitudinal reinforcement provided to the walls were below the limits that are specified by both ACI 318 and NZS 3101 (refer to Table 2). ACI 318 stipulates the minimum longitudinal reinforcement ratio for earthquake force-resisting RC walls to be 0.25% if Vu exceeds 0.83Acv√fc′ (MPa) (10Acv√fc′ [psi]), and the tested walls satisfy this condition. In addition to the minimum ratio, ACI 318 requires at least two 16 mm (5/8 in.) diameter bars to be provided around all openings. The requirement of NZS 3101 is dependent on concrete strength and reinforcement yield strength. For the walls tested, the minimum required reinforcement ratio was, on average, 0.3%. NZS 3101 also requires additional reinforcement with yield strength equal to or greater than 600 N/mm (3426 lb/in.) of wall thickness to be provided around all openings. This requirement is approximately equivalent to two 12 mm (1/2 in.) and three 12 mm (1/2 in.) diameter Grade 500 bars for the 150 and 230 mm (6 and 9 in.) thick walls, respectively. Due to the additional two 12 mm (1/2 in.) diameter boundary reinforcing bars, the wall pier specimens that were tested in double bending (WPS3 to WPS10) achieved more strength and energy dissipation when compared to the wall pier specimens having no boundary reinforcement (WPS1 and WPS2). However, even with these additional bars, the quantity of longitudinal reinforcement provided resulted in a level of applied shear force that was insufficient to induce a shear mode of failure. Similar findings were previously reported in studies12,13 conducted on the behavior of existing RC walls detailed following pre-1970s’ detailing techniques, but having relatively more longitudinal reinforcement than used in the test specimens discussed herein.
ACI Structural Journal/March-April 2014
Flexural failure is the principal failure mode for existing RC walls constructed in New Zealand before the amendment of NZSS 9514 in 1955, mainly because in NZSS 95 the contribution of concrete to the shear strength of RC structural components is underestimated.23 Consequently, in the absence of boundary frame elements, walls of this era are generally expected to have sufficient shear strength to develop flexural overstrength. However, due to the provision of a low quantity of reinforcement and a lack of transverse confinement reinforcement, this type of wall has low flexural strength and exhibits a low ductility capacity. The test specimens dissipated a significant amount of energy through yielding of longitudinal reinforcing bars during cycles to drifts of less than 1%. However, the energy dissipation capacity of the test specimens reduced considerably as the drift demands increased, due to a lack of any dissipative mechanism except sliding friction at the wall-foundation block interfaces. The bar slip that occurred over the splice lengths did not significantly alter the energy dissipation capacity for those test specimens that incorporated lap splices. After 1% drift demand, the stiffness of the test specimens had typically degraded significantly to less than 10% of the initial stiffnesses, with continuing degradation until reaching approximately 1% of the initial stiffnesses at drift demands in excess of 2.5%. The rapid and significant loss of stiffness observed during testing indicates that, after large earthquakes, this type of wall becomes too soft to develop significant ongoing resistance and therefore will undergo larger displacements when subjected to small lateral forces associated with either a long-duration event or aftershocks having significant intensity at the site.
285
Fig. 6—Lateral-force, top-displacement responses of test specimens. COMPARISON OF RESULTS WITH ASCE 41-06 PROVISIONS Section C6.7.1 of ASCE/SEI 41-06,16 “Seismic Rehabilitation of Existing Buildings,” categorizes the response of RC walls based on aspect ratio. According to ASCE/SEI 41-06, walls with an aspect ratio of less than 1.5 are considered to be squat and their response is assumed to be controlled by shear. Conversely, walls with an aspect ratio of greater than 3 are assumed to be slender and their response is considered to be controlled by flexure. The response of walls with intermediate aspect ratios is considered to be controlled by both flexure and shear. As the walls presented herein had
286
aspect ratios ranging between 1.35 and 1.85, the response of the walls was supposed to be controlled by shear and by both shear and flexure, respectively, according to ASCE/SEI 41-06. Wall strength ASCE/SEI 41-06 refers to Chapter 21 of ACI 318-11 to determine the shear strength of existing walls. The nominal shear strength of walls is given in ACI 318-11, Eq. (21-7), as
Vn = Acv (a c fc′ + ρt f yt )
(1)
ACI Structural Journal/March-April 2014
This nominal shear strength is limited to 0.083Acv√fc′ (MPa) (Acv√fc′ [psi]). The coefficient αc is 0.25 for hw/lw ≤ 1.5, is 0.17 for hw/lw ≥ 2.0, and varies linearly between 0.25 and 0.17 for intermediate hw/lw values. When determining the yield and nominal shear strengths, ASCE/SEI 41-06 limits the strength of the transverse reinforcing bars fyt to the specified yield strength. The nominal shear-friction strength of walls across a sliding plane perpendicular to shear-friction reinforcing bars is given by ACI 318-11, Eq. (11-25), as
Vn = (Avf fy + N*)μ (2)
The nominal shear-friction strength given in Eq. (2) is limited to the smaller of 0.2Ac fc′ (N) (0.2Ac fc′ [lb]) and 5.5Ac (N) (800Ac [lb]). For the flexural strength of existing walls, ASCE/SEI 41-06 refers to the basic principles outlined in Chapter 10 of ACI 318-11, but requires the use of expected yield strengths of the longitudinal reinforcing bars instead of specified minimum yield strengths. When determining flexural yield strengths of walls with no boundary members, ASCE SEI 41-06 requires considering only the longitudinal reinforcing bars within the outer 25% of the wall cross section, but when determining the nominal flexural strengths, the contributions of all longitudinal reinforcing bars within the wall component cross section need to be considered. As shown in Table 3, the lateral-force-carrying capacity of the test specimens was limited by their flexural strength and, thus, categorizing the response of RC walls by ASCE/SEI 41-06 based on aspect ratio only is found to be misleading. The results also show that the “plane sections remain plane” hypothesis, which was used during the calculation of the flexural strengths, provided strengths that agree well with those determined experimentally, even for squat walls with an aspect ratio of 1.35. In addition, prior to the peak strength of the test specimens being attained, the strain gauge readings from longitudinal reinforcement of most test specimens generally varied linearly across the section. Required length of splices Current provisions for the required length of splices are based on studies conducted to determine bond-slip relationships between isolated reinforcing bars and the surrounding concrete. Transfer of force between starter and main reinforcing bars over the provided splice length involves a different force transfer mechanism than that occurring between an isolated reinforcing bar and the surrounding concrete, but it is widely accepted that the required length of splices is the same as the required development lengths of single embedded reinforcing bars.24 Accordingly, ASCE/ SEI 41-06 refers to the provisions for required length of tension splices of ACI 318-11, which are based on requirement for tension development length. ASCE/SEI 41-06 specifies that the required splice length of plain round reinforcing bars to be taken as twice that required for deformed reinforcing bars. According to ACI 318-11, Eq. (12-1), the required length of Class B deformed reinforcing bar splices
ACI Structural Journal/March-April 2014
Table 4—Ratios of maximum stress to yield stress for spliced bars Test specimen
φ10 reinforcing bars *
φ12 reinforcing bars
fs/fy
fs/fy
†
fs/fy*
fs/fy†
WPS5
0.51
0.80
0.44
0.73
WPS6
0.51
0.80
0.44
0.73
WPS7
0.51
0.80
0.77
1.00
WPS8
0.51
0.80
0.77
1.00
*
Ratio according to Eq. (5).
†
Ratio according to Eq. (6).
subjected to tension, which is required to be at least 300 mm (12 in.), is
fy ld = 1.3 1.1l fc′
ψt ⋅ ψe ⋅ ψs ⋅ l db cb + K tr d b
(3)
The length of deformed reinforcing bar splices subjected to compression can be determined from Section 12.16.1 of ACI 318-11 as
f y ≤ 420 0.071 f y db , ld = (0.13 f y − 24)db , f y > 420
(4)
This development length is required to be at least 300 mm (12 in.) and is required to be increased by one-third for a concrete compressive strength of less than 21 MPa (3.0 ksi). When the splice length of reinforcing bars within an existing wall is found to be inadequate, ASCE/SEI 41-06 stipulates the maximum stress that can be developed within the spliced bars to be determined as follows
fs = (lb/ld)fy ≤ fy (5)
Ratios of the maximum stresses, which can be developed by spliced plain round bars according to Eq. (5) to the corresponding yield strengths of the spliced bars, are presented in Table 4. Although the provided splice lengths were significantly less than those required by Eq. (5) to develop the yield strength of the spliced bars, the walls were able to develop 97 to 102% of their computed flexural strength (refer to Table 3), which was determined assuming that the lap splices would develop the yield strength of the spliced bars. Peak strengths reached by the test specimens with lap-spliced reinforcing bars were underestimated by an average of 41% (refer to Table 5) by predictions made using Eq. (5). Similar findings were previously reported in studies24,25 undertaken to investigate the behavior of columns with short lap splices. The lateral force capacity of columns investigated by Cho and Pincheira24 was underestimated using Eq. (5) by an average of 28%. Similarly, columns tested by Melek and Wallace25 were reported to have achieved 97 to 103% 287
Table 5—Measured and calculated strengths of test specimens with spliced longitudinal reinforcement Test specimen
VTest, kN
Vn,F-A/S*, kN
Vn,F-PS†, kN
Vn,F‡, kN
VTest/Vn,F-A/S
VTest/Vn,F-PS
VTest/Vn,F
WPS5
199
91
129
195
2.14
1.51
1.02
WPS6
194
91
144
197
2.16
1.37
0.98
WPS7
231
181
208
233
1.29
1.12
0.99
WPS8
271
234
262
278
1.19
1.06
0.97
Average
1.70
1.27
0.99
Standard deviation
0.46
0.18
0.02
†
Nominal flexural capacity according to ASCE/SEI 41-06.
‡
Nominal flexural capacity according to proposed supplement26 to ASCE 41-06.
*
Nominal flexural capacity according to ACI 318-11 and assuming splices would develop yield strength of spliced bars.
Note: 1 kN = 0.225 kip.
Fig. 7—Normalized maximum bond stresses that developed between spliced bars and surrounding concrete. of their yield strengths, which were calculated assuming that the lap splices would develop the yield strengths of the spliced bars, but the provided splice lengths were approximately 67% of that required by ASCE/SEI 41-06. Because Eq. (5) was found to be excessively conservative, the provided splice lengths used in the study reported herein were also compared with those implied by a proposed supplement26 to ASCE/SEI 41-06. The proposed equation, which is a modified version of Eq. (5) and based on the work of Cho and Pincheira,24 is
l fs = 1.25 b ld
u=
f s db 4ld
(7)
Using Eq. (3) and (7), the ASCE/SEI 41-06 implied maximum bond stress that was expected to develop between a plain round bar subjected to tension and the surrounding concrete was determined as
0.67
fy ≤ fy
(6)
In most cases, the provided splice lengths were shorter than required by Eq. (6) (refer to Table 4) to develop the full strength of the spliced bars. Predictions made using Eq. (6) underestimated the peak strengths by an average of 21%. As discussed previously, both Eq. (5) and Eq. (6) predict slip to occur at force levels less than the yield strength of the spliced bars. However, during testing, all of the monitored splices developed tensile stresses that were greater than the experimentally determined yield strength of the spliced bars.
288
The maximum stresses that were measured during testing were converted to maximum bond stresses as follows
u=
1 1 1.1 fc′ cb + K tr 2 4 ψ t ψ e ψ s l db
(8)
Maximum bond stresses developed between the spliced bars and the surrounding concrete are compared in Fig. 7, with maximum bond stress values implied by ASCE/SEI 41-06 and the proposed supplement to ASCE/SEI 41-06. The ASCE/SEI 41-06 implied average maximum bond stress of 0.29√fc′ (MPa) (3.49√fc′ [psi]) is significantly less than the measured average bond stress of 0.57√fc′ (MPa) (7.95√fc′ [psi]). The average maximum bond strength implied by the proposed supplement to ASCE/SEI 41-06, ACI Structural Journal/March-April 2014
which was dependent on the provided splice lengths, was 0.46√fc′ (MPa) (5.54√fc′ [psi]). The performance of the splices reported herein was better than had been expected, principally because of the excessively conservative requirement of current design codes19,20 and assessment recommendations16 for the required splice length of plain round bars. For example, ACI 318 requires the length of splices to be increased by one-third if all of the longitudinal bars are spliced at the same location. This requirement is not based on strength criteria,27 but is primarily intended to encourage designers to stagger bar splices. This requirement alone results in underestimating the capacity of spliced reinforcing bars in existing structures by 23%. In some cases encountered herein, the compression splice length requirements of ACI 318 governed the required length of splices. The compression splice length requirements of ACI 318 have remained essentially the same since the 1963 version of the code and appear to be conservative. Required tension splice lengths are expected to govern the required length of splices, as the formation of transverse tension cracks around a splice that is subjected to tension reduces bond strength and, thus, increases the length that is required to allow the splice to transfer the desired magnitude of stress. Chun et al.28 have recently reported a better performance of compression splices than tension splices, which was principally attributed to end bearing of reinforcing bars when subjected to compression. Similarly, Cairns29 has found the equations contained in ACI 318-11 to be conservative, and has proposed that the length of compression splice for deformed bars be taken as 30% shorter than that required by the equations. In addition to the aforementioned excessively conservative requirements of ACI 318 for deformed bars, ASCE 41-06 recommends taking the required splice length of plain round bars as twice that required for deformed bars, which results in significantly underestimating the capacity of plain round splices located in existing structures. The good performance of the splices reported herein was not considered to be influenced by the thick concrete cover that the splices were provided with. ACI 318 employs parameters for concrete cover/reinforcement spacing cb and transverse reinforcement index Ktr to account for the confinement term (cb + Ktr)/db, and in ACI 318, it is assumed that an increase in the value of this confinement term, above the maximum allowed 2.5, is not likely to increase anchorage capacity and is not likely to prevent a pullout failure, which is a failure mode typically exhibited by plain round bars. Similarly, Eligehausen et al.30 reported that an increase in concrete cover, reinforcement spacing, or transverse confinement can prevent concrete splitting failures only, which is a failure mode typically sustained when using spliced deformed bars. The maximum allowed value of (cb + Ktr)/db = 2.5 was employed when calculating the ASCE/SEI 41-06 implied bond strength of the plain round bars discussed herein. CONCLUSIONS Twelve test specimens replicated from wall segments of an existing building were experimentally tested to assess the ACI Structural Journal/March-April 2014
seismic behavior of RC walls constructed before the introduction of seismic design requirements in the New Zealand Standard Model Building By-law.14 The results of the experimental tests were evaluated and compared with current assessment provisions. Based on the study presented herein, the following conclusions are drawn: 1. The lateral-force-carrying capacity of lightly reinforced existing walls is limited by their flexural strength. Owing to the low quantity of reinforcing bars provided, yielding of the longitudinal reinforcing bars dictates the strength of this wall type. 2. The strength and the stiffness of this type of wall degrade rapidly and significantly. The walls have limited energy dissipation capacity, principally due to the provision of few longitudinal reinforcing bars. In addition, the walls suffer from a lack of transverse confinement reinforcement to contain concrete in compression zones and to prevent longitudinal reinforcing bars from buckling. 3. During testing, the wall pier specimens having no axial load exhibited cracks that were wide during low-level drift cycles, but the cracks, which were located near the supports, closed up and appeared inconspicuous after the tests were completed, with longitudinal reinforcement that had previously yielded in tension hidden in the cracks. This type of crack could easily be overlooked and the walls may appear intact during post-earthquake inspections, even if the stiffness and the strength of the walls deteriorated significantly. 4. From peak stresses measured during testing, it was shown that the provisions contained in ASCE/SEI 41-06 significantly underestimate the maximum stresses that can be developed by plain round reinforcing bar lap splices. The relatively recent recommendations of a proposed supplement to ASCE/SEI 41-06 also underestimate the maximum stresses that can be developed, but to a lesser extent. 5. During testing, the lap splices were able to develop bond stresses that were significantly higher than the maximum possible bond stresses implied by ASCE/SEI 41-06. Further research is recommended, as the provisions of ASCE/SEI 41-06 for required splice lengths of plain round reinforcing bars are based on studies conducted for deformed bars. The provisions are excessively conservative and potentially lead to unnecessary or expensive seismic retrofitting solutions. The provisions also lead to the potential for overlooking the danger of existing walls failing in shear during an earthquake, before the actual strength of the tension splices is exceeded. ACKNOWLEDGMENTS
The authors would like to gratefully acknowledge the financial support provided by the New Zealand Foundation for Research, Science and Technology (FRST) through Grant UOAX0411.
AUTHOR BIOS
Adane Gebreyohaness is a Structural Engineer at Beca Limited in New Zealand. His research interests include the seismic assessment, strengthening, and design of reinforced concrete and steel structures. Charles Clifton is an Associate Professor at the University of Auckland, Auckland, New Zealand. His research interests include the performance of steel and composite steel/concrete buildings in severe earthquakes and severe fires.
289
John Butterworth is an Associate Professor at the University of Auckland. His research interests include nonlinear structural and solid mechanics; stability; buckling behavior of thin-walled sections; structural dynamics; earthquake engineering; base isolation using rolling, sliding, and rocking mechanisms; passive control of structure response (especially by energy dissipating joints); experimental dynamics; pounding of bridges and buildings; and assessment and retrofit of steel structures. ACI member Jason Ingham is an Associate Professor and Deputy Head (Research) of the Department of Civil and Environmental Engineering at the University of Auckland. His research interests include seismic assessment, retrofit and design of reinforced and prestressed concrete structures, and sustainable concrete technology.
Ab Ac Acv Al A t Avf cb
= = = = = = =
db = fc′ = fs = fult = fy = fyt = hw = Ktr = l = lb = ld = lw = M/Vlw = N* = u = Vn = VTest = Vu = λ = μ = ρl = ρt
=
ψe ψs ψt
= = =
NOTATION
area of boundary reinforcement area of concrete section resisting shear transfer shear area area of longitudinal reinforcing bar area of transverse reinforcing bar area of shear friction reinforcement smaller of: (a) distance from center of bar or wire to nearest concrete surface; and (b) one-half the center-to-center spacing of bars or wires being developed nominal bar diameter specified compressive strength of concrete splice strength ultimate strength of reinforcement yield strength of reinforcement yield strength of shear reinforcement height of wall transverse reinforcement index length of splice provided splice length required splice length according to ACI 318-11 horizontal length of wall shear span-to-depth ratio design axial load bond stress nominal shear strength peak strength of test specimen factored shear force modification factor related to density of concrete coefficient of friction ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement modification factor based on reinforcement coating modification factor based on reinforcement size modification factor based on reinforcement location
REFERENCES
1. NZSEE, “Assessment and Improvement of the Structural Performance of Buildings in Earthquake: Recommendations of a NZSEE Study Group on Earthquake Risk Buildings,” New Zealand Society for Earthquake Engineering Inc., Wellington, New Zealand, 2012, 343 pp. 2. FEMA, “Pre-standard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 356),” Federal Emergency Management Agency, Washington, DC, 2000, 519 pp. 3. Wood, S. L.; Wight, J. K.; and Moehle, J. P., “The 1985 Chile Earthquake—Observations on Earthquake-Resistant Construction in Vina Del Mar,” Structural Research Series No. 532, University of Illinois at Urbana-Champaign, Champaign, IL, 1987, 192 pp. 4. Sezen, H.; Whittaker, A. S.; Elwood, K. J.; and Mosalam, K. M., “Performance of Reinforced Concrete Buildings during the August 17, 1999 Kocaeli, Turkey Earthquake, and Seismic Design and Construction Practise in Turkey,” Engineering Structures, V. 25, No. 1, 2003, pp. 103-114. 5. EERI, “EERI Special Earthquake Report: The Mw 8.8 Chile Earthquake of February 27, 2010,” Earthquake Engineering Research Institute, Oakland, CA, 2010, 20 pp. 6. Kam, W. Y., and Pampanin, S., “The Seismic Performance of RC Buildings in the 22 February 2011 Christchurch Earthquake,” Structural Concrete, V. 12, No. 4, 2011, pp. 223-233.
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7. New Zealand Police, “List of Deceased,” http://www.police.govt.nz/ list-deceased. (last accessed Jan. 12, 2012) 8. IPENZ, “Christchurch Earthquake—An Overview,” http://www.ipenz. org.nz/ipenz/forms/pdfs/ChChFactSheets-Overview.pdf. (last accessed Aug. 25, 2011) 9. Beca Carter Hollings & Ferner Ltd (Beca), “Investigation into the Collapse of the Pyne Gould Corporation Building on 22nd February 2011,” Prepared for Department of Building and Housing (DBH), 2011, 51 pp. 10. Orakcal, K.; Massone, L. M.; and Wallace, J. W., “Shear Strength of Lightly Reinforced Wall Piers and Spandrels,” ACI Structural Journal, V. 106, No. 4, July-Aug. 2009, pp. 455-465. 11. Kuang, J. S., and Ho, Y. B., “Seismic Behavior and Ductility of Squat Reinforced Concrete Shear Walls with Nonseismic Detailing,” ACI Structural Journal, V. 105, No. 2, Mar.-Apr. 2008, pp. 225-231. 12. Ireland, M.; Pampanin, S.; and Bull, D. K., “Experimental Investigations of a Selective Weakening Approach for the Seismic Retrofit of RC Structural Walls,” NZSEE Conference, Palmerston North, New Zealand, Mar. 30-Apr. 1, 2007, 8 pp. 13. Greifenhagen, C., and Lestuzzi, P., “Static Cyclic Tests on Lightly Reinforced Concrete Shear Walls,” Engineering Structures, V. 27, No. 11, 2005, pp. 1703-1712. 14. NZ Standards Institute, “NZSS 95: New Zealand Standard Model Building By-Law, Sections I to X,” NZ Standards Institute, Wellington, New Zealand, 1935, 39 pp. 15. Gebreyohaness, A. S.; Clifton, G. C.; and Butterworth, J. W., “Assessment of Soil-Foundation-Structure Interaction Effects on the Seismic Performance of an Old Dual Wall-Frame Building,” 14th ECEE Conference, Ohrid, Macedonia, Aug. 30-Sept. 4, 2010, 8 pp. 16. ASCE/SEI 41, “Seismic Rehabilitation of Existing Buildings,” American Society of Civil Engineers, Reston, VA, 2007, 428 pp. 17. Oyarzo-Vera, C.; McVerry, G.; and Ingham, J. M., “Seismic Zonation and Default Suite of Ground-Motion Records for Time-History Analysis in the North Island of New Zealand,” Earthquake Spectra, V. 28, No. 2, 2012, pp. 1-22. 18. DBH, “Building Act 2004,” Department of Building and Housing, Wellington, New Zealand, 2004, 353 pp. 19. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp. 20. NZS 3101:2006, “Concrete Structures Standard: Part 1—The Design of Concrete Structures,” Standards New Zealand, Wellington, New Zealand, 2006, 696 pp. 21. Paulay, T., “Seismic Response of Structural Walls: Recent Developments,” Canadian Journal of Civil Engineering, V. 28, No. 6, 2001, pp. 922-937. 22. ACI Innovation Task Group 1 and Collaborators, “Acceptance Criteria for Moment Frames Based on Structural Testing (ACI T1.1-01),” American Concrete Institute, Farmington Hills, MI, 2001, 10 pp. 23. Brunsdon, D. R., “Seismic Performance Characteristics of Buildings Constructed between 1936 and 1975,” University of Canterbury, Christchurch, New Zealand, 1984. 24. Cho, J. Y., and Pincheira, J. A., “Inelastic Analysis of Reinforced Concrete Columns with Short Lap Splices Subjected to Reversed Cyclic Loads,” ACI Structural Journal, V. 103, No. 2, Mar.-Apr. 2006, pp. 280-290. 25. Melek, M., and Wallace, J. W., “Cyclic Behavior of Columns with Short Lap Splices,” ACI Structural Journal, V. 101, No. 6, Nov.-Dec. 2004, pp. 802-811. 26. Elwood, K. J.; Matamoros, A. B.; Wallace, J. W.; Lehman, D. E.; Heintz, J. A.; Mitchell, A. D.; Moore, M. A.; Valley, M. T.; Lowes, L. N.; Comartin, C. D.; and Moehle, J. P., “Update to ASCE/SEI 41 Concrete Provisions,” Earthquake Spectra, V. 23, No. 3, 2007, pp. 493-523. 27. ACI Committee 408, “Bond and Development of Straight Reinforcement in Tension (ACI 408R-03),” American Concrete Institute, Farmington Hills, MI, 2003, 49 pp. 28. Chun, S. C.; Lee, S. H.; and Oh, B., “Compression Lap Splice in Unconfined Concrete of 40 and 60 MPa (5800 and 8700 psi) Compressive Strengths,” ACI Structural Journal, V. 107, No. 2, Mar.-Apr. 2010, pp. 170-178. 29. Cairns, J., “Strength of Compression Splices: A Reevaluation of Test Data,” ACI Journal, V. 82, No. 4, July-Aug. 1985, pp. 510-516. 30. Eligehausen, R.; Popov, E. P.; and Bertero, V. V., “Local Bond Stress-Slip Relationships of Deformed Bars under Generalized Excitations,” University of California, Berkeley, Berkeley, CA, 1983, 180 pp.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S25
Behavior of Epoxy-Injected Diagonally Cracked Full-Scale Reinforced Concrete Girders by Matthew T. Smith, Daniel A. Howell, Mary Ann T. Triska, and Christopher Higgins Many cast-in place reinforced concrete deck-girder (RCDG) bridges in the national inventory contain diagonal cracks typically associated with shear-moment interaction. Many transportation agencies use epoxy injection as a prophylactic to seal cracks. The shear-dominated performance of girders treated with epoxy injection is not well understood and the existing data regarding performance of members injected with epoxy have been gathered from reduced-scale test specimens. To provide new data on the shear performance of girders with epoxy-injected diagonal cracks, five full-scale RCDG specimens were constructed to reflect 1950s proportions and details. The specimens were loaded to produce diagonal cracks, injected with epoxy under varying degrees of axial tension and service loading, and tested to failure. The test data indicated that epoxy injection resulted in minimal increased shear capacity. However, the epoxy-injected specimens exhibited increased load magnitudes prior to crack re-initiation and reduced stirrup stresses at serviceability levels compared to the cracked condition prior to repair. Keywords: bridges; cracking; epoxy; full-scale testing; reinforced concrete; repair; shear.
INTRODUCTION AND BACKGROUND Large numbers of cast-in-place reinforced concrete deckgirder (RCDG) bridges remain in the national inventory and are reaching the end of their originally intended design lives. Many of these bridges are exhibiting varying degrees of diagonal-tension cracking in the girders and supporting bent caps. Diagonal cracks can be attributed to many sources, including insufficient reinforcing and poor flexural detailing, increasing service load magnitude and volume, and temperature or shrinkage strains. These cracks are generally of concern to engineers due to the nonductile nature of shear failure and limited reserve shear strength. Further, diagonal cracks can expose the embedded reinforcing steel to chlorides, moisture, and oxygen, which promote corrosion, thereby weakening the structure. Several methods exist that can seal diagonal cracks and possibly restore or increase capacity, such as externally bonded steel and carbon fiber materials, applied ferrocement, cement grouting, and epoxy injection. Epoxy, in particular, has been widely used for the rehabilitation of concrete structures. The first record of epoxy material testing for highway applications was performed by the California Division of Highways Materials and Research Department (Rooney 1963). The application was focused on highway maintenance patching of damaged roadways and securing reflective traffic markers. An earlier study using small-sized plain concrete prisms demonstrated that the bond strength of epoxy permitted rupture in the concrete and not in the adhe-
ACI Structural Journal/March-April 2014
sive bond layer irrespective of the loading conditions (shear, flexure, or tension) (Tremper 1960). As epoxy materials became more widely used, researchers began to investigate the use of epoxy injection for reinforced concrete members. Early tests to evaluate the performance of epoxy-injected reinforced concrete beams were performed by Chung (1975) with 125 x 200 mm (5 x 8 in.) beam specimens on a clear span of 2754 mm (9 ft). Longitudinal and transverse reinforcement were provided, and each specimen was first loaded to failure and then all major cracks exceeding 0.08 mm (0.003 in.) were injected with epoxy resin. Chung observed that epoxy restored the flexural capacity of the failed specimens. Another study conducted by Popov and Bertero (1975) examined the behavior of full-scale and halfscale cantilever reinforced concrete beam-column specimens injected with epoxy and exposed to reversed cyclic loading. The steel detailing and member proportions were typical of large-sized, short-span cantilevers and beam-column subassemblages for buildings. Epoxy injection improved the original shear strength of the specimens, but the specimens exhibited reduced overall stiffness following repair when compared with the uncracked condition. At locations where severe reinforcing bar-concrete bond degradation occurred, the epoxy did not perform as well. Additional research by Chung (1981) noted that epoxy injection of small 200 x 300 x 2000 mm (7.9 x 11.8 x 78.7 in.) reinforced concrete beams was not an effective means to restore or improve reinforcing bar-concrete bond strength. Basunbul et al. (1990) compared several flexural repair methods for reinforced concrete beams, including epoxy injection. Nine epoxy-injected specimens measuring 150 x 150 mm (5.9 x 5.9 in.) in cross section and 1250 mm (49.2 in.) in length, with longitudinal and transverse reinforcement, were loaded to induce varying degrees of flexural damage. Vertical cracks were injected with epoxy resin and allowed to cure before each specimen was loaded to failure. The loads required to reinitiate cracking were observed to be approximately 20% higher for the injected specimens compared to the original member response. In more recent years, the effects of environment and fatigue have been included in studies of epoxy-injected specimens. Abu-Tair et al. (1991) investigated concrete beams reinforced with transverse and longitudinal steel measuring 205 x 140 mm (8 x 5.5 in.) in cross section with a 2300 mm ACI Structural Journal, Vol. 111, No. 2, March-April 2014. MS No. S-2012-083, doi:10.14359.51686521, was received March 6, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
291
(90.6 in.) span. Seven specimens were loaded to failure in flexure and then injected with epoxy resin. Several of the specimens were loaded monotonically to failure, while others were fatigue loaded at varying magnitudes. Additionally, three of the specimens (two monotonically and one fatigue-loaded) were soaked in 38°C (100°F) water to investigate the effect of water absorption on durability and post-repair specimen performance. The results of the study indicated that epoxy injection restored the original strength and stiffness of the beams regardless of the loading conditions, while the four months of water immersion had insignificant effects on specimen durability, strength, or stiffness. The preceding limited research on the structural performance of epoxy-injected reinforced concrete specimens has focused on flexural response of reduced-sized specimens. No data are available for the shear response of epoxy-injected reinforced concrete girders, and few researchers have investigated loading conditions on the curing and bonding of epoxy resin. Furthermore, reduced-sized specimens may not accurately replicate strain fields and behavior of large reinforced concrete members. Other important issues to consider are in-service loading responses and localized behavioral effects, incorporation of service-induced diagonal cracks, and the effects of temperature and shrinkage strains on epoxy-injected member performance. RESEARCH SIGNIFICANCE Epoxy injection is widely used for remediation of cracked RC bridges and other structures, but the efficacy of the method on shear performance has not been established. An experimental program was conducted using realistic fullscale bridge girders constructed with mid-twentieth century design methods, details, and materials. Diagonal cracks were produced under quasi-static loading. The girders were then epoxy-injected and tested under different loading conditions to determine the effects of epoxy injection on structural performance. Research results improve the understanding of the behavior of epoxy-injected diagonally cracked RC girders and help engineers make better decisions regarding rehabilitation alternatives.
Fig. 1—Specimen reinforcing details and typical instrumentation placement.
EXPERIMENTAL PROGRAM Test specimens Five laboratory specimens were constructed and tested to characterize the behavior and capacity of 1950s vintage reinforced concrete deck girders with diagonal cracks after being injected with epoxy resin. Previous work by Higgins et al. (2004) identified standard details, materials, and proportions used in 1950s vintage bridge construction. Specimens in the current study used an inverted-T (IT) configuration to place the deck in flexural tension. This arrangement is representative of negative moment in high-shear locations near continuous supports such as piers and bent caps. Each specimen had the following geometry: 1219 mm (48 in.) overall height, a stem width of 356 mm (14 in.), and a flange of 152 mm (6 in.) thick by 914 mm (36 in.) wide. Member proportions and reinforcing steel are illustrated in Fig. 1. The
292
Fig. 2—Specimen naming convention. specimen naming convention used in the study is illustrated in Fig. 2. Longitudinal reinforcing steel consisted of ASTM A615/ A615M-05a Grade 420 No. 36 (Grade 60, No. 11) bars, while transverse reinforcement consisted of Grade 300 No. 13 (Gr. 40, No. 4). Intermediate grade steel, with a yield stress of 300 MPa (43.5 ksi), was typically used in 1950s construction. However, this grade is not readily available for large-diameter reinforcing bars. Therefore, Grade 240 (Grade 60) flexural bars were used but the area was reduced ACI Structural Journal/March-April 2014
Table 1—Concrete and steel material properties Reinforcing steel Concrete Specimen
fc′ at failure, MPa (psi)
No. 13, Grade 300 fct at initial loading, MPa (psi)
28.5 (4130)
3.2 (460) at 28-day
2-EC
36.2 (5250)
2.8 (410)
3-ED
28.3 (4104)
2.6 (377)
4-EL
29.5 (4279)
2.6 (377)
5-EA
35.4 (5141)
2.8 (410)
1-C
No. 36, Grade 420
fy, MPa (ksi)
fu, MPa (ksi)
fy, MPa (ksi)
fu, MPa (ksi)
350 (50.7)
544 (78.9)
477 (69.2)
712 (103)
492 (71.4)
741 (107)
484 (70.2)
728 (106)
473 (68.6)
694 (101)
492 (71.3)
741 (108)
357 (51.8)
570 (82.7)
Note: Values are for failure test unless otherwise indicated.
to produce the same tension resultant as the original designs that used Grade 300 (Grade 40) steel. This results in a smaller area of dowel steel in the specimens compared to the original designs. Tension tests were performed according to ASTM E8-04 to determine the reinforcing steel properties, which are summarized in Table 1. Concrete was provided by a local ready-mixed concrete supplier. The concrete mixture design was based on 1950s AASHO “Class A” concrete (Higgins et al. 2003). Specified compressive strength was 21 MPa (3000 psi), which is comparable to the specified design strength in the original 1950s bridges. Actual concrete compressive strengths were determined from 152 x 305 mm (6 x 12 in.) cylinders tested for 28-day and day-of-test strengths in accordance with ASTM C39M/C 39M-05 and ASTM C617-05. Day-of-test concrete cylinder strengths for each specimen are shown in Table 1. Split cylinder tests in accordance with ASTM C496/ C496M-04e1 were conducted the same day each specimen was precracked, as reported in Table 1. Instrumentation Internal and external sensors were positioned on the specimens to record the local and global member responses. Strain gauges were placed at midheight on the stirrups located within the critical shear section near midspan. Additional strain gauges were mounted to the flexural reinforcement at midspan in the flexural-tension region. Diagonal displacement sensors were placed at three locations along the shear span, as shown in Fig. 1. Midspan displacement and support settlements were also measured with additional displacement sensors. The actual centerline displacement presented in subsequent figures was calculated by removing the support deformations from the overall centerline deformation during each load cycle. Typical instrumentation is illustrated in Fig. 1. Testing methodology A simply-supported four-point loading configuration was used with a span length of 6604 mm (260 in.) from the centerline of supports. Force was applied from a hydraulic actuator at a quasi-static rate of 8.9 kN/s (2.0 kip/s) and was measured by a 2224 kN (500 kip) capacity load-cell. A spreader beam distributed the applied actuator force to 102 mm (4 in.) wide plates spaced 610 mm (24 in.) symmetriACI Structural Journal/March-April 2014
cally about the midspan. Load was applied in incremental steps followed by unloading, and repeating cycles until failure. Load magnitudes increased each cycle by 222 kN (50 kip). At each load peak, the load was reduced by 10% to minimize creep effects while visible cracks were marked and recorded. Three tests were performed on each specimen: precrack, baseline, and failure (with the exception of the control specimen, 1-C, which was loaded to failure in a single test). An initial loading sequence, or precrack test, was performed to produce diagonal cracks similar to those observed from field inspections of RCDG bridges and of sufficient size for epoxy injection. A target diagonal crack range of 0.65 to 1.25 mm (0.025 to 0.05 in.) was selected based on the earlier work of Higgins et al. (2004). When diagonal cracks reached a suitable size, the precrack loading cycle was terminated and a baseline test was performed to establish a reference for the specimens in the cracked condition for comparison to the post-injection response. The baseline test of the cracked specimens used the same loading sequence as the precrack test described previously. In the failure test, specimens were loaded to failure using the same load steps as the previous two tests. Injection and curing procedures The epoxy resin selected is a commercial, two-part, ultralow-viscosity liquid epoxy. The specified material tensile strength is 55.2 MPa (8000 psi). The surface sealant used is a commerical, two-part, 100% solids epoxy. These two materials are commonly used, are preapproved for use by transportation agencies in several states, and are representative of similar epoxy materials. All injection materials were provided by local suppliers. Additional installation guidance was provided by qualified contractors to establish a repair protocol that satisfied the installation recommendations of the manufacturer. The procedure that was established is summarized as follows. The concrete surfaces around the diagonal cracks were cleaned with a wire brush and vacuumed to remove loose particles and dirt. The crack perimeter was sealed with the surface epoxy and injection ports were surface-mounted every 356 mm (14 in.), or roughly equal to the width of the girder web. The surface epoxy cured for 24 hours before the injection process was initiated. To allow for the release of 293
Table 2—Specimen experimental summary Specimen
VINITIAL, kN (kip)
VAPP, kN (kip)
VDL, kN (kip)
VR2K, kN (kip)
VEXP/VR2K
Failure mode
1-C
N/A
902 (203)
16.9 (3.80)
919 (207)
952 (214)
0.97
Shear-compression
2-EC
723 (162)
983 (221)
20.3 (4.56)
1001 (225)
983 (221)
1.02
Shear-compression
3-ED
778 (175)
992 (223)
17.2 (3.87)
1009 (227)
965 (217)
1.05
Shear-compression
4-EL
778 (175)
1046 (235)
16.7 (3.75)
1063 (239)
947 (213)
1.12
Shear-compression
5-EA
778 (175)
1112 (250)
18.4 (4.14)
1130 (254)
943 (212)
1.20
Shear-compression
entrapped air, diagonal cracks were injected starting from the lowest port working up the crack. “Window” ports were placed on the backside of the beam to serve as a visual aid for assurance of epoxy penetration through the beam web. A specialized injection machine, commonly used by local contractors, was needed to mix the two-part liquid epoxy in the proportions recommended by the manufacturer and to deliver the mixture into the beam under low pressure. Each port was injected to a maximum pressure of 690 kPa (100 psi). As liquid epoxy began to seep from the next higher injection port, the lower port was capped and the injection nipple was moved to the next position. Near the top of each diagonal crack, the injection pressure climbed more quickly to 690 kPa (100 psi), and would take longer to dissipate, signaling that there was little available void space to pump additional resin. When the maximum pressure was maintained, the final port was capped. After injection, all specimens were allowed to cure for at least 7 days. A heated plastic enclosure was placed around the specimen to ensure that temperatures were maintained above 4.5°C (40°F), as recommended by the epoxy manufacturers. Thermocouples outfitted with data loggers were placed into a small void cast into the end of the specimens and on the exterior to record temperatures throughout the curing cycle. Specimen variables To simulate the effects of different in-service stress conditions, each specimen was subjected to a distinct loading scenario during the injection and curing phases. Specimen 2-EC was injected and cured with no applied loads other than specimen self-weight. Simulated superstructure dead load was applied to Specimen 3-ED before epoxy injection. A total load of 356 kN (80 kip) was applied to induce a service level dead load shear of 178 kN (40 kip). This shear magnitude is representative of an interior girder for a typical 1950s vintage three-span continuous RCDG bridge having 15.2 m (50 ft) spans and a uniform dead load of 23.3 kN/m/ girder (1.6 kip/ft/girder). Varying live load stress was applied to Specimen 4-EL in addition to the superstructure dead load. The live loading was representative of average shear magnitudes produced by ambient traffic and a fully loaded AASHTO Type 3-3 unit truck having five axles and a gross vehicular weight of 356 kN (80 kip) moving across the bridge described for Specimen 3-ED. Realistic shear distribution factors developed by Potisuk and Higgins (2007) from field studies were used 294
VEXP, kN (kip)
Mean
1.07
Coefficient of variation
0.08
to determine the live load magnitude. Force was applied at 0.3 Hz with an amplitude of 160 kN (36 kip) and a mean of 463 kN (104 kip). This loading amplitude represents the maximum girder shear caused by the dead load of the bridge and the truck live load with impact, as well as a minimum force resulting from hogging due to live load moving onto an adjacent span. The loading rate represents the truck traveling over the prototype bridge at approximately 33.8 kph (21 mph), which was controlled by the hydraulic loading system in the laboratory. The fifth specimen, 5-EA, had simulated locked-in drying and thermal shrinkage strains induced by applying a uniform tension load to the specimen. The axial load was applied to a level of approximately 890 kN (200 kip) before the initial precrack transverse loading cycles began. The axial load was held at a constant magnitude of 645 kN (145 kip) during the injection and curing phases, and then returned to 890 kN (200 kip) for the post-injection failure loading. For additional detail on the axial force application and loading protocol, refer to Smith (2007). EXPERIMENTAL RESULTS The performance of the epoxy-injected specimens was evaluated through the shear-midspan deflection and sheardiagonal displacement responses, flexural and shear reinforcement strains, and crack deformations. The data collected from the three phases of testing were compared to assess the local and global responses before and after epoxy injection. Results were also compared with an otherwise similar un-injected specimen. All of the specimens exhibited shear-compression failures and the applied shear at failure for each specimen is summarized in Table 2. Shear-midspan displacement response Applied shear-midspan displacement responses are shown in Fig. 3 and demonstrate the overall specimen behavior of the initial, baseline, and post-injection tests. The post-injection response of each injected specimen showed decreased residual deformations and greater stiffness during the first two or three load steps as compared to the baseline response. As the applied shear magnitudes increased, the specimens began to soften due to the development of new cracks, often adjacent to the repaired diagonal cracks. Specimens 3-ED and 4-EL were similar, especially in the service load range indicated in Fig. 3, and both had greater stiffness than Specimen 2-EC. ACI Structural Journal/March-April 2014
Fig. 3—Applied shear-midspan displacement response. shear decreased, the specimen shortened along the axis of the axial loading apparatus and the axial tension increased again. Like Specimen 4-EL, Specimen 5-EA had decreased residual deformations for many of the load cycles and did not begin to soften until near failure.
Fig. 4—Applied shear-axial load variability of Specimen 5-EA. The axially loaded specimen exhibited a unique shear-midspan displacement response. The curve has a slender S-shape resulting from the specimen stiffening and then softening during each load cycle. The axial load as a function of the applied shear for Specimen 5-EA is displayed in Fig. 4. As the applied shear increased, the specimen length increased at the level of the axial apparatus, thereby reducing the hydraulic pressure in the axial load actuators, and thus reducing the externally applied axial tension. As the applied ACI Structural Journal/March-April 2014
Shear-diagonal displacement response The post-injection diagonal displacement data are shown in Fig. 5. All of the post-injection tests for the epoxy specimens had greater stiffness and smaller permanent deformations during the initial load steps than the control specimen. Specimens 3-ED and 4-EL were stiffer than Specimen 2-EC, with Specimen 4-EL performing slightly better than 3-ED. Specimen 5-EA showed significantly improved stiffness and reduced permanent deformations after unloading following epoxy injection. For all the specimens except 4-EL and 5-EA, the north and south diagonal deformations were essentially identical, showing similar stiffness and exhibiting increasing diagonal deformation at approximately the same shear magnitude. For the remaining two specimens, however, one end of the specimen produced a substantially larger diagonal deformation than the other side. Diagonal cracking behavior The orientation and location of the diagonal cracks produced during precrack and post-injection loading 295
Fig. 5—Control and post-injection shear-diagonal displacement response recorded near centerline of specimens. sequences are shown in Fig. 6. The locations of diagonal cracks that were epoxy-injected are also shown in Fig. 6. Diagonal cracks that were injected did not reopen during post-injection tests. Instead, new cracks formed adjacent to the injected cracks and propagated at similar angles. Non-repaired cracks propagated along the original paths. The applied loads required to reinitiate diagonal cracking are shown in Fig. 7. The load required to reinitiate diagonal cracking was determined from the applied shear magnitude at the moment the stirrup strain showed an abrupt increase. The pre- and post-injection diagonal cracking shears were compared with the precrack diagonal cracking shear on the abscissa and the post-injection cracking shear serving on the ordinate. Solid symbols represent stirrup strain gauges located near injected diagonal cracks, while hollow symbols represent stirrup strain gauges located away from injected diagonal cracks, as described in the next section. Injected diagonal cracks required higher applied shear than the original specimen to produce strains in the stirrups due to new diagonal cracking. Data above the reference line show that larger shear loads were required, while points below the line required smaller loads to propagate or reinitiate diagonal cracking. Non-injected cracks typically behaved similarly to the baseline tests, where stirrup strains began increasing immediately upon application of applied shear.
296
Reinforcement strains The largest relative influences of epoxy injection were seen in the individual stirrup strains, but these effects were highly influenced by the proximity of injected diagonal cracks to the embedded strain gauge locations. Strain gauges located near diagonal cracks that were injected had lower strains after injection at similar shear magnitude. Strain gauges located between diagonal cracks or far from cracks that were not injected displayed relatively little change. This behavior was observed for all injected specimens. Diagonal cracks were considered to be “near” the stirrup strain gauge if the vertical distance that the crack crossed the stirrup with the strain gauge was within the AASHTO-LRFD (AASHTO 2005) calculated development length of the Grade 300 No. 13 (Grade 40, No. 4) stirrup (203 mm [8 in.]). An example of strains measured for a stirrup located near a diagonal crack and a stirrup located at a distance greater than the development length from a diagonal crack is shown in Fig. 8. The strain behavior depicted in Fig. 9 shows the baseline and post-injection stirrup strains at the maximum service load range. In the figure, the baseline strains serving as the abscissa are plotted against the post-injection strains on the ordinate. Solid symbols represent stirrup strain gauges located near injected diagonal cracks, while hollow symbols represent stirrup strain gauges located away from injected diagonal cracks, as defined previously. The dashed referACI Structural Journal/March-April 2014
Fig. 6—Crack pattern locations on east face of specimens. Figure includes precracking, epoxy-injected cracks, post-injection cracks, and final failure crack. ence line marks the boundary between improved and unimproved behavior. Points above the line had higher strains at the same service load after injection, whereas the points below the line had lower strains after injection. Most stirrup strains near injected diagonal cracks showed significantly reduced strains after injection, whereas uninjected regions were generally unaffected.
ACI Structural Journal/March-April 2014
Interaction of epoxy curing process and cyclic live load Data were collected continuously for Specimen 4-EL during curing of the epoxy with cyclic service-level live load being applied. An example of the diagonal deformation throughout the first 3 days of curing is shown in Fig. 10. The deformation range of a representative displacement sensor crossing the injected diagonal crack is shown in Fig. 11. As seen in Fig. 10, within the first several hours of curing, 297
the average diagonal crack deformation reduced from 1.39 to 1.27 mm (0.0547 to 0.0500 in.) and remained relatively constant for the remainder of the curing process. However, the diagonal deformation range continued to reduce over the period of about 3 days, during which the deformation range decreased by nearly 75% (Fig. 11). An example of the stirrup strain throughout the curing period and the internal and external temperature recordings is shown in Fig. 12. The
stirrup is located in the same section as the example diagonal deformation shown in Fig. 11, and the strain range decreased by over 50% within the first 18 hours, while little additional effects were observed for the remainder of the curing process. The curing time reported by the epoxy manufacturer is 7 days at 4°C (40°F) and 2 days at 25°C (77°F). The average curing temperature for Specimen 4-EL was 10°C (50°F), which correlates to a required curing time of approximately 6 days. The stirrup strain was also observed to fluctuate with the external temperature with significant time lag between surface temperature and strain changes (Fig. 12). DISCUSSION The results of this study indicate that epoxy injection affected the structural behavior of the RC specimens in several ways. Overall, the most dramatic effects were observed for Specimens 3-ED, 4-EL, and 5-EA, as described in the following discussion.
Fig. 7—Applied shear at diagonal cracking initiation before and after injection.
Shear capacity of specimens In this study, a computer program call Response 2000 (R2K) (Bentz 2000) was used to estimate the strength of the specimens (neglecting any influence of the epoxy injection) as well as the strength of the control specimen. In a previous study, R2K, which uses the Modified Compression Field Theory (MCFT) (Vecchio and Collins 1986), was used to predict shear capacity for a series of 31 similar full-size RC specimens within 0.98 of the actual capacity with a coeffi-
Fig. 8—Applied shear-stirrup strain behavior for Specimen 3-ED. Strain gauges located near: (a) injected diagonal cracks; and (b) uninjected diagonal cracks. 298
ACI Structural Journal/March-April 2014
Fig. 11—Diagonal deformation range during curing of Specimen 4-EL. (Note: Zero was taken as a reference value.) Fig. 9—Stirrup strains at service level shear before and after injection. Shear magnitude taken as 311 kN (70 kip).
Fig. 10—Diagonal deformations reduced during curing of Specimen 4-EL. cient of variation under 8% (Higgins et al. 2004). The R2K predicted member capacities are shown in Table 2. The experimental shear strength is the applied actuator force at failure combined with the self-weight of the specimen acting at the failed section. Except for two specimens, the epoxyinjected specimens exhibited slightly larger shear capacities than predicted, ranging from 1.02 to 1.12. However, all but 4-EL and 5-EA fall within a standard deviation (68% prediction interval) of the expected shear strength ignoring the effects of epoxy injection. This is within the expected variability of shear testing results. Specimens 4-EL and 5-EA exhibited shear strengths significantly above the predicted unaltered shear capacity. The shear strength of Specimen 4-EL was above the 95% prediction interval, and Specimen 5-EA was above the 99% prediction interval for the expected shear strength without epoxy injection and indicates the increase is not likely attributed to the inherent variability of shear strength testing of large reinforced concrete girders of the type studied herein. These two specimens received the least amount of epoxy injection in comparison to the other specimens, because they only exhibited three major diagonal crack systems injected on each specimen. Axial load was accounted for in the R2K capacity prediction of Specimen 5-EA but not 4-EL, and the differences in shear capacity for each of the specimens is described subsequently. ACI Structural Journal/March-April 2014
Fig. 12—Stirrup strain during curing of Specimen 4-EL. (Note: °C = [°F × 1.8] + 32.) Interaction of epoxy repair and superimposed dead load Specimen 3-ED exhibited a higher capacity than the predicted baseline capacity. Specimen 3-ED also achieved higher load prior to reinitiation of nonlinear response compared to the epoxy-injected control specimen, 2-EC. The dead load serves to keep the diagonal cracks open, allowing for more penetration of the epoxy at the crack tips. It further allows the epoxy to only carry superimposed live loads and leaves dead load stresses locked into the reinforcement and concrete. This tends to further delay crack reinitiation. This was observed by the reduced stirrup steel demand at injected diagonal cracks for otherwise similar load levels. Cured epoxy characteristics following cyclic live load The live load magnitudes, rates, and curing conditions considered in this program for Specimen 4-EL did not reduce the effectiveness of the epoxy injection compared to the specimen with dead load alone and, in fact, resulted in higher observed shear capacity. The cyclic loading acted as an internal pumping mechanism that enabled the epoxy to enter and fill finer cracks than in either Specimen 3-ED or Specimen 2-EC. It was observed during the injection process of Specimen 4-EL that the epoxy pump pressures built and dissipated in-phase with the actuator loading cycle, which is 299
Fig. 13—Photographs of cores taken from Specimens 3-ED and 4-EL: (a) core taken from Specimen 3-ED; and (b) core taken from Specimen 4-EL with small voids. consistent with the epoxy being pushed out of the diagonal cracks as the cracks closed upon unloading. Concrete cores measuring 102 mm (4 in.) in diameter were taken from epoxy-injected diagonal cracks for both Specimens 3-ED and 4-EL after failure. Both cores showed that the epoxy was well distributed through the cracks and even filled hairline subcracks within the cored region. The core taken from Specimen 4-EL had small visible voids, which were evidence of bubble formations likely caused by the cyclic loading noted previously. Examples of the porous epoxy matrix observed in Specimen 4-EL compared to the solid epoxy matrix observed in Specimen 3-ED are shown in Fig. 13. The development of bubbles within the epoxy did not diminish the performance of Specimen 4-EL compared to Specimen 3-ED. It is important to note that the cyclic live loading was representative of loads moving across a typical 15.2 m (50 ft) span continuous bridge at an approximate speed of 33.8 kph (21 mph). Additionally, due to setting of the epoxy at a larger average crack width (dead load plus average live load range), as compared to Specimens 2-EC and 3-ED, the cross section was effectively induced with compressive stresses that must be overcome before additional cracking may occur. This post-tensioning effect also accounts for the increased shear strength observed for Specimen 4-EL. Further research is needed to study the effects of higher loading rates and other load magnitudes applied simultaneously during epoxy injection, as well was possible lower-range curing temperatures. However, based on these observations, it may be possible to inject cracks on existing bridges while positioning static superimposed live loads on the bridge (such as loaded maintenance trucks) to effectively open the cracks to their maximum service-level width. After curing the epoxy and removing the live load, compressive stresses would be induced in the cross section. If the live load used during repair is above the maximum expected service loads, this could effectively prevent or significantly delay future cracking. Interaction of epoxy repair and axial load The axially loaded specimen, 5-EA, exhibited the most dramatic change between the pre- and post-injection response. The specimen was injected with a constant externally applied axial tension force of 645 kN (145 kip), which coincided with the load magnitude at the end of the precrack test. The applied axial force maintained larger diagonal and vertical cracks during injection, allowing for increased pene300
tration of the epoxy into microcracks within the concrete matrix, similar to Specimens 3-ED and 4-EL. More importantly, as the vertical loading was applied, the axial force decreased during the failure test to a magnitude of 267 kN (60 kip) at ultimate load, resulting in a net compressive force of 378 kN (85 kip) induced into the epoxy-injected section. Had the axial load not diminished with increasing transverse load, the specimen may have failed at lower load levels. R2K predicted a capacity of 853 kN (192 kip) for a similar specimen with 890 kN (200 kip) total axial tension force. Reducing the steel yield stress by an amount equivalent to the 267 kN (60 kip) axial tension and applying a 378 kN (85 kip) axial compression force on the section, R2K estimated a shear capacity of 987 kN (222 kip), which is closer to the observed shear capacity. This situation of loading and curing would represent a structure with shrinkage and/or temperature-induced tensile strains that are recovered after epoxy injection. The strain recovery (release of restraints at supports or temperature change, for example) produces a post-tensioning effect for the injected cross section. However, the beneficial temperature effect could not be relied upon in the field and would vary during daily and seasonal changes. CONCLUSIONS Five RC deck girder specimens were fabricated to reflect the design and construction materials of the 1950s for RCDG bridges lightly reinforced for shear. The specimen tests were designed to study the effects of epoxy on diagonal-tension, shear-dominated cracked girders. Specimens were precracked to similar levels observed in the field, subjected to baseline tests in the cracked condition, injected with epoxy resin at varying levels of applied dead and/or live load, and then, after curing the epoxy, were tested to failure. The results of the initial cracking, baseline, and postinjection responses were compared. Factors included in the study were superimposed dead load, service live load plus dead load, and externally applied axial tension during epoxy curing. Based on the experimental observations and analytically predicted shear strengths, the following conclusions are presented: • Most of the epoxy-injected specimens exhibited marginal increases in shear strength compared to well-correlated analytically predicted strengths of unrepaired specimens. The largest capacity increases were observed for specimens subjected to superimposed cyclic live load and externally applied static axial tension during epoxy curing (which was due principally to an unintended post-tensioning effect). These showed that the epoxy injection did not effectively strengthen the specimens, as they would have failed very close to the observed capacity with or without epoxy injected cracks. • Superimposed cyclic live loading during injection and curing of Specimen 4-EL produced dynamic pressure during injection and pumping of the epoxy within the diagonal cracks. Fine bubbles were formed within the epoxy matrix but did not reduce structural performance at service or ultimate states. In addition, the curing of the epoxy at larger average diagonal crack ACI Structural Journal/March-April 2014
•
• • •
•
widths introduced compressive stresses in the cross section that increased the threshold load for recracking. The compressive stresses in the stem also resulted in increased shear capacity. Consequently, this finding may permit strategic placement of loaded maintenance trucks to widen cracks at certain locations during the injection and curing process. Initial stiffness after injection was improved and development of residual deformations was delayed prior to recracking by epoxy injection compared with the cracked performance prior to injection. Epoxy injection increased the threshold load level required to form additional diagonal cracks or extend the existing cracks within the stem. Injected diagonal cracks did not reopen. Instead, new cracks formed adjacent to the original injected cracks. Epoxy injection reduced service-level stirrup strains compared to uninjected diagonal cracks prior to recracking. This may reduce bond fatigue, thereby slowing or preventing additional diagonal crack growth and help maintain force transfer across diagonal cracks. Careful and methodical epoxy installation procedures following industry best practices enabled epoxy penetration through the depth of the web. Based on the observed penetration and uniformity of the epoxy within the diagonal cracks, it is likely that the epoxy would restrict access of moisture and chlorides to the embedded stirrups and thereby delay or diminish corrosion potential at the injected crack locations. ACKNOWLEDGMENTS
This research was funded by the Oregon Department of Transportation. The findings and conclusions are those of the authors and do not necessarily reflect those of the project sponsors.
AUTHOR BIOS
Matthew T. Smith is an Associate Engineer at CH2M-Hill, Corvallis, OR. He received his BS and MS from Oregon State University, Corvallis, OR. His research interests include the design of hydraulic and building structures. Daniel A. Howell is a Project Manager with the Bridge Design Division of the St. Louis County Department of Highways and Traffice, Creve Coeur, MO. He received his BS and MS from the University of Delaware, Newark, DE, and his PhD from Oregon State University. His research interests include the design of bridges and other structures. Mary Ann T. Triska is a Bridge Engineer at HDR Engineering, Portland, OR. She received her BS from the University of Portland, Portland, OR, and her MS from Oregon State University. Her research interests include evaluation, rehabilitation, and sustainable design of infrastructure. Christopher Higgins is the Slayden Construction Faculty Fellow and Professor of Structural Engineering in the School of Civil and Construction Engineering at Oregon State University. He received his BS from Marquette University, Milwaukee, WI; MS from the University of Texas at Austin, Austin, TX; and PhD from Lehigh University, Bethlehem, PA. His research interests include evaluation and rehabilitation of bridges and other structures.
ACI Structural Journal/March-April 2014
fc′ fct fu fy VAPP VDL
NOTATION = = = = = =
compressive strength of concrete, MPa (psi) tensile strength of concrete, MPa (psi) ultimate tensile stress of reinforcing steel, MPa (ksi) yield stress of reinforcing steel, MPa (ksi) applied shear from actuator, kN (kip) applied shear from portion of self-weight acting at failure plane, kN (kip) VEXP = total applied shear, kN (kip) VINITIAL = maximum applied shear during precracking phase of testing, kN (kip) VR2K = predicted shear capacity, kN (kip)
REFERENCES
AASHTO, 2005, “AASHTO-LRFD Bridge Design Specification,” third edition with 2005 interims, American Association of State Highway and Transportation Officials, Washington, DC, 654 pp. Abu-Tair, A. I.; Rigden, S. R.; and Burley, E., 1991, “The Effectiveness of the Resin Injection Repair Method for Cracked RC Beams,” The Structural Engineer, V. 69, No. 19, Oct., pp. 335-341. ASTM A615/A615M-05a, 2005, “Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 6 pp. ASTM C39/C39M-05, 2005, “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 7 pp. ASTM C496/C496M-04e1, 2004, “Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 5 pp. ASTM C617-05, 2005, “Standard Practice for Capping Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 6 pp. ASTM E8-04, 2004, “Standard Test Methods for Tension Testing of Metallic Materials,” ASTM International, West Conshohocken, PA, 28 pp. Basunbul, I. A.; Gubati, A. A.; Al-Sulaimani, G. J.; and Baluch, M. H., 1990, “Repaired Reinforced Concrete Beams,” ACI Materials Journal, V. 87, No. 4, July-Aug., pp. 348-354. Bentz, E. C., 2000, “Section Analysis of Reinforced Concrete Members,” PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada. Chung, H. W., 1975, “Epoxy-Repaired Reinforced Concrete Beams,” ACI Journal, V. 72, No. 5, May, pp. 233-234. Chung, H. W., 1981, “Epoxy Repair of Bond in Reinforced Concrete Members,” ACI Journal, V. 78, No. 1, Jan.-Feb., pp. 79-82. Higgins, C.; Farrow III, W. C.; Potisuk, T.; Miller, T. H.; Yim, S. C.; Holcomb, G. R.; Cramer, S. D.; Covino, B. S.; Bullard, S. J.; ZiomekMoroz, M.; and Matthes, S. A., 2003, “SPR 326 Shear Capacity Assessment of Corrosion-Damaged Reinforced Concrete Beams,” Oregon Department of Transportation, Salem, OR, 19 pp. Higgins, C.; Miller, T. H.; Rosowsky, D. V.; Yim, S. C.; Potisuk, T.; Daniels, T. K.; Nicholas, B. S.; Robelo, M. J.; Lee, A.-Y.; and Forrest, R. W., 2004, “Research Project SPR 350 SR 500-91: Assessment Methodology for Diagonally Cracked Reinforced Concrete Deck Girders,” Oregon Department of Transportation, Salem, OR, Oct., 328 pp. Popov, E. P., and Bertero, V. V., Oct.-Dec. 1975, “Repaired R/C Members Under Cyclic Loading,” Earthquake Engineering & Structural Dynamics, V. 4, No. 2, pp. 129-144. Potisuk, T., and Higgins, C., 2007, “Field Testing and Analysis of CRC Girder Bridges,” Journal of Bridge Engineering, V. 12, No. 1, Jan.-Feb., pp. 53-63. Rooney, H. A., 1963, “Epoxy Resins as a Structural Repair Material,” State of California Department of Public Works Division of Highways, Jan., 15 pp. (http://www.dot.ca.gov/hq/research/researchreports/1961-1963/63-23.pdf) Smith, M. T., 2007, “Investigation of the Behavior of Diagonally Cracked Full-Scale CRC Deck-Girders Injected with Epoxy Resin and Subjected to Axial Tension,” MS thesis, Oregon State University, Corvallis, OR. (http:// scholarsarchive.library.oregonstate.edu.) Tremper, B., 1960, “Repair of Damaged Concrete with Epoxy Resins,” ACI Journal, V. 57, No. 2, Feb., pp. 173-182. Vecchio, F. J., and Collins, M. P., 1986, “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal, V. 83, No. 2, Feb., pp. 219-231.
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NOTES:
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S26
High-Performance Fiber-Reinforced Concrete Bridge Columns under Bidirectional Cyclic Loading by Ady Aviram, Bozidar Stojadinovic, and Gustavo J. Parra-Montesinos An experimental and analytical study was carried out on circular column specimens representing cantilever bridge piers constructed with tensile strain-hardening, high-performance fiber-reinforced concrete (HPFRC). Two column specimens with different longitudinal reinforcement details in the expected plastic hinge zone were tested under bidirectional displacement reversals, and the results were compared with those of a geometrically identical specimen constructed using regular concrete and designed according to current Caltrans bridge design specifications. The results demonstrate the considerable benefits of using tensile strain-hardening fiberreinforced concrete in typical highway overpass bridge columns. These benefits include: improved cyclic response; substantial reduction in transverse reinforcement and corresponding construction benefits; and increased damage tolerance and reduction of post-earthquake repair costs. Keywords: bidirectional cyclic load; bond stress; bridge column; drift; fiber-reinforced concrete; plastic hinge; shear; steel fibers.
INTRODUCTION Numerous cast-in-place and precast reinforced concrete structures suffered significant damage or collapse during historical and recent earthquakes, primarily due to deficient structural design. Code-mandated reinforcement detailing required for critical bridge and building members to ensure adequate seismic behavior often leads to substantial reinforcement congestion and construction difficulties. Therefore, it is not surprising that many recent research efforts have been directed to the development and implementation of innovative materials in new structures for improved seismic performance while simplifying the required reinforcement detailing. Fiber-reinforced concretes that exhibit a tensile strain-hardening behavior are now possible with the use of relatively low fiber-volume fractions Vf (in the range of 1.5 to 2.0%). These tensile strain-hardening materials are typically referred to as high-performance fiber-reinforced concrete (HPFRC). In addition to their tensile strain capacity, which often exceeds 0.5%, HPFRCs exhibit a compression response that resembles that of well-confined concrete. Hooked and twisted steel fibers, as well as ultra-high-molecular-weight polyethylene fibers, are among the fiber types investigated for use in earthquake-resistant construction.1 When used in structural elements subjected to large displacement reversals, HPFRCs enable significant deformation capacity with superior damage tolerance compared with geometrically identical, well-detailed reinforced concrete members.1-5 Further, substantial reductions in transverse reinforcement required for confinement and shear resistance have been possible in elements subjected to large shear stress reversals.1 There is ACI Structural Journal/March-April 2014
substantial experimental evidence that supports the use of HPFRC materials to enhance structural response of elements subjected to large deformation demands caused by ground motions, such as bridge piers with either flexural-dominated behavior or with strong flexure-shear interaction. Evaluation of the use of HPFRC in bridge piers to substantially relax transverse reinforcement requirements while leading to increased damage tolerance, shear strength, and energy dissipation under cyclic loading compared with regular concrete piers was the main focus of this research. An experimental and analytical study was carried out on two approximately 1/4-scale column specimens built with HPFRC and subjected to bidirectional displacement reversals. The behavior of these specimens was compared with that of a geometrically identical conventionally reinforced concrete (RC) column.6 Additional information about the tests, calibrated finite element models, and the repair cost and repair time analysis of typical highway bridges in California constructed using HPFRC columns can be found elsewhere.7 RESEARCH SIGNIFICANCE Experiments were performed to characterize the cyclic response of circular HPFRC bridge columns subjected to bidirectional lateral displacements and to compare their response with that of conventionally reinforced concrete columns. This experimental study is one of the first of its kind, and was aimed at assessing the effectiveness of fiber reinforcement as partial replacement of transverse reinforcement used for shear resistance and confinement while increasing column flexural ductility. The experiments performed also allowed an evaluation of the enhanced damage tolerance of HPFRC columns, which is important for reducing post-earthquake repair cost and repair time assessment, and performance-based evaluation of structural systems using HPFRC. TEST PROGRAM The column specimens represented the bottom half of a typical bridge column deforming in double curvature with an assumed inflection point at midheight. The specimen geometry was selected so as to represent circular column prototypes used by Caltrans for typical highway overpass bridges in California. The length scale of the specimens was approximately 1/4. Columns of both HPFRC specimens, ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-092, doi:10.14359.51686522, was received March 10, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
303
Table 1—Summary of specimen geometry, reinforcement, and material properties Parameter
*
S1: HPFRC
S2: HPFRC
BC: Plain
Column diameter Dcol
400 mm (16 in.)
400 (16 in.)
400 mm (16 in.)
Total column height Hcol
1625 mm (64 in.)
1625 mm (64 in.)
1625 mm (64 in.)
Shear span-to-diameter ratio
4
4
4
Longitudinal reinforcement
12 No. 4/13M + 8 No. 4/13M dowels
12 No. 4/13M + 8 No. 4/13M dowels
12 No. 4/13M
Longitudinal reinforcement ratio ρl
2% (base), 1.2% (rest)
2% (base), 1.2% (rest)
1.2%
Debonding sleeves
Dowels, L = 250 mm (10 in.), 250 mm (10 in.) above base
Main reinforcing bar, L = 100 mm (4 in.), 200 mm (8 in.) above base
—
Transverse reinforcement
W3.5* at 64 mm (2.5 in.)
W3.5 at 64 mm (2.5 in.)
W3.5 at 32 mm (1.25 in.)
Volumetric transverse reinforcement ratio ρs
0.75%
0.75%
1.5%
Specified concrete compressive strength
34.5 MPa (5.0 ksi)
34.5 MPa (5.0 ksi)
34.5 MPa (5.0 ksi)
Days from concrete casting to test date
60
49
49
Concrete compressive strength at test day
47.3 MPa (6.86 ksi)
47.1 MPa (6.83 ksi)
35.1 MPa (5.09 ksi)
W3.5: diameter = 5.3 mm (0.21 in.).
denoted as S1 and S2 in Table 1, were built using the same HPFRC material, reinforced with a 1.5% volume fraction of commercially available high-strength (2410 MPa [350 ksi]) hooked steel fibers with a length of 30 mm (1.2 in.), and an aspect ratio of 80. A fiber-volume fraction of 1.5% (120 kg/m3 [200 lb/yd3]) was selected such that a tensile strain-hardening behavior could be achieved. Ready mix concrete was used in both columns, and the fibers were added to the concrete truck on site. HPFRC casting was performed using a bucket and stick vibrator. The results from the test of a reference base column specimen (BC), designed according to the Caltrans Seismic Design Criteria (SDC)8 and built with regular concrete, were used for comparison purposes.6 All three specimens were tested following the same predetermined bidirectional cyclic displacement pattern. The transverse reinforcement of both HPFRC specimens was approximately half of that required by Caltrans Seismic Design Criteria (SDC),8 counting on the HPFRC material to contribute significantly to shear resistance and confinement. The longitudinal reinforcement of the columns in Specimens S1 and S2, shown in Fig. 1, was detailed to prevent concentration of inelastic deformation at the cold joint between the HPFRC column and the base block, which was constructed with regular concrete. Such cold joint is typical for conventional reinforced concrete bridge columns in California. Concentration of deformations at this joint is not desirable because it can lead to a premature sliding shear failure at the base of the column, fracture of column longitudinal reinforcement, or both. The cold joint at the base of HPFRC columns is more vulnerable to damage localization than a similar joint in reinforced concrete construction because of the higher flexural strength of the immediately adjacent HPFRC column sections and the excellent bond between HPFRC and reinforcing bars.9 Thus, the HPFRC column-foundation interface of the test specimens was strengthened with dowel reinforcement to force most of the inelastic deformations to occur within the HPFRC column.
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Two different debonding schemes, shown in Fig. 1, were devised to minimize damage localization at the section where the dowel reinforcement was terminated. In Specimen S1, the upper portion of the dowels was debonded using plastic tubes to avoid premature damage localization that could occur because of the termination of the bars within the plastic hinge zone. In Specimen S2, the dowels were terminated within the plastic hinge region, and the main longitudinal bars were debonded over a length of 4 in. (10 cm) to prevent large strain concentration and premature reinforcing bar fracture at the section where the dowels were terminated. Loading pattern The HPFRC specimens were tested using a bidirectional circular load pattern (Fig. 2). This pattern was similar to that used for the BC specimen.6 A cycle in this pattern comprised circles, one clock-wise and the other counterclockwise, while return paths were sequenced to minimize the bias in any particular loading direction; however, this resulted in a very demanding displacement pattern characterized by long specimen travel along circles with constant ductility demand. The quasi-static cyclic tests were conducted by incrementally increasing the radius of the circular pattern. The target displacement ductility demand for each cycle in the displacement history is presented in Table 2. The target ductility demand, termed nominal ductility demand μ, was computed with respect to the yield displacement of the BC column, estimated at 14.0 mm (0.55 in.) (0.86% drift), to enable a direct comparison between the BC and HPFRC specimens. Each post-yield primary cycle (that is, cycle to a new maximum drift level) was followed by a small displacement cycle with amplitude equal to 1/3 of that of the primary cycle to evaluate the column stiffness degradation throughout the loading history. Similar displacement rates among the different test cycles were applied, not exceeding 25 mm/min (1.0 in./min). A gravity load equivalent to 0.1fc′Ag of the BC column, where Ag is the column gross cross-sectional area, was applied at the column top through a spreader beam ACI Structural Journal/March-April 2014
Table 2—Nominal ductility level used at each cycle of displacement history, defined with respect to BC column yield displacement Cycle
Nominal ductility
Displacement, mm (in.), (drift, %)
Cycle
Nominal ductility
Displacement, mm (in.), (drift, %)
1
NA
1.0 mm (0.04 in.) (0.07)
10
3
41.9 mm (1.65 in.) (2.6)
2
NA
2.8 mm (0.11 in.) (0.17)
11
1
14.0 mm (0.55 in.) (0.86)
3
NA
5.6 mm (0.22 in.) (0.34)
12
4.5
63.0 mm (2.48 in.) (3.9)
4
1
14.0 mm (0.55 in.) (0.86)
13
1.5
21.1 mm (0.83 in.) (1.3)
5
0.33
4.6 mm (0.18 in.) (0.28)
14
6.25
87.4 mm (3.44 in.) (5.4)
6
1.5
21.1 mm (0.83 in.) (1.3)
15
2
27.9 mm (1.10 in.) (1.7)
7
0.5
7.1 mm (0.28 in.) (0.43)
16
8
112 mm (4.40 in.) (6.9)
8
2
27.9 mm (1.10 in.) (1.7)
17
2
27.9 mm (1.10 in.) (1.7)
9
0.67
9.4 mm (0.37 in.) (0.58)
18
12.5
175 mm (6.88 in.) (10.7)
Fig. 1—Reinforcement detailing of HPFRC specimens. (Note: Dimensions in mm; 1 mm = 0.0394 in.) and post-tensioned rods tensioned through hydraulic jacks. This load is typically used to represent the average dead and service live loads carried by typical column bents of overpass bridges in California. Test setup and instrumentation The bidirectional quasi-static cyclic testing of the two HPFRC column specimens was carried out. The lateral and gravity load test setup is shown in Fig. 3. The lateral load was applied using two horizontal servo-controlled hydraulic actuators at an initial angle of 90 degrees with respect to each other reacting against a rigid frame. The actuators were attached to the column top using a steel jacket. The actuator commands were computed to follow the circular load pattern considering actual actuator elongations. The HPFRC specimen instrumentation scheme comprised internal and external instruments. Strain gauges were installed on longitudinal and transverse reinforcement to trace the strain history at various locations along the column height and to correlate internal strains to observed damage, such as bar buckling and fracture. Five levels of linear displacement potentiometers were placed on two stiff ACI Structural Journal/March-April 2014
Fig. 2—Normalized displacement cycle: (a) plan view; and (b) displacement history for normalized cycle. instrumentation frames located on the sides of the specimen. These absolute displacement measurements were used to obtain the deflected shape of the column and relative deflections between various column sections, and to monitor the torsion of the column top. Additional linear potentiometers were attached to instrumentation rods anchored in the column core at various sections to measure the relative displacements necessary for determination of flexural rota305
Fig. 3—(a) Plan; and (b) elevation views of experimental setup for HPFRC column specimens. Table 3—Reinforcing steel mechanical properties Parameter Specification
Continuous longitudinal bar 11
Dowel reinforcement 11
Spiral reinforcement ASTM A8212
ASTM A706
ASTM A706
Size
No. 4/13M
No. 4/13M
W3.5
Elastic modulus Es
190.3 GPa (27,600 ksi)
185.5 GPa (26,900 ksi)
198.3 GPa (28,800 ksi)
Yield stress Fy
448 MPa (65 ksi)
*
483 MPa (70 ksi)
638 MPa* (92 ksi)
Ultimate stress Fu
621 MPa (90 ksi)
705 MPa (102 ksi)
709 MPa (102 ksi)
Yield plateau, strain
0.25 to 1.33
—
—
*
Yield strength determined using 0.2% offset line parallel to corresponding elastic modulus.
tions, average curvatures, and shear deformations, as well as average column axial deformations. Load cells were used to monitor the forces in the two horizontal actuators and the two post-tensioned rods used for simulation of gravity load. Reinforcing steel The mechanical properties of the longitudinal and spiral reinforcement used for the HPFRC columns, obtained through ASTM A37010 standard tension tests, are summarized in Table 3. The fracture strain was not determined in these coupon tests because the bars were unloaded before fracture due to laboratory safety regulations. Instead, fracture strain values specified in Caltrans SDC8 were used in analytical models of the HPFRC cantilever columns. Fiber-reinforced concrete The concrete mixture used for the construction of the fiber-reinforced concrete columns and plain concrete foundation had a specified 28-day strength of 34.5 MPa (5.0 ksi). This mixture proportion, with a proportion by weight of 0.45:1:2.3:1.86 (water:cement:fine aggregate:coarse aggregate), was adjusted from that used in previous tests6 to incorporate the steel fibers with acceptable workability. Hooked steel fibers were added to the concrete mixture at a 1.5% volume fraction (120 kg/m3 [200 lb/yd3]) by direct pouring into the truck mixer and mixing for 4 minutes. Mixture quantities for 0.765 m3 (1 yd3) of concrete are listed in Table 4. A similar mixture was successfully used in HPFRC slab-column connection tests.13 A high-range water reducing admixture was added during the mixing process to maintain
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acceptable workability. The column concrete had a slump of 140 mm (5.5 in.) following the addition of the high-range water reducing admixture and before the addition of fibers. Fiber-reinforced concrete 150 x 300 mm (6 x 12 in.) cylinders were cast during the construction of the specimens to assess the development of concrete compressive strength through ASTM C39/C39M14 tests. In addition, 150 x 150 x 600 mm (6 x 6 x 24 in.) beams were tested under thirdpoint loading (457 mm [18 in.] span length) following ASTM C1609/C1609M15 to assess the flexural performance (and indirectly tensile performance) of the HPFRC material used. Failure occurred inside the middle third of the spans for all beam specimens tested. The elastic modulus for the HPFRC material, Ec,FRC, corresponding to the secant modulus up to 0.45fc,FRC′, determined from fiber-reinforced concrete cylinder tests, was also verified through ASTM C1609/ C1609M15 beam tests. Average compressive strength test results for plain and fiber-reinforced concrete at various days after casting, obtained directly from ASTM C39/C39M14 cylinder tests or from linear interpolation of results at other days, are listed in Table 5. Measured cylinder compressive strengths at test day are listed in Table 1. Despite having the same specified strength, measured cylinder compressive strength at test day for the HPFRCs was approximately 20% higher than that of the regular concrete used in the BC specimen (Table 1). The elastic modulus, and peak and residual flexural strength at various deflection levels for the fiber-reinforced concrete material determined according to ASTM C39/C39M14 and ASTM C1609/C1609M,15 respectively, are also listed in Table 5.
ACI Structural Journal/March-April 2014
TEST RESULTS The damage progress in the HPFRC and BC specimens throughout the loading history is shown in Table 6. The HPFRC specimens, particularly Specimen S1, exhibited enhanced damage tolerance compared with the geometrically identical plain concrete Specimen BC. Both HPFRC columns behaved elastically up to a drift ratio of approximately 1.3% (nominal ductility μ = 1.5 based on first yielding of Specimen BC). The actual ductility of the tested HPFRC columns μa is, therefore, two-thirds that of the BC column. The HPFRC specimens developed relatively similar damage states as the reference BC specimen, but at higher displacement levels. For example, damage observed in Specimens S1 and S2 at 3.9% drift ratio (μ = 4.5) was smaller than that in Specimen BC, as seen in Table 6. Large portions of the BC column cover had already spalled off at this displaceTable 4—Fiber-reinforced concrete mixture quantities Item
Value
w/c
0.45
Coarse aggregate weight (9.5 mm [3/8 in.] maximum size)
602 kg/m3 (1324 lb/yd3)
Top sand weight
551 kg/m3 (1212 lb/yd3)
Blend sand weight
194 kg/m3 (426 lb/yd3)
Total fine aggregate weight
745 kg/m3 (1638 lb/yd3)
Cement
324 kg/m3 (712 lb/yd3)
High-range water-reducing admixture
621 mL/m3 (21 oz/yd3)
Water
145 kg/m3 (320 lb/yd3)
Fibers
88 kg/m3 (194 lb/yd3)
Note: Specified 28-day compressive strength: 34.5 MPa (5.0 ksi); slump: 140 mm (5.5 in.); 1 yd3 = 0.765 m3; 1 lb = 0.45 kg.
ment level, while the HPFRC columns sustained relatively minor damage with no spalling despite experiencing relatively large flexural cracks. At a nominal ductility level of 6.25 (5.4% drift), the spiral reinforcement in the S1 column fractured at an approximate height of 150 mm (6 in.) above the column base. This spiral fracture resulted in longitudinal bar buckling and significant concrete cover spalling and core degradation in the subsequent displacement cycles. All the continuous longitudinal bars in Specimen S1 underwent buckling and fractured by the end of the cycle, corresponding to a nominal ductility level of 12.5 (10.7% drift). The dowels in Specimen S1 did not buckle or fracture. Specimen S2, on the other hand, experienced longitudinal bar buckling and spiral fracture at two locations, followed by fracture of two continuous longitudinal reinforcement bars during the cycle at a nominal ductility demand level of 6.25 (5.4% drift). The BC specimen did not experience spiral fracture, bar buckling, or longitudinal reinforcing bar fracture because the spiral spacing was half that provided in the HPFRC specimens, and the column was only cycled up to a nominal ductility level of 4.5 (3.9% drift) because it was subsequently tested under monotonically increased axial load.6 The maximum displacement ductility level attained during the test of Specimens S1 and S2 without substantial loss of gravity load-carrying capacity was 12.5 and 6.25, respectively (10.7 and 5.4% drift ratio). Tests of Specimens S1 and S2 were terminated after several of the longitudinal bars fractured, compromising the safety of the test setup. The length of the plastic deformation zone Lp in Specimen S1 was approximately 450 mm (18 in.) at the end of the test, which is slightly larger than the column diameter. Inelastic deformations in Specimen S1 first developed at approximately 350 mm (14 in.) from the base, and propagated upwards as well as down towards the base of the column.
Table 5—Average values of HPFRC mechanical properties
*
Parameter
11 days
28 days
49 days
60 days
Regular concrete compressive strength fc′ used for BC specimen
28.3 MPa* (4.10 ksi)
34.0 MPa (4.93 ksi)
35.0 MPa (5.07 ksi)
35.2 MPa* (5.10 ksi)
Regular concrete compressive strength fc′ used for HPFRC specimens
33.0 MPa (4.78 ksi)
41.9 MPa (6.07 ksi)
42.1 MPa (6.11 ksi)
41.9 MPa (6.08 ksi)
HPFRC compressive strength fcFRC′
37.0 MPa (5.37 ksi)
46.7 MPa (6.77 ksi)
47.1 MPa* (6.83 ksi)
47.3 MPa* (6.86 ksi)
HPFRC elastic modulus Ec-FRC
22.9 GPa* (3323 ksi)
28.9 GPa* (4190 ksi)
29.2 GPa* (4227 ksi)
29.3 GPa* (4246 ksi)
HPFRC first peak flexural strength f1
—
5.44 MPa (0.79 ksi)
6.67 MPa (0.97 ksi)
6.37 MPa (0.92 ksi)
HPFRC absolute peak flexural strength f
—
6.69 MPa (0.97 ksi)
7.10 MPa (1.03 ksi)
7.58 MPa (1.10 ksi)
HPFRC residual flexural strength at L/600 deflection fres,L/600
—
6.37 MPa (0.92 ksi)
6.49 MPa (0.94 ksi)
7.29 MPa (1.06 ksi)
HPFRC residual flexural strength at L/150 deflection fres,L/150
—
4.69 MPa (0.68 ksi)
5.58 MPa (0.81 ksi)
5.38 MPa (0.78 ksi)
Obtained indirectly from linear interpolation of test results performed on other days.
ACI Structural Journal/March-April 2014
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Table 6—Comparison of damage progress in HPFRC and BC specimens S1: HPFRC
S2: HPFRC
BC: Plain concrete
State of column specimens at nominal ductility demand of 1.5 (1.3% drift)
State of column specimens at nominal ductility demand of 2.0 (1.7% drift)
State of column specimens at nominal ductility demand of 3.0 (2.6% drift)
State of column specimens at nominal ductility demand of 4.5 (3.9% drift)
State of column specimens at nominal ductility demand of 6.25 (5.4% drift)
Test terminated.
State of column specimens at nominal ductility demand of 8.0 (6.9% drift)
Test terminated.
State of column specimens at nominal ductility demand of 12.5 (10.7% drift)
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ACI Structural Journal/March-April 2014
Fig. 4—Force-deformation response of HPFRC and BC specimens: (a) total shear stress versus total drift; and (b) shear stress ratio versus total drift. The S2 column, on the other hand, developed a primary crack at a height of 250 mm (10 in.) above the foundation at the cutoff point of the dowel bars, resulting in a concentration of deformation and damage in that region with limited spreading of the plastic deformation zone towards the base of the column. The extent of the BC column plastic deformation zone was estimated at 300 mm (12 in.), equivalent to 3/4 of the column diameter.6 Force-displacement response The force-deformation response of the HPFRC and BC specimens is shown in Fig. 4. Only the primary cycles corresponding to the nominal ductility level of 1 and higher are shown. The deformation axis is expressed in terms of resultant drift ratio (displacement of the column top divided by the distance between the top of the column base to the actuator axes). The force axis is expressed in terms of resultant shear stress (Fig. 4(a)) and shear stress ratio (Fig. 4(b)). The resultant shear stress was calculated as the resultant shear force applied by the two actuators divided by the effective area in shear, defined by Caltrans SDC8 as 0.8 times the gross area of the column. The shear stress ratio was obtained by dividing the total shear force in the column by the assumed nominal shear strength provided by the transverse steel reinforcement at yielding Vs, calculated according to Caltrans SDC8 as follows
Vs =
Av f yh D ′ s
(1)
where Av = (π/2)Ab is the area of shear reinforcement, Ab is the area of the spiral reinforcement, fyh is the corresponding yield strength, D′ is the cross-sectional dimension of confined concrete core measured between the centerline of the spiral, and s is the spiral pitch. Figure 4 shows a three-fold increase in shear stress ratio demand in the HPFRC specimens compared with the BC specimen due to: 1) half as much transverse reinforcement in the HPRFC columns than in the BC column; and 2) dowels in the plastic hinge region of the HPRFC specimens that added flexural resistance and moved up the plastic hinge region, increasing the shear demand at flexural yielding. From Fig. 4, it can be seen that even though the shear demand on the HPFRC specimens increased significantly ACI Structural Journal/March-April 2014
and the amount of transverse reinforcement was reduced by half compared with that in the BC specimen, the HPFRC specimens maintained a stable hysteretic behavior governed by flexure throughout the entire loading history. The degradation of lateral resistance with the progression of damage in the HPFRC specimens, which initiated at a nominal displacement ductility of 6.25 (5.4% drift), was governed by the loss of flexural capacity (concrete crushing, bar buckling, and finally bar fracture), and not by shear-related cracking or damage. Sliding of the column along the cold joint at the column-foundation interface or significant shear distortions of the column plastic hinge zone were not observed. A conventional shear force versus nominal displacement ductility envelope, derived by plotting the peak lateral force at each nominal displacement ductility level imposed, is shown in Fig. 5(a). This plot was computed using the peak resultant force of the specimens in the x- and y-directions, to reconcile the differences in the response produced by the circular load pattern. Both HPFRC specimens remained in the elastic response range up to a nominal ductility demand of 1.5 (based on first yielding of Specimen BC). The peak applied force remained generally constant between nominal ductility levels of 1 and 4.5 for the BC column, and between 1.5 and 6.25 for the HPFRC columns. The S1 column was slightly stronger than the S2 column. The secant lateral stiffness of the specimens, computed using the resultant peak force and corresponding displacement value attained during each new primary cycle, is shown in Fig. 5(b). The cracked elastic stiffness of the two HPFRC specimens was comparable, and higher than that of Specimen BC. However, the stiffness degradation rate for Specimen BC was somewhat lower than that for the HPFRC specimens up to nominal displacement ductility of 4.5. This is likely due to the use of twice as much transverse reinforcement (and tighter spiral spacing) in Specimen BC. Column plastic hinge deformations Measurements of cross section rotation relative to the column base about the x- and y-axes were obtained at four levels along the height of the column (0.375Dcol, 0.75Dcol, 1.125Dcol, and 4.5Dcol above the column base). From these rotations, average curvatures for each segment between two adjacent rotation measurements were calculated to evaluate the spread of inelastic deformations along the column
309
Fig. 5—(a) Shear force-displacement envelope; and (b) lateral stiffness degradation versus nominal displacement ductility (or drift) demand.
Fig. 6—Curvature profiles from experiments for: (a) S1; (b) S2; and (c) BC. height. Profiles of these curvatures for all three specimens are shown in Fig. 6. The significant difference in the length of the plastic deformation zones among these three specimens, discussed previously and evident in Fig. 6, shows that it is possible to design and detail the longitudinal reinforcement of an HPFRC column to achieve a highly desirable spreading of plastic deformation. In particular, the addition of dowel reinforcement elevated the center of the plastic hinge zone from the column base, thus providing more space for its spreading. Debonding of the dowel reinforcement (thus avoiding termination of dowels within the plastic hinge) in the column of Specimen S1 allowed for very effective spreading of bar yielding along the column height and formation of several flexural cracks in the plastic hinge region. The less successful detail used in Specimen S2, on the other hand, shows that there are significant unexplored opportunities to develop improved designs to ensure adequate spread of yielding in 310
HPFRC plastic hinges. It should be noted, however, that increased curvature demands were imposed on the HPRFC specimens for a given displacement level, compared with those imposed on the BC specimen, due to the upward shift of the plastic deformation region. Bond stress In both HPFRC specimens, the bonded region of dowel reinforcement started at 250 mm (10 in.) above the foundation. Strain gauge measurements along the dowel reinforcement recorded peak strain values exceeding the steel yield strain at a height of 100 mm (4 in.) above the foundation or 150 mm (6 in.) from the bar termination point, resulting in a length Ld as small as 150 mm (6 in.) or 12 bar diameters required to develop the yield strength of the No. 4 dowel bars. The peak average bond stress up to first yielding of the reinforcement in the HPFRC specimens was determined based on force equilibrium between the resultant force from ACI Structural Journal/March-April 2014
Fig. 7—Curvature profiles for calibrated plastic hinge model of Column S1: (a) formulation; and (b) results for different displacement ductility demands of HPFRC columns. an average uniform bond stress ub acting on the surface of the dowel reinforcement along a length measured from the bar termination point to the section at which first yielding occurred, and the yield strength of the bar. It is important to note that dowel bar yielding occurred after substantial cracking occurred around the cover of the HPFRC specimens. The resulting peak average bond stress ub was 10.2 MPa (1.5 ksi), which can be rewritten in terms of the unconfined HPFRC compressive strength results obtained from cylinder tests, fc′,FRC = 47.3 MPa (6.86 ksi). The degradation of bond stress with increasing bar inelastic strains could not be evaluated due to lack of data. Thus, the peak bond stress for reinforcing bar strains not exceeding the yield strain was approximately ub,max = 1.5 fc′, FRC , MPa (ub,max = 18 fc′, FRC , psi). This value is significantly higher than bond strengths reported in the literature for regular concrete16 of 1.0√fc′, MPa (12√fc′, psi) and 0.5√fc′, MPa (6√fc′, psi) for deformed bars at slip values smaller and larger than the slip measured at bar yield strain, respectively. These measurements thus indicate that reinforcement development lengths in HPFRC columns could be shorter than those in conventional concrete columns. Similar conclusions were established in recent studies.9 Conservative development lengths for conventional concrete, however, should be used for HPFRC until more test data on the subject become available. CALIBRATED HPFRC COLUMN MODELS An idealized curvature profile for columns with reinforcement detailing similar to that used in Specimen S1 is shown in Fig. 7. Based on the curvature distribution shown in Fig. 6(a), the length of the plastic hinge zone Lp was set at 400 mm (16 in.), equal to the column diameter. The middle of the plastic hinge was centered at approximately the middle of the debonded region of the column dowel bars, by setting the distance between the column base and the bottom of the plastic hinge zone, hLP, to 150 mm (6 in.). The yield curvatures φy,Top and φy,Bottom were defined at a height of 560 and 150 mm (22 and 6 in.) above the column base (top and bottom ends of the plastic hinge zone), respectively. These yield curvatures were computed using moment-curvature analyses of the corresponding cross sections with different longitudinal reinforcement details. For displacements beyond first ACI Structural Journal/March-April 2014
flexural yielding, a uniform curvature over the plastic hinge length is assumed, dependent on the actual ductility level of the HPFRC column μa. Curvature over the length hLP is also assumed constant, as shown in Fig. 7, and equal to 1/4 of the curvature over Lp. Additional information about the material models and parameters used for calibration of the HPFRC plastic hinge model can be found elsewhere.6,7 A difference of less than 10% was obtained in the computation of lateral displacements, u, when using the experimentally (Fig. 6(a)) and analytically (Fig. 7) obtained curvatures. In the idealized curvature profile shown in Fig. 7(a), the term HTot is the height of the column measured from the base block top to the actuator centerline. SUMMARY AND CONCLUSIONS Experimental findings obtained from tests of strain-hardening, high-performance fiber-reinforced concrete (HRFRC) bridge columns under highly demanding bidirectional cyclic displacements are presented. Two approximately 1/4-scale circular cantilever HPFRC column specimens (S1 and S2) were tested, and the results were compared with those of a geometrically identical baseline regular concrete specimen, denoted as Specimen BC. The HPFRC column specimens were constructed using a ready mix concrete with a 1.5% volume fraction of high-strength hooked steel fibers. The plastic hinge region of the HPFRC specimens was detailed using dowels in combination with bar debonding, either of the dowel ends or of the main longitudinal reinforcement at the end of the dowels to prevent concentration of damage at the column base and increase the spread of yielding. The transverse reinforcement spacing in the HPFRC specimens was twice that of the BC specimen. The HPFRC specimen with long dowels, Specimen S1, developed an extended plastic deformation zone with an approximate length of one column diameter, improved ductile behavior, high-damage tolerance, and high energy dissipation compared with the regular concrete Specimen BC. This specimen was cycled up to a 10.7% drift ratio while sustaining the applied gravity load. The HPFRC specimen with short dowels and debonding of main longitudinal reinforcement, Specimen S2, exhibited less deformation capacity compared with Specimen S1. The reason for such 311
behavior was the development of a single major crack at the cutoff point of the dowel bars, resulting in a concentration of rotation and damage at that location and limited spreading of the plastic hinge zone towards the base of the column. Even though the HPFRC specimens were subjected to larger shear force demands and the amount of transverse reinforcement was half that of the conventional Specimen BC, the HPFRC specimens exhibited a stable hysteretic behavior governed by flexure up to large drift demands with negligible shear-related damage. Such desirable structural response of the tested HPFRC columns indicates that HPFRC has great potential for use in flexural elements subjected to large shear reversals. The results of these unique tests demonstrate several other advantages of HPFRC and call for additional research on the design and detailing of plastic hinge regions in HPFRC flexural members to best achieve improved seismic performance and reduced post-earthquake repair costs of bridge structures. Furthermore, the use of HPFRC is expected to simplify the construction of critical regions in bridges by allowing for a substantial increase in transverse reinforcement spacing compared with that required in regular concrete construction without compromising seismic performance. While the additional shear strength provided by the steel fibers is helpful in ensuring a flexural-dominated behavior, the adverse consequences of increased hoop spacing, particularly reduction of lateral support of longitudinal reinforcing bars, should be carefully considered during design of HPFRC elements. The efficiency of HPFRC cover to provide support to the longitudinal bars is as yet unknown, and should not be relied upon until results from research on this topic become available. AUTHOR BIOS
ACI member Ady Aviram is a Structural Engineer with Simpson Gumpertz & Heger, Inc., in San Francisco, CA. She received her BS in civil engineering from the University of Costa Rica, San Pedro, Costa Rica, and her MEng and PhD in structural engineering from the University of California, Berkeley, Berkeley, CA. Her research interests include performance-based earthquake-resistant design of steel and reinforced-concrete structures, base-plate connections, bridge modeling and analysis, structural reliability, fiber-reinforced concrete, and blast-resistant design of wall systems. Bozidar Stojadinovic, FACI, is a Professor and Chair of structural dynamics and earthquake engineering at the Swiss Federal Institute of Technology (ETH), Zürich, Switzerland. He received his Dipl. Ing. from the University of Belgrade, Belgrade, Serbia; his MS from Carnegie Mellon University, Pittsburgh, PA; and his PhD from the University of California, Berkeley. He is a member of ACI Committees 335, Composite and Hybrid Structures; 341, Earthquake-Resistant Concrete Bridges; 349, Concrete Nuclear Structures; and 374, Performance-Based Seismic Design of Concrete Buildings. His research interests include probabilistic performance-based seismic design of composite and reinforced concrete structures.
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Gustavo J. Parra-Montesinos, FACI, is the C. K. Wang Professor of Structural Engineering at the University of Wisconsin-Madison, Madison, WI. He is Chair of ACI Committee 335, Composite and Hybrid Structures; and a member of ACI Committees 318, Structural Concrete Building Code, and 544, Fiber-Reinforced Concrete, and Joint ACI-ASCE Committee 352, Joints and Connections in Monolithic Concrete Structures. His research interests include seismic behavior and design of reinforced concrete, fiber-reinforced concrete, and hybrid steel-concrete structures.
REFERENCES
1. Parra-Montesinos, G. J., “High-Performance Fiber-Reinforced Cement Composites: An Alternative for Seismic Design of Structures,” ACI Structural Journal, V. 102, No. 5, Sept.-Oct. 2005, pp. 668-675. 2. Billington, S. L, and Yoon, J. K., “Cyclic Response of Unbonded Post-Tensioned Precast Columns with Ductile Fiber-Reinforced Concrete,” Journal of Bridge Engineering, ASCE, V. 9, No. 4, July-Aug. 2004, pp. 353-363. 3. Harajli, M. H., and Rteil, A. M., “Effect of Confinement Using Fiber-Reinforced Polymer or Fiber-Reinforced Concrete on Seismic Performance of Gravity Load-Designed Columns,” ACI Structural Journal, V. 101, No. 1, Jan.-Feb. 2004, pp. 47-56. 4. Canbolat, B. A.; Parra-Montesinos, G. J.; and Wight, J. K., “Experimental Study on Seismic Behavior of High-Performance Fiber-Reinforced Cement Composite Coupling Beams,” ACI Structural Journal, V. 102, No. 1, Jan.-Feb. 2005, pp. 159-166. 5. Parra-Montesinos, G. J., and Chompreda, P., “Deformation Capacity and Shear Strength of Fiber-Reinforced Cement Composite Flexural Members Subjected to Displacement Reversals,” Journal of Structural Engineering, ASCE, V. 133, No. 3, 2007, pp. 421-431. 6. Terzic, V., and Stojadinovic, B., “Post-Earthquake Traffic Capacity of Modern Bridges in California,” PEER Report 2010/103, Pacific Earthquake Engineering Research Center, Berkeley, CA, 2010, 218 pp. 7. Aviram, A.; Stojadinovic, B.; Parra-Montesinos, G. J.; and Mackie, K. R., “Structural Response and Cost Characterization of Bridge Construction Using Seismic Performance Enhancement Strategies,” PEER Report 2010/01, Pacific Earthquake Engineering Research Center, Berkeley, CA, 2009, 363 pp. 8. Caltrans, “Seismic Design Criteria 1.3,” Report, California Department of Transportation, Sacramento, CA, 2004, 101 pp. 9. Chao, S.-H.; Naaman, A. E.; and Parra-Montesinos, G. J., “Bond Behavior of Reinforcing Bars in Tensile Strain-Hardening Fiber Reinforced Cement Composites,” ACI Structural Journal, V. 106, No. 6, Nov.-Dec. 2009, pp. 897-906. 10. ASTM A370, “Standard Test Methods and Definitions for Mechanical Testing of Steel Products,” ASTM International, West Conshohocken, PA, 2012, 48 pp. 11. ASTM A706/A706M, “Standard Specification for Low-Alloy Steel Deformed and Plain Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 2009, 6 pp. 12. ASTM A82, “Standard Specification for Steel Wire, Plain, for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 2007, 4 pp. 13. Cheng, M.-Y.; Parra-Montesinos, G. J.; and Shield, C. K., “Shear Strength and Drift Capacity of Fiber Reinforced Concrete Slab-Column Connections Subjected to Bi-Axial Displacements,” Journal of Structural Engineering, ASCE, V. 136, No. 9, 2010, pp. 1078-1088. 14. ASTM C39/C39M, “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 2012, 7 pp. 15. ASTM C1609, “Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam With Third-Point Loading),” ASTM International, West Conshohocken, PA, 2012, 9 pp. 16. Eligehausen, R.; Popov, E. P.; and Bertero, V. V., “Local Bond Stress-Slip Relationships of Deformed Bars under Generalized Excitations,” Report 82/23, Earthquake Engineering Research Center, University of California, Berkeley, Berkeley, CA, 1983, 169 pp.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S27
Analysis of Early-Age Thermal and Shrinkage Stresses in Reinforced Concrete Walls by Barbara Klemczak and Agnieszka Knoppik-Wróbel The issues related to thermal and shrinkage stresses arising in reinforced concrete walls at the stage of their construction are discussed. The cause of these stresses is inhomogeneous volume changes associated with temperature rise caused by the exothermic hydration process of cement, as well as moisture exchange with the environment. The induced thermal-shrinkage stresses can reach significant levels, and in some cases, cracks appear in structural elements. The article presents the results of a numerical analysis of a reinforced concrete wall cast against an old set foundation, subjected to early-age thermal and shrinkage deformations. Development of stresses and character of cracks is briefly described. The presented analysis focuses on evaluation of the contribution of self-induced and restraint stresses to the total stresses induced in the wall. The contribution and development of thermal and shrinkage stresses is investigated. Walls with different dimensions are considered. Keywords: cracking; early-age concrete; reinforced concrete wall; thermalshrinkage stresses.
INTRODUCTION The cause of thermal and shrinkage stresses arising in early-age concrete are the volume changes due to the temperature and moisture variations during the hardening process. The variations of concrete temperature during curing are the result of the exothermic nature of the chemical reaction between cement and water. In structural elements with thin sections, the generated heat dissipates quickly, and causes no problem. In thicker sections, the internal temperature can reach a significant level. Furthermore, due to the poor thermal conductivity of concrete, high temperature gradients may occur between the interior and the surface of thick structural elements. Concrete curing is also accompanied by moisture exchange with the environment in conditions of variable temperatures. The loss of water through evaporation at the surface of the element results in shrinkage, which is classified as an external drying shrinkage. There is also internal drying resulting from the reduction in material volume as water is consumed by hydration, which is classified as autogenous shrinkage. Additionally, the chemical shrinkage is also distinguished, which occurs because the volume of hydration products is less than the original volume of cement and water. The volume changes due to the temperature and moisture variations have consequences in arising stresses in a concrete element. Two natures of these stresses can be distinguished: self-induced stresses and restraint stresses. The self-induced stresses are related to internal restraints of the structure, resulting from nonuniform volume changes in a cross section. In internally restrained elements, during ACI Structural Journal/March-April 2014
the phase of temperature increase, tensile stresses originate in the surface layers of the element, and compressive stresses are observed inside the element. An inversion of stress body occurs during the cooling phase: inside, tensile stresses are observed; in the surface layers, compressive stresses are observed. Considerable self-induced stresses can be expected, for example, within thick foundation slabs, thick walls, dams, and in each element with interior temperatures considerably greater than surface temperatures. A concrete element can also be externally restrained. For example, such a restraint exists along the contact surface of mature concrete against which a new concrete element has been cast. Because of the limited possibility of deformations of the structure, restraint stresses occur in that case. The restraint stresses are often observed in medium-thick elements, such as a wall cast against an old set concrete. It should also be noted that the stresses resulting from an external restraint of a structure add to the effects of an internal restraint. The problem of thermal-shrinkage stresses—and consequently, in some cases, cracking of early-age concrete structures—is well known in massive concrete elements.1-3 Nevertheless, high thermal-shrinkage stresses and cracks are also observed in newly constructed medium-thick concrete elements, such as reinforced concrete (RC) walls cast against an old set foundation (tank walls or abutments4,5) or walls cast in stages (massive container walls6). These cracks, which are particularly deep or thorough cracks, may adversely affect the serviceability, lifespan, or even bearing capacity of a concrete structure. Cracking in tank walls endangers their tightness.5 The problem of thermal-moisture cracking is also dangerous in the case of nuclear containments executed in stages, where a previously cast layer of mature concrete restrains younger concrete layers.6 The formation of cracks promotes the leakage of radioactive elements into the environment during the service life of the containment. Early-age thermal-shrinkage cracking may even influence thin-walled structures, such as shell roof covers, which reduces their capacity, and may lead to structural collapse as a result of unforeseen overpressure.7 RESEARCH SIGNIFICANCE Considerable early-age thermal-shrinkage stresses and consequent cracks at the construction stage are frequently ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-096.R2, doi:10.14359.51686523, was received December 14, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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Fig. 1—(a) Temperature; (b) thermal stresses; (c) moisture content; and (d) shrinkage stress development in time for externally restrained concrete wall.10 observed in RC walls. Correct prediction and counteracting negative effects of these stresses is of great importance to ensure the desired service life and function of structures. It is particularly important in structures such as tanks, which require a solid concrete that prevents water leakage. This article studies distribution of the discussed stresses in RC walls with different dimensions. The contribution of self-induced and restrained stresses to the total induced stresses is also investigated. DEVELOPMENT OF THERMAL AND SHRINKAGE STRESSES Two main phases can be distinguished when observing a temperature change in time during the concrete curing process (Fig. 1(a)): a phase of concrete temperature increase (self-heating), and a cooling phase of the element down to the temperature of the surrounding air. In the first phase, the wall extends being opposed by the foundation, which results in the formation of compressive stresses (Fig. 1(b)), usually within the first 1 to 3 days. As soon as the maximum self-heating temperature is reached, the wall begins to cool down, which takes another few days, restrained by a cooled foundation. This leads to development of tensile stresses in the wall (Fig. 1(b)). In case of moisture migration, a monotonic moisture removal from the wall is observed (Fig. 1(c)). The resulting stresses are tensile stresses in the whole curing process (Fig. 1(d)). It should be noted that the graphs in Fig. 1 are shown only for illustration of the phenomena that arise in the discussed RC walls. In fact, the values of generated temperature and the loss of moisture will be different in each point of the wall according to the temperature and moisture exchange with environment. Similarly, the values of generated stresses vary in particular areas of the wall due to the different thermal and shrinkage strains, as well as due to the different level of the restraint of the wall in the foundation, which is changing 314
with the height of the wall. Nevertheless, the main character of temperature, moisture, and stress development presented in Fig. 1 is kept in most areas of the wall. The detailed analysis of the temperature, moisture, and stress distribution in the walls with different dimensions are presented in following sections of the article. Shrinkage stresses resulting from moisture migration reach relatively low values, so the character of total thermal-shrinkage stresses is analogical to thermal stresses; shrinkage stresses increase total tensile stress values in the second phase. Figure 2 presents total thermal-shrinkage stress maps with resulting deformations in the right half of the 70 cm (27.56 in.) thick wall in a heating phase after 1.3 days (Fig. 2(a)) and a cooling phase after 18.3 days (Fig. 2(b)). The described tensile stresses occurring in the cooling stage often reach considerable values, and can lead to cracking of the wall. A typical pattern of cracking due to an edge restraint of a wall is shown in Fig. 3, assuming that the base is rigid. Without restraint, the section would contract along the line of the base; thus, with a restraint, a horizontal force develops along the construction joint. This leads to vertical cracking at the midspan area, but splayed cracking towards the ends of the section where a vertical tensile force is required to balance the tendency of the horizontal force to warp the wall. In addition, a horizontal crack may occur at the construction joint at the ends of the walls due to this warping restraint. Generally, it is thought that a basic cracking pattern is independent of the amount of reinforcement provided.4,5,8 When sufficient reinforcement is provided, the widths of the cracks are controlled, although secondary cracks may be induced. The extent and size of cracking will then depend on the amount and distribution of reinforcement provided. The cracks can reach 1/3, 1/2, or even 2/3 of the height of the wall, depending on the length and height of the wall, and ACI Structural Journal/March-April 2014
Fig. 2—Distribution of thermal-shrinkage stresses in right half of reinforced concrete wall in: (a) heating phase; and (b) cooling phase. •
Fig. 3—Image, spacing, and height of cracks in reinforced concrete wall.4 are usually spaced every 1.5 to 3.0 m (4.9 to 9.8 ft).4 The cracks start at the wall-foundation interface and widen up to the wk,max value, and then decrease in width. The maximum width of the crack wk,max is approximately 0.3 to 0.5 mm (12 to 20 mil) (in walls with a low horizontal reinforcement ratio), and is localized at some level above the construction joint (at 1/3 of the height of the crack, according to Reference 4; at a height equal to the thickness of the wall, according to References 9 and 10). Another interesting property of the cracks is their distribution: the greatest height of the crack can be observed in the middle of the wall length, and it declines towards free edges of the wall or towards the expansion joints, as presented in Fig. 3. PREDICTION OF THERMAL AND SHRINKAGE STRESSES Prediction and control of thermal and shrinkage stresses, along with possible cracking in early-age RC walls, is a complicated problem due to the complex nature of interacting phenomena and a large number of contributing factors.11-14 One of the important factors is the geometry of the RC wall (length, height, and the length-height ratio), as well as a degree of its restraint in a foundation. Additionally, the crucial factor is the temperature development in the concrete member. The complex variables that affect the rate of temperature rise, the maximum temperature, and the temperature gradients over sections of the wall are: • Thermal properties of early-age concrete, such as the rate of heat evolution, the total amount of heat, specific heat, and thermal conductivity, are strongly dependent on the amount and properties of concrete components, especially the amount and type of cement; ACI Structural Journal/March-April 2014
Conditions during concreting and curing of concrete, such as the initial temperature of concrete, type of formwork, and use of insulation or pipe cooling; • Technology of concreting, such as segmental concreting; • Environmental conditions, such as ambient temperature, temperature of neighboring elements, wind, and humidity; and • Dimensions of wall, especially the width of the wall. Furthermore, deformations originating from the material from which a wall is made and occurring in the erection stage are essential loads. The problems arise from the material itself as concrete is subjected to transformations caused by cement hydration and its mechanical properties develop as its maturity progresses. Therefore, first the nonlinear and non-stationary temperature and moisture fields and corresponding strains should be determined in the analyzed wall considering the real technological and material conditions. The stresses are calculated in the second step of the analysis. METHOD OF ANALYSIS The applied original numerical model can be classified as a phenomenological model. The influence of mechanical fields on the temperature and moisture fields was neglected, but thermal-moisture fields were modeled using coupled equations of thermodiffusion. Therefore, the complex analysis of a structure consists of three steps. The first step is related to determination of temperature and moisture development. In the second step, thermal-shrinkage strains are calculated, and these results are used as an input for computation of stress in the last step. With respect to the engineering application of the theoretical model, computer codes were also developed. Details of the model are given in Appendix A,* and a full description of the model and computer programs, TEMWIL and MAFEM_VEVP, can be found in References 15 through 17. Some results of the validation of the model are presented in Appendix B,* where the cracking image obtained in the numerical analysis is compared with the cracking observed in the real tank walls. For presentation of results, an opensource application PARAVIEW was adopted. * The Appendix is available at www.concrete.org/publications in PDF format, appended to the online version of the published paper. It is also available in hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.
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Table 1—Thermal and moisture coefficients Thermal fields Coefficient of thermal conductivity
λ, W/mK (Btu/s·ft°F)
2.52 (4.04 × 10–4)
Specific heat
cb, kJ/kgK (Btu/lb°F)
0.95 (0.227)
Density of concrete
ρ, kg/m (lb/ft )
2400 (149.80)
Coefficient of thermal diffusion
αTT, m /s (ft /s)
11.1 × 10–7 (1.19 × 10–5)
Coefficient representing influence of moisture concentration on heat transfer
αTW, m2K/s (ft2·°F/s)
9.375 × 10–5 (1.81 × 10–3)
αp, W/m2K (Btu/ft2s°F)
6.00 (29.41 × 10–5) surface without protection, without considering wind 3.58 (17.56 × 10–5) surface with plywood 5.80 (28.45 × 10–5) surface with foil 0.81 (3.97 × 10–5) bottom surface: soil
Thermal transfer coefficient
Heat of hydration*
3
2
3
2
According to equation Q (T , t ) = Q∞ e
− ate−0 ,5
Q∞ = kJ/kg (218.90 Btu/lb); a = 513.62te–0.17
Moisture fields Coefficient of water-cement proportionality
K, m3/J (ft3/Btu)
0.3 × 10–9 (1.12 × 10–5)
Coefficient of moisture diffusion
αWW, m2/s (ft2/s)
0.6 × 10–9 (6.46 × 10–9)
Thermal coefficient of moisture diffusion
αWT, m2/sK (ft2/s°F)
2 × 10–11 (1.20 × 10–10)
βp, m/s (ft/s)
2.78 × 10–8 (91.21 × 10–9) surface without protection 0.18 × 10–8 (5.90 × 10–9) surface with plywood 0.10 × 10–8 (3.28 × 10–9) surface with foil 0.12 × 10–8 (3.93 × 10–9) bottom surface: soil
Moisture transfer coefficient
*
Approximation made on basis of experimental results of heat of hydration.
Fig. 4—Dimensions of analyzed walls with finite element mesh. ANALYSIS OF STRESSES: RESULTS AND DISCUSSION Assumption of geometrical, material, and technological data The wall of 4 m (13.12 ft) height was analyzed for the length of 10, 15, or 20 m (32.81, 49.21, or 65.62 ft) and two thicknesses: 40 and 70 cm (15.75 and 27.56 in.). The length-height ratios of these walls were, respectively, 2.5, 3.75, and 5. Six examples of combinations of these cases were considered. The analyzed walls were supported on a 4 m (13.12 ft) wide and 70 cm (27.56 in.) deep strip foundation of the same length. The wall and the foundation were assumed to be reinforced with a near-surface reinforcing net of ø16 bars (0.63 in.). The wall was reinforced at both surfaces with horizontal spacing of 20 cm (7.87 in.) and vertical spacing of 15 cm (5.91 in.). The foundation was reinforced with 20 x 20 cm (7.87 x 7.87 in.) spacing at the top and bottom surface. Due to a double symmetry of the wall, the model for finite element analysis was created for 1/4 of the walls. A uniform mesh was prepared and densified 316
at the free edges of the wall and within the contact surface between the wall and the foundation. A final geometry of the wall with a mesh of finite elements for one exemplary wall is presented in Fig. 4. It was assumed that the analyzed wall was made of the following concrete mixture: cement CEM I 42.5R 375 kg/m3 (23.41 lb/ft3), water 170 L/m3 (10.61 lb/ft3), and aggregate (granite) 1868 kg/m3 (116.60 lb/ft3). Thermal and moisture coefficients necessary for calculations were set in Table 1. The development of mechanical properties in time was assumed according to CEB-FIP MC90.18 The final values for 28-day concrete were assumed as follows: compressive strength fcm = 35 MPa (5.08 ksi), tensile strength fctm = 3.0 MPa (0.44 ksi), and modulus of elasticity Ecm = 32.0 GPa (4.64 Mpsi). It was also assumed that the foundation was erected earlier and had hardened, so the material properties were taken as for 28-day concrete, with the same final values as the wall. Environmental and technological conditions were taken as: ambient temperature 20°C (68°F), initial temperature of fresh concrete mixture 20°C (68°F), wooden formwork of 1.8 cm (0.71 in) plywood on the side surfaces, and foil protection of the top surface. It was also assumed that formwork was removed 28 days after concrete casting. Thermal and shrinkage stresses First, the temperature and moisture development in time was determined. Figure 5 presents a juxtaposition of temperature and moisture content development diagrams for two areas in the walls (Fig. 4) with different dimensions. Although the character of both temperature and moisture content are independent of the dimensions of the wall, their magnitudes depend directly on these dimensions. Only the ACI Structural Journal/March-April 2014
thickness, not the length, of the wall is influenced by the temperature and moisture content development. The greatest temperatures are reached in the thicker walls, while the moisture removal rates are almost the same; only slightly greater loss of moisture was observed in thinner walls. For the known thermal-moisture fields and strains, the stress state can be determined. The following cases were analyzed, and the results of stress distribution at the height of the wall in its internal midspan cross section were presented: 1. Thermal stresses with assumed uniform distribution of temperature in the wall (development of temperature in time was only considered) (Fig. 6(a) and (c)); 2. Shrinkage stresses with assumed uniform moisture content distribution in the wall (moisture content change in time was only considered) (Fig. 6(b) and (d)); 3. Thermal stresses with assumed real distribution of temperature in the wall (development of temperature in time was also considered) (Fig. 7(a), (c), and (e)); 4. Shrinkage stresses with assumed real distribution of moisture content in the wall (moisture content change in time was also considered) (Fig. 7(b), (d), and (f)); and 5. Coupled thermal and shrinkage stresses with assumed real distribution of both temperature and moisture content (Fig. 8(a)). The diagrams of nonuniform temperature distribution at the height of the wall (Fig. 7(a)) are presented at the moment the maximum hardening temperature is reached; in case of uniform distribution of temperature, the values of temperature from the interior of the wall are applied the entire wall (Fig. 6(a)). Similarly, the moisture distribution is presented at the moment the maximum hardening temperature is reached. Figure 6 presents distribution of thermal (Fig. 6(c)) and shrinkage (Fig. 6(d)) stresses in the midspan cross section of the interior of the wall under the assumption of uniform temperature and moisture content distribution in the wall. Such an assumption is very common in the analysis of medium-thick externally restrained structures, especially when analytic methods of thermal-shrinkage stresses determination are used, but also in numerical analyses in which a model is reduced to a two-dimensional problem. It is believed that such an approach provides a good approximation because both the temperature and moisture content differences within the body of the wall are relatively small. The resultant stress distribution at the height of the section is approximately linear with the maximum values of stresses at the joint between the wall and the foundation. On such a simple example, it can be observed that both the length and the thickness of the wall influence the resulting stresses. The thickness of the wall determines the maximum value of stress; it should be noted that greater values of thermal stresses occur in thicker walls, which results from higher exerted temperatures; shrinkage stresses are greater in thinner walls, which is caused by a higher rate of water removal. The length of the wall (linear restraint) determines the distribution of stress at the height of the wall. For the analyzed walls characterized by length-height ratio (L/H) ≥ 2.5, tensile stresses occur at the whole height of the wall; in high walls—that is, the walls with L/H < 2.5—compression of top areas may be expected. ACI Structural Journal/March-April 2014
Fig. 5—Temperature distribution: (a) in interior and (b) on surface of wall; and moisture content development: (c) in interior and (d) on surface of wall. Nevertheless, heat and moisture are transported within the element and to the surrounding environment in the process of concrete curing. Therefore, the values of temperatures 317
Fig. 6—Case of uniform distribution of: (a) temperature; (b) moisture; (c) thermal; and (d) shrinkage stress distribution at height of wall in midspan cross section after 18.3 days. and moisture content vary in different zones of the wall, as do the resulting stresses. Figure 7 shows thermal (Fig. 7(c)) and shrinkage (Fig. 7(d)) stress distribution at the height of the wall in its interior taking into account the real (nonuniform) temperature and moisture content distribution. It is also noted that temperature and moisture content difference at the thickness of the wall leads to stress diversification in the internal and near-surface areas (Fig. 7(e) and (f)). It can be observed that the length of the wall influences the occurring stresses as much as its thickness in such a way that the length determines the character of stress distribution, while the thickness determines the maximum values of stresses. It should be emphasized that considering real distribution of temperature and moisture the maximum stresses, and consequently the highest cracking risk, is observed at some distance above the joint, which complies with observations in References 4, 9, and 10. The observation diagrams in Fig. 8 were prepared to present coupled thermal-shrinkage stress distribution in 318
the wall. The character of total thermal-shrinkage stresses results mainly from the character of their thermal component (Fig. 7(b) versus Fig. 8(a)); shrinkage stresses only add to the final value. Thus, the aforementioned conclusions remain valid. The location of the maximum stresses varied; generally, it was the closest to the construction joint for the thinnest and the shortest walls (0.4 m = 1.31 ft), and was elevated as the thickness and the length of the wall increased (even up to 1.2 m [3.94 ft]). Thus, the results comply with observations in Reference 4, while the observations from References 9 and 10 seem more accurate for high walls (walls with a low L/H ratio). In all analyzed cases, because the formwork was detained for the whole process, greater total stresses were observed in the interior of the wall, which explains the occurrence of first cracks in the interior of the wall.5 It should be noted that Fig. 6 presents stress distribution at the height of the wall in the midspan cross section after 18.3 days under the assumption of uniform distribution ACI Structural Journal/March-April 2014
Fig. 7—Stress distribution at height of wall in midspan cross section after 18.3 days under assumption of real (nonuniform) distribution of: (a) temperature and (b) moisture content in wall; (c) thermal and (d) shrinkage stresses in the interior of the wall; and (e) thermal and (f) shrinkage stress in interior and on surface of 20 m (65.6 ft) long wall. of temperature in the wall, while in Fig. 7 and 8, the real, nonuniform distribution of temperature is taken into account. It accounts for the visible differences in the obtained stress distribution, especially in thermal stress near the joint. In this case, the self-induced stress arises in the wall due ACI Structural Journal/March-April 2014
to the nonuniform distribution of temperature in the wall. The importance of the self-induced stresses is discussed in a following section. It is interesting that the same differences in the stress distribution can be obtained with the use
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Fig. 8—Coupled thermal-shrinkage stress distribution at height of wall in midspan cross section after 18.3 days under assumption of real (nonuniform) temperature and moisture content distribution in wall: (a) total stress in interior of wall; and (b) stresses in interior and on surface of 20 m (65.6 ft) long wall.
Fig. 9—Thermal-shrinkage stress development in time: (a) self-induced stresses; and (b) total stresses in 20 m (65.6 ft) long wall. of analytical methods when the nonuniform distribution of temperature at the height of the wall is taken.19 Self-induced versus restraint stresses In the next stage, the computations were made to evaluate the share of self-induced stresses in total stresses exerted
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in the wall. Total stresses exerted in the wall supported on a stiff foundation due to the thermal-shrinkage effects are a sum of self-induced and restraint stresses. To assess the contribution of self-induced stresses in the analyzed walls, the impact of restraint in a form of foundation was minimized by reduction of the foundation’s stiffness to EF = 100 MPa (14.5 ksi) (flexible foundation was assumed). Diagrams in Fig. 9 present development of self-induced (Fig. 9(a)) and total (Fig. 9(b)) stresses in time for the location in which the maximum value of stress was observed for the 20 m (65.6 ft) long walls of 70 and 40 cm (2.3 and 1.3 ft) thickness, assuming that both walls were detained in the formwork. Stress development was presented for one length of the wall for better visibility, as the values are similar. The resulting self-induced stresses reach relatively low values compared with the total stresses. Moreover, their character is different and is closer to the behavior of typical massive concrete structures. In the first phase, the interior of the wall is subjected to compression, while surface layers are tensioned; in the second phase, stress body inversion is observed. This behavior is especially visible in thicker walls; temperature and moisture content differences at the thickness of the thinner walls are smaller, so the resulting stresses are of lower value. It is worth noting that the generation of self-induced stresses is the cause of total stress difference in different zones of the wall. Figure 10 presents a comparison of the diagrams of self-induced (Fig. 10(a)) and total stress (Fig. 10 (b)) distribution in the midspan cross section of the wall in both the heating (after 1.2 days) and cooling phase (after 18.3 days). The character of the observed stresses is similar in each wall, so the diagrams are presented on the example of one wall (L_20,d_0.7) only. Massive concrete-like behavior can be observed in unrestrained walls, while the signs of total stresses are the same at the whole height of the wall.
ACI Structural Journal/March-April 2014
Fig. 10—(a) Self-induced and (b) total stress distribution at height of 20 m (65.6 ft) long, 70 cm (2.3 ft) thick wall in midspan cross section in heating (ph_I) and cooling (ph_II) phase.
Fig. 11—Stress distribution in midspan cross section of 20 m (65.6 ft) long, 70 cm (2.3 ft) thick wall after 18.3 days from which formwork was removed after 3 and 7 days. Influence of time of formwork removal on stress distribution Finally, an analysis was performed that investigated the influence of early formwork removal (3 and 7 days after concrete casting). Diagrams in Fig. 11 show stress development in time, while Fig. 12 shows stress distribution after 18.3 days in the midspan cross section for the walls from which the formwork was removed after 3 and 7 days. Because of the similar character, diagrams were also presented for one exemplary wall (L_20,d_0.7). If the wall is kept in the formwork long enough for the concrete to cool completely, the heat concentration in the interior of the wall leads to higher stress and possible first crack development in the internal parts of the wall (Fig. 9(b) and 10(b)). When formwork is removed in early phases of concrete curing, greater stresses are observed on the surface of the wall as a result of rapid cooling of the wall surface, which may lead to first crack formation in the near-surface areas (Fig. 11 and 12). It should be noted that in both cases, cracks may extend to the entire wall thickness. It is important to note that formwork removal accelerates moisture loss near the surface, which is why a significant increase of tensile stresses is observed in the vicinity of the top surface if it is no longer protected. ACI Structural Journal/March-April 2014
Fig. 12—Stress distribution in midspan cross section of 20 m (65.6 ft) long, 70 cm (2.3 ft) thick wall after 18.3 days from which formwork was removed after 3 and 7 days. CONCLUSIONS The problem with high temperatures arising during the hardening of concrete has been known since the 1930s, when dams were first built in the United States. Much effort has been focused on the creation of efficient methods for mitigation of the negative effects of concrete curing in massive structures; this problem is well known in concrete elements with considerable thickness. Nevertheless, formation of cracks is also observed in medium-thick concrete elements, such as RC walls cast against an old set foundation. Such walls can also be sensitive to early-age cracking of thermal and shrinkage origins. Control of thermal and shrinkage cracking in early-age concrete is of great importance to ensure a desired service life and function of structures. It is a complicated problem due to the complex nature 321
of interacting phenomena and a large number of contributing factors. Important factors include the dimensions of structural elements and the length-height ratio, which directly affect the level of a wall restraint in a foundation. The contribution of self-induced and restrained stresses to total stresses induced in the wall with different dimensions was investigated. The results obtained with the use of the original numerical model were discussed. Very limited analysis of the stress distribution in the walls could be found in the literature concerning early-age concrete. This paper is an attempt to fill the vacancy in this field, in particular by providing information about development of stresses and the importance of self-induced stresses in externally restrained structures. Knowledge about the distribution of stresses is necessary in many practical cases, for example, in the evaluation of crack risk of early-age concrete structures. The results of the analysis can be summarized as follows: 1. Thermal stresses play a predominant role in the total thermal-shrinkage stress development; 2. The total thermal-shrinkage stresses arising in an RC wall result mainly from restraint stresses generated by limited possibility of the wall deformation; the share of self-induced stresses increases with the increasing thickness of the wall, but even in relatively thin elements, it has an influence on total stress distribution in the wall; and 3. Three-dimensional numerical analysis results explain the following phenomena observed in externally restrained elements: • The greatest thermal-shrinkage stress does not occur at the interface between the wall and the restraint but at some level above the restraint joint. That fact results from nonuniform distribution of temperature and moisture within the element which concentrate in its central parts. In this case, the self-induced stress is also considered. The first crack can consistently be observed at some level above the restraint joint; and • When the wall is detained in formwork until it cools down, stresses develop towards the interior of the wall; thus, internal cracking may initially develop. When formwork is removed in early phases of concrete curing, an increased cooling rate leads to greater stresses in the surface zones, and first cracks can develop on the surface of the wall. AUTHOR BIOS
Barbara Klemczak is an Associate Professor in the Department of Civil Engineering at the Silesian University of Technology, Gliwice, Poland. She received her PhD and DSc from the Silesian University of Technology in the field of numerical modeling of early-age massive concrete. Her research interests include nonlinear analysis of reinforced concrete structures, particularly numerical modeling of thermal and shrinkage effects in concrete structures at early ages.
ACKNOWLEDGMENTS
This paper was done as a part of a research Project N N506 043440 entitled, “Numerical Prediction of Cracking Risk and Methods of Its Reduction in Massive Concrete Structures,” funded by the Polish National Science Centre. The co-author of the paper, Agnieszka Knoppik-Wróbel, is a scholar under the Project SWIFT, co-financed by the European Union under the European Social Fund.
REFERENCES
1. ACI Committee 207, “Report on Thermal and Volume Change Effects on Cracking of Mass Concrete (ACI 207.2R-07),” American Concrete Institute, Farmington Hills, MI, 2007, 28 pp. 2. Branco, F. A.; Mendes, P. A.; and Mirambell, E., “Heat of Hydration Effects in Concrete Structures,” ACI Materials Journal, V. 89, No. 2, Mar.-Apr. 1992, pp. 139-145. 3. De Schutter, G., “Fundamental Study of Early Age Concrete Behaviour as a Basis for Durable Concrete Structures,” Materials and Structures, V. 35, Jan.-Feb. 2002, pp. 15-21. 4. Flaga, K., and Furtak, K., “Problem of Thermal and Shrinkage Cracking in Tanks Vertical Walls and Retaining Walls Near Their Contact with Solid Foundation Slabs,” Architecture–Civil Engineering–Environment, V. 2, No. 2, June 2009, pp. 23-30. 5. Zych, M., “Analiza pracy scian zbiorników zelbetowych we wczesnym okresie dojrzewania betonu w aspekcie ich wodoszczelnosci (Analysis of Work of RC Tank Walls in Early Ages of Concrete Curing in the View of Their Water Tightness),” PhD thesis, Faculty of Civil Engineering, Cracow Technical University, 2011. (in Polish) 6. Benboudjema, F., and Torrenti, J. M., “Early-Age Behaviour of Concrete Nuclear Containments,” Nuclear Engineering and Design, V. 238, No. 10, Oct. 2008, pp. 2495-2506. 7. Estrada, C. F.; Godoy, L. A.; and Prato, T., “Thermo-Mechanical Behaviour of a Thin Concrete Shell during Its Early Age,” Thin-Walled Structures, V. 44, No. 5, May 2006, pp. 483-495. 8. De Borst, R., and Van den Boogaard, A. H., “Finite Element Modeling of Deformation and Cracking in Early-Age Concrete,” Journal of Engineering Mechanics, ASCE, V. 120, No. 12, Dec. 1994, pp. 2519-2534. 9. Nilsson, M., “Restraint Factors and Partial Coefficients for Crack Risk Analyses of Early Age Concrete Structures,” PhD thesis, Department of Civil and Mining Engineering, Luleå University of Technology, Sweden, 2003. 10. Larson, M., “Thermal Crack Estimation in Early Age Concrete. Models and Methods for Practical Application,” PhD thesis, Department of Civil and Mining Engineering, Luleå University of Technology, Sweden, 2003. 11. ACI Committee 207, “Guide to Mass Concrete (ACI 207.1R-05),” American Concrete Institute, Farmington Hills, MI, 2005, 30 pp. 12. RILEM TC 119-TCE, “Recommendations of TC 119-TCE: Avoidance of Thermal Cracking in Concrete at Early Ages,” Materials and Structures, V. 30, Oct. 1997, pp. 451-464. 13. RILEM Report 25, “Early Age Cracking in Cementitous Systems,” Final Report of RILEM Technical Committee TC 181-EAS, 2002. 14. Mihashi, H., and Leite, J. P., “State-of-the-Art Report on Control Cracking in Early Age Concrete,” Journal of Advanced Concrete Technology, V. 2, No. 2, June 2004, pp. 141-154. 15. Majewski, S., “MWW3—Elasto-Plastic Model for Concrete,” Archives of Civil Engineering, V. 50, No. 1, 2004, pp. 11-43. 16. Klemczak, B., “Adapting of the Willam-Warnke Failure Criteria for Young Concrete,” Archives of Civil Engineering, V. 53, No. 2, June 2007, pp. 323-339. 17. Klemczak, B., “Prediction of Coupled Heat and Moisture Transfer in Early-Age Massive Concrete Structures,” Numerical Heat Transfer. Part A: Applications, V. 60, No. 3, Sept. 2011, pp. 212-233. 18. Comité Euro-International du Béton, “CEB-FIP Model Code 1990,” Thomas Telford, London, UK, 1991, 437 pp. 19. Klemczak, B., and Knoppik-Wróbel, A., “Comparison of Analytical Methods for Estimation of Early-Age Thermal-Shrinkage Stresses in RC Walls,” Archives of Civil Engineering, V. 59, No. 1, 2013, pp. 97-117.
Agnieszka Knoppik-Wróbel is a PhD Student in the Department of Civil Engineering at the Silesian University of Technology. Her research interests include cracking risk in early-age externally restrained concrete structures.
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S28
Effects of Casting Position and Bar Shape on Bond of Plain Bars by Montserrat Sekulovic MacLean and Lisa R. Feldman Twenty-five lap splice specimens were reinforced with plain round or square longitudinal bars in the top or bottom position to evaluate the effects of casting position and bar shape on bond. All specimens failed in bond, and the bond of square bars may be evaluated by calculating their equivalent round diameter. Top cast factors of 0.3 and 0.6 for round and square bars, respectively, reasonably capture the reductions in bond resistance. Maximum load predictions based on the CEB-FIP draft Model Code 2010 provisions for bond are overly conservative for all combinations of bar shape and casting position, whereas CEB-FIP Model Code 1990 provisions for bond reasonably and conservatively capture the behavior of specimens with bottom-cast round bars, but do not appear to capture the behavior of specimens with bottom- or top-cast square bars or top-cast round bars. Keywords: bar shape; bond; casting position; lap splice; plain reinforcement; stress.
INTRODUCTION Recently published works highlight case studies of historic reinforced concrete structures with plain reinforcement,1 and reviews of structural inventories include many structures with reinforcing bar details and types that do not meet current requirements.2 Many concrete structures with plain reinforcement have reached an age where they require remediation,3,4 and so it is crucial for forensic engineers to have an understanding of their behavior and capacity. Of particular note, ACI Committee 562, organized in 2004, has a goal of developing a code and commentary for the evaluation, repair, and rehabilitation of existing concrete structures, and will likely need to include provisions for the bond evaluation of plain reinforcement. Plain reinforcement does not possess lugs or other surface deformations, and cannot transfer bond forces by mechanical interlock. Instead, bond is transferred through adhesion between the concrete and the reinforcement before slip occurs, and by wedging of small particles that break free from the concrete upon slip.5 Moreover, both plain square and round bars have been used to reinforce concrete structures,6 though only round bars were included in Abrams’ historic study.5 The extent of void formations beneath top-cast round and square bars due to the upward migration of water and mortar that occurs during concrete placement operations, and differences in concrete consolidation around the two bar shapes, might cause different relationships between the required lap splice length and the depth of concrete cast under the bar. Plain bars may also be more affected by casting position than deformed bars because the adhesion component of bond is a more dominant factor in the transfer of bond force for plain bars. ACI Structural Journal/March-April 2014
This paper presents the design and results of an experimental program to evaluate the effects of casting position and bar shape on plain steel bars longitudinally cast in lap splice specimens. RESEARCH SIGNIFICANCE Both round and square plain steel reinforcing bars are regularly encountered in historical structures, and criteria for assessing their bond strength are necessary. The results of an experimental investigation of lap splice specimens reinforced with plain bars are presented to evaluate the effects of bar shape and casting position on bond behavior. Such knowledge will aid in the development of bond provisions for the evaluation of concrete structures reinforced with plain steel bars. EXPERIMENTAL INVESTIGATION The description of the specimens, materials, and test setup are similar to those described by Hassan and Feldman,7 but are briefly described herein for comprehensiveness. Figure 1 shows the cross sections, elevation, and plan view for the 25 specimens in this study. Ten of the specimens, as identified in Table 1, were originally reported by Hassan and Feldman.7 All specimens had identical cross-sectional dimensions and span lengths. Figure 1(a) and (b) show the cross section of specimens with the round or square longitudinal reinforcement cast in the bottom and top positions, respectively. These cross sections show that the cover was held constant at 50 mm (2 in.) regardless of the size of the longitudinal reinforcing bars used in the various specimens. Earlier works2,8 suggested that the bond strength of plain reinforcement is independent of concrete cover because these bars lack mechanical interlock with the surrounding concrete; thus, the likelihood of a splitting failure is reduced. Specimens cast with top reinforcement were inverted before testing such that Fig. 1(c) shows the elevation of all specimens as tested, including the span length, loading, and reinforcing steel arrangement. The shear span-depth ratio, a/d, was approximately equal to 3.94 for all specimens. Figure 1(d) shows a plan view of the specimens and illustrates the arrangement of the spliced longitudinal bars. All specimens were designed to fail in bond, and had lap splice lengths Ls ranging from 12.8 to 32.1 times the longitudinal bar diameter for round bars or the side face dimenACI Structural Journal, Vol. 111, No. 2, March-April 2014. MS No. S-2012-097.R1, doi:10.14359.51686524, was received August 3, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
323
Table 1—Actual and predicted failure loads Predicted normalized maximum load Pmax /√fc′, kN/√MPa (lb/√psi)
Specimen identification*
Splice length as a function of bar size (Ls/db)
Concrete compressive strength fc′, MPa (psi)
Bar surface roughness Ry, μm (× 10–3 in.)
Maximum normalized load, Pmax /√fc′, kN/√MPa (lb/√psi)
19l-305↓†
16.1
17.4 (2520)‡
9.54 (0.376)
8.50 (159)
18.0 (337)
29.1 (544)
4.98 (93.0)
0.96 (17.9)
21.6
17.4 (2520)
‡
9.67 (0.381)
9.14 (171)
18.0 (337)
29.1 (544)
7.72 (144)
2.33 (43.5)
18.7 (2710)
‡
9.86 (0.388)
9.58 (179)
17.5 (327)
28.4 (530)
10.5 (196)
3.71 (69.2)
21.0 (3040)
‡
9.44 (0.372)
17.8 (332)
16.7 (311)
27.1 (507)
13.9 (259)
5.36 (100)
23.7 (3440)
‡
8.88 (0.350)
16.2 (302)
28.1 (524)
45.0 (840)
12.5 (233)
4.12 (76.9)
24.0 (3480)
‡
8.43 (0.332)
18.4 (343)
27.7 (518)
44.5 (831)
16.1 (300)
5.74 (107)
22.8 (3310)
‡
8.71 (0.343)
20.6 (384)
28.5 (532)
45.6 (851)
19.8 (370)
7.52 (140)
§
†
19l-410↓
†
19l-510↓
†
19l-610↓
†
25l-410↓
†
25l-510↓
†
25l-610↓
26.8 32.1 16.4 20.4 24.4
Neglecting strain hardening of reinforcement
Including strain hardening of reinforcement
CEB-FIP Model Code 1990
Draft CEB-FIP Model Code 2010
25l-410↑
16.4
27.1 (3930)
9.19 (0.362)
6.55 (122)
28.1 (524)
42.2 (788)
8.39 (157)
0.91 (17.0)
25l-510↑
20.4
28.0 (4060)§
9.09 (0.358)
4.69 (87.5)
27.7 (517)
41.7 (778)
11.1 (207)
1.76 (32.8)
25l-610↑
24.4
35.8 (5190)§
9.21 (0.362)
7.07 (132)
25.1 (468)
38.0 (710)
14.8 (276)
2.91 (54.3)
32l-410↓†
12.8
19.8 (2870)‡
9.92 (0.390)
15.6 (291)
44.5 (827)
63.2 (1180)
14.1 (263)
4.43 (82.7)
32l-610↓†
19.1
19.8 (2870)‡
9.72 (0.383)
25.1 (468)
44.3 (827)
63.2 (1180)
22.1 (412)
7.94 (148)
32l-810↓†
25.3
15.8 (2290)‡
10.1 (0.398)
31.8 (594)
46.9 (876)
64.0 (1190)
28.0 (523)
10.9 (203)
16.4
25.5 (3700)
§
8.79 (0.346)
16.1 (300)
38.3 (714)
55.3 (1030)
14.8 (276)
4.85 (90.5)
25.0 (3620)
§
8.83 (0.348)
20.0 (373)
38.3 (714)
55.2 (1031)
18.6 (347)
6.50 (121)
28.1 (4080)
§
8.86 (0.349)
26.8 (500)
36.6 (684)
53.4 (996)
22.9 (427)
8.24 (154)
33.0 (4790)
§
9.06 (0.357)
8.97 (167)
31.3 (585)
50.2 (937)
10.5 (196)
1.47 (27.4)
33.5 (4860)
§
9.17 (0.361)
11.2 (209)
31.1 (581)
49.9 (932)
13.6 (254)
2.37 (44.2)
33.0 (4790)
§
9.16 (0.361)
12.2 (228)
31.3 (585)
50.2 (937)
16.6 (310)
3.26 (60.8)
25.5 (3700)
§
9.36 (0.368)
17.4 (325)
50.6 (944)
73.7 (1380)
17.3 (323)
5.69 (106)
25.5 (3700)
§
9.24 (0.364)
20.1 (375)
50.8 (948)
74.0 (1380)
26.6 (496)
9.63 (180)
26.9 (3900)
§
9.17 (0.361)
28.3 (528)
49.5 (924)
72.9 (1360)
35.6 (664)
13.4 (250)
27.5 (4000)
§
9.29 (0.366)
12.6 (235)
49.4 (922)
73.0 (1360)
11.6 (216)
1.66 (31.0)
§
9.52 (0.375)
14.3 (267)
50.4 (941)
73.8 (1380)
17.9 (334)
3.54 (66.1)
9.34 (0.368)
16.2 (302)
50.4 (941)
73.8 (1380)
24.5 (457)
5.50 (103)
25n-410↓ 25n-510↓ 25n-610↓ 25n-410↑ 25n-510↑ 25n-610↑ 32n-410↓ 32n-610↓ 32n-810↓ 32n-410↑
20.4 24.4 16.4 20.4 24.4 12.8 19.1 25.3 12.8
32n-610↑
19.1
26.2 (3800)
32n-810↑
25.3
26.2 (3800)§
*
First number in specimen identification represents nominal diameter for round bars or side face dimension for square bars. Solid circle (l) or square (n) identifies shape of longitudinal reinforcement. Number following hyphen denotes lap splice length, in millimeters, with an up arrow (↑) showing that longitudinal bars were cast in top position, and down arrow (↓) showing that bars were cast in bottom position. † Originally reported by Hassan and Feldman (2012). ‡ Specimens cast with Concrete Mixture Proportion 1. § Specimens cast with Concrete Mixture Proportion 2.
sion for square bars. Specimen dimensions and lap splice lengths were selected to match those reported by Idun and Darwin9 for tests of specimens with deformed bars. A direct comparison of the specimens with plain and deformed bars is reported elsewhere.7 Figure 2 shows that a vertical load was applied using a spreader beam with a self-weight that exerted a load P of 1.77 kN on the specimens to establish the four-point loading arrangement. Loading was applied at a rate of 0.0015 mm/s (0.0006 in./s) to failure. Concrete The concrete had a target compressive strength of 20 MPa (2900 psi). General purpose (Type GU) portland cement was used without admixtures. Table 1 indicates the mixture 324
proportion used to cast each specimen. Mixture Proportion 1 consisted of a crushed limestone and granite coarse aggregate blend and a silica sand fine aggregate. The mixture proportion per cubic meter (cubic yard) of concrete was: 250 kg (421 lb) cement, 1100 kg (1854 lb) sand, 1100 kg (1854 lb) crushed coarse aggregate, and 140 L (28.3 gal.) water. Mixture Proportion 2 consisted of a carbonate, gneiss, and granite coarse aggregate blend and a washed silica sand fine aggregate. The mixture proportion per cubic meter (cubic yard) of concrete was: 270 kg (455 lb) cement, 993 kg (1674 lb) sand, 1039 kg (1751 lb) crushed coarse aggregate, and 145 L (29.3 gal.) water. The maximum size of the coarse aggregate used in both mixture proportions was 20 mm (0.8 in.), and all aggregates conformed to CAN/ CSA A23.1-09.10 It should be noted that the effect of mixture ACI Structural Journal/March-April 2014
Fig. 1—Splice specimen geometry: (a) cross section for specimens with bottom-cast longitudinal reinforcement; (b) cross section for specimens with top-cast reinforcement; (c) elevation; and (d) plan view. (Note: Dimensions are given in mm [in.].)
Fig. 2—Test setup. ACI Structural Journal/March-April 2014
325
Table 2—Longitudinal reinforcing steel properties Bar identification
Static yield strength fys, MPa (ksi)
Dynamic yield strength fyd, MPa (ksi)
Ultimate strength fu, MPa (ksi)
Modulus of elasticity Es, GPa (ksi)
19l↓
326 (47.3)
355 (51.5)
520 (75.4)
203 (29,400)
25l↓
322 (46.7)
346 (50.2)
534 (77.4)
196 (28,400)
25l↑
340 (49.3)
364 (52.8)
522 (75.7)
243 (35,200)
32l↓
318 (46.1)
348 (50.5)
504 (73.1)
204 (29,600)
25n↓
357 (51.8)
381 (55.2)
544 (78.9)
192 (27,800)
25n↑
325 (47.1)
349 (50.6)
542 (78.6)
207 (30,000)
32n↓ and 32n↑
320 (46.4)
343 (49.7)
527 (76.4)
196 (28,400)
proportion on bond strength was not within the scope of the current investigation. Rather, the change in mixture proportions resulted from a change in ready-mix suppliers. Bleed water measurements were not conducted as part of this investigation. Table 1 shows the concrete compressive strength of the specimens at the time of testing as established from the results of companion concrete cylinders stored under the same conditions and tested on the same day as the corresponding splice specimen. Specimens were moist cured using wet burlap and plastic sheets for 7 days following casting, and were then stored in the laboratory until testing. Reinforcement All principal longitudinal reinforcement was hot-rolled CSA G40.21 300W steel. Figure 1(c) shows that the bars had 180-degree hooks at the ends adjacent to the beam supports to ensure that the bond failure occurred within the lap splice length. The material properties were established from coupons obtained from surplus bar lengths and tested in accordance with ASTM A370.11 Table 2 shows the static yield strength fys calculated in accordance with Rao et al.,12 dynamic yield strengths fyd, ultimate strength fu, and modulus of elasticity Es for all longitudinal bar sizes used. The longitudinal reinforcing bars were sandblasted using 220-grit aluminum oxide, a nozzle distance of 125 mm (5 in.), and a blast pressure of 698 kPa (100 psi) to increase the surface roughness and make them more representative of historical bars.8 The surface roughness of each bar was characterized by the maximum height of profile Ry, established as the distance between the highest peak and the deepest valley on the bar surface.13 Table 1 shows the average Ry values for the longitudinal reinforcing bars in each specimen based on a total of 30 roughness measurements on each bar using a surface roughness tester and a single 0.25 mm (0.01 in.) stroke. The shear reinforcement consisted of 12.7 mm (0.5 in.) diameter hot-rolled CSA G40.21 300W plain steel bars spaced at 200 mm (8 in.) on center within the shear spans, and 250 mm (10 in.) on center within the constant moment region outside of the lap splices (Fig. 1(d)). Two additional stirrups were placed in the splice region one-quarter of the splice length, but not exceeding 150 mm (6 in.), from the ends of the splice to prevent prying action of the longitudinal reinforcement. The specimens had considerably more shear reinforcement than strictly necessary to ensure that failure 326
would be governed by bond between the longitudinal reinforcement and the surrounding concrete. EXPERIMENTAL RESULTS Table 1 shows the observed maximum loads attained by the specimens and those predicted assuming yielding of the reinforcement, both neglecting and including strain hardening, and predicted loads based on average bond stress provisions for plain reinforcement included in the CEB-FIP Model Code 199014 and the CEB-FIP draft Model Code 2010.15 The predicted loads have been reduced by the weight of the spreader beam and the specimen self-weight to allow for a direct comparison with the maximum loads that were recorded during testing. All reported loads have been normalized by the square root of the concrete compressive strength given that a previous work8 showed that it is valid for plain reinforcement and is consistent with familiar equations for deformed bars. The specimens are identified by mark numbers that include two numbers and associated symbols separated by a hyphen. The first number represents the nominal diameter for round bars or the nominal side face dimensions for square bars db, in millimeters, used to longitudinally reinforce the specimens. A solid circle (l) or square (n) following this number identifies the shape of the longitudinal reinforcement. The number following the hyphen denotes the lap splice length Ls in millimeters, with an up arrow (↑) showing that the longitudinal bars were cast in the top position (Fig. 1(b)), or a down arrow (↓) showing that the bars were cast in the bottom position (Fig. 1(a)). Table 1 shows that the maximum normalized load reported for Specimen 25l-510↑ was only 72% that of Specimen 25l-410↑, a specimen cast from the same batch of concrete. This result was considered suspect because specimens with longer splice lengths should be able to resist higher loads when all other variables are held constant. Removal of the concrete surrounding the longitudinal reinforcement was completed for Specimen 25l-510↑ following testing; however, no voids were identified that would have impaired the bond between the reinforcement and the surrounding concrete. This specimen therefore could not be identified as a physical outlier, and is included in the regression analysis as will be presented in a subsequent section. Table 1 shows that all but Specimen 19l-610↓ failed at loads well below those predicted using the flexural resistance procedures in ACI 318-1116 with resistance factors set ACI Structural Journal/March-April 2014
equal to unity, and thus suggest that these specimens failed in bond. The load-deflection behavior and crack patterns for all specimens is consistent with that described by Hassan and Feldman,7 including that of Specimen 19l-610↓, which, based upon its load-deflection behavior, failed in bond even though it attained a maximum load of 106% that predicted assuming yielding of the reinforcement. Comparison of test results with predictions based on European code provisions Both the CEB-FIP Model Code 199014 and the draft Model Code 201015 provide equations for the average bond stress for plain reinforcement, and thus allow for a prediction of the maximum normalized load resisted by the specimens in the study, as reported in Table 1. The design average bond stress uave for reinforcing bars is specified in the CEB-FIP Model Code 199014 as
uave = η1η2 η3 fctd
(1)
where η1 is a factor that accounts for the reinforcing type, and is equal to 1.0 for plain bars; η2 considers the casting position of the reinforcement, and is equal to 1.0 and 0.7 for bottom and top cast reinforcement, respectively; η3 considers the bar size, and is equal to 1.0 for bars with a diameter db of 32 mm (1.25 in.) or less and (132 – db)/100 for db > 32 mm (1.25 in.); and fctd is the design tensile strength of the concrete in MPa. Bond provisions have changed markedly in the CEB-FIP draft Model Code 2010.15 The basic average bond strength uave, which can be used to assess plain reinforcement, is uave = η1η2 η3 η4 ( fck 20 )
0.5
γc
(2)
where η1 is equal to 0.9 for plain bars; η2 is equal to 1.0 and 0.5 for plain bars cast in the bottom and top positions, respectively; η3 is equal to 1.0 for db ≤ 20 mm (0.79 in.) and (20/db)0.3 for larger bar sizes; η4 accounts for the characteristic yield stress of the reinforcement and is equal to 1.2 for reinforcement with a yield stress equal to, and presumably less than, 400 MPa (58.0 ksi); fck is the characteristic value of the cylinder compressive strength of the concrete, in MPa; and γc is a partial factor for the concrete compressive strength set equal to unity for the case of using Eq. (2) as a predictive, rather than design, equation. Neither edition of the CEB-FIP Model Code14,15 specifically provides for square reinforcing bars. An analysis of archival test results of pullout specimens reinforced with historical round and square bars whose deformation patterns did not conform to ASTM A305-4917 was performed by Howell and Higgins18 and showed that the simplified ACI development length equations19 provided a lower bound for both bar shapes, where square bars were evaluated by calculating their equivalent round diameter db,EQ
db, EQ =
4 db 2 π
ACI Structural Journal/March-April 2014
(3)
The bar size factor η3 in Eq. (1) and (2) was therefore calculated assuming db = db,EQ for the case of specimens longitudinally reinforced with square bars. The predicted maximum normalized loads for all specimens tested were then calculated assuming a linear strain distribution along the height of the specimen and the stress versus strain distribution for the concrete as obtained from companion specimens tested in conjunction with each splice specimen. The neutral axis location was established from cracked transformed section properties because all specimens failed in bond, and, with the exception of Specimen 19l-610↓, at loads well below those predicted based on yielding of the longitudinal reinforcement. Figure 3(a) shows the ratio of the test-to-predicted maximum loads based on the CEB-FIP Model Code 199014 provisions, Pmax /(Pmax)CEB,1990, for all specimens. Values of Pmax /(Pmax)CEB,1990 > 1.0 suggest that the predicted values are conservative, whereas values of Pmax /(Pmax)CEB,1990 < 1 suggest that the same values are unconservative. The average Pmax /(Pmax)CEB,1990 for all specimens with bottom-cast round bars is equal to 1.2, and so suggests that the CEB-FIP Model Code 199014 provisions reasonably and conservatively capture the bond behavior of these bars. The same code provisions, however, do not appear to capture the behavior of specimens with bottom- (average Pmax /(Pmax)CEB,1990 = 0.98) or top-cast square bars (average Pmax /(Pmax)CEB,1990 = 0.83), or specimens reinforced with top-cast round bars (average Pmax /(Pmax)CEB,1990 = 0.56). Figure 3(b) shows that the ratio of the test-to-predicted loads based on the CEB-FIP draft Model Code 201015 provisions, Pmax /(Pmax)CEB,2010, for all specimens. All values of Pmax /(Pmax)CEB,2010 exceed 2.0, which suggests that the CEB-FIP draft Model Code 201015 provisions are overly conservative. Figure 3(b) does suggest that these provisions are also more conservative when estimating the capacity of specimens cast with the longitudinal reinforcement in the top position, and that the provisions tend to be more conservative for specimens with shorter lap splice lengths for both bar shapes and casting positions. Top casting effects Figure 4 shows the ratio of the maximum normalized loads for each pair of specimens for which the same size, shape, and lap splice length were provided for longitudinal reinforcement, but with this reinforcement cast in the top position for one specimen, and cast in the bottom position for the other specimen. Figure 4 shows that all specimens with top cast reinforcement failed at loads well below those for bottom cast reinforcement, with a resulting average ratio of the normalized maximum loads equal to 0.51. The results of this limited investigation suggest that square reinforcement, with an average ratio of 0.60, is less sensitive to casting position than round bars, with a resulting average ratio of 0.33. Furthermore, the larger square reinforcing bar size, db = 32 mm (1.25 in.), used to longitudinally reinforce the specimens, appears to be less sensitive to casting position than the smaller square bars with db = 25 mm (1 in.). Current American16 and Canadian20 code provisions for reinforced concrete require a 30% increase in development 327
Fig. 4—Ratio of normalized maximum loads for pairs of specimens with longitudinal reinforcement in top versus bottom cast position. below the bottom face of the bar only and will affect a much smaller portion of the overall perimeter.
Fig. 3—Test-to-predicted ratio of maximum normalized loads: (a) predicted loads based on CEB-FIP 1990 code provisions; and (b) predicted loads based on CEB-FIP 2010 draft code provisions. length for deformed bars cast in the top position (that is, when more than 300 mm [12 in.] of fresh concrete is placed below the reinforcement), whereas the CEB-FIP Model Code 199014 provides a multiplier of 0.7 to the average bond stress in such cases. The modifiers in all three of these codes appear to be unconservative for plain bars in light of the results discussed in the previous paragraph. Furthermore, a previous investigation conducted by Chana21 also concludes that the bond of plain bars is more affected by casting position than that of deformed bars. This conclusion appears justified upon consideration of the mechanics of bond. The adhesion between the concrete and the reinforcement is a more dominant factor in the transfer of bond forces for plain reinforcement, because they cannot transfer these forces by mechanical interlock.22 In contrast, the CEB-FIB draft Model Code 201015 provides a multiplier of 0.5 specifically for plain bars cast in the top position, and appears to be more reasonable when compared with the results in the current investigation. The test results presented herein, however, also show that square bars are less sensitive to casting position than round bars due to differences in the shape of voids that form beneath these two bar shapes. For round bars, the concrete tends to settle such that a void forms under the bottom half of the perimeter23; whereas for square bars, assuming construction allows them to be placed perfectly square within the reinforcing cage as shown in Fig. 1(a) and (b), the void will form
328
Effect of bar shape as assessed using predictive equations for maximum normalized load A regression analysis of the 25 specimens yields the following empirical equation for the normalized maximum load Pmax
fc′
= 9.38 × 10 −5 Ls db Ry +
Ls (0.24 + 0.15kb − 0.50kc ) (4) db
where Ls is the lap splice length, in mm; db is the longitudinal bar size, in mm, reported as the measured bar diameter for round bars or the measured side face dimension for square bars; Ry is the surface roughness of the longitudinal reinforcement, in μm; kb is an indicator variable for the shape of the longitudinal bars, and is equal to zero for round bars and 1 for square bars; and kc is an indicator variable for the casting position of the longitudinal reinforcement, and is equal to 0 if the bars are cast in the bottom position (Fig. 1(a)), and 1 if the bars were cast in the top position (Fig. 1(b)). The root mean square error for Eq. (4) is 2.91 kN/√MPa (54.3 lb/√psi). Using an equivalent round diameter db,EQ, as described by Eq. (3), results in the following predictive equation that allows for the elimination of the indicator variable kb Pmax
fc′
= 3.36 × 10 −4 Ls Ry db, EQ 0.5 (2.12 − kc )
(5)
where db,EQ is the diameter for round bars and the equivalent round diameter of square bars. The resulting root-meansquare error of 3.01 kN/√MPa (56.2 lb/√psi) for Eq. (5) is similar to that reported for Eq. (4), and suggests that using the equivalent round diameter for plain square bars is reasonable. Results of a previous investigation8 have shown that the average surface roughness, Ry = 9.26 μm, for the 25 specimens included in the regression analysis is a lower bound for ACI Structural Journal/March-April 2014
Fig. 5—Comparison of recorded normalized maximum loads to those predicted empirically using Eq. (6) for: (a) specimens cast with round longitudinal bars; and (b) specimens cast with square longitudinal bars. that of historical bars. Furthermore, the analysis presented in the previous section suggests that multipliers of 0.3 and 0.6 for round and square longitudinal bars, respectively, reasonably capture the reduction in bond resistance provided by bars in the top cast position. The following simplified predictive normalized maximum load equation therefore results
Pmax
fc′
= 6.63 × 10 −3 Ls ψ t db, EQ 0.5
(6)
where ψt is a factor used to modify the lap splice length based on the location of the longitudinal reinforcement, and is equal to 1.0 for both round and square bars cast in the bottom position, 0.3 for round bars cast in the top position, and 0.6 for square bars cast in the top position. The resulting root-mean-square error for Eq. (6) is 2.44 kN/√MPa (45.5 lb/√psi). Figure 5 shows the fit of Eq. (6) with the experimental test data, with Fig. 5(a) showing all data for specimens longitudinally reinforced with round bars, and Fig. 5(b) showing all data for specimens longitudinally reinforced with square bars. It should be noted that a linear and proportional relationship, with Pmax /√fc′ = 0 for Ls = 0, is the best fit. This finding differs from the linear, but not proportional, relationship reported for deformed bars16 and prestressing strands.24 An alternate method of evaluating the goodness of fit of Eq. (6) to the test data is presented in Fig. 6, which shows the predicted normalized load calculated in accordance with Eq. (6) versus the recorded maximum normalized load for all 25 specimens in the test database. Also shown is the proportional line, which represents the theoretical case that the predicted maximum normalized load exactly equals that recorded during specimen testing. Specimen markers falling above this line represent cases for which the maximum normalized load, predicted in accordance with Eq. (6), exceeds the maximum normalized load recorded during specimen testing. Similarly, markers falling below the proportional line represent cases for which Eq. (6) underestimates the maximum normalized load recorded during specimen testing. A review of the data presented in Fig. 6 shows that the mean and standard deviation obtained for specimens longitudinally reinforced with square bars cast in the bottom position were 1.04 and 0.154, respectively. Similarly, specimens ACI Structural Journal/March-April 2014
Fig. 6—Predicted versus recorded maximum normalized loads. cast with square longitudinal bars cast in the top position attained a mean predicted-recorded maximum normalized load ratio of 1.02, and a standard deviation of 0.151. Results for specimens longitudinally reinforced with round bars in the bottom position had a mean predicted-recorded load ratio of 0.983, and a standard deviation of 0.159. In contrast, specimens longitudinally reinforced with round bars cast in the top position attained a mean value and standard deviation for the predicted-recorded applied load ratios of 1.22 and 0.340, respectively. The higher standard deviation obtained for specimens cast with round longitudinal bars in the top position is likely due to the limited number of such specimens in the test database and the sensitivity of round bars to casting position, as outlined in the previous section. SUMMARY AND CONCLUSIONS Twenty-five lap splice specimens with a shear span-depth ratio approximately equal to 3.94 were reinforced with plain round or square longitudinal steel bars in the top or bottom position to evaluate the effects of casting position and bar shape on bond. Specimens were 305 mm (12 in.) wide by 410 mm (16 in.) tall, with a span length of 4570 mm (15 ft), and were subjected to four-point loading. Lap splice lengths ranged from 12.8 to 32.1 times the longitudinal bar diameter or side face dimension for the case of round and square longitudinal bars, respectively. The following significant observations and conclusions were noted: 329
• •
•
• •
•
All specimens failed due to bond loss between the longitudinal reinforcement and the surrounding concrete; Square longitudinal bars may be evaluated by calculating their equivalent round diameter, based on equal cross-sectional areas of the actual square reinforcing bar and the equivalent round bar; Predictions of the maximum applied load based on CEB-FIP Model Code 1990 provisions for bond reasonably and conservatively capture the behavior of specimens with bottom cast round bars, but do not appear to capture the behavior of specimens with bottom- or top-cast square bars or specimens with top-cast round bars; Maximum load predictions based on the CEB-FIP draft Model Code 2010 provisions for bond are overly conservative for all combinations of bar shapes and casting positions; Square bars appear to be less sensitive to casting position than round bars. Top cast factors of 0.3 and 0.6 for round and square bars, respectively, reasonably capture the reductions in bond resistance based on the range of parameters evaluated in this study; and A regression analysis of the specimens shows that a linear and proportional relationship for maximum load as a function of lap splice length, casting position, and equivalent diameter provides a best fit for the test data. ACKNOWLEDGMENTS
Financial support was provided by a Natural Science and Engineering Council of Canada Discovery Grant for the second author and by scholarship support for the first author from the University of Saskatchewan.
AUTHOR BIOS
Montserrat Sekulovic MacLean is a Junior Engineer with KTA Structural Engineers Ltd., Calgary, AB, Canada. She received her MSc in the Department of Civil and Geological Engineering at the University of Saskatchewan, Saskatoon, SK, Canada. Lisa R. Feldman, FACI, is an Associate Professor in the Department of Civil and Geological Engineering at the University of Saskatchewan. She is a member of ACI Subcommittee 318-R, Code Reorganization, and Chair of Joint ACI-ASCE Committee 408, Development and Splicing of Deformed Bars.
330
= = =
NOTATION
shear span effective depth of reinforced splice specimens diameter for round bars or side face dimension for square bars db,EQ = equivalent diameter for square bars E s = modulus of elasticity of reinforcement fc′ = concrete compressive strength fck = characteristic value of cylinder compressive strength of concrete fctd = design value of concrete tensile strength fu = ultimate strength of reinforcement fyd = dynamic yield strength of reinforcement fys = static yield strength of reinforcement kb = indicator variable for bar shape kc = indicator variable for casting position Ls = spliced length of longitudinal reinforcing bars P = applied load Pmax = maximum applied load (Pmax)CEB,1990 = maximum applied load predicted using CEB-FIP Model Code 1990 provisions (Pmax)CEB,2010 = maximum applied load predicted using CEB-FIP draft Model Code 2010 provisions R y = bar surface roughness uave = average bond stress γc = partial factor for concrete compressive strength η1 = factor to describe reinforcing type a d db
η2 η3 η4 ψt l, n ↑, ↓
= = = = = =
factor to account for bond conditions factor to account for bar size factor to account for characteristic yield strength of reinforcement modification factor for bar shape and casting position symbols identifying bar shape symbols identifying casting position of reinforcement
REFERENCES
1. Feldman, L. R.; MacFarlane, D. C.; Kroman, J. A.; and Bartlett, F. M., “Construction Staging of the Centre Street Bridge Rehabilitation to Accommodate Emergency Vehicle Traffic,” 31st Annual Conference of the Canadian Society for Civil Engineering, 2003, 10 pp. (CD-ROM) 2. Baldwin, M. I., and Clark, L. A., “The Assessment of Reinforcing Bars with Inadequate Anchorage,” Magazine of Concrete Research, V. 47, No. 171, June 1995, pp. 95-102. 3. Hassanain, M. A., and Loov, R. E., “Cost Optimization of Concrete Bridge Infrastructure,” Canadian Journal of Civil Engineering, V. 30, No. 5, Oct. 2003, pp. 841-849. 4. Mirza, M. S., and Haider, M., The State of Infrastructure in Canada: Implications for Infrastructure Planning and Policy, McGill University, Montreal, QC, Canada, 2003, 53 pp. 5. Abrams, D. A., “Tests of Bond Between Concrete and Steel,” University of Illinois Bulletin No. 71, University of Illinois at Urbana-Champaign, Urbana, IL, 1913, 240 pp. 6. Feldman, L. R., and Bartlett, F. M., “Design of a Testing Program for Bond of Plain Reinforcement,” 5th International PhD Symposium in Civil Engineering, Delft, the Netherlands, 2004, pp. 145-153. 7. Hassan, M. N., and Feldman, L. R., “Behavior of Lap-Spliced Plain Steel Bars,” ACI Structural Journal, V. 109, No. 2, Mar.-Apr. 2012, pp. 235-243. 8. Feldman, L. R., and Bartlett, F. M., “Bond Strength Variability in Pullout Specimens with Plain Reinforcement,” ACI Structural Journal, V. 102, No. 6, Nov.-Dec. 2005, pp. 860-867. 9. Idun, E. K., and Darwin, D., “Improving the Development Characteristics of Steel Reinforcing Bars,” SM Report No. 41, University of Kansas Center for Research, Lawrence, KS, 1995, 267 pp. 10. CAN/CSA-A23, 1/A23.2-09, “Concrete Materials and Concrete Construction/Test Methods and Standard Practices for Concrete,” Canadian Standards Association, Mississauga, ON, Canada, 2009, 582 pp. 11. ASTM A370-97a, “Standard Test Methods and Definitions for Mechanical Testing of Steel Products,” ASTM International, West Conshohocken, PA, 1997, 52 pp. 12. Rao, N. R. M.; Lohrmann, M.; and Tall, L., “Effects of Strain Rate on the Yield Stress of Structural Steels,” ASTM Journal of Materials, V. 1, No. 1, May 1966, pp. 241-262. 13. Mitutoyo, “SJ-201 Surface Roughness Tester User’s Manual No. 99MBB0796A,” Mitutoyo Corporation, Kanagawa, Japan, 2006, 190 pp. 14. CEB-FIP, “CEB-FIP Model Code (1990),” Comité Euro-Internationale du Béton (CEB), Thomas Telford Ltd., London, UK, 1993, 437 pp. 15. CEB-FIP, “fib Bulletin 55: Model Code 2010, First Complete Draft— Volume 1,” Comité Euro-Internationale du Béton (CEB), International Federation for Structural Concrete (fib), Lausanne, Switzerland, 2010, 292 pp. 16. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp. 17. ASTM A305-49, “Minimum Requirements for the Deformations of Deformed Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 1949, 3 pp. 18. Howell, D. A., and Higgins, C., “Bond and Development of Deformed Square Reinforcing Bars,” ACI Structural Journal, V. 104, No. 3, May-June 2007, pp. 333-343. 19. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05),” American Concrete Institute, Farmington Hills, MI, 2005, 430 pp. 20. CAN/CSA-A23, 3-04, “Design of Concrete Structures,” Canadian Standards Association, Mississauga, ON, Canada, 2004, 258 pp. 21. Chana, P. A., “A Test Method to Establish a Realistic Bond Stress,” Magazine of Concrete Research, V. 24, No. 151, 1990, pp. 83-90. 22. Feldman, L. R., and Bartlett, F. M., “Bond Stresses Along Plain Steel Reinforcing Bars in Pullout Specimens,” ACI Structural Journal, V. 104, No. 6, Nov.-Dec. 2007, pp. 685-692. 23. Söylev, T. A., “The Effect of Fibres on the Variation of Bond Between Steel Reinforcement and Concrete with Casting Position,” Construction & Building Materials, V. 25, No. 4, Apr. 2011, pp. 1736-1746. 24. Barnes, R. W.; Burns, N. H.; and Kreger, M. E., “Development Length of 0.6-Inch Prestressing Strands in Standard I-Shaped Pretensioned Concrete Beams,” Research Report 1388-1, Center for Transportation Research, University of Texas at Austin, Austin, TX, 2000, 338 pp.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S29
Performance of Glass Fiber-Reinforced Polymer-Doweled Jointed Plain Concrete Pavement under Static and Cyclic Loadings by Brahim Benmokrane, Ehab A. Ahmed, Mathieu Montaigu, and Denis Thebeau Glass fiber-reinforced polymer (GFRP) dowel bars are a non-corrodible and maintenance-free alternative that will potentially reduce the life-cycle cost of jointed plain-concrete pavement (JPCP), especially in harsh environmental conditions. This paper investigates the performance of GFRP dowels in JPCP under static and cyclic loads. In addition, it compares their behavior with that of commonly used epoxy-coated steel dowels. GFRP and epoxy-coated steel dowels were employed in fabricating a total of six JPCP prototypes (slab-joint). The test prototypes measured 2440 mm long x 610 mm wide x 254 mm deep (96 x 24 x 10 in.). The slabs were cast with a butted joint; each test prototype contained two dowel bars. The test parameters included: 1) dowel-bar type (GFRP and epoxy-coated steel); 2) dowel-bar diameter (34.9 and 38.1 mm [1.38 and 1.50 in.] for GFRP; 28.6 mm [1.13 in.] for epoxy-coated steel); and 3) loading scheme (static and cyclic). The test results revealed that both 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels showed crack patterns and failure modes similar to those of the epoxy-coated steel dowels. The 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels and 28.6 mm (1.13 in.) epoxy-coated steel dowels were not affected by 1,000,000 cycles between 10 and 50 kN (2.25 and 11.24 kip). In addition, both the 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels showed higher joint effectiveness than that of the 28.6 mm (1.13 in.) epoxy-coated steel dowels. This paper also discusses the results of a field application in which the GFRP dowels were implemented in a new concrete-pavement highway in Mirabel, QC, Canada. Keywords: cyclic; design; dowel; fiber-reinforced polymers; field application; joint; joint effectiveness; pavement; static.
INTRODUCTION Jointed plain-concrete pavements (JPCPs) are commonly constructed with contraction joints to accommodate slab movements due to temperature and moisture variations (Ioannides and Korovesis 1992). The joints may either be longitudinal, parallel to traffic, or transverse, perpendicular to traffic. Transverse joints are placed at regular intervals, creating discontinuities in the pavement and forming a series of slabs. Load transfer within a series of concrete slabs takes place across these joints. Thus, an effective load-transfer device should be present to transfer the loads between adjacent slabs (Porter 2005). Dowel bars are installed at the transverse joints of the concrete slabs to reduce the deflections and stresses at the joints while transferring the traffic load from one slab to the adjacent slab (Westergaard 1928). In addition, the dowel-bar system works well with both narrow and wide joints (Maitra et al. 2009). The load-transfer efficiency of a joint is assessed by joint effectiveness E, as specified by the American Concrete Pavement Association (ACPA 1991). ACI Structural Journal/March-April 2014
Joint effectiveness E based on the measured deflections of loaded and unloaded sides of the joint is given by Eq. (1)
E = 2 ⋅ δ u (δ l + δ u ) × 100 (1)
where E is the joint effectiveness; δu is the deflection of the unloaded slab; and δl is the deflection of the loaded slab. When the deflections of the slabs on both sides of the joint are equal, the joint is considered 100% effective. On the other hand, if the unloaded side of the joint experiences no deflection, the joint is considered 0% effective. ACPA (1991) recommends an adequate effectiveness of 75% in pavement joints. Load-transfer efficiency LTE (AASHTO 1993) is another quantitative measure for assessing joint efficiency. Equation (2) provides deflection-based LTE
LTE = δ u δ l × 100 (2)
ACPA (1991) considers corrosion of steel dowels as one of the main reasons of premature concrete failure, resulting from corrosion initiated by the chloride from deicing salts infiltrating the joints. Because the smooth dowel bars are assumed to be frictionless and permit free relative movement of slabs due to temperature changes, the corrosion causes the steel surface to exfoliate, so that the dowels lock in the joint. Locking, in turn, exerts excessive tensile loads on the surrounding concrete with attendant stress concentration on the concrete and greater movement around the joint, which hasten the rate of joint failure (FRP Dowel Bar Team 1998). Furthermore, corrosion of the steel dowels may restrain free movement under temperature variations. The restriction of free movement of slabs with respect to the dowels produces high tensile stresses, which, in turn, result in mid-slab cracking (William and Shoukry 2001). A common method to make steel dowels more durable is coating them with fusion-bonded epoxy. Unfortunately, epoxy-coated steel dowels exhibit the same performance problems normally associated with surface coating, including voids and damage during transportation and handling. The concentrated corrosive mechanisms at defects have led, in some cases, to more rapid failure than the same ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-098, doi:10.14359.51686525, was received March 16, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
331
steel reinforcement without an epoxy coating (FRP Dowel Bar Team 1998). Glass fiber-reinforced polymer (GFRP) dowels do not corrode, and are maintenance-free. Consequently, employing GFRP dowels in JPCP as an alternative to the commonly used epoxy-coated dowels will eliminate the potential of corrosion and extend the service life of jointed concrete pavements. A few studies have been conducted to investigate the feasibility of GFRP dowel bars as an alternative to steel in jointed concrete pavements (Porter et al. 1996; Davis and Porter 1998; Porter et al. 2001; Eddie et al. 2001; Smith 2001). These investigations supported the use of GFRP dowels as a potential solution to the corrosion issues of steel dowels in JPCP. Unlike the United States, which has the Federal Highway Administration (FHWA), Canada has no single agency responsible for funding pavement construction and rehabilitation or for setting pavement design standards. Pavement design for Canada’s primary highway network comes under provincial jurisdiction, while the federal government retains responsibility for national-park roadways. Each agency is free to use whatever design procedure it chooses for JPCP design and rehabilitation (Canadian Strategic Highway Research Program 2002). The Ministry of Transportation of Quebec (MTQ) has attempted to overcome corrosion-associated problems when steel dowels are used. More than 350 km (217.5 miles) of JPCP has been built in Quebec since 1994. The method commonly employed for more durable pavement has been using epoxy-coated steel dowels. These dowels, however, have evidenced performance problems normally associated with surface coating, including voids, corrosion, and damage during transportation and handling. Through an extended collaborative project between the MTQ and the University of Sherbrooke, new GFRP dowels were developed, and their long-term durability performance was assessed (Montaigu et al. 2013). In this investigation, the GFRP dowels were conditioned in harsh environments at high temperatures for different duration periods. The findings of this investigation demonstrated the high stability of vinylester-based GFRP dowels in concrete environment. This paper, however, investigated the performance of these newly developed vinylester-based GFRP dowels in JPCP under static and cyclic loadings in laboratory conditions. In addition, it compared their structural performance with that of epoxy-coated steel dowels in JPCP. This paper also discusses the results of a field application in which the GFRP dowels tested were installed in a new concrete-pavement highway (Hwy 15 North) in Mirabel, QC, Canada. RESEARCH SIGNIFICANCE GFRP dowels appeared as a possible cost-effective solution for JPCP. Few studies have investigated the feasibility of using GFRP dowels in pavements. The reported study investigated the structural performance and effectiveness of the newly developed vinylester-based GFRP dowel bars (34.9 and 38.1 mm [1.38 and 1.50 in.]) under static and cyclic loadings, and in a field application. In addition, it compared the behavior of JPCP with either GFRP or epoxycoated steel dowels in transverse joints. 332
Fig. 1—Details of test prototypes and GFRP dowels. EXPERIMENTAL PROGRAM GFRP dowel characterization The research involved GFRP dowels measuring 34.9 and 38.1 mm (1.38 and 1.50 in.) in diameter (Fig. 1) and epoxycoated steel reference dowels 28.6 mm (1.13 in.) in diameter. The GFRP dowels were made of continuous E-glass fibers in vinylester resin using the pultrusion process. The fiber content was 80.6% by weight. The physical and mechanical properties of the GFRP dowels were determined using the appropriate test methods provided in CSA S807 (Canadian Standards Association 2010) and ACI 440.6 (ACI Committee 440 2008). Mechanical characterization included testing representative specimens of the GFRP dowel bars to determine transverse shear strength (ACI 440.3R [ACI Committee 440 2004], Test Method B.4), interlaminate shear (short-beam test) (ASTM D4475), flexural strength, and flexural modulus of elasticity (stiffness) (ASTM D4476). Table 1 presents the physical and mechanical properties of the GFRP dowels obtained from testing. Test prototypes A total of six JPCP prototypes were constructed and tested. The prototypes included two reinforced with GFRP dowels 34.9 mm (1.38 in.) in diameter, two reinforced with GFRP dowels 38.1 mm (1.50 in.) in diameter, and two reinforced with epoxy-coated steel dowels 28.6 mm (1.13 in.) in diameter. For each dowel type and diameter, one prototype was tested under monotonic load (Phase I), while the second one was tested using a cyclic-load scheme (Phase II). The test prototypes were 2440 mm long x 610 mm wide x 254 mm deep (96 x 24 x 10 in.). The slabs were cast with a 19 mm (0.75 in.) butt joint, and each test prototype had two dowel bars spaced 305 (12 in.) mm apart. Figure 1 shows the dimensions and details of the pavement prototypes. The length of the specimens was selected based on finite-element modeling (Maitra et al. 2009), which simulated the experimental study conducted by the U.S. Naval Civil Engineering Research and Evaluation Laboratory (Keeton and Bishop 1957). This study revealed that the vertical shear force in a dowel beyond a distance of approximately 1200 mm (4 ft) from the center of the load was insignificant. Thus, 2440 mm (8 ft) was selected as the total length for the jointed slab prototypes for this study. The geometry
ACI Structural Journal/March-April 2014
Table 1—Physical and mechanical properties of GFRP dowel bars Physical properties GFRP dowel diameter, mm
34.9
Mechanical properties GFRP dowel diameter, mm
34.9
38.1
Fiber type
Glass E-type
38.1
Transverse shear strength, MPa
184 ± 2
173 ± 3
Resin type
Vinyl ester resin
Short beam shear strength, MPa
61 ± 0
54 ± 2
Fiber content, %
80.7
80.6
Four-point flexural strength, MPa
1210 ± 50
1077 ± 61
Cure ratio, %
100
100
Flexural modulus of elasticity, GPa
50.3 ± 0.5
51.6 ± 0.8
Tg, oC
124
123
—
—
—
Moisture uptake, %
0.06
0.07
—
—
—
Notes: 1 mm = 0.0394 in.; 1 MPa = 0.145 ksi; 1 GPa = 145 ksi; °C = 5/9(°F – 32).
and dimensions of the slab prototypes were consistent with jointed slab prototypes tested elsewhere (Eddie et al. 2001). The prototypes were fabricated with a MTQ Type III-A concrete with a target 28-day compressive strength of 35 MPa (5.1 ksi), as specified in Standard 3101 for MTQ normal-density mass concrete (MTQ 2009a). The concrete mixture contained 380 kg/m3 (23.7 lb/ft3) of GUb-SF cement, and had a water-cement ratio (w/c) of 0.42, with high-range water-reducing admixture to maintain a mixture slump of 120 ± 30 mm (4.7 ± 1.18 in.) (MTQ 2009a). The pavement prototypes were cast at the structural laboratory using three concrete batches. The average concrete strength of the concrete batches was 48.0 ± 3.5 MPa (7.0 ± 0.5 ksi) based on testing of three concrete cylinders (150 x 300 mm [5.9 x 11.8 in.]) from each batch.
Table 2—Loading schemes of test prototypes
Subgrade base layer The granular base consisted of three 100 mm (4 in.) thick layers of limestone aggregate compacted using a 90 kg (198 lb) vibrating plate. The granular mixture was prepared according to AASHTO specifications (Class A). The granular subgrade mixture consisted of 50% sand (0 to 5 mm [0 to 0.2 in.]), 20% 10 mm (0.4 in.) crushed rock (5 to 14 mm [0.2 to 0.6 in.]), and 30% 20 mm (0.8 in.) crushed rock (14 to 28 mm [0.6 to 1.1 in.]). Aggregates were dampened before placing to maximize the compaction efficiency. Once the base was completed, a thin layer of sand was applied to the final surface to provide contact between the concrete surface and subgrade. The base was extended by 300 mm (12 in.) on all sides to allow for load distribution and prevent failure of the base-layer container. The overall dimensions of the base layer were 1.52 m wide x 3.35 m long x 0.30 m deep (5 x 11 x 1 ft). Upon completing the base, the base modulus (stiffness) was measured using a Briaude Compacting Device (BCD), and was 110 MPa/m (4.9 ksi/ft).
Table 2 summarizes the loading schemes, while Fig. 2 shows the test setup. For static testing (Phase I), the monotonic load was applied with a stroke-controlled rate of 0.01 mm/sec (0.02 in./min) to allow for progressive contact and loading. The load was applied using a 1000 kN (225 kip) hydraulic actuator on one side of the joint over a loading plate of 306 mm (12 in.) in diameter. The prototypes were loaded up to 200 kN (45 kip), then the load was released. Thereafter, the prototypes were loaded again at the same rate until failure. E and LTE were calculated at an applied load of 40 kN (9 kip) (service load, which is equal to one half the equivalent axle load) from the deflection measurements of two linear variable differential transducers (LVDTs) on both joint sides (loaded and unloaded). For the fatigue testing (Phase II), the prototypes were tested up to 1 million cycles. The load followed a sinusoidal waveform that varied from 10 to 50 kN (2.25 to 11.24 kip). The minimum load (10 kN [2.25 kip]) was required to maintain contact between the slab and loading plate and to minimize the impact on the subgrade. The maximum load (50 kN [11.24 kip]) was set to achieve the service load and keep 40 kN (9 kip) as the cyclic test amplitude, which is equal to one-half the equivalent axle load (service load). It should be mentioned that this loading scheme closely represents field conditions under which load is applied and removed as a vehicle approaches the joint or moves away from it. The load was applied with the same hydraulic actuator (1000 kN [225 kip]) with a load-controlled scheme. The loading
Testing loads and procedures The JPCP prototypes were tested under two different loading conditions: static (Phase I) and cyclic (Phase II). During Phase I, the prototypes were monotonically loaded to 200 kN (45 kip) to induce cracks at the joints. Thereafter, the load was released, and the prototypes were loaded again up to failure. During Phase II, the prototypes were subjected to 1 million cycles ranging from 10 to 50 kN (2.25 and 11.24 kip), followed by monotonic loading up to failure. ACI Structural Journal/March-April 2014
Phase
Number and prototypes
Loading scheme
One 34.9 mm (1.38 in.) GFRP I Static
One 34.9 mm (1.50 in.) GFRP
Monotonic to 200 kN (45 kip), unloading, monotonic reloading to failure.
One 28.6 mm (1.13 in.) epoxy-coated steel One 34.9 mm (1.38 in.) GFRP II Cyclic
One 34.9 mm (1.50 in.) GFRP One 28.6 mm (1.13 in.) epoxy-coated steel
One million cycles between 10 and 50 kN (2.24 to 11.24 kip) at 15 Hz. Thereafter, static testing until failure.
333
Fig. 2—Test setup: (a) overall view; and (b) loading plate and linear variable displacement transducers. Table 3—Summary of test results Cracking and failure loads of jointed pavement prototypes Phase
Load at
Steel, 28.6 mm
GFRP, 34.9 mm
GFRP, 38.1 mm
I Static
Cracking, kN (kip)
140.7 (31.6)
100.0 (22.5)
124.8 (28.1)
Failure, kN (kip)
506.6 (113.9)
460.0 (103.4)
478.0 (107.5)
II Cyclic
Cracking, kN (kip)
250 (56.2)
178 (40.0)
145 (32.6)
Failure, kN (kip)
622 (139.8)
526 (118.2)
413 (92.8)
Joint effectiveness and load-transfer efficiency at service load, 40 kN (9 kip) Steel, 28.6 mm
GFRP, 34.9 mm
GFRP, 38.1 mm
Phase
Load type
E, %
LTE, %
E, %
LTE, %
E, %
I Static
First loading
86
75
89
81
95
Reloading
65
45
64
47
74
II Cyclic
First loading
95
90
95
90
96
After cycling
92
85
93
87
95
Note: 1 mm = 0.0394 in.
and unloading was applied at a frequency of 15 Hz. This frequency is equivalent to the time that a vehicle needs to cross the joint, assuming a speed of 65 to 80 kph (37.3 to 49.7 mph) (MTQ 2009b). Because the test prototypes did not fail after 1 million cycles, the prototypes were retested under monotonic static load until failure. Before cycling, as well as after predetermined sets of cycles (1; 1000; 10,000; 100,000; 500,000; and 1,000,000), the load cycling was interrupted, and a monotonic loading test up to 40 kN (9 kip) (service load) was conducted to assess joint performance. TEST RESULTS Static testing (Phase I) Cracking and failure—When the JPCP prototypes were submitted to 200 kN (45 kip), cracks appeared in the loaded slabs. The unloaded slabs, however, did not evidence any cracks during the test. Table 3 gives the cracking and failure loads of the test prototypes. Figure 3 shows the cracking patterns and failure modes of the three prototypes tested in 334
Phase I: 28.6 mm (1.13 in.) steel dowels, 34.9 mm (1.38 in.) GFRP dowels, and 38.1 mm (1.50 in.) GFRP dowels. In the case of the 28.6 mm (1.13 in.) diameter steel dowels, the first crack appeared in the loaded slab at 140.7 kN (31.6 kip) on one side, and at 197.0 kN (44.3 kip) on the other. The crack appeared at the level of dowel bars, and continued to the surface. The second crack appeared under a load of approximately 380 kN (85.4 kip). The slab prototype failed at 506.6 kN (113.9 kip) by shear failure of the loaded slab beyond the dowel bars. The GFRP-doweled prototypes showed crack patterns and failure modes similar to the steel-doweled prototype. The cracking loads were 100 and 124.8 kN (22.4 and 28.1 kip) for both 34.9 and 38.1 mm (1.38 and 1.50 in.) diameter GFRP dowels, respectively. These loads represent 71 and 89% of the cracking load of the steel-doweled prototype. On the other hand, the failure loads for the 34.9 and 38.1 mm (1.38 and 1.50 in.) diameter GFRP dowels were 460 and 478 kN (103.4 and 107.4 kip), respectively, which represent 91 and 94% of the failure load of the steel-doweled prototype. ACI Structural Journal/March-April 2014
Fig. 3—Cracking at failure of Phase I prototypes: (a) 28.6 mm steel dowels; (b) 34.9 mm GFRP dowels; and (c) 38.1 mm GFRP dowels. (Note: 1 mm = 0.0394 in.)
Fig. 4—Results of Phase I prototypes (static testing up to 200 kN): (a) joint effectiveness; (b) load-transfer efficiency; and (c) relative deflection. (Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.) Joint effectiveness E and load-transfer efficiency LTE— E and LTE were calculated using the deflection measurements recorded by the two LVDTs placed on the unloaded and loaded sides of the joint. Table 3 gives the calculated E and LTE at service load (40 kN [9 kip]) for the tested JPCP prototypes with steel and GFRP dowels. All tested prototypes showed E and LTE higher than 75 and 60%, respectively, which meets ACPA (1991) requirements. Both GFRP dowel diameters (34.9 and 38.1 mm [1.38 and 1.50 in.]) displayed E and LTE higher than the 28.6 mm diameter (1.13 in.) steel dowels. The 34.9 mm (1.38 in.) diameter GFRP dowels showed E of 89% and LTE of 81%, while the 38.1 mm (1.50 in.) diameter GFRP dowels showed E of 95% and LTE of 92%. The values in Table 3 reveal that using 34.9 mm (1.38 in.) diameter GFRP dowels instead of 28.6 mm diameter (1.13 in.) steel dowels increased E and LTE by 9 and 8%, respectively. On the other hand, replacing 28.6 mm diameter (1.13 in.) steel dowels with 38.1 mm diameter (1.50 in.) GFRP dowels increased E and LTE by 10 and 23%, respectively. In addition, E and LTE values revealed that the behavior of the jointed pavement with 34.9 mm (1.38 in.) diameter GFRP dowels was almost the same as that with 28.6 mm (1.13 in.) diameter steel dowels. Furthermore, Table 3 shows that reloading the specimens after cracking during the initial loading phase (200 kN [45 kip]) yielded very low E and LTE because of the cracks. The 38.1 mm (1.50 in.) diameter GFRP dowels evidenced joint effectiveness E of 74%, which is very close to 75%, as provided for by ACPA (1991). Therefore, JPCP stability and performance is dependent on the slabs remaining uncracked to achieve efficient joints. E and LTE were plotted against applied load in Fig. 4(a) and (b). It should be mentioned that LTE corresponding to E = 75% was 60%. Figure 4(a) and (b) demonstrate that, after an initial loading interval till about 50 kN (11.24 kip), E and LTE stabilized. Besides, there was no significant differACI Structural Journal/March-April 2014
ence between the two prototypes with 35.9 mm (1.38 in.) GFRP dowels and 28.6 mm (1.13 in.) steel dowels after 50 kN (11.24 kip). The differences between the two prototypes under 50 kN (11.24 kip) may be related to the better compaction of the subgrade base after testing the first prototype, which had 28.6 mm (1.13 in.) steel dowels. Furthermore, increasing the GFRP dowels to 38.1 mm (1.50 in.) increased E and LTE. Figure 4(a) also shows that cracking during the first loading did not affect E, because the load was not released until it reached 200 kN (45 kip). Relative deflection—Figure 4(c) provides the relative deflection of loaded and unloaded slabs of three prototypes with 28.6 mm (1.13 in.) epoxy-coated steel dowels, 34.9 mm (1.38 in.) GFRP dowels, and 38.1 mm (1.50 in.) GFRP dowels. The relative deflection of the 28.6 mm (1.13 in.) steel dowels was between those of the 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels. Figure 4(c) shows immediate deflection at the beginning of the test ranging from 0.2 to 0.45 mm (0.01 to 0.02 in.). This immediate deflection occurred because the specimens were not cast directly on the subgrade base and, when the load was applied to the pavement prototypes, the immediate deflection occurred until complete contact between the concrete surface and the subgrade base layer was achieved. The steel-doweled pavement prototype showed the highest immediate deflection (≈0.45 mm [0.02 in.]) because it was the first tested, and may have been affected by the compressibility of the subgrade layer. The immediate deflection was less in the case of the GFRP-doweled pavement prototypes (≈0.20 mm [0.01 in.]). This immediate deflection increase might not occur in field applications in which the pavement is cast directly on the subgrade. At service load (40 kN [9 kip]), the 28.6 mm (1.13 in.) steel dowels showed a relative deflection of 0.58 mm (0.02 in.). The 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels evidenced relative deflections of 0.82 and 0.36 mm (0.03 and 0.01 in.), respectively. The relative deflections 335
Fig. 5—Cracking at failure of Phase II prototypes: (a) 28.6 mm steel dowels; (b) 34.9 mm GFRP dowels; and (c) 38.1 mm GFRP dowels. (Note: 1 mm = 0.0394 in.) of the 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels were 1.41 and 0.62 times that of the 28.6 mm (1.13 in.) steel dowels, respectively. After the service load, the difference between the relative deflections of the 28.6 mm (1.13 in.) steel dowel and 34.9 mm (1.38 in.) GFRP dowels decreased. At approximately 70 kN (15.7 kip), the difference between the two prototypes was less than 0.1 mm (0.004 in.). On the other hand, the relative deflection of the 38.1 mm (1.50 in.) GFRP dowels was very small compared with that of the 28.6 mm (1.13 in.) epoxy-coated steel dowels. Cyclic testing (Phase II) Cracking and failure—The three prototypes with steel and GFRP dowels did not experience any cracking after 1,000,000 cycles at 40 kN (9 kip) (between 10 and 50 kN [2.25 and 11.24 kip]). Thus, using durable dowel bars in jointed pavements will yield efficient joints with extended service life under service load. This confirms the findings of the static testing (Phase I): JPCP efficiency will not be altered as long as the concrete does not crack. After 1,000,000 cycles, the three prototypes were retested under monotonic load up to failure. Table 3 lists the cracking and failure loads. The cracking load of the prototypes in Phase II was higher than those in the Phase I prototypes. The cyclic testing of the three prototypes affected the subgrade base, and resulted in very high compaction. That, in turn, affected the cracking loads of the test prototypes. Similarly, the failure loads in Phase II were also higher than those in Phase I, except for the prototype with 38.1 mm (1.50 in.) GFRP dowels, which showed 413 kN (92.9 kip) compared with 478 kN (107.4 kip) in Phase I (static testing). Table 3 shows that the prototype with 28.6 mm (1.13 in.) epoxy-coated dowels experienced the highest cracking load among the tested prototypes. The prototypes with 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels had cracking loads of 71 and 58% of that of the prototype with steel dowels. As with Phase I prototypes, the first cracks appeared at the joints at the level of the dowel bars, and then extended to the surface. Compared with Phase I, Phase II prototypes showed more cracks at failure, except in the case of the 38.1 mm (1.50 in.) GFRP-doweled prototype, which showed one major crack. The cracks led to the splitting of concrete around the dowels before failure, which occurred due to shear failure of the loaded slabs past dowel length. The 28.6 mm (1.13 in.) steel-doweled prototype failed at 622 kN (139.8 kip). The prototypes with 34.9 and 38.1 mm 336
(1.38 and 1.50 in.) GFRP dowels showed failure loads equal to 85 and 66% of the failure load of the steel-doweled prototype. Figure 5 shows the cracking patterns and failure modes of the three prototypes tested in Phase II: 28.6 mm (1.13 in.) steel dowels, 34.9 mm (1.38 in.) GFRP dowels, and 38.1 mm (1.50 in.) GFRP dowels. In addition, Table 3 also shows that the prototype with 38.1 mm (1.50 in.) GFRP dowels yielded lower cracking load and failure load compared with that of the prototype with 34.9 mm (1.38 in.) GFRP dowels. The normal variance in the concrete strength between the different batches may have had an effect on the lower cracking and failure loads. Joint effectiveness E and load-transfer efficiency LTE— Before cycling, as well as after predetermined sets of cycles (1; 1000; 10,000; 100,000; 500,000; and 1,000,000), the load cycling was interrupted, and a monotonic loading test up to 40 kN (9 kip) (service load) was conducted to assess joint performance. Table 3 lists the calculated E and LTE at service load (40 kN [9 kip]) for the JPCP prototypes with steel and GFRP dowels. All tested prototypes showed E and LTE higher than 75 and 60%, respectively, which meets ACPA (1991) requirements. Table 3 shows that E and LTE in Phase II were higher than in Phase I. Once again, this is related to the excessive compaction resulting from the cyclic testing of the prototypes. The continued cycling resulted in further compaction of the base layer, which increased joint effectiveness. E and LTE were plotted against applied load for a selected number of cycles in Fig. 6. The 38.1 mm (1.50 in.) GFRP dowels showed the highest E and LTE, which were 96 and 92%, respectively. Figure 6 also reveals no significant difference in E and LTE after 1,000,000 cycles. There was no significant difference between the two prototypes with 34.9 mm (1.38 in.) GFRP dowels and 28.6 mm (1.13 in.) steel dowels (E and LTE equal 95 and 90%, respectively). DESIGN OF GFRP DOWELS Because the properties of GFRP dowel are different from those of steel, directly replacing steel dowels with GFRP dowels of the same diameter and at the same spacing is not valid. The required diameter and spacing can be determined by equating the relative deflection of a joint doweled with steel to that of a joint doweled with GFRP (Davis and Porter 1998). The effective design steps for GFRP-doweled JPCP are: 1) determine the load transferred by the critical dowel; 2) determine the relative deflection for a joint with ACI Structural Journal/March-April 2014
Fig. 6—Results of Phase II prototypes (cyclic loading) at 40 kN: (a) joint effectiveness; (b) load-transfer efficiency. (Note: 1 mm = 0.0394 in; 1 kN = 0.225 kip.) steel dowels; 3) determine the relative deflection for a joint with GFRP dowels; 4) determine the required diameter and spacing for GFRP dowels; and 5) check the bearing stresses. This design procedure is summarized as follows. When a load is applied to the edge of a slab, a portion of the load is transferred to the adjacent slab through the dowels by shear. Tabatabie et al. (1979) suggested that only the dowels located within a distance of lr from the load point contributes to transferring the load (Fig. 7(a)), where lr is the radius of relative stiffness as defined in Eq. (3) by Westergaard (1925)
(
)
lr = 4 Ec h3 12 1 − µ 2 k (3)
where Ec is the modulus of elasticity of the pavement concrete; h is the pavement thickness; μ is the Poisson’s ratio of the pavement concrete; and k is the modulus of subgrade reaction. Corresponding to the contribution of the dowels located in the lr distance, the load transferred by the critical dowel Pt is given by Eq. (4)
Pt =
Design Load Transfer ( Pd ) Number of Effective Dowels
(4)
Yoder and Witczak (1975) reported that a 5 to 10% reduction in load transfer occurred due to the formation of voids beneath the dowels at the joint face. Accordingly, a design load transfer of 45% of the applied wheel load is recommended. Thus, the design load transfer Pd is calculated from Eq. (5) as a function of the applied wheel load Pw
Pd = 0.45Pw (5)
Considering the schematic shown in Fig. 7(b), the relative deflection between the jointed slabs Δ is calculated from Eq. (6), neglecting the deflection due to the slope and flexure along the joint width
∆ = 2yo + δ (6)
where yo is the dowel deflection relative to or within the concrete at the face; and δ is the shear deflection of the dowel across the joint.
ACI Structural Journal/March-April 2014
Fig. 7—Load-transfer distribution and relative deflection between jointed slabs. According to Friberg (1938), yo is calculated as in Eq. (7). This equation is derived assuming the dowel bars have a semi-infinite length. Albertson (1992), however, showed that this equation can be applied to dowel bars with a βL value greater than 2 with a minor error, where L is the length of dowel bar on one side of the slab
yo =
Pt (2 + b z ) such that βL > 2.0 4 b3 E I
(7a)
b = 4 Kb 4 EI (7b)
where yo is the dowel deflection relative to or within concrete at the face; Pt is the load transferred by the critical dowel; β is the relative stiffness of the dowel bar encased in the concrete; L is the length of dowel bar on one side of the slab; E is the flexural modulus of elasticity; I is the moment of inertia; b is the dowel diameter; and K is the modulus of dowel support or reaction. It should be mentioned that K is an important parameter in the Friberg (1938) design equation. K is determined empirically because of the difficulty in establishing it theoretically (Friberg 1938). Yoder and Witczak (1975) found 337
that K ranges between 81.43 and 407.17 N/mm3 (3 × 105 and 1.5 × 106 lb/in.3). For the analytical calculations herein, a value of 407.17 N/mm3 (1.5 × 106 lb/in.3) has been used as suggested to simulate the worst-case scenario (Yoder and Wiczak 1975). The shear deflection of the dowel across the joint is then calculated as shown in Eq. (8)
δ = lPt z AG (8)
where δ is the dowel’s shear deflection across the joint; l is the shear shape factor; Pt is the load transferred by the critical dowel; z is the joint width; A is the area of dowel bar; and G is the shear modulus, which is assumed as 3.3 GPa (478.6 ksi) based on the literature. The bearing stress developed due to slab deformation was calculated as shown in Eq. (9), which should be less than the permissible bearing stress underneath the pavement provided by ACI Committee 325 (1956)
σ b = Kyo < fb = 1 3 ⋅ ( 4 − b ) fc′ (9)
where σb is the developed bearing stress; K is the dowel’s modulus of support; yo is dowel deflection as the concrete face; fb is the permissible bearing stress; b is the dowel diameter; and fc′ is the concrete compressive strength. Considering the geometries and material properties of the dowels used in this investigation, a comparable design was conducted to determine the diameter of GFRP dowels that could replace 28.6 mm (1.13 in.) diameter epoxy-coated steel dowels. The design included the three diameters of GFRP dowels used herein: 31.8, 34.9, and 38.1 mm (1.25, 1.38, and 1.50 in.). Provided in Table 4, it shows that replacing 28.6 mm (1.13 in.) epoxy-coated steel dowels with 31.8 mm (1.25 in.) GFRP dowels increased the bearing stress and relative deflection by 23 and 88%, respectively. Using 34.9 mm (1.38 in.) GFRP dowels yielded almost the same bearing stress as that of 28.6 mm (1.13 in.) epoxy-coated dowels, while the relative deflection was 58% higher. On the other hand, using 38.1 mm (1.50 in.) GFRP dowels yielded 29% lower bearing stress than the 28.6 mm (1.13 in.) epoxy-coated steel dowels, while the relative deflection was 33% higher. Considering the bearing stress as reference, the 34.9 mm (1.38 in.) GFRP dowels may be considered as a direct alternative to the 28.6 mm (1.13 in.) epoxy-coated dowels when the materials and conditions in this investigation prevail. FIELD APPLICATION Based on the results of this research project and the characteristics provided in Table 1, the MTQ has issued new materials specifications for GFRP dowels as minimum requirements for their use in JPCP in the province of Quebec (Montaigu et al. 2013): 1) the fiber type should be (E-glass) or (ECR-glass); 2) vinylester resin; 3) glass-fiber content (ASTM D3171, Procedure G) ≥ 75%; 4) moisture absorption (ASTM D570) ≤ 0.15%; 5) glass transition temperature (ASTM D3418) ≥ 110°C (230°F); 6) cure ratio (CSA S807) ≥ 98%; 7) shortbeam shear strength (ASTM D4475) ≥ 59 MPa (8.6 ksi); and
338
8) transverse shear strength (ACI 440.3R [ACI Committee 440 2004], Test Method B.4) ≥ 170 MPa (24.7 ksi). To take a step forward toward employing GFRP dowels in field applications, MTQ has implemented the use of GFRP dowels in a demonstration section on Hwy 15 North in Mirabel, QC, Canada (just to the north of HW 50). The traffic volume on this highway is approximately 100,000 vehicles per day, with trucks approaching 6%. The experimental section is in the right lane and the center of a length of 500 m (1640 ft) divided into two parts: 250 m (820 ft) for 38.1 mm (1.50 in.) GFRP dowels, and 250 m (820 ft) for 34.9 mm (1.38 in.) steel dowels. Figure 8 shows the GFRP dowel arrangement during the construction of the highway. Both the GFRP and steel dowels were 450 mm (18 in.) long and spaced at 300 mm (12 in.). The pavement thickness was 260 mm (10.2 in.), while the length of the jointed slabs was set at 5000 mm (197 in.). The joints at the dowel locations were sawn within a few hours of casting and allowed to crack due to thermal contraction and shrinkage. The JPCP was cast using MTQ Type IIIA concrete with a 28-day compressive strength of 35 MPa (5.1 ksi) according to MTQ requirements (MTQ 2009a). As part of an ongoing MTQ effort, the performance of the experimental section with the GFRP and steel dowels is being assessed with a falling-weight deflectometer (FWD) (ASTM D4694) to locate and quantify weak areas that can be corrected before premature damage occurs. The FWD is a nondestructive field test that involves applying impact loads to the pavement surface and monitoring the pavement deflection response through a series of velocity transducers placed on the pavement at specified distances from the load, as illustrated in the FWD test diagram in Fig. 9(a). To simulate moving-axle loads, the FWD load is applied by releasing a mass from a selected height to impact the road surface. The mass and drop height of the load determine the peak contact pressure applied to the road surface. The FWD test was conducted using the MTQ testing vehicle (Fig. 9(b)). The falling weight is lifted to the desired height and dropped on an anvil fitted with rubber shock absorbers, inducing an impact of 40 kN (9 kip). The anvil transmits the force of impact to the pavement through a plate placed on the road surface. A series of sensors simultaneously measure pavement vertical movement resulting from a shock wave. This movement is very subtle, because it lasts only 30 ms, and is measured in microns. The specifications of the MTQ testing apparatus are load-plate diameter: 300 mm (12 in.); falling weight: 250 kg (551 lb); impact strength: 40 kN (9 kip); and location of sensors: 0 to 1.8 m (0 to 5.9 ft) from the center of the plate (seven to 15 sensors). In 2011, 20 FWD tests were conducted on each section (steel and GFRP). The maximum, minimum, and average LTE for the GFRP-doweled sections were 85.2, 93.6, and 88.6 ± 2.6%, respectively. The maximum, minimum, and average LTE for the steel-doweled sections were 85.3, 91.6, and 87.9 ± 1.8%, respectively. In addition, core samples were extracted from the experimental sections during the FWD testing, yielding an average compressive strength of 49.6 MPa (7.2 ksi). These results indicate that the steel- and GFRP-doweled slabs had almost the same performance with ACI Structural Journal/March-April 2014
Table 4—Design for alternative GFRP dowel bar diameter Design parameter
Reference steel
Alternative 1 GFRP
Alternative 2 GFRP
Alternative 3 GFRP
Dowel diameter b, mm
28.6
31.8
34.9
38.1
Dowel area A, mm2
642.42
794.23
956.62
1140.09
Moment of inertia I, mm4
32,842
50,197
72,824
103,436
200,000
52,600
50,300
51,600
Dowel shear modulus G, MPa
78,000
3300
3300
3300
Dowel length L, mm
457
457
457
457
Dowel spacing s, mm
305
305
305
305
Concrete strength fc′, MPa
48
48
48
48
Concrete’s modulus of elasticity Ec, MPa
32,909
32,909
32,909
32,909
Concrete’s Poisson’s ratio μ
0.2
0.2
0.2
0.2
Pavement thickness h, mm
254
254
254
254
110
110
110
110
407.17
407.17
407.17
407.17
19
19
19
19
808
808
808
808
Number of dowels
1.87
1.87
1.87
1.87
Design load transfer = 0.45Pw, kN
18
18
18
18
Load transferred by critical dowel Pt
9.63
9.63
9.63
9.63
0.026
0.033
0.031
0.029
5.90
7.60
7.17
6.67
Pt (2 + b z ) , mm 4 b3 E I
0.053
0.065
0.055
0.046
l Pt z , mm AG
0.004
0.078
0.064
0.054
Δ = 2yo + δ, mm
0.110
0.208
0.175
0.147
σb = Kyo, MPa
21.63
26.51
22.47
18.84
63.54
63.49
63.44
63.39
σb GFRP/σb steel
—
1.23
1.04
0.71
Δ GFRP/Δ steel
—
1.88
1.58
1.33
Geometry and material properties
Dowel modulus of elasticity E, MPa *
Modulus of subgrade reaction k, MPa/m Modulus of dowel support K, N/mm
3
Joint width z, mm
Design
lr =
4
b=
Ec h 3
(
)
12 1 − µ 2 k
4
, mm
Kb , mm–1 4E I
βL > 2.0 (ok) yo =
δ=
fb =
(4 − b) fc′ , MPa 3
Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip; 1 MPa = 0.145 ksi; 1 mm2 = 0.00155 in.2; 1 N/mm3 = 0.2714 kip/in.3; 1 MPa/m = 0.0442 ksi/ft; 1 mm–1 = 25.4 in.–1
an average LTE of 87.9 ± 1.8% and 88.6 ± 2.6% for the steel- and GFRP-doweled slabs, respectively. The LTE of both the steel- and GFRP-doweled slabs were higher than
ACI Structural Journal/March-April 2014
the 75% specified by ACPA (1991). This indicates that the GFRP dowels tested performed efficiently in transferring loads in JPCP.
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SUMMARY AND CONCLUSIONS Through an extensive collaboration project between the Ministry of Transportation of Quebec (MTQ) and the University of Sherbrooke, new GFRP dowels were developed, and their long-term durability characteristics were assessed (Montaigu et al. 2013). This study, however, investigated the performance of the newly developed GFRP dowels (34.9 and 38.1 mm [1.38 and 1.50 in.]) in JPCP under static and cyclic loadings. In addition, it compared their structural performance with that of epoxy-coated steel dowels in JPCP. Based on the test results presented and discussed herein, the following conclusions concerning the tested GFRP dowels can be drawn: 1. The GFRP dowel bars provided suitable and effective alternatives to the common epoxy-coated steel dowels to overcome corrosion problems and related deterioration under static and cyclic loading conditions; 2. Under the static testing in Phase I, the pavement prototype with 28.6 mm (1.13 in.) steel dowels showed its first crack at 140.7 kN (31.6 kip), while the prototypes with 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels showed their first cracks at 100 and 124.8 kN (22.4 and 28.1 kip), respectively. The cracking loads of the prototypes with 34.9 and
Fig. 8—GFRP dowel arrangement during construction (Hwy 15, Mirabel, QC, Canada).
38.1 mm (1.38 and 1.50 in.) GFRP dowels were 2.5 and 3.1 times the service load (40 kN [9 kip]), respectively; 3. Under the static testing in Phase I, the pavement prototype with 28.6 mm (1.13 in.) steel dowels and those with 34.9 and 38.1 mm (1.38 and 1.50 in.) GFRP dowels showed similar crack patterns and modes of failure. The capacities of the three prototypes were 506.6, 460.0, and 478.0 kN (113.9, 103.4, and 107.5 kip), respectively; 4. Under the cyclic testing in Phase II, the prototypes resisted 1 million cycles at service load without cracking. Thus, providing durable dowel bars capable of withstanding the environmental conditions and deterioration will yield pavements with extended service lives; 5. Phase II produced higher cracking and ultimate loads compared with Phase I. The results were similar for joint effectiveness E and load-transfer efficiency LTE. This can be accounted for by excessive compaction resulting from prototype cyclic testing, which tended to increase joint effectiveness; 6. The pavement prototypes with GFRP dowels (34.9 and 38.1 mm [1.38 and 1.50 in.]) showed joint effectiveness E and load-transfer efficiency LTE similar to or higher than that of the prototypes with steel dowels (28.6 mm [1.13 in.]); 7. Achieving stability and good performance in the GFRP-doweled JPCP requires that slabs remain uncracked to enable achieving efficient joints and maintain efficient load transfer; 8. Considering the tested material and setup configuration, the 34.9 mm (1.38 in.) diameter GFRP dowels behaved very similarly to the 28.6 mm (1.13 in.) diameter steel dowels. Thus, the 34.9 mm (1.38 in.) GFRP dowels may be viable alternatives to the 28.6 mm (1.13 in.) epoxy-coated steel dowels subjected to the same loading and boundary conditions. The test design also indicates that the 34.9 mm (1.38 in.) GFRP dowels could be direct alternatives to the 28.6 mm epoxy-coated steel dowels; and 9. The field application showed similar LTE values for of the 38.1 mm (1.50 in.) GFRP dowels and 34.9 mm (1.38 in.) steel dowels in real service conditions. The steel- and GFRP-doweled slabs had average LTEs of 87.9 ± 1.8% and
Fig. 9—In-place falling-weight deflectometer (FWD) test (Hwy 15, Mirabel, QC, Canada): (a) schematic; and (b) in-place test. 340
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88.6 ± 2.6%, respectively, which were higher than the 75% specified by ACPA (1991). ACKNOWLEDGMENTS
The authors wish to acknowledge the financial support of Quebec’s Ministry of Transport (MTQ), the Natural Sciences and Engineering Research Council of Canada (NSERC), and Quebec’s Fonds québécois de la recherche sur la nature et les technologies (FQRNT). The authors are grateful to Pultrall Inc. for providing the GFRP dowel bars and RocTest Inc. for providing the Briaude Compacting Device (BCD). Special thanks to the technical staff at the Department of Civil Engineering for their help in fabricating and testing the specimens.
AUTHOR BIOS
Brahim Benmokrane, FACI, is Tier-1 Canada Research Chair Professor in Advanced Composite Materials for Civil Structures and an NSERC Research Chair Professor in Fiber-Reinforced Polymer Reinforcement for Concrete Infrastructure in the Department of Civil Engineering at the University of Sherbrooke, Sherbrooke, QC, Canada. He is a member of ACI Committee 440, Fiber-Reinforced Polymer Reinforcement. ACI member Ehab A. Ahmed is a Postdoctoral Fellow in the Department of Civil Engineering at the University of Sherbrooke, and Lecturer at Menoufiya University, Shebin El-Kom, Minoufiya, Egypt. He received his PhD in civil engineering from the University of Sherbrooke. His research interests include structural analysis, design and testing, and structural health monitoring of fiber-reinforced polymer concrete structures. Mathieu Montaigu is an MSc Student in the Department of Civil Engineering at the University of Sherbrooke. His research interests include concrete durability and performance evaluation of glass fiber-reinforced polymer dowel bars for concrete pavement. Denis Thebeau is a Professional Engineer with the Ministry of Transportation of Quebec (Pavement Division), Quebec City, QC, Canada. His research interests include the design, construction, rehabilitation, and long-term monitoring of the performance of concrete pavements.
REFERENCES
AASHTO, 1993, “Guide for Design of Pavement Structures,” American Association of State Highway and Transportation Officials, Washington, DC, 624 pp. ACI Committee 325, 1956, “Structural Design Considerations for Pavement Joints,” ACI Journal, V. 53, No. 7, July, pp. 1-29. ACI Committee 440, 2008, “Metric Specification for Carbon and Glass Fiber-Reinforced Polymer Bar Materials for Concrete Reinforcement (ACI 440.6M-08),” American Concrete Institute, Farmington Hills, MI, 10 pp. ACI Committee 440, 2004, “Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures (ACI 440.3R-04),” American Concrete Institute, Farmington Hills, MI, 39 pp. American Concrete Pavement Association (ACPA), 1991, “Design and Construction of Joints for Concrete Highways,” ACPA, Skokie, IL, 24 pp. Albertson, M. D., 1992, “Fibercomposite and Steel Pavement Dowels,” master’s thesis, Iowa State University, Ames, IA, 268 pp. ASTM D3171, 2011, “Standard Test Methods for Constituent Content of Composite Materials,” ASTM International, West Conshohocken, PA, 10 pp. ASTM D3418-12e1, 2012, “Standard Test Method for Transition Temperatures and Enthalpies of Fusion and Crystallization of Polymers by Differential Scanning Calorimetry,” ASTM International, West Conshohocken, PA, 7 pp. ASTM D4475, 2008, “Standard Test Method for Apparent Horizontal Shear Strength of Pultruded Reinforced Plastic Rods by the Short Beam Method,” ASTM International, West Conshohocken, PA, 4 pp. ASTM D4476, 2009, “Standard Test Method for Flexural Properties of Fiber Reinforced Pultruded Plastic Rods,” ASTM International, West Conshohocken, PA, 5 pp. ASTM D4694, 2009, “Standard Test Method for Deflections with a Falling-Weight-Type Impulse Load Device,” ASTM International, West Conshohocken, PA, 3 pp.
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ASTM D570, 2010, “Standard Test Method for Water Absorption of Plastics,” ASTM International, West Conshohocken, PA, 4 pp. CAN/CSA S807-10, 2010, “Specification for Fibre-Reinforced Polymers,” Canadian Standards Association (CSA), Rexdale, ON, Canada, 27 pp. Canadian Strategic Highway Research Program (C-SHRP), 2002, “Pavement Structural Design Practices Across Canada,” C-SHRP Technical Brief No. 23, Ottawa, ON, Canada, 10 pp. Davis, D., and Porter, M. L., 1998, “Evaluation of Glass Fiber Reinforced Polymer Dowels as Load Transfer Devices in Highway Pavement Slabs,” Proceedings of Transportation Conference, Ames, IA, pp. 78-81. Eddie, D.; Shalaby, A.; and Rizkalla, S., 2001, “Glass Fiber-Reinforced Polymer Dowels for Concrete Pavements,” ACI Structural Journal, V. 98, No. 2, Mar.-Apr., pp. 201-206. Friberg, B. F., 1938, “Load and Deflection Characteristics of Dowels in Transverse Joints of Concrete Pavements,” Proceedings of Highway Research Board No. 18, National Research Council, Washington, DC, pp. 140-154. FRP Dowel Bar Team (DBT), 1998, “Fiber-Reinforced Polymer (FRP) Composite Dowel Bars—15 Years of Durability Study,” Market Development Alliance, Composites Institute, Harrison, NY, 18 pp. Ioannides, A. M., and Korovesis, G. T., 1992, “Analysis and Design of Doweled Slab-on-Grade Pavement Systems,” Journal of Transportation Engineering, V. 118, No. 6, pp. 745-768. Keeton, J. R., and Bishop, J. A., 1957, “Load Transfer Characteristics of a Dowelled Joint Subjected to Aircraft Wheel Loads,” Proceedings of the Highway Research Board, No. 36, Transportation Research Board, Washington, DC, pp. 190-198. Maitra, S. R.; Reddy, K. S.; and Ramachandra, L. S., 2009, “Load Transfer Characteristics of Dowel Bar System in Jointed Concrete Pavement,” Journal of Transportation Engineering, V. 135, No. 11, pp. 813-821. Ministry of Transportation of Québec (MTQ), 2009a, “Bétons de masse volumique normale,” Norme 3101, Ministère des Transports du Québec, Québec, Canada, 8 pp. Ministry of Transportation of Québec (MTQ), 2009b, “Bulletin Innovation Transport,” No. 34, Ministère des Transports du Québec, Quebec, Canada, Jan., 42 pp. Montaigu, M.; Robert, M.; Ahmed, E.; and Benmokrane, B., 2013, “Laboratory Characterization and Evaluation of the Durability Performance of New Polyester and Vinylester E-Glass GFRP Dowels for Jointed Concrete Pavement,” Journal of Composites for Construction, ASCE, V. 17, No. 2, pp. 176-187. Porter, M. L., 2005, “Structural Dowel Bar Alternative and Gaps of Knowledge,” Proceedings of the Mid-Continent Transportation Research Symposium, Ames, IA, Aug., 13 pp. Porter, M. L.; Davis, D.; Guinn, R.; Lundy, A.; and Rohner. J., 2001, “Investigation of Glass Fiber Composite Dowel Bars for Highway Pavement Slabs,” Final Report TR-408, submitted to Highway Division of the Iowa Department of Transportation and Iowa Highway Research Board, Iowa State University, Engineering Research Institute, Ames, IA, 168 pp. Porter, M. L.; Hughes, B. W.; and Barnes, B. A., 1996, “Fiber Composite Dowels in Highway Pavements,” Proceedings of the Semisequicentennial Transportation Conference, May, Iowa State University, Ames, IA, 6 pp. Smith, K. D., 2001, “Alternative Dowel Bars for Load Transfer in Jointed Concrete Pavements,” FHWA Technical Report Draft, Washington, DC, 16 pp. Tabatabie, A. M.; Barenberg, E. J.; and Smith, R. E., 1979, “Longitudinal Joint Systems in Slip-formed Rigid Pavements: V. II-Analysis of Load Transfer Systems for Concrete Pavements,” Report No. DOT/ FAA RD-79/4, Federal Aviation Administration, U.S. Department of Transportation, Washington, DC, 193 pp. Westergaard, H. M., 1925, “Computation of Stresses in Concrete Roads,” Proceedings of the 5th Annual Meeting of the Highway Research Board, Washington, DC, pp. 91-112. Westergaard, H. M., 1928, “Spacing of Dowels,” Proceedings of the Highway Research Board, No. 8, Transportation Research Board, Washington DC, pp. 154-158. William, G. W., and Shoukry, S. N., 2001, “3D Finite Element Analysis of Temperature Induced Stresses in Dowel Jointed Concrete Pavements,” International Journal of Geomechanics, V. 1, No. 3, pp. 291-307. Yoder, E. J., and Witczak, M. W., 1975, Principles of Pavement Design, second edition, John Wiley & Sons, Inc., New York, 736 pp.
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ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S30
Nonlinear Static Analysis of Flat Slab Floors with Grid Model by Dario Coronelli and Guglielmo Corti A grid model has been set up for the nonlinear response of a flat slab subjected to gravity and lateral cyclic loading. The model requires the definition of the grid geometry and properties of point hinges in beam finite elements, and modelling the nonlinear response in bending, torsion, and shear. The simulation is carried out for experimental tests on a floor under gravity and lateral biaxial cyclic loading of increasing amplitude. Pushover analyses have been performed under gravity and horizontal loads in the two principal directions. Predictions are shown of the global response and the connections of different column shapes and slab reinforcement with the strength, drift capacity, and failure modes. The accuracy is different in the two directions of loading due to the damage of the test slab for biaxial cyclic loading. The results show the potential of the model for design and analysis of existing flat slab structures. Keywords: flat slabs; grid models; punching shear; slab-column connections.
INTRODUCTION Reinforced concrete slabs, supported by columns and walls, are among the most common structures for floors, and their diffusion is continuously increasing all over the world. Their use is advantageous for speed in construction, the possibility to realize flat intrados without beams, and their low thickness in relation to the span. One of the leading aspects in slab design is to guarantee adequate punching shear resistance of slab-column connections when the structure is subjected to both gravity and seismic loads. A wide variety of literature is available on this topic, with code provisions accompanied by several constructions in seismic zones.1 A grid model was previously developed and validated for the nonlinear behavior of flat slab-column connections.2 The grid is composed by linear beam finite elements; the inelastic response of the structure is concentrated in nonlinear point hinges. A model2 has been proposed for static pushover analyses that permit evaluation of flexural, torsional, and shear internal forces and moments in the whole plate structure, with particular attention to the state of slab-column joints. The description of their nonlinear behavior allows evaluation of the whole slab structural response up to failure. In particular, it is possible to assess the safety of connections with respect to punching and structural deformability, in terms of interstory drift ratio under lateral loads. The aim of this paper is to show the efficiency of the model2 for flat slab floors under gravity and horizontal loads. The grid model2 was used to simulate the experimental tests on a scaled model of a flat-plate structure.3 A rather demanding case study, including structural irregularity and the effects of biaxial loading, was chosen.
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The test slab consists of a rectangular floor with 16 slabcolumn joints under gravity and biaxial cyclic quasi-static horizontal loading increased up to failure. Due to the different column cross sections and slab reinforcement, the structure is symmetric in one direction and nonsymmetric in the orthogonal direction. The experimental response showed significant effects of the biaxial loading.3 The maximum connection moments were reached at 4% drift in the north-south (N-S) direction, whereas in the east-west (E-W) direction, for most connections, the maximum moments were recorded at 2% drift and punching failures occurred for drifts at approximately 3%. Following this, the test was stopped. Biaxial loading effects have also been documented in tests on connections,4 with a reduction of drift capacity in both directions with respect to the case of uniaxial loading. This effect has also been measured in connections with rectangular cross sections of the column.5,6 The first section of the paper briefly describes the experimental tests.3 The second section presents the setup of the grid model; in particular, the definition of the grid geometry, nonlinear hinges, and loads applied. In the third section, results of nonlinear analyses under gravity and lateral loads are shown and compared with experimental results.3 The conclusions assess the adequacy of the modeling of the global response and of the individual connections, with attention given to prediction of the ultimate load and drift capacity, and the failure modes. RESEARCH SIGNIFICANCE A grid model developed for slab-column connections is validated for the pushover analysis of a flat slab floor tested experimentally under gravity and cyclic lateral loading. The performance for a nonsymmetrical geometry is studied, with four different types of column cross sections arranged nonsymmetrically with respect to one principal direction of the plan; the reinforcement layout varies accordingly. The approximation of the slab behavior with biaxial load cycles of increasing amplitude up to failure is investigated, with a strong damage accumulation effect. The results corroborate the potential of the model for design and analysis of existing flat slab structures.
ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-103.R2, doi:10.14359.516686526, was received April, 8 2013, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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Fig. 1—Geometry of test slab, plan view, in. (cm); positions of slab column connections (letters A through D and numbers 1 through 4).3 EXPERIMENTAL RESULTS The tests regard the scaled model of a flat-plate structure subjected to gravity and lateral loads designed following ACI 318-83.3 The prototype slab represents a portion of a typical flat-plate floor of an intermediate story of a multistory office building. The slab has three bays in each direction, and a 203 mm (8 in.) thickness. The bay widths are 6.86 and 4.57 m (22.5 and 15 ft) for long and short directions, respectively. The story height is 3.05 m (10 ft). The scaled model (Fig. 1) used for the experimental study has dimensions equal to 40% of those of the prototype. The length of each bay is 2.74 and 1.83 m (108 and 72 in.) for the long and short directions, respectively. The slab is 81 mm (3.2 in.) thick. Columns extend above and below the slab. The column stubs above the slab were 0.3 m (12 in.) long, and their purpose was to anchor the column longitudinal reinforcement and to provide continuity of the columns themselves through the floor; the inferior columns stubs were 1.46 m (4.8 ft) long with pinned connections at the extremities. Four different column cross-sectional shapes were used to collect data related to the effects of column rectangularity on the structural response: rectangular columns with an aspect ratio of 2:1 in the east half of the floor and square columns in the west half. With this layout, the structure is symmetric about the floor centerline along the long direction and nonsymmetric in the orthogonal direction. The concrete had a mean cylinder compressive strength of 21.8 MPa (3160 psi). The self-weight of the slab was 1.9 kN/m2 (40 lb/ft2), corresponding to 23.6 kN/m3 (150 lb/ft3). Slab longitudinal reinforcement (Appendix A*) was made of No. 2 deformed bars with cross-sectional area Al = 32 mm2 (0.05 in.2) (Φ = 6.4 mm [0.25 in.]), with fy = 462.6 MPa (67.1 ksi). The layout of the reinforcement reflects the changes in the cross sections of the columns (Appendix A). No transverse reinforcement was used for the slab. * Appendixes are available at www.concrete.org/publications in PDF format, appended to the online version of the published paper. It is also available in hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.
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Fig. 2—Experimental crack pattern of top and edge of slab following test at 4% drift in E-W direction3 and representation of the numerical deformations and position of the nonlinear hinges activated for W loading direction. Testing of the model slab included gravity load tests, construction load tests, and lateral load tests up to failure (Appendix B). A uniform gravity loading of 3.73 kN/m2 (78 lb/ft2) was provided by weights placed on the slab, with a total vertical uniform load with the self-weight of the structure equal to 5.65 kN/m2 (118 lb/ft2). Construction loads were then applied in sequence on each panel of the model slab; their approximated value is equal to 2.63 kN/m2 (55 lb/ft2), then removed for all subsequent tests. The total vertical uniform load with the self-weight of 5.65 kN/m2 (118 lb/ft2) was used for the lateral load testing described in the following, resulting in a gravity shear ratio Vg/Vc close to 0.2 (Table B2). The lateral loads were applied to the test slab in two principal directions (N-S and E-W) using four reversible hydraulic actuators supported on a reaction frame. Increasing lateral drifts from 1/400 to 1/25 were imposed, with lateral drift first imposed in the S direction, then reversed to the N direction, and finally returned to zero drift. The cycle was repeated once. The same sequence was then immediately applied in E-W direction. These alternating loadings in the two orthogonal directions were then repeated, doubling the lateral drift (Fig. B1). No torsional effects leading to rotation of the floor were observed in the tests. The experimental response to the biaxial horizontal loading showed relevant differences in the two orthogonal directions as a consequence of the loading history.3 The connections in the N-S direction of loading reached their strength at 4% drift. Loading in the E-W direction then took place, and the expected connection strengths were not developed. The ACI Structural Journal/March-April 2014
recorded maximum moments for most connections were those of the previous load cycle at 2% drift, followed by severe strength deterioration and punching failures around 3% drift. The crack pattern of the entire slab at the end of these tests is shown in Fig. 2. NUMERICAL MODEL In the following, the description of the setup of the grid model for the particular study case previously explained and the comparison between test results and numerical outputs will be presented. The grid model2 was developed using a commercial finite element software7 to perform nonlinear static analyses under displacement control. The slab is represented by a grid of linear beam finite elements, fixed at joints, arranged in two orthogonal directions; the columns are modeled with two beam elements, one above and one below the slab level, fixed to the plate. The beam finite elements have been defined as beam-column elements, thus including the effects of flexural, torsional, and shear deformations. Each joint has six degrees of freedom. The in-plane shear due to the lateral loads is modeled by the flexural stiffness of the elements around the axis perpendicular to the slab plane, together with the in-plane shear and axial stiffness. Grid geometry—To design the grid geometry, guidelines given by CIRIA Report 1108 have been considered as a reference point, resulting in the choices for the grid detailed in the following. The grid spacing must be sufficiently close near to the columns to obtain a good approximation of the load effects in the slab, since concentration of internal forces and moments exists in these zones; the elements can be more widely spaced elsewhere. For the size of the grid spacing, generally a width equal to c + d is adequate,2 where c is the column dimension, and d is the effective height of the slab. It should be noted that c + d is the width of the shear critical section of connection, as considered in the grid model2 according to the definition of ACI 3189; further details are given in the following section. Observing the layout of the test slab (Fig. 1), it is evident that the structure is asymmetrical in regards to the column sections; four different column sections were used by authors of the experimental test.3 For beam elements placed on the axes connecting the connections, a width equal to the major c + d along the axes themselves was chosen (Appendix B). The nearby elements have the same width, with some adjustments to have the sum of the widths of all cross sections equal to the slab dimensions in the plan. The depth of the beam elements modeling the slab is equal to the slab thickness. The portions of grid corresponding to the column crosssection dimensions are modeled by four beam elements positioned along the four column semi-axes. A high stiffness is specified to these elements, to model the support given to the slab by the column. In the analyses, the elements had the column width and a depth equal to three times the slab thickness. As already specified, columns are modeled with two beam elements: one below the slab grid with a length of 1.260 m (4.13 ft), and one above with a length of 0.345 m (1.13 ft). The columns stubs below the slab are pinned at their bases. ACI Structural Journal/March-April 2014
Fig. 3—Grid model geometry: (a) overall view of grid and columns; and (b) detail of model at connection of slab and column. Columns sections are taken with the same dimensions of those effectively used in the test slab. Loads—The structure is subjected to gravity and lateral loads. From the total uniformly distributed gravity load per unit of surface (comprising self-weight), the total load per unit length acting in the two principal directions is calculated for each element of the grid. With regard to the imposed displacements, these have been applied in the same positions of the experimental test compatibly to the refinement of the grid. A displacement control analysis is carried out. Nonlinear hinges—Each grid element is composed of an elastic part and nonlinear hinges. The cracked stiffness, depending on the quantity of reinforcement, is used for the elastic part of all elements to consider the effect of shrinkage and construction stresses,3 causing cracking in the slab previous to the action of lateral loads. The hinges are points in which the nonlinear properties of the elements themselves are lumped, and are characterized by relations that link bending moment, shear, and torsion with the inelastic curvature, shear distortion, and twist angle, respectively. 345
Fig. 4—Shear nonlinear hinge: relation of shear force and inelastic strain. The elements (Fig. 3(b)) are made of a linear elastic beam element with a nonlinear hinge at each end for flexure. Each element has one hinge for shear and one for torsion, both at the center of the element. The elements are connected together at their end nodes in the intersection points of the grid. The simplified phenomenological approach adopted to define the hinge properties is summarized herein; more details can be found in the references.2 Point hinges were assigned to frame elements lying on the center lines connecting joints and on the immediately adjacent axes. This choice was made to make the model more computationally light. The level of internal forces was checked a posteriori, indicating that the cracking moments were not reached in the internal part of the slab panels. Three types of hinges are defined according to the grid model2: flexural, shear, and torsional. Their properties depend on the geometry of each element’s cross section, on concrete properties, and on longitudinal bottom and top reinforcement of the slab. Bending—Flexural nonlinear hinge properties are computed analytically for each beam element using a sectional model10 with nonlinear constitutive relations based on perfect bond and plane section assumptions; the moment-curvature relations thus obtained are then approximated with trilinear relationships. Normalized diagrams with respect to ultimate capacity Mu and associated ultimate curvature Φu are provided as input to the model, together with the values of Mu and Φu. The hinge length is defined equal to d, based on test results.2 Shear—The shear force-distortion relation is input as a normalized diagram with respect to the ultimate shear capacity Vu and to the associated ultimate distortion γu (Fig. 4). The shear capacity of each side of the critical perimeter was computed as Vu = vn(c + d)d according to ACI 318-05,9 with the strength vn = 1/3(fc)1/2 MPa [4(fc′)1/2 psi] for elements without shear reinforcement. Experiments show that this can vary with the slab thickness, reinforcement ratio, and the effects of cyclic loading.11 For this case, the slab had a low thickness that would increase vn; the cyclic loading could cause strength deterioration. Hence vn = 1/3(fc)1/2 [4(fc′)1/2 psi] was used for the analyses. The values of ultimate shear distortion γu for slabs without shear reinforcement were obtained by a linear interpolation of 346
the optimal values for modeling the experimental punching in tests carried out on slab-column connections,2 with γu = 0.0092[pfy/(1/3fc0.5)] – 0.011, where p is the longitudinal reinforcement ratio and fc′ and fy are the strength of materials. The expression in customary units is given by γu = 0.00229[pfy /(fc′0.5)] – 0.011, where fc′ and fy are expressed in psi. A trilinear relation was defined for the shear force-strain relation (Fig. 4); the behavior is obtained with the sectional shear model,10 normalized with respect to the maximum shear force and the correspondent strain. The normalized diagrams with the associated shear capacity Vu and the corresponding ultimate shear distortion γu are used as input to the model. The first point of the trilinear diagram corresponds to cracking. The second point (γ1, V1/Vu) is determined by the intersection of the portion in the cracked stage of the curve determined by the sectional model10 with the level of 80% of the strength. The third point corresponds to the shear strength, followed by the last point at the end of the softening branch determined using the shear sectional model.10 The third point corresponds to the shear strength, followed by the last point at the end of the softening branch determined using the shear sectional model.10 The hinge length is taken equal to 2d.2 Shear nonlinear hinges were applied only to the grid elements framing into the columns; this choice is based on the fact that shear forces in other elements of the grid are much lower. Torsion—The definition of torsion nonlinear hinges in the grid model2 relates torque and twist; normalized diagrams with respect to the ultimate torsional capacity Mtu and the corresponding ultimate twist ψu are provided. Mtu0 is the torsional capacity without interaction effects, and Mtu considers the interaction of the torsional strength with the bending moment and shear acting in the connection due to gravity loads. These are determined according to the model for slab-column connections proposed by Park and Choi,12 where Mtu0 is the product of the polar moment of inertia at the sides [J′ = 2(c + d)d3/12 + 2d(c + d)3/12] by a strength vus = 5.0vn. To consider the interaction with the bending moment and shear acting in the connection due to gravity loads, a reduced torsional capacity Mtu is calculated by reducing the strength to vus,red = vn[5.0 – 2.5(σn/fc)] – Vg/(c + d)/d, where σn is the maximum flexural stress in the concrete at the sides of the connection and Vg/(c + d)/d is the gravity shear stress. With regard to the ultimate twist angle ψu0, values measured experimentally for specimens without transverse steel13 are used2; a value of 0.02 is adequate.14 When the interaction with shear and bending moment determines a capacity reduction from Mtu0 to Mtu, the twist angle ψu0 is reduced to ψu, proportionally to Mtu/Mtu0. For the normalized torque and twist relation, a trilinear diagram is used; the behavior is obtained with the torsional model of Collins and Mitchell,15 normalized with respect to the maximum torque and the correspondent twist. The piecewise linear diagram is obtained by connecting the points at cracking, yielding, and ultimate (Fig. 5). Torsional nonlinear hinges computed by the aforementioned method are used in elements framing into the columns. For grid elements that are not at the interface with ACI Structural Journal/March-April 2014
Fig. 5—Torsion nonlinear hinge: relation of torque and inelastic twist angle.
Fig. 7—Comparison between numerical pushover curve and experimental lateral load-drift envelope curve for E-W direction (experimental cycles in small figure)
Fig. 6—Comparison between numerical pushover curve and experimental lateral load-drift envelope curve for N-S direction (experimental cycles in small figure). the columns, the model prescribes an elastic-perfectly plastic behavior, with a torsional strength16 equal to 0.58(fc′)0.5 MPa [6.99(fc′)0.5 psi]. Comparison between numerical and experimental results The procedure followed for the analysis of the model slab is the following: a load-controlled nonlinear analysis is first performed under gravity loads specified previously; then, starting with these results, nonlinear static analyses for horizontal loads with displacement control up to failure in each principal direction are carried out. It should be noted that both positive (S and W) and negative (N and E) verses of loading are considered in the analyses, with a total of four analyses for horizontal load, each starting after the gravity load analysis. The experimental study3 provides data for the total lateral load and drift applied to the structure (Fig. 6 and 7). Envelopes of peak values of the lateral loads and the corresponding deflections in each cycle are well suited to be compared with pushover curves of the model for the two orthogonal
ACI Structural Journal/March-April 2014
directions of loading. The experimental responses in the two orthogonal directions are shown in Fig. 6 and 7. As a consequence of the orientation of a part of the columns with the strong axis in the E-W direction, the sum of the column stiffness in the E-W direction is the double that in the N-S direction. This has a limited impact on the global stiffness of the structure resulting from the assemblage of columns and slab. For the first cycles at low drift, the stiffness in the E-W direction was only 20 to 30% higher than in the N-S direction (Table B1). The curves up to 1% drift are rather close in the two directions, whereas they differ both in terms of resistance and ultimate drift. As previously mentioned, this difference can be explained by the degradation of slabcolumn connections due to the biaxial cyclic loading.3,4 In Fig. 6 and 7, the model predicts an ultimate drift capacity of 4% in both directions. The prediction in the N-S direction is accurate; a slight difference shows in the N direction with negative forces. It should be considered that experimentally, the – 4% drift was reached after that the same drift was attained in the S direction, with some damage accumulation. In the E-W directions, differences between tests and model response show starting from 2% drift. The ultimate drift and load capacity are overestimated, with the model reaching ultimate drift at 4%; the tests showed strength deterioration beyond 2% drift, followed by several punching failures at drifts around 3% on average. The high level of damage inflicted by the two cycles at 4% drift in the N-S direction should be considered. This is not taken into account by the model. A similar analytical overestimation of the load capacity was obtained by the authors of the tests3 using the ACI 318-83 model for the strength of the connections; the experimental interior connection strengths were, on average, 87% of the analytical values in the E-W direction, whereas the model was slightly conservative (experimental results are 110% on average of the analytical) in the N-S direction. The model approximates the response, taking into account the global behavior of the structure with different column 347
Fig. 8—Comparison between numerical and experimental moment-rotation curve of Connection C3 for: (a) N-S; and (b) E-W directions. Positive drifts S and W. Experimental envelope up to connection strength. Experimental E-W 4% drift cycles, including cycles beyond failure. cross-section shapes, with the nonsymmetry highlighted in the description of the structure. Figure 2 shows the experimental crack pattern at failure with the slab numerical deformed shape and the nonlinear hinges activated in the elements for the W loading direction. The most damaged zones—that is, where hinges are beyond yielding—are those around connections corresponding to the experimental damage. A more detailed analysis of the prediction of damage is carried out as follows. Punching failure of a connection is reached after the formation of a shear hinge, when the torsion capacity at the sides of the connection is exceeded. In the analyses presented herein, the structure reached failure with punching in part of the connections; several others were very close to this stage. This reflects the experimental behavior where failure occurred with punching occurring in several connections within a short interval of time.3 Unbalanced moment versus rotation envelopes of connections The behaviors of each connection obtained numerically and experimentally3 were compared. The test report3 provides unbalanced moment-rotation envelopes for each joint up to the drift corresponding to connection strength for both the loading directions. Experimental cycles for the E-W 4% drift test are also presented, including the cycles beyond failure. For the model, the moments were obtained by the product of the numerical base shear and the column height3; rotations are an output of the analysis in the nodes connecting the slab and columns. The behavior of connections depends on their position (internal, edge, and corner) and the direction of loading (N-S and E-W). The figures in the following show examples of the comparison of numerical and experimental moment-rotation curves of connections, representative of three different typology of joints, discussed previously: the interior Connection C3 (Fig. 8 and 9), the lateral Connection D3 loaded parallel to the free edge (Fig. 10 and 11), and the corner Connection A4 (Fig. 12 and 13).
348
With regard to the interior Connection C3 and considering the N-S loading direction (Fig. 8(a)), the numerical curve fits very well the experimental one for positive and negative verse of loading. For the E-W loading direction (Fig. 8(b)), a fair approximation is obtained, though some difference between the numerical and the experimental curve shows from approximately 1.5 to 2% drift, overestimating the strength; this is due to the previously mentioned deterioration of the test slab subjected to the biaxial cyclic loading. The model reproduces the connection failure modes that were experimentally observed. Connection C3 failed for punching shear during the final test in the E-W direction, for both positive and negative directions of loading at a drift of 3.1%. Numerical results effectively confirm these data, because punching of the connection is not detected during analyses for the N-S loading direction (Fig. 9, left), whereas punching is predicted in the E-W loading direction (Fig. 9, right) for both positive and negative drifts of 3.9 and 4.0%, respectively. The difference between experimental and numerical punching drift is ascribed to the biaxial loading. For the lateral Connection D3, when loaded parallel to the free edge (N-S), good correspondence is obtained with the pushover (Fig. 10(a)) in terms of force and drift. For the E-W cycles, the experimental failure was punching in both E and W directions at 3 and 2% drift, respectively. Strength is overestimated in the W loading (Fig. 10(b)) at a maximum drift very close to the experimental. Punching failure is predicted in the E (negative) direction (Fig. 11, right), though strength and drift capacity are overestimated. With regard to corner connections, for A4 (Fig. 12), the numerical curve predicts drift capacity accurately in the N-S and W directions, but overestimates the drift capacity in the E (negative) direction. The connection strength is overestimated in the N (negative) and E-W directions. The tests showed that all corner connections, including A4, survived the E-W 4% drift test, except D1 in the W direction. The numerical model correctly shows that punching is not reached, whereas the torsion capacity is reached for both S and W directions, corresponding to the experimental crack patterns (Fig. 13). ACI Structural Journal/March-April 2014
Fig. 9—State of hinges around column of Connection C3 for N-S (left) and E-W (right) loading at ultimate drift. Experimental crack pattern on top surface after punching (with line surrounding damaged zone).
Fig. 10—Comparison between numerical and experimental moment-rotation envelope of Connection D3 for: (a) N-S; and (b) E-W direction. Positive drifts S and W. Experimental envelope up to connection strength. Experimental E-W 4% drift cycles, including cycles beyond failure. Summing up, the model provides a good approximation of the experimental behavior for the N-S direction, where the biaxial loading effects were lower. In the E-W direction, the strength and ultimate drift capacity were affected by the ACI Structural Journal/March-April 2014
accumulation of damage with biaxial loading, and the model provides non-conservative results. The same results were reached for strength of the connections using ACI 318-83,
349
and showing the experimental ultimate drift capacities reduction in the E-W direction compared with N-S.3
Fig. 11—State of hinges around column of Connection D3 for N-S (left) and E-W (right) loading at ultimate drift.
CONCLUSIONS A grid model has been set up to reproduce the nonlinear response of a flat slab structure subjected to gravity and lateral cyclic loading. Experimental tests carried out on a scaled model were analyzed. The slab was tested under gravity and lateral biaxial cyclic loading. Both principal directions were loaded alternatively, with a sequence of cycles of increasing amplitude. Nonlinear static analyses under gravity loads have been performed, followed by pushover analyses under horizontal loads in the two principal directions of the slab on the numerical model. The model is efficient in showing several aspects of the response of the test slab considered: 1. The experimental global behavior is approximated differently in the two orthogonal directions of biaxial loading: the pushover curves in N-S directions are very close to the experimental in terms of path, maximum load, and maximum drift; for the E-W direction, a numerical overestimation of lateral load and drift is detected that is due to the experimental degradation of the test slab due to biaxial cyclic loading. 2. The model captures the ultimate drift capacity of the test slab in both N and S directions, the first loaded up to 4% drift. The drift capacity in the E and W direction is overestimated by the model, predicting a maximum drift close to 4% in both E and W directions against experimental values close to 2%. 3. Experimental moment-rotation curves of internal connection are well approximated by numerical curves for the N-S loading direction; for the E-W direction, an overestimation of load and drift capacity is detected. A similar result is obtained for lateral connections loaded parallel to the free edge. The difference is attributed to the slab degradation observed experimentally, due to the damage accumulation with biaxial loading. 4. For lateral connections loaded perpendicular to the free edge and corner connections, the numerical analysis is less accurate for both the N-S and E-W directions. In the
Fig. 12—Comparison between the numerical and experimental moment-rotation envelope of joints A4 for: (a) N-S, and (b) E-W direction. Positive drifts S and W. Experimental envelope up to connection strength. Experimental E-W 4% drift cycles, including cycles beyond failure. 350
ACI Structural Journal/March-April 2014
Guglielmo Corti is a Civil Engineer. He received his MSc in civil engineering from Politecnico di Milano in 2010. His research interests include design of reinforced concrete structures.
c d J′ Mtu Mtuo Mu Vc Vg
= = = = = = = =
Vu = vc = vn = vus = vus,red = Φu σn γu ψu ψuo
= = = = =
NOTATION
column side slab average effective depth polar moment of inertia at sides of connection reduced torsion capacity (with interaction effects) torsion capacity without interaction effects flexural capacity punching shear capacity of flat slab-column connection shear force transferred between slab and column under gravity loads shear force at capacity of critical sections concrete shear strength, ACI 318-059 shear strength, ACI 318-059 eccentric shear strength at the sides of connection reduced eccentric shear strength, by interaction with flexure and shear ultimate curvature maximum flexural stress in concrete, compression inelastic shear strain corresponding to shear capacity reduced twist angle at maximum torque (with interaction effects) twist angle at maximum torque
REFERENCES
Fig. 13—State of hinges around column of Connection A4 for N-S (left) and E-W (right) loading at ultimate drift. Experimental crack patterns (side and top). latter case, the accumulation of damage with the biaxial loading affects the results. Improvements are needed for the parameters in the model for the strength of these types of connections. 5. The model reproduces the experimental failure modes of connections. The tests considered herein showed the effects of biaxial loading as a reduction of ultimate drift and capacity at punching of the slab-column connections, with respect to those for a one-directional loading. These punching failures are predicted by the model in correspondence of ultimate moment and drift values higher than the experimental. The developments of the research should improve the model to consider the biaxial loading effect. These results show the performance of the model in a rather demanding case study, including some structural irregularity and the effects of cyclic loading in two orthogonal directions. The results for biaxial loading indicate the need for further research developments. AUTHOR BIOS
Dario Coronelli is an Assistant Professor in the Department of Civil and Environmental Engineering at Politecnico di Milano, Milan, Italy, where he received his PhD in 1998. His research interests include the structural effects of corrosion and seismic design of reinforced structures.
ACI Structural Journal/March-April 2014
1. Joint ACI-ASCE Committee 421, “Seismic Design of Punching Shear Reinforcement in Flat Plates (ACI 421.2R-07),” American Concrete Institute, Farmington Hills, MI, 2007, 24 pp. 2. Coronelli, D., “A Grid Model for Flat Slab Structures,” ACI Structural Journal, V. 107, No. 6, Nov.-Dec. 2010, pp. 645-665. 3. Hwang, S. J., and Moehle, J. P., “An Experimental Study of FlatPlate Structures under Vertical and Lateral Loads,” Technical Report UCB/ EERC-93/03, Earthquake Engineering Research Center, University of California at Berkeley, Berkeley, CA, Feb. 1993, 278 pp. 4. Pan, A. D., and Moehle, J. P., “Lateral Displacement Ductility of Reinforced Concrete Flat Plates,” ACI Structural Journal, V. 86, No. 3, May-June 1989, pp. 250-258. 5. Tan, Y., and Teng, S., Interior Slab-Rectangular Column Connections under Biaxial Lateral Loadings, SP-232, M. A. Polak, ed., American Concrete Institute, Farmington Hills, MI, 2005, pp. 147-174. 6. Anggadjaja, E., and Teng, S., “Edge-Column Slab Connections under Gravity and Lateral loading,” ACI Structural Journal, V. 105, No. 5, Sept.-Oct. 2008, pp. 541-551. 7. CSI, CSI Analysis Reference Manual—SAP 2000 Advanced Research v.10, Computers and Structures Inc., Oct. 2005, 433 pp. 8. Whittle, R. T., “Design of Reinforced Concrete Flat Slabs to BS 8110,” Report 110, CIRIA, 1994. 9. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05),” American Concrete Institute, Farmington Hills, MI, 2005, 430 pp. 10. Bentz, E. C., Sectional Analysis of RC Members, University of Toronto, Toronto, ON, Canada, 2000, 198 pp. 11. Dilger, W. H., “Flat Slab-Column Connections,” Progress in Structural Engineering and Materials, V. 2, 2000, pp. 386-399. 12. Park, H., and Choi, K., “Improved Strength Model for Interior Flat Plate-Column Connections Subjected to Unbalanced Moment,” Journal of Structural Engineering, ASCE, V. 132, No. 5, May 2006, pp. 694-704. 13. Kanoh, Y., and Yoshizaki, S., “Strength of Slab-Column Connections Transferring Shear and Moment,” ACI Journal, V. 76, No. 3, Mar. 1979, pp. 461-468. 14. Tian, Y.; Jirsa, J. O.; and Bayrak, O., “Nonlinear Modeling of SlabColumn Connections under Cyclic Loading,” ACI Structural Journal, V. 106, No. 1, Jan.-Feb. 2009, pp. 30-38. 15. Collins, M. P., and Mitchell, D., “Shear and Torsion Design of Prestresses and Non-Prestressed Concrete Beams,” PCI Journal, Sept.-Oct. 1980, pp. 32-100. 16. Park, R., and Paulay, T., Reinforced Concrete Structures, John Wiley & Sons, Inc., New York, 1975, 769 pp.
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NOTES:
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ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S31
Effect of Steel Stirrups on Shear Resistance Gain Due to Externally Bonded Fiber-Reinforced Polymer Strips and Sheets by Amir Mofidi and Omar Chaallal This paper presents the results of an experimental investigation of reinforced concrete (RC) T-beams strengthened in shear with externally bonded (EB) carbon fiber-reinforced polymer (CFRP) strips and sheets. The main objective of this study was to gain insight, by varying the test parameters, into the interaction between the internal transverse steel reinforcement and the externally bonded CFRP used for strengthening of RC beams in shear. The test parameters of this study were: 1) the CFRP ratio (that is, the spacing of the CFRP strips); 2) the presence or absence of transverse steel; 3) the transverse steel ratio (that is, the spacing of the stirrups); and 4) the use of CFRP strips versus CFRP sheets. In total, 10 tests were performed on 4520 mm (14 ft, 10 in.) long T-beams. The study showed that the presence of internal transverse steel reinforcement resulted in a significant decrease in the gain due to CFRP for all strengthened specimens. It also showed that the steel yielded before failure for all test specimens with transverse steel. Finally, the presence of CFRP did not result in a significant decrease in transverse steel strain. It can be concluded that the contribution of transverse steel to shear resistance is not affected by the addition of EB CFRP. These results are in good agreement with the assumptions made by existing codes and design guidelines, which are based on the yielding of transverse steel at ultimate strain for RC beams strengthened in shear with EB CFRP. Keywords: carbon fiber-reinforced polymer (CFRP); CFRP sheet; reinforced concrete beam; shear strengthening; strip; transverse steel reinforcement.
INTRODUCTION In recent years, shear strengthening of reinforced concrete (RC) beams with externally bonded (EB) fiber-reinforced polymer (FRP) material has attracted attention and has been studied by several researchers (Uji 1992; Chaallal et al. 1998; Triantafillou 1998; Khalifa et al. 1998; Bousselham and Chaallal 2004; Chaallal et al. 2011; Mofidi and Chaallal 2011a,b). These experimental and analytical studies have provided valuable insights and results. Several questions, however, still linger in the area of shear strengthening of RC beams with FRP composites (Bousselham and Chaallal 2004; Mofidi and Chaallal 2011a). For instance, a comparison between the experimental shear resistance due to FRP and the values predicted by the analytical models used in existing codes and guidelines shows that major aspects of shear strengthening with FRP material are still not captured by the predictive models used in the codes and guidelines (Bousselham and Chaallal 2008; Mofidi and Chaallal 2011a). This is mainly because the calculated shear contribution of FRP according to the codes and guidelines does not account for the effect of certain parameters that have experimentally been found to have a major influence ACI Structural Journal/March-April 2014
on the contribution of FRP to shear resistance. The effect of internal transverse steel reinforcement is one of these influential parameters. The adverse effect of transverse steel on the effectiveness of externally bonded FRP used for shear strengthening and retrofit of RC beams is well established (Bousselham and Chaallal 2008; Chaallal et al. 2011; Mofidi and Chaallal 2011a,b). In contrast, the effect of adding EB FRP for shear retrofit on the performance of internal steel stirrups has not been thoroughly documented. Moreover, in most modern codes and guidelines, the contribution of steel stirrups to the shear resistance Vs at the ultimate state is calculated on the premise that the steel stirrups have yielded. The premature debonding failure observed in RC beams strengthened in shear with FRP, however, has prompted legitimate questions and concerns as to whether the assumption that the steel stirrups yield before failure holds true (Chen et al. 2010). RESEARCH SIGNIFICANCE Researchers have not yet reached a commonly accepted agreement on the effect of transverse steel in RC beams retrofitted with FRP. Therefore, this effect is not yet considered in the design codes and guidelines, including ACI 440.2R-08 (ACI Committee 440 2008). Consequently, current design codes and guidelines may overestimate the shear resistance of RC beams with transverse steel that are strengthened using EB FRP sheets and strips. Such uncertainties in shear strengthening of RC beams using EB FRP have provided the key impetus for conducting the current research study, the objective of which was to gain insight into the interaction between internal transverse steel reinforcement and externally bonded FRP strips and sheets used for shear strengthening of RC beams. This insight has been achieved based on results obtained from an experimental program carried out on full-size T-beam specimens, described as follows. EXPERIMENTAL PROGRAM The experimental program (Table 1) involved 10 tests performed on full-scale RC T-beams. The control specimens, which were not strengthened with carbon FRP (CFRP), were labeled NF (for No FRP), whereas the specimens retrofitted with a layer of EB CFRP sheet were labeled ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-104.R2, doi:10.14359.51686527, was received November 12, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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Table 1—Experimental results Total shear resistance, kN
Resistance due to concrete, kN
Resistance due to steel, kN
Resistance due to CFRP, kN
Gain due to CFRP, %
Deflection at loading point, mm
Specimen
FRP type
wf /sf
Load at rupture, kN
NR-NF
—
0
122.7
81.2
81.2
0.0
0.0
0
2.6
NR-ST-LF
Strips
87.5/175
203.1
134.5
81.2
0.0
53.3
66
6.2
NR-ST-HF
Strips
87.5/125
227.3
150.6
81.2
0.0
69.3
85
7.2
NR-SH
Sheet
1
181.2
120.0
81.2
0.0
38.7
48
4.2
HR-NF
—
0
350.6
232.2
81.2
151.0
0.0
0
11.9
HR-ST-LF
Strips
87.5/175
372.5
246.7
81.2
151.0
14.5
6
15.9
HR-ST-HF
Strips
87.5/125
383.4
253.9
81.2
151.0
21.7
9
15.7
HR-SH
Sheet
1
378.3
250.6
81.2
151.0
18.4
8
15.2
MR-NF
—
0
294.0
194.7
96.2
98.5
0
0
11.2
MR-SH
Sheet
1
335.2
222.0
96.2
98.5
27.3
14
11.3
Notes: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.
Fig. 1—Test setup configuration: (a) cross section of tested RC beams; and (b) side view of loading configuration. (Note: 1 mm = 0.0394 in.) SH (for SHeet), and the specimens strengthened with FRP strips (strip width = 87.5 mm = 3-7/16 in.) were labeled ST (for STrips). Specimens strengthened with narrowly spaced FRP strips (spacing equal to 125 mm [5 in.]) were labeled HF (for Heavily strengthened with FRP), whereas the specimens strengthened with widely spaced strips (spacing equal to 175 mm [6 7/8 in.]) were labeled LF (for Lightly strengthened with FRP). Series NR (Not Reinforced with transverse steel) consisted of specimens with no internal transverse steel reinforcement (that is, no stirrups). Series HR (Heavily Reinforced with transverse steel) and MR (Moderately Reinforced with transverse steel) contained specimens with internal transverse steel stirrups spaced at s = d/2 and s = 3d/4, respectively, where d = 350 mm (13-3/4 in.) represents the effective depth of the cross section of the beam. Therefore, for instance, Specimen NR-ST-HF featured a beam with no transverse steel retrofitted using CFRP strips spaced at 125 mm (5 in.). The specimen details are provided in Table 1, together with the identification codes used hereafter. Description of specimens The T-beams were 4520 mm (14 ft, 10 in.) long, and their T-sections had overall dimensions of 508 x 406 mm (20 x 16 in.). The width of the web and the thickness of the flange were 152 and 102 mm (6 and 4 in.), respectively (Fig. 1(a) and (b)). It should be noted that the web of the strengthened beams is chamfered at the outer corners. The longitudinal steel reinforcement consisted of four 25M bars (diameter 354
25.2 mm [1 in.], area 500 mm2 [0.78 in.2]) laid in two layers at the bottom, and six 10M bars (diameter 10.3 mm [ 0.4 in.], area 100 mm2 [0.16 in.2]) laid in one layer at the top. The bottom bars were anchored at the support with 90-degree hooks to prevent premature anchorage failure. The internal steel stirrups (where applicable) were 8 mm (5/16 in.) in diameter (area 50 mm2 [0.08 in.2]). To apply the EB FRP sheets and strips to the RC specimens, the following steps were implemented: 1) the area of the specimens where the CFRP sheets and strips was to be epoxy-bonded was sand-blasted to remove any surface cement paste and to round off the beam edges; 2) the specimen corners were chamfered to provide a radius of 12.7 mm (0.5 in.) to avoid stress concentration in the FRP sheets during the tests; 3) residues were removed using compressed air; and 4) layers of U-shaped CFRP sheets and strips were glued to the bottom and lateral faces of the RC beam using a two-component epoxy resin. Materials A commercially available concrete delivered to the structural laboratory by a local supplier was used in this project. The average 28-day concrete compressive strength was 25 MPa (3626 psi), which is very close to the average compressive strength of 27 MPa (3916 psi) obtained during the tests. It should be noted that the specimens of the MR series were cast using a different concrete batch, the compressive strength of which was 35 MPa (5076 psi).
ACI Structural Journal/March-April 2014
location as the transverse steel. The load was applied using a 2000 kN (449 kip) capacity MTS hydraulic jack. All tests were performed under displacement-control conditions at a rate of 2 mm/min (approximately 3/16 in./min). ANALYSIS OF RESULTS All the specimens failed in shear. The control specimens failed due to diagonal tension failure of the concrete cross section. The specimens strengthened with CFRP failed by premature FRP debonding followed by diagonal tension failure (Fig. 4(a) through (d)). Local CFRP fracture was observed in few specimens (NR-ST-LF and NR-ST-HF); this local failure is attributed to stress concentration at the web corners. Fig. 2—Side view of strengthened specimen using FRP sheet U-jacket with crack gauges on CFRP strips. The scatter between the results of compression tests on the cylinder specimens was insignificant. The longitudinal steel reinforcement consisted of 25M bars (modulus of elasticity 187 GPa [27,122,057 psi], and yield stress 500 MPa [72,519 psi]), and the transverse steel reinforcement consisted of deformed 8 mm (13/16 in.) bars (modulus of elasticity 206 GPa [29,877,774 psi] and yield stress 650 MPa [94,275 psi]). The composite material was a unidirectional carbon-fiber fabric epoxy-bonded over the test zone in a U-shape around the web (Fig. 2). The dry CFRP sheet had an ultimate tensile strength of 3450 MPa (500,380 psi), an elastic modulus of 230 GPa (33,358,697 psi), and an ultimate strain of 1.5%, as reported by the manufacturer. The thickness of the CFRP fabric used was 0.11 mm. Test setup All 10 tests were conducted in three-point load flexure (Fig. 1(b)). This loading configuration was chosen because it enabled two tests to be performed on each specimen. Specifically, while one end zone was being tested, the other end zone was overhung and unstressed. The load was applied at a distance a = 3d from the nearest support, a configuration which was representative of a slender beam. Instrumentation The measuring equipment used in this research study was carefully designed to meet the objectives of this study. The vertical displacement was measured at the position under the applied load and at midspan, using a linear variable differential transformer (LVDT) with a 150 mm (5-7/8 in.) stroke. Different types of strain gauges were installed on the longitudinal reinforcement, on the steel stirrups, and embedded in the concrete to measure the strains experienced by the various materials as the loading increased and to monitor thereby the yielding of the steel. The strain gauges on the stirrups were installed along the anticipated plane of the major shear crack. Displacement sensors, also known as crack gauges, were used to measure the strains experienced by the CFRP strips and sheets (Fig. 2 and 3). These gauges were fixed vertically onto the lateral faces of the specimens at the same ACI Structural Journal/March-April 2014
Deflection response Figure 5 compares the deflection response for RC beams without transverse steel reinforcement. It reveals that the NR-SH and NR-ST-HF specimens exhibited slightly greater overall stiffness than the other beams. Specimen NR-ST-HF exhibited the highest deflection at the loading point and a higher maximum load at failure than the other specimens (Fig. 5). The beams strengthened with FRP strips exhibited more deformability than the beams strengthened with FRP sheets. This occurred mainly because in RC beams strengthened with FRP strips, local FRP debonding did not result in a complete debonding failure. Each local strip-debonding event resulted in a drop in the load-carrying capacity of the beam (Fig. 5), but the load continued to increase as the cracks propagated in the RC beams web, engaging the unloaded CFRP strips in their path. In specimens strengthened with FRP strips, and unlike beams strengthened with FRP sheets, local debonding of FRP cannot propagate from one FRP strip to the next. Therefore, using FRP strips results in a more progressive type of failure, and a sudden and brittle failure is prevented. Figure 6 shows the load versus maximum deflection curves for RC beams with transverse steel reinforcement. It reveals that each of the specimens in Series HR and MR exhibited an overall stiffness relatively similar to that of the other beams. The maximum load at failure and the maximum deflection attained at the loading point for each specimen are provided in Table 1. Specimen HR-ST-HF reached the highest maximum load at failure. Meanwhile, the HR-ST-LF and HR-SH specimens exhibited a slightly higher deflection at the loading point than the other strengthened and unstrengthened specimens (Table 1). It should be mentioned that in Table 1, the shear contributions of concrete and steel were calculated based on the measured experimental results for the control beams. Strain analysis This part of the study investigated the behavior of CFRP and transverse steel during loading of the specimens. As mentioned previously, extensive instrumentation for strain monitoring was carefully planned and implemented to provide the data needed to gain a better understanding of the effect of transverse steel on the contribution of FRP to
355
Fig. 3—Location of strain gauges on transverse steel reinforcement and FRP sheets/strips. Positions of strain gauges on FRP sheets/strips are identical in specimens strengthened with similar FRP strengthening configurations. the shear resistance of RC beams retrofitted in shear with EB FRP. CFRP strain—The distribution of the maximum strains attained in the CFRP is shown in Fig. 7 for all strengthened test specimens. It should be noted that these strain values are the maximum measured values, but not necessarily the absolute maximum values, experienced by the CFRP U-jackets. The two values may differ in cases where the strain gauges did not intercept the main cracks. From Fig. 7, the following observations can be made: 1. All curves presented in these figures show that the CFRP did not contribute to load-carrying capacity in the initial stage of loading. 2. For specimens of Series NR, the measured strains were greater for specimens strengthened with FRP strips than for similar beams strengthened with FRP sheets. 3. For the beams strengthened with a layer of FRP sheet (NR-SH, MR-SH, and HR-SH), the maximum strain in the CFRP increased as the amount of transverse reinforcement was increased. In fact, for Specimen HR-SH, the maximum strain attained by the FRP sheet was approximately 48% of the ultimate strain value, whereas the corresponding 356
maximum strain values for Specimens NR-SH and MR-SH were 17 and 27%, respectively, of the ultimate strain. 4. For specimens strengthened with FRP strips in Series NR (no steel stirrups), the maximum measured FRP strain values were approximately equal. This is also true for the specimens strengthened with FRP strips in the HR series. 5. For all specimens strengthened with FRP strips in both Series NR and HR, the maximum FRP strain was greater than 5000 με. It may be of interest to note that ACI 440.2R-08 (ACI Committee 440 2008) limits the maximum design FRP strain value to 4000 με. On the basis of the results achieved in this study, this limit appears to be conservative for RC beams strengthened with FRP strips. Transverse steel reinforcement strain—Figure 8 shows the measured strain in the transverse steel reinforcement for the test specimens with internal steel reinforcement. The vertical line identifies the strains corresponding to the yielding of the transverse steel, as obtained by tests (εy = 3250 με). From Fig. 8, the following observations can be made: 1. Like the CFRP, the steel stirrups did not contribute to load-carrying capacity in the initial stage of loading. The
ACI Structural Journal/March-April 2014
Fig. 4—Failure mode and multiline cracking pattern of strengthened specimens: (a) NR-ST-HF; (b) NR-SH; (c) HR-ST-LF; and (d) HR-ST-HF after failure.
Fig. 5—Load versus deflection at load point: Series NR. (Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.)
Fig. 6—Load versus deflection at load point: Series HR and MR. (Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.)
transverse steel contribution to shear resistance started after the formation of diagonal cracking initiated. 2. All monitored stirrups were significantly strained. This is also reflected by the cracking pattern observed in the beams with transverse steel (Fig. 4(a) through (d)). 3. Yielding of transverse steel was observed in all cases. This observation is in good agreement with existing code specifications and guidelines, which assume that the trans-
verse steel yields at ultimate strain for RC beams strengthened in shear with EB FRP. Figure 8 shows that addition of EB FRP did not result in a decrease of transverse steel strain. For all the specimens with transverse steel, the steel yielded well before the RC beam reached ultimate failure. Therefore, it can be concluded that at the ultimate state the contribution of internal steel stirrups to shear resistance was not affected by the addition of
ACI Structural Journal/March-April 2014
357
Fig. 7—Load versus strain in FRP for all strengthened specimens. (Note: 1 kN = 0.225 kip.)
Fig. 8—Load versus strain in transverse steel: Series HR and MR. (Note: 1 kN = 0.225 kip.)
externally bonded FRP. It follows that the shear contribution of internal steel reinforcement Vs should be calculated using the same formula for both FRP-strengthened and unstrengthened RC beams, which confirms the assumptions of the design guidelines (ACI 440.2R-08; CSA S806-02; Oehlers et al. 2008). These results are not in agreement with those based on finite-element simulations reported by Chen et al. (2010, 2012); these researchers found that for RC beams strengthened in shear with FRP, the internal steel stirrups did not reach the yield point. Based on their finite-element model, they concluded that the yield strength of the internal steel stirrups in such strengthened RC beams cannot be fully used. The models by Chen et al. (2010, 2012) were originally generated based on a single crack failure pattern assumption. Single crack failure pattern was adopted by most design models to simplify the calculation and design of strengthening FRP sheets and strips. Experimental observations, however, clearly show that for RC beams strengthened with EB FRP, the cracking pattern on the FRP-concrete interface is rather distributed (Mofidi and Chaallal 2011a). Eventually, the distributed cracks at the concrete cover merge together at the concrete core to form one major shear crack at ultimate. Therefore, it is believed that assuming a single crack pattern is overly simplistic when considering such a precise finite element modeling tool. Considering the fact that the crack width plays a governing role in the Chen et al. (2010, 2012) models, the discrepancies between the results produced by Chen et al. (2010, 2012) models and the experimental results are to be expected.
The experimental contribution of transverse steel Vs is calculated as the sum of the contributions corresponding to the stirrups crossing the plane of rupture using the following equation
Shear resistance under increasing load In accordance with most codes and standard guidelines, the nominal shear resistance Vn can be expressed as follows Vn = Vc + Vs + Vf
358
(1)
Vs = As Es ∑ e s ,i (2)
where As is the section area of one stirrup; Es is the elastic modulus of the transverse steel; and εs,I (≤εy) is the measured strain in stirrup i in the failure zone, where εy is the yield strain of the stirrups. The experimental contribution of FRP Vf can be calculated as follows
V f = 2 E f t f ∑ (wi e f ,i ) (3)
where Ef is the elastic modulus of the CFRP; tf is the thickness of the CFRP; εf,i is the measured strain in the CFRP corresponding to instrumented section i in the failure zone; and wi is the tributary width of the strengthening FRP strips intercepted by the major shear crack, where the CFRP strain εf,i is assumed constant. The CFRP strengthening width represents the portion of the CFRP that effectively contributes to shear resistance. Figure 9 shows the experimental evolution under increasing load of the contributions to the shear resistance of the two components (Vs and Vf) for Specimens HR-NF, HR-ST-LF, HR-ST-HF, and HR-SH. The specimens shown in this figure had the same degree of transverse steel reinforcement (highly reinforced), but were strengthened using different amounts of externally bonded FRP strips and sheet. The behavior of the transverse steel under increasing load exhibited a similar pattern for both the unstrengthened beam (HR-NF) and the beams retrofitted with different amounts of EB FRP strips and sheet (HR-ST-LF, HR-ST-HF, and HR-SH). This result indicates that strengthening of RC beams with EB FRP does not alter the behavior of internal ACI Structural Journal/March-April 2014
Table 2—Coefficient of determination (R2) between values of Vf as calculated by each of the models and experimental values of Vf
Specimen
Vfexp
Vf cal by ACI 440.2R (2008)
NR-ST-LF
53.3
20.5
32.5
43.7
NR-ST-HF
69.3
28.6
39.8
37.9
NR-SH
38.7
40.9
45.9
35.5
HR-ST-LF
14.5
20.5
32.5
7.3
HR-ST-HF
21.7
28.6
39.8
8.3
HR-SH
18.4
40.9
45.9
10.2
27.3
44.1
50.7
14.4
0.04
0.03
0.81
MR-SH
Fig. 9—Transverse steel and FRP contributions under increasing load for Specimens HR-NF, HR-ST-LF, HR-ST-HF, and HR-SH. (Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.)
Fig. 10—Transverse steel and FRP contributions under increasing load for Specimens HR-NF, MR-SH, and HR-SH. (Note: 1 kN = 0.225 kip.) transverse steel. It also reveals that addition of EB FRP does not attenuate the shear contribution of the transverse steel reinforcement. Figure 10 shows the experimental progression of the shear contributions of the two components (Vs and Vf) under increasing load for Specimens HR-NF, MR-SH, and HR-SH. The strengthened specimens illustrated in this figure were both retrofitted with one layer of CFRP sheet, but reinforced with different amounts of transverse steel reinforcement. The behavior of the FRP under increasing load followed different patterns for the strengthened beams depending on the amount of internal transverse steel reinforcement (MR-SH and HR-SH). This clearly shows that the behavior of EB FRP depends on the amount of transverse steel used in
ACI Structural Journal/March-April 2014
Vf cal by HB 305 (2008)
Vf cal by Mofidi and Chaallal (2011a)
2
R
Notes: Vfexp is experimental shear resistance due to FRP; Vfcal is calculated shear resistance due to FRP (not factored); 1 kN = 0.225 kip.
RC beams. This result confirms that increasing the amount of transverse steel leads to a reduction in the contribution of the FRP during loading and at the ultimate state. COMPARISON OF TEST RESULTS WITH SHEAR DESIGN EQUATIONS The shear resistance due to CFRP as obtained by tests Vfexp is compared in Table 2 to the nominal shear resistance Vfcal predicted by ACI 440.2R (2008), HB 305 (Oehlers et al. 2008), and Mofidi and Chaallal (2011a). Mofidi and Chaallal (2011a) proposed a model for calculating the contribution of FRP to shear resistance, taking into consideration the attenuating effect of transverse steel as well as of the cracking pattern on the EB FRP contribution in shear. Based on their study, it was determined that the presence of transverse steel favors the formation of a multi-line shear-cracking pattern in the RC beam, which decreases the anchorage length of the FRP fibers and hence the available effective width of FRP wfe and bonding area between the FRP and the concrete. In the calculation of wfe, it is assumed that the cracking pattern of the RC beam becomes more propagated with the increase in the amount of internal steel and external FRP shear reinforcement as measured by their respective rigidities. On the other hand, the cracking pattern influences the anchorage length of the fibers. As the cracking pattern becomes more propagated, fewer fibers will provide the minimum effective anchorage length. Therefore, the effective width, that is the width of the fibers long enough to attain the effective anchorage length, decreases. Using a computational analysis based on the available test results in the literature (Mofidi and Chaallal 2011a), the effective width is defined as a function of the sum of the rigidities of transverse steel reinforcement and that of transverse FRP sheets (Eq. (9) and (10)).
w fe =
0.6 ρ f ⋅ E f + ρs ⋅ E s
× df
for U-jacket (4)
359
w fe =
0.43 × d f for side bonded ρ f ⋅ E f + ρs ⋅ E s
(5)
With wfe defined, the cracking modification factor can then be calculated as kc = wfe/df—that is kc =
kc =
w fe 0.6 = df ρ f ⋅ E f + ρs ⋅ E s
w fe 0.43 = df ρ f ⋅ E f + ρs ⋅ E s
for U-jackets
(6)
for side bonded
(7)
The effect of kL for beams with an anchorage length less than the effective length and that of kf counting for the wf /sf ratio of the FRP strips are considered in the equation for effective strain, as follows
k ⋅k ⋅k ⋅τ ⋅L fc′ e fe = c L f eff e = 0.31kc ⋅ kL ⋅ k f ≤ e fu (8) tf ⋅ Ef tf Ef
It should be noted that kL and kf can be calculated using Eq. (9) and (11), as follows
if l ≥ 1 1 kL = − ⋅ ( 2 l ) l if l < 1
l=
Lmax Le
(9)
where
Lmax
df for U-jackets sin b = df for side plates 2 sin b
kf =
wf 1 1+ − sf 2
2
wf 1 − 1− sf 2
2
(10)
(11)
In addition, Vf can be calculated as a function of εfe using the following equation that accounts for the effect of the cracking angle θ (the cracking angle can be taken equal to 45 degrees for simplicity) Vf =
2t f ⋅ w f ⋅ e fe ⋅ E f ⋅ (cot θ + cot a ) ⋅ sin a ⋅ d f sf (12)
360
= ρ f ⋅ E f ⋅ e fe ⋅ b ⋅ d f ⋅ (cot θ + cot a ) ⋅ sin a
Fig. 11—FRP contribution: values as calculated by ACI 440.2R-08, HB 305-08, and Mofidi and Chaallal (2011a) models versus experimental values. (Note: 1 kN = 0.225 kip.) The Mofidi and Chaallal (2011a) model justifies premature FRP debonding in RC beams with internal transverse steel reinforcement compared with beams with no transverse steel and explains the superior gain achieved due to FRP in beams with few or no steel stirrups compared with beams with moderate to high amounts of internal transverse steel. To test the correlation between the experimental results and the predicted results by the models, the best fit of the nominal predicted results versus the experimental results was considered. The following assumptions were made when calculating the experimental results: 1) the shear resistance due to concrete was assumed constant for beams with or without transverse steel reinforcement; 2) the shear resistance due to concrete was assumed constant for both retrofitted and unstrengthened specimens; and 3) the contribution of the transverse steel was assumed constant for both retrofitted and unstrengthened specimens. For specimens with no transverse steel strengthened using FRP strips (NR-ST-LF and NR-ST-HF), all three models underestimated the shear resistance due to FRP. This effect was more significant when using ACI 440.2R-08 (ACI Committee 440 2008), where, for example, for NR-ST-HF, the shear resistance predicted was 28 kN (6.3 kip), compared with 69.3 kN (15.6 kip) obtained by test. On one hand, for the specimen with no transverse steel strengthened using an FRP sheet (NR-SH), the ACI 440.2R-08 (ACI Committee 440 2008) and HB 305-08 (Oehlers et al. 2008) models slightly overestimated the shear resistance due to FRP. On the other hand, the Mofidi and Chaallal (2011a) model slightly underestimated the FRP contribution to shear resistance (Table 2). For all strengthened specimens with transverse steel reinforcement, the ACI 440.2R-08 and HB 305-08 models provided unconservative predictions and therefore overestimated results (Table 2). In contrast, results produced by Mofidi and Chaallal (2011a) for specimens strengthened with transverse steel reinforcement correlate fairly well with ACI Structural Journal/March-April 2014
the test results. Figure 11 shows that the Mofidi and Chaallal (2011a) model predicted the experimental shear contribution of FRP (R2 = 0.81) with a high level of accuracy. The ACI 440.2R-08 and HB 305-08 models produced low coefficients of determination (0.04 and 0.03, respectively). In general, current design guidelines models (including ACI 440.2R-08 and HB 305-08) fail to consider the effect of the transverse steel (Mofidi and Chaallal 2011a,b). Therefore, they may predict conservative results for beams without transverse steel reinforcement. In contrast, current design guidelines models may overestimate the shear contribution of FRP for the specimens with transverse steel reinforcement and hence, the shear resistance. Such unconservative results are exemplified in the results predicted by ACI 440.2R-08 and HB 305-08 for Specimens HR-ST-LF, HR-ST-HF, HR-SH, MR-SH in the current study. The presence of the transverse steel has a significant effect on the shear resistance of RC beams strengthened with FRP, and therefore, should ultimately be considered in design models. CONCLUSIONS This paper presents the results of an experimental investigation involving 10 tests on RC T-beams strengthened in shear with EB FRP strips and sheets. The effects of the following parameters were studied: 1) the CFRP ratio (that is, the spacing of the CFRP strips); 2) the presence or absence of transverse steel; 3) the transverse steel ratio (that is, the spacing between the stirrups); and 4) the use of CFRP strips versus CFRP sheets. The following conclusions can be drawn: 1. The addition of internal transverse steel reinforcement resulted in a significant decrease in the gain due to FRP for all the strengthened specimens. 2. For all test specimens with transverse steel reinforcement, the steel yielded before the specimen failed. The presence of externally bonded FRP for shear retrofit did not cause a significant decrease in transverse steel strain. Overall, the contribution of steel stirrups to shear resistance was not adversely affected by the addition of FRP. 3. Comparison of the resistance predicted by the ACI 440.2R-08 (ACI Committee 440 2008), HB 305-08 (Oehlers et al. 2008), and Mofidi and Chaallal (2011a) models with test results showed that the guidelines failed to capture the influence of transverse steel on the shear contribution of FRP. The model proposed by Mofidi and Chaallal (2011a) showed a better correlation with experimental results than the guidelines mentioned. 4. The maximum measured strain values in CFRP strips, and hence the gain in shear strength due to CFRP strips, were significantly greater than for CFRP continuous sheets. In addition, the maximum deflection was slightly greater for beams retrofitted with CFRP strips than for beams strengthened with continuous CFRP sheets. 5. In all the specimens strengthened with FRP strips, the maximum attained FRP strain was greater than 5000 με. It follows that the ACI 440.2R-08 limit for maximum FRP
ACI Structural Journal/March-April 2014
strain (that is, 4000 με) seems conservative for RC beams strengthened in shear with FRP strips. AUTHOR BIOS
Amir Mofidi is a Postdoctoral Fellow in the Department of Civil Engineering and Applied Mechanics of McGill University, Montreal, QC, Canada. He received his PhD from University of Quebec, École de Technologie Supérieure, Montreal, QC, Canada. His research interests include the use of fiber-reinforced polymer composites for strengthening and retrofitting of concrete structures. Omar Chaallal, FACI, is a Professor of construction engineering, University of Quebec, École de Technologie Supérieure. He is a member of ACI Committee 440, Fiber-Reinforced Polymer Reinforcement. His research interests include experimental and analytical research on the use of fiber-reinforced polymer composites for reinforcement and repair of concrete structures.
ACKNOWLEDGMENTS
The financial support of the National Science and Engineering Research Council of Canada (NSERC), the Fonds québécois de la recherche sur la nature et les technologies (FQRNT), and the Ministère des Transports du Québec (MTQ) is gratefully acknowledged. The efficient collaboration of J. Lescelleur (Senior Technician) and J. M. Rios (Technician) at ÉTS in conducting the tests is acknowledged.
REFERENCES
ACI Committee 440, 2008, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (440.2R-08),” American Concrete Institute, Farmington Hills, MI, 76 pp. Bousselham, A., and Chaallal, O., 2004, “Shear-Strengthening Reinforced Concrete Beams with Fiber-Reinforced Polymer: Assessment of Influencing Parameters and Required Research,” ACI Structural Journal, V. 101, No. 2, Mar.-Apr., pp. 219-227. Bousselham, A., and Chaallal, O., 2008, “Mechanisms of Shear Resistance of Concrete Beams Strengthened in Shear with Externally Bonded FRP,” Journal of Composites for Construction, ASCE, V. 12, No. 5, pp. 499-512. Chaallal, O.; Mofidi, A.; Benmokrane, B.; and Neale, K., 2011, “Embedded Through-Section FRP Rod Method for Shear Strengthening of RC Beams: Performance and Comparison with Existing Techniques,” Journal of Composites for Construction, ASCE, V. 15, No. 3, pp. 374-383. Chaallal, O.; Nollet, M. J.; and Perraton, D., 1998, “Strengthening of Reinforced Concrete Beams with Externally Bonded Fiber-Reinforced-Plastic Plates: Design Guidelines for Shear and Flexure,” Canadian Journal of Civil Engineering, V. 25, No. 4, pp. 692-704. Chen, G. M.; Teng, J. G.; and Chen, J. F., 2012, “Shear Strength Model for FRP-Strengthened RC Beams with Adverse FRP-Steel Interaction,” Journal of Composites for Construction, ASCE, DOI: 10.1061/(ASCE) CC.1943-5614.0000313. Chen, G. M.; Teng, J. G.; Chen, J. F.; and Rosenboom, O. A., 2010, “Interaction between Steel Stirrups and Shear-Strengthening FRP Strips in RC Beams,” Journal of Composites for Construction, ASCE, V. 14, No. 5, pp. 498-509. Khalifa, A.; Gold, W. J.; Nanni, A.; and Aziz, A., 1998, “Contribution of Externally Bonded FRP to Shear Capacity of RC Flexural Members,” Journal of Composites for Construction, V. 2, No. 4, pp. 195-203. Mofidi, A., and Chaallal, O., 2011a, “Shear Strengthening of RC Beams with Epoxy-Bonded FRP—Influencing Factors and Conceptual Debonding Model,” Journal of Composites for Construction, ASCE, V. 15, No. 1, pp. 62-74. Mofidi, A., and Chaallal, O., 2011b, “Shear Strengthening of RC Beams with Externally Bonded FRP Composites: Effect of Strip-Width to StripSpacing Ratio,” Journal of Composites for Construction, ASCE, V. 15, No. 5, pp. 732-742. Oehlers, D. J.; Seracino, R.; and Smith, S. T., 2008, Design Guideline for RC Structures Retrofitted with FRP and Metal Plates: Beams and Slabs, HB 305-2008, Standards Australia, Sydney, Australia, 73 pp. Triantafillou, T. C., 1998, “Shear Strengthening of Reinforced Concrete Beams Using Epoxy-Bonded FRP Composites,” ACI Structural Journal, V. 95, No. 2, Mar.-Apr. pp. 107-115. Uji, K., 1992, “Improving Shear Capacity of Existing Reinforced Concrete Members by Applying Carbon Fiber Sheets,” Transactions of the Japan Concrete Institute, V. 14, pp. 253-266.
361
NOTES:
362
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S32
Punching of Reinforced Concrete Flat Slabs with DoubleHeaded Shear Reinforcement by Maurício P. Ferreira, Guilherme S. Melo, Paul E. Regan, and Robert L. Vollum Twelve slabs, 11 of which contained double-headed studs as shear reinforcement, were tested supported by central column and loaded concentrically. Their behavior is described in terms of deflections, rotations, strains of the concrete close to the column, strains of the flexural reinforcement across the slab width, and strains of the studs. All failures were by punching, in most cases within the shear reinforced region. The treatments of punching resistance in ACI 318, Eurocode 2 (EC2), and the critical shear crack theory (CSCT) are described, and their predictions are compared with the results of the present tests and 39 others from the literature. The accuracy of predictions improves from ACI 318 to EC2 to CSCT—that is, with increasing complexity. However, the CSCT assumptions about behavior are not well supported by the experimental observations. Keywords: codes; flat slabs; punching; shear studs.
INTRODUCTION There is no generally accepted theoretical treatment of punching, and design is based on empirical methods given in codes of practice. While there is similarity between them in terms of general approach, there are considerable differences in their assumptions and the resulting equations, which leads to uncertainties about their reliability. A further cause of uncertainty is the wide variety of types of shear reinforcement, such as stirrups of various forms, bent-up bars, welded fabric, and stud systems. Comparisons of design equations with the results of tests using different types of shear reinforcement can result in a wide scatter, while comparisons of slabs with only one type are often limited by the restricted data available. This paper presents the results of tests1 of slabs with double-headed studs as shear reinforcement, followed by a short review of the design methods of ACI 318,2 Eurocode 2 (EC2),3 and the critical shear crack theory (CSCT) of Muttoni et al.,4,5 which is the basis of the punching clauses of the fib Model Code 2010 draft.6 The results of the present tests and of others on slabs with double-headed shear reinforcement are then compared with the three design methods. RESEARCH SIGNIFICANCE There are considerable differences between the design methods for punching in ACI 318, EC2, and the CSCT. The primary objective of the experimental study described in this paper was to assess the realism of the assumptions underlying these design methods. The principal variables in the test series were the sizes and spacings of the studs, and the size and shape of the columns. Extensive measurements were made of slab rotations and strains in the concrete, and flexural and shear reinforcement. Comparisons between ACI Structural Journal/March-April 2014
Fig. 1—Test arrangements. (Note: Dimensions in mm; 1 mm = 0.0394 in.) experimental and calculated strengths for the present tests and others are presented to evaluate the accuracies of the methods. EXPERIMENTAL PROGRAM Twelve tests were made at the University of Brasilia. The specimens were square slabs 2.5 x 2.5 m (8.2 x 8.2 ft) on plan and 180 mm (7.1 in.) thick supported centrally by circular or square columns (Type C and S slabs, respectively). Equal downward loads were applied at eight points close to the slab edges, as shown in Fig.1. ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-119, doi:10.14359.51686535, was received April 4, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
363
The main variables were the shape and size of the column, the amount and distribution of the shear reinforcement, and some details of the main reinforcement. The concrete was made with ordinary portland cement, natural sand, and crushed limestone aggregate with a maximum size of 9.5 mm (3/8 in.). The concrete strength was determined from 100 x 200 mm (4 x 8 in.) control cylinders that were tested at the same time as the slabs. The arrangement of flexural reinforcement was basically the same in all but two of the specimens (Slabs C5 and C6). The general arrangement of the upper tension reinforcement was 16 mm (No. 5) bars with fy = 540 MPa (78 ksi) and Es = 213 GPa (30,893 ksi) at spacings of 100 mm (4 in.) in the outer layer and 90 mm (3.54 in.) in the inner layer, providing almost equal flexural resistances in two directions. The bottom reinforcement was 8 mm (0.315 in.) bars positioned directly below alternate top bars. At the edges, each top bar was lapped with a 12.5 mm (No. 4) hair-pin shaped bar with 500 mm (20 in.) horizontal legs. Only minor adjustments to this arrangement were needed to avoid clashes with shear reinforcement. In Slab C5, the tension reinforcement in the central parts of the widths was increased to 20 mm (No. 6) bars with fy = 544 MPa (79 ksi) and Es = 208 GPa (30,168 ksi) and that in the outer parts was decreased, to obtain a higher reinforcement ratio near the column without significantly altering the flexural capacity. The details of this slab are shown in Fig.2. As the failures of some of slabs appeared to be influenced by crushing of the soffit near the column, Slab C6 was provided with compression reinforcement comprised of four 16.0 mm (No. 5) bars through the column in each direction, and 12.5 mm (No. 4) bars below all the top bars in the rest of the width. The shear reinforcement was double-headed studs made of deformed 10 mm (No. 3) bars with fyw = 535 MPa (78 ksi) and Es = 211 GPa (30,603 ksi), or 12.5 mm (No. 4) bars with fyw = 518 MPa (75 ksi) and Es = 204 GPa (29,588 ksi). The heads, with diameters three times the bar size, were welded to the shanks, and the completed studs were spot-welded to nonstructural carrier rails, which were 10 mm (3/8 in.) wide and 3.2 mm (1/8 in.) thick. The shear reinforcement was positioned from above, with the carrier rails sitting on the upper tension bars either directly or via cross rails. Tests of studs, in which the loading was applied via the heads, showed that the welds between the heads and shanks were able to develop the full strengths of the bars with ductile failures away from the welds. In all but one of the slabs, the lines of studs ran outward from the columns along equally spaced radial lines (radial arrangement). The exception was Slab C4, where a cruciform arrangement was used. Typical details are shown in Fig. 3. Table 1 summarizes the characteristics of all slabs. TEST RESULTS Deflections and rotations Deflections of the top surfaces of the slabs were measured along their centerlines by dial gauges mounted from frames spanning over the slabs and supported on the laboratory 364
Fig. 2—Flexural reinforcement of Slab C5. (Note: Dimensions in mm; 1 mm = 0.0394 in.) floor. An example of the deflected profiles is shown in Fig. 4, where it can be seen that segments of the slab rotated about axes at or very close to the column face, and the top surfaces remained more or less straight on radial lines. The displacements of the slab very close to the column, visible in Fig. 4, were likely due mostly to movements in the support of the column, and were not deflections of the slab relative to the column. Figure 5 shows envelopes of the experimental loadrotation relationships, and the theoretical ones according to CSCT. The experimental rotations plotted are the averages of values determined from deflections, measured on the centerline of the slabs at distances 274 and 1049 mm (10.8 and 41.3 in.) from the slab center in the North, South, East, and West directions. The CSCT values have been calculated from Eq. (13) and (14). The correlations between experimental and calculated results are good. Strains of concrete Strain gauges were used to measure the strains of the bottom surfaces of the concrete close to the columns. The general responses were similar to those observed by others. At low loads, the compression strains in both directions were similar, and increased with increasing load. As loading continued, the radial strains stabilized and then decreased, sometimes becoming tensile before failure. The tangential compressions increased at progressively higher rates. At circular columns, the maximum compression strains were from 2.5 to 2.8‰, where the gauges were 20 mm (0.8 in.) from the column faces, and 3.1 to 3.2‰, where the gauges were 40 mm (1.6 in.) from the faces. In the slabs with square columns, the maximum compressions recorded were lower, but this was probably due to their being on the slab centerlines, while the greatest strains were likely at the corners of the columns. ACI Structural Journal/March-April 2014
Table 1—Characteristics of test slabs Shear reinforcement Slab No.
Column size , mm (in.)
d, mm (in.)
ρ,%
fc, MPa (ksi)
Studs
so, mm (in.)
sr, mm (in.)
C1
270 (10.6)
143 (5.6)
1.48
47.8 (6.9)
10 φ10.0 x 6
70 (2.8)
100 (3.9)
C2
360 (14.2)
140 (5.5)
1.52
46.9 (6.8)
10 φ10.0 x 6
70 (2.8)
100 (3.9)
C3
450 (17.7)
142 (5.6)
1.49
48.9 (7.1)
10 φ10.0 x 6
70 (2.8)
100 (3.9)
C4
360 (14.2)
140 (5.5)
1.52
47.9 (6.9)
12 φ10.0 x 6
70 (2.8)
100 (3.9)
C5
360 (14.2)
140 (5.5)
2.00
49.7 (7.2)
10 φ10.0 x 6
70 (2.8)
100 (3.9)
C6
360 (14.2)
143 (5.6)
1.48
48.6 (7.0)
10 φ10.0 x 6
70 (2.8)
100 (3.9)
C7
360 (14.2)
144 (5.7)
1.47
49.0 (7.1)
10 φ10.0 x 7
55 (2.2)
80 (3.1)
C8
360 (14.2)
144 (5.7)
1.47
48.1 (7.0)
12 φ10.0 x 6
70 (2.8)
100 (3.9)
S1
300 (11.8)
145 (5.7)
1.46
48.3 (7.0)
12 φ10.0 x 2
70 (2.8)
100 (3.9)
S2
300 (11.8)
143 (5.6)
1.48
49.4 (7.2)
12 φ10.0 x 4
70 (2.8)
100 (3.9)
S5
300 (11.8)
143 (5.6)
1.48
50.5 (7.3)
—
—
—
S7
300 (11.8)
143 (5.6)
1.48
48.9 (7.1)
12 φ12.5 x 4
70 (2.8)
100 (3.9)
*
*
Diameter in Series C, side length in Series S.
†
Calculated as
‡
Number of studs per perimeter, stud size (mm) by number of perimeters.
†
‡
ρx ρy . In all slabs except C5, reinforcement distributed uniformly across widths. For C5, 2.00% is ratio in central (c + 6d), and 1.56% is ratio for full width.
Fig. 3—Shear reinforcement. (Note: Dimensions in mm; 1 mm = 0.0394 in.) The difference in maximum strains at distances of 20 and 40 mm (0.8 and 1.6 in.) points to restraint from the columns, and the strains 40 mm (1.6 in.) from the columns were probably high enough to indicate distress of the concrete due to tangential stresses, except in the one slab without shear reinforcement. ACI Structural Journal/March-April 2014
Fig. 4—Load-displacement of Slab C3. (Note: 1 mm = 0.0394 in.) 365
Fig. 5—Load-rotation behavior of tested slabs. (Note: 1 kN = 0.2248 kip.) Figure 6 shows the developments of strains measured in Slabs C2 and C6, the former having only nominal bottom steel, and the latter being the slab with considerable compression reinforcement. In C6, the maximum strain of 3.2‰ was reached at a load equal to the failure load of C2. Thereafter, the strain in C6 decreased as the load was increased to failure. This suggests that the 12% higher ultimate strength was achieved with the compression reinforcement locally taking over the function of the failing concrete. Strains of flexural reinforcement Strains of the flexural tension reinforcement were measured by pairs of strain gauges at opposite ends of diameters of the upper bars, at a section just outside the column. The resulting profiles of tangential strains for Slabs C1 through 4 and C8 are shown in Fig. 7. Strains beyond yield were recorded in considerable parts of the slab widths, but the yielding never reached the slab edge, that is, a yield line was never developed. Strains of shear reinforcement Strains were measured at the midheight of the shear studs in four lines of the shear reinforcement in all slabs. 366
Fig. 6—Strains of concrete at soffits of Slabs C2 and C6. (Note: 1 kN = 0.2248 kip.) The strains were measured in the inner three rings of shear reinforcement in the slabs with circular columns, and at all perimeters for the slabs with square columns. The average stresses (strain × Es) in the shear reinforcement are summarized in Table 2. Typical profiles of stud stresses along radial lines are shown in Fig. 8. The stud stresses summarized in Table 2 are thought to be reasonably close to the maximum stresses in the studs because the studs were short. The difference between the measured and maximum stress depends on the product of the bond stress and the distance from the shear crack to the midheight of the studs. Allowing for bond along lengths between cracks and strain gauges, it appears that the first perimeter of shear reinforcement is likely to have yielded in all the tests except C6, C7, and S7. Ultimate loads and modes of failure All of the slabs failed by punching, and Table 2 gives the ultimate loads and summarizes data from relevant strain measurements at or close to failure. The slabs with shear reinforcement failed inside the shear reinforced areas in all cases but S1, where there were only two perimeters of studs, and S7, where the diameter of the studs was 12.5 mm (No. 4). ACI Structural Journal/March-April 2014
Fig. 7—Strains of flexural reinforcement. (Note: 1 mm = 0.0394 in.; 1 kN = 0.2248 kip.)
ACI Structural Journal/March-April 2014
Fig. 8—Average stud stresses at Perimeters 1 to 3. (Note: 1 kN = 0.2248 kip; 1 MPa = 0.1450 kip.) 367
Specimens C2, C5, and C6 (Table 1) were similar apart from the detailing of the flexural reinforcement. Comparison of the shear strengths of C2 and C5 shows that the punching resistance was increased by approximately 15% by concentrating 60% of the flexural reinforcement into a 1 m (39 in.) wide band centered on the column whilst maintaining the same flexural capacity across the slab width as in the other tests. The shear strength of C6 was increased by approximately 12% relative to C2 through the provision of additional compression steel.
The specimens were saw-cut half width in two orthogonal directions to reveal the failure surfaces. For the inside failures, most of the surfaces ran from the soffit at the column face to reach the level of the top steel at the second perimeter of studs, but there were exceptions. In both sections of Slab C1 and one of Slab C2, the failure surfaces crossed the inner studs very close to their upper heads. In Slabs C5, C6, and S2, they reached to the level of the top bars at the third or fourth perimeter of studs. In C7, there were multiple cracks reaching the main steel from the third to the fifth perimeter in one section, while in the perpendicular direction, the surface ran just above the lower heads of the studs out to the fourth layer and reached the top steel at the sixth layer. In the outside failures, the surface was entirely outside the studs in S1, but did cross them just above their lower heads in S7. In some slabs, most notably C6, there was spalling of the slab around the column that commenced before failure. METHODS OF CALCULATION All three approaches considered herein take the punching strength of a slab with shear reinforcement as the least of VR,cs, VR,out, and VR,max, but not less that VR,c, where VR,c is the resistance of an otherwise similar slab without shear reinforcement; VR,cs is the combined resistance of the concrete and shear reinforcement; VR,out is the resistance from the concrete alone just outside the shear reinforcement; and VR,max is the maximum resistance possible for a given column size, slab effective depth and concrete strength. These resistances correspond to failures of the types shown in Fig. 9. The calculations are made for perimeters at specified distances from supports: uo is the perimeter at the outline of the support; u1 is the perimeter used in the calculation of VR,c and VR,cs; and uout is the perimeter used in the calculation of VR,out.
Fig. 9—Types of punching failure. Table 2—Summary of test results
Average stud stresses‡, MPa (ksi) Slab No.
εc,max , ‰
ry , mm (in.)
1
2
3
Vu§, kN (kip)
Failure mode
*
†
C1
2.66
450 (17.7)
535 (77.6)
317 (46.0)
137 (19.9)
858 (192.9)
In
C2
2.81
550 (21.7)
530 (76.9)
235 (34.1)
121 (17.5)
956 (214.9)
In
C3
2.54
625 (24.6)
511 (74.1)
362 (52.5)
189 (27.4)
1077 (242.1)
In
C4
||
770 (30.3)
535 (77.6)
461 (66.8)
297 (43.1)
1122 (252.2)
In
2.28
C5
3.24
490 (19.3)
504 (73.1)
264 (38.3)
160 (23.2)
1117 (251.1)
In
C6
3.20
750 (29.5)
479 (69.5)
421 (61.0)
474 (68.7)
1078 (242.3)
In
C7
3.14
540 (21.3)
386 (56.0)
419 (60.8)
167 (24.2)
1110 (249.5)
In
C8
3.14
660 (26.0)
535 (77.6)
436 (63.2)
179 (26.0)
1059 (238.1)
In
S1
2.37
560 (22.0)
535 (77.6)
473 (68.6)
—
1021 (229.5)
Out
S2
2.15
570 (22.4)
535 (77.6)
514 (74.5)
216 (31.3)
1127 (253.4)
In
S5
1.47
130 (5.1)
—
—
—
779 (175.1)
—
S7
2.67
600 (23.6)
238 (34.5)
285 (41.3)
137 (19.9)
1197 (269.1)
Out
εc,max is maximum tangential strain of concrete (measured 20 mm from columns in C1 to C4, S1 and S2, and 40 mm from columns in C5 to C8 and S7). For slab Type S, strains measured on centerlines. *
†
ry is radius in which tangential strain > εy.
‡
Averages of Esεs ≤ fyw in Perimeters 1, 2, and 3.
§
Ultimate shear force including self-weights of slabs and loading system.
||
Measured at 0.85Vu.
368
ACI Structural Journal/March-April 2014
Fig. 12—Control perimeters: CSCT. Fig. 10—Detailing and control perimeters: ACI 318.
VR,cs = 0.75VR,c + VR,s (2) VR,s =
d ⋅ Asw f yw with fyw ≤ 414 MPa (60,000 psi) (3) sr VR,out = 1 6
VR,max = 2 3 VR,max = 1 2
fc uout d (4)
fc u1 d if sr ≤ 0.5d (5a)
fc u1 d if 0.5d ≤ sr ≤ 0.75d (5b)
fc is limited to ≤ 69 MPa (10,000 psi) for calculation purposes. Fig. 11—Detailing and control perimeters: EC2.
EC2-04
The locations and lengths of u1 and uout vary with the method of calculation. The symbols used for spacings of shear reinforcement are as follows: so is the distance from column to inner studs; sr is the radial spacing of studs; and st is the tangential spacing of studs at a perimeter. The effective depth d is taken as the average for orthogonal directions, d = (dx + dy)/2. The expressions for punching resistances are given below in SI units (N and mm) without any explicit safety factors. Those from ACI 318 are for nominal resistances, and the others are for characteristic resistances. The perimeters u1 and uout and the detailing requirements, in relation to the spacings of shear reinforcement, are illustrated by Fig. 10, 11, and 12 for ACI 318, EC2, and the CSCT, respectively.
k = 1 + 200 / d ≤ 2
VR.cs = 0.75VR,c + VR,s (8)
ACI 318-08 As double-headed studs are not considered explicitly, the equations used herein are those for studs with heads at their top ends and bottom anchorages provided by welds to structural rails
fc u d (12) VR,max = 0.3 fc 1 − 250 o
VR,c = 1 3
fc u1 d (1)
ACI Structural Journal/March-April 2014
VR,c = 0.18k(100ρfc)1/3u1d (6)
VR,s = 1.5
(7)
d Asw f yw,ef (9) sr
fyw,ef = 1.15(250 + 0.25d) ≤ fyw ≤ 600 MPa (87,000 psi) (10) VR,out = 0.18k(100ρfc)1/3uout,efd (11)
ρ is the ratio of flexural reinforcement calculated as ρx ρy , where ρx and ρy are the ratios in orthogonal directions determined for widths equal to those of the column plus 3d to
369
VR,s = ΣAswσsi(ψ) ≤ ΣAswfyw (16)
VR,cs = VR,c + VR,s (17) VR,out =
0.75uout dv fc 1 + 15ψd / (16 + dg )
(18)
VR,max = 3VR,c (19)
Fig. 13—Punching strengths according to CSCT: Slab C1. (Note: 1 kN = 0.2248 kip.) either side. ρ ≤ 0.02 for calculation purposes, and the scope of EC2 is limited to fc ≤ 90 MPa (13,000 psi). Critical shear crack theory In the CSCT, punching resistances are related to the rotation ψ of the slab, outside a critical crack. Half of this rotation is assumed to occur in the critical shear crack and, as the slab rotates, the concrete component of shear resistance at the crack is assumed to decrease, while the component from the shear reinforcement increases up to yield. The rotation ψ is related to the ratio V/Vflex, where V is the acting shear, and Vflex is the shear force corresponding to the flexural capacity, calculated by yield-line theory. Values of VR,c, VR,cs, VR,out, and VR,max can be determined as shown in Fig. 13, by plotting the resistances against ψ and finding their intersections with Eq. (13) 3
r fy V 2 ψ = 1.5 s d Es V flex (13)
where rs is the distance from the column center to the line of radial contraflexure; and ψ is in radians. For typical punching test specimens, rs is the distance from the column center to the slab edge. The flexural failure load Vflex is approximated by5 rs Vflex = 2πmR r − r (14) q c where mR is the moment resistance per unit length of yield line; rq is the radius at which loading is applied; and rc is the radius of the column and for square columns can be taken as 2c/π, where c is the side length of the column. In the CSCT average method given in Reference 5 0.75u1 d fc
370
VR,c =
1 + 15ψd / (16 + dg )
(15)
where σsi is the stress in the i-th perimeter of shear reinforcement which is related to the width of the critical shear crack, where it crosses the shear reinforcement.5 The summations ΣAsw and ΣAswσsi(ψ) are for all the shear reinforcement within a distance d from the column. The CSCT average method is intended to give approximately mean strengths. In it, the stresses in studs at different distances (≤d) from the column are calculated assuming that the width of the critical shear crack increases linearly, from zero at the slab soffit to the width corresponding to a slab rotation ψ and a crack opening angle of 0.5ψ, at the level of the tension reinforcement. The stress in a stud is then obtained by equating the vertical component of the crack opening to the elongation of the stud for a given stress at the crack. COMPARISONS OF TESTS AND CALCULATIONS General Experimental strengths from the present tests and from others reported in the literature have been compared with resistances calculated by the three methods described previously. The shear reinforcement in the tests by Regan,7 Regan and Samadian,8 Beutel,9 and Birkle10 was double-headed studs made from either deformed or plain round bars. In the tests by Gomes and Regan,11 it was slices of steel I-beams with the flanges acting as anchorages. The shear reinforcement was positioned radially unless noted as ACI type in Table A1 in Appendix A. The calculations of punching resistances were made using the expressions given previously, with their limits generally respected. Exceptions to this were as follows. For ACI 318 and EC2, the limits on so/d and sr/d were given a little tolerance. Values of sr/d up to 0.8 were treated as acceptable, and for EC2 the lower limit so/d < 0.3 was waived with values going down to 0.24. EC2 does not envisage the use of plain round shear reinforcement, but this has been ignored, and lower limits on d for the use of shear reinforcement were ignored. (The least effective depth in the tests used was 124 mm [4.9 in.] in six slabs by Birkle.10) The CSCT shear strengths were calculated using slab rotations calculated with Eq. (13), in which Vflex was calculated with Eq. (14). The stresses in the shear reinforcement were calculated in accordance with the recommendations in (5). The resulting slab rotations were slightly greater than the measured slab rotations, as illustrated in Fig. 5. The predicted shear strengths typically increase by less than 5% for the slabs tested in this program if measured rotations are used instead of calculated rotations. For the CSCT, there ACI Structural Journal/March-April 2014
Table 3—Comparisons with test results for slabs without shear reinforcement Vu/Vcalc Slab No. d, mm (in.) ρ, %
ACI 318
EC2
CSCT
*
EC2
Table 4—Statistics of Vu /Vcalc for slabs with shear reinforcement No. of tests
ACI 318 Mean
EC2
COV
143 (5.6)
1.48
1.30
Gomes and Regan 1 1A
159 (6.3) 159 (6.3)
1.27 1.27
1.16 1.20
1.20
1.24
1.10
0.89 0.92
1.30 1.12 0.88
1.11 0.94 0.78
1.10 1.02 0.86
0.96 0.93 0.78
Mean
1.16
0.99
1.04
0.93
Coefficient of variation
0.13
0.15
0.12
0.11
Birkle10
*
1.53 1.29 1.10
Mean
COV
1.47
0.148
9
1.56
0.100
are only a few cases in which there were two perimeters of shear reinforcement within a distance d from the support, but there are some where a second layer was not much further out (all of the slabs by Gomes and Regan11 where the distances varied from 1.0d to 1.04d and Slabs 2, 3, 9, and 12 by Birkle10 where the distances were from 1.09d to 1.18d). The second perimeter has been included in ΣAsw, where the distance was less than 1.05d. Details of the individual slabs and the results obtained are given in Appendix A, while Tables 3 and 4 summarize the results of the comparisons for slabs without and with shear reinforcement. Although there are only six results in Table 3, it is noteworthy that, for all the methods of calculation, Vu/Vcalc decreases with increasing effective depth. This is not surprising for ACI 318, which has no size factor, or for EC2, where the size factor is constant for d ≤ 200 mm (7.9 in.). It is surprising for the CSCT, which includes a size factor taking account of the effective depth and the maximum size of aggregate. The best correlation in the table is that for EC2*, which is the same as EC2, but without the limit on k = 1 + (200 / d ). With this modification, however, the mean Vu/Vcalc is low, and the coefficient of 0.18 in Eq. (7) would need to be reduced. Table 4 summarizes the results of the comparisons with the 45 slabs with shear reinforcement, and all three methods of calculation are broadly satisfactory. The coefficient of variation of Vu/Vcalc decreases with increasing complexity in the method. The ACI method is the simplest and gives a coefficient of variation of 0.162. The EC2 method is slightly more complex, and reduces the coefficient by 0.026, while the CSCT is considerably more complicated, but gives a further reduction of 0.015. There are no unsafe predictions from ACI 318, but there are four from EC2 and the CSCT, with the lowest values of Vu/Vcalc being 0.88 for EC2, and 0.90 for the CSCT. An overall reduction of Vcalc by 4% would make each of these methods safe in the sense of limiting the probability of an unsafe prediction to 5%, assuming a statistically normal distribution of Vu/Vcalc.
1.06 Beutel
6
1.72
0.093
0.160
1.23
0.108
0.087
1.05
0.102
0.087
1.16
0.101
0.081
1.28
0.083
0.105
1.06
0.050
0.136
1.16
0.121
9
1.34
Gomes and Regan11 10
1.76
0.134
1.28 Birkle
9
1.35
0.185
EC2 calculations as for EC2, but with no upper limit on k = 1+√(200/d).
ACI Structural Journal/March-April 2014
1.20
Regan7 and Regan and Samadian8 1.00 1.03
124 (4.9) 190 (7.5) 260 (10.2)
11
11
0.96 1.01
1 7 10
COV
Ferreira1
Ferreira1 S5
Mean
CSCT
10
1.09 Total
45
1.56
0.162
1.19
ACI 318 and EC2 are basically empirical, but the CSCT claims a rational basis. Unfortunately, its modeling of slab deformations is incorrect. The rotation ψ is predicted satisfactorily by Eq. (13), but, as can be seen from Fig. 4, it is not divided equally into movements at the column face and in a shear crack. In addition, the surfaces at which failure occurs are not at 45 degrees to the slab plane, but have variable geometries. Refer to the section entitled, “Ultimate loads and modes of failure.” In nine tests by Ferreira1 and five by Birkle,10 EC2 predicts outside failures for slabs that actually failed in the shear-reinforced zones. Its predictions of failure modes in the other series are generally good. The main cause of the problem seems to be the overestimation of VR,cs. For the slabs by Ferreira,1 the mean Vu/VR,cs is 0.98, and the coefficient of variation is 0.061. For Birkle’s tests,10 the corresponding figures are 0.88 and 0.101, but would be improved if the four slabs with so/d less than 0.3 were excluded. The situation could be improved by either a reduction of VR,c or by interpreting the code’s expression for the design value of the stud stress (fywd,ef) as not requiring a safety factor so long as fywd,ef is less than fyw/1.15—that is, by taking fyw,ef as (250 + 0.25d) ≤ fyw. The EC2 predictions of VR,out for slabs with radial arrangements of shear reinforcement are generally satisfactory, though perhaps over-conservative for the slabs by Gomes and Regan.11 In these slabs, the 0.64d widths of the I-beam flanges reduced the clear tangential spacing of the shear reinforcement. This could be allowed for, and would make Vu/VR,out for these tests similar to those for other series. The strength of Ferreira’s1 Slab C4 with an ACI cross arrangement of studs which failed inside is predicted very conservatively with Vu/VR,out = 1.69. For Birkle’s10 slabs with the ACI layout, which failed outside, the strengths are well predicted with Vu/VR,out = 1.21. Slab C4 was unrealistic in relation to EC2 design because it had six perimeters of studs, while the same strength would be calculated for a slab with two perimeters of studs. The performance of C4 is in marked 371
Fig. 14—Influence of slab rotation on Vu/Vcalc CSCT. contrast to that of slabs by Mokhtar et al.,12 with up to eight perimeters of studs on stud rails. Their strengths are quite well predicted by EC2. Influence of slab rotation on shear resistance provided by concrete Unlike ACI 318 and EC2, the CSCT predicts that the shear resistance provided by concrete reduces with slab rotation, which is assumed to be proportional to (V/Vflex)1.5. This has significant implications for design because Vu/Vflex may be close to one for practical slabs. Consequently, the CSCT can require significantly greater areas of shear reinforcement than EC2. The influence of slab rotation on Vu/Vcalc for the CSCT is illustrated by Fig. 14, where the ratio is plotted against the normalized rotation ψd/(16 + dg), with ψ calculated by Eq. (13). There is a clear tendency for the CSCT to become more conservative with increasing slab rotation, which suggests that Vu is either independent of ψ, or that the CSCT overestimates the influence of rotation. In the case of outside failure, this is to be expected as the rotation develops close to the column and not within a crack outside the shear reinforcement. Muttoni4 plots Vu/u1d fc against ψd/(16 + dg) for 99 tests of slabs without shear reinforcement, and shows that experimental strengths are close to the predictions of Eq. (15), which may appear to contradict the preceding paragraph. This, however, is not the case. Figure 15 shows Vu/u1d fc plotted against ψd/(16 + dg) for slabs similar to Ferreira’s1 C2, but without shear reinforcement, and with ρ from 0.4 to 4.0%. The values of Vu have been calculated by EC2 and the CSCT, u1 is the CSCT control perimeter, and ψ is the rotation calculated by Eq. (13). It can be seen that the effect shown in Muttoni’s figure can be accounted for by the EC2 relationship between VR,c and ρ1/3 without involving ψ in the calculations. Failure surface and locations of shear reinforcement ACI 318 and the CSCT assume punching surfaces to be inclined at 45 degrees, while EC2 assumes an inclination of 26.6 degrees. These are simplifications of a reality in which the angle increases with increasing shear reinforcement
372
Fig. 15—Influence of slab rotation on shear strength. (refer to Carvalho et al.13). Reasonable results can, however, be obtained in most instances with fixed angles, provided the expressions for VR,c and VR,s are constructed appropriately. This seems to be the case with ACI 318 and EC2, with the former considering d/sr perimeters of studs acting at fyw, and the latter assuming 1.5d/sr perimeters acting at fyw,eff, which is typically approximately 0.7fyw for test slabs. The situation is more complex in the CSCT, as its numbers of perimeters depend on the exact distances of studs from the column. There are cases where the use of different failure surfaces has a significant effect. Slabs 2, 3, 10, and 11 by Gomes and Regan11 are an example. In these slabs so = sr ≅ 0.5d, Asw = 226 mm2 (0.36 in.2) in Slabs 2 and 10, and 325 mm2 (0.5 in.2) in Slabs 3 and 11. Slabs 2 and 3 had two perimeters of shear reinforcement, while Slabs 10 and 11 had three. Thus, for ACI 318, two perimeters are taken into account for all the slabs, while in EC2, two perimeters are active in Slabs 2 and 3, but three are active in Slabs 10 and 11. All four slabs failed inside their shear reinforced zones. The EC2 ratios Vu/VR,cs are 1.26 and 1.21 for Slabs 2 and 3, and 1.28 and 1.31 for Slabs 10 and 11. The ACI ratios are 1.39 and 1.28 for Slabs 2 and 3, and 1.58 and 1.61 for Slabs 10 and 11, showing that the extra perimeter of shear reinforcement had an effect. The same slabs illustrate a problem with the CSCT’s considering the active shear reinforcement to be exactly that within a distance d from a column rather than using an expression in d/sr. Because of variations of effective depths, (so + sr) = 1.05d in three cases instead of the intended 1.0d. This discrepancy has been ignored in the calculations for Table A1, but if the CSCT were applied strictly the ratios Vu/VR,cs, which are already unusually high for Slabs 10 and 11, would be significantly increased. CONCLUSIONS Comparisons have been made between the punching strengths of 45 slabs with and six slabs without shear reinforcement and those predicted by ACI 318, EC2, and the CSCT. ACI 318 is the simplest method, and gives only one unsafe prediction, which is for a slab without shear reinforcement. Its mean value of Vu/Vcalc for slabs with shear reinforcement is rather high, and the coefficient of variation is 0.162. The ACI Structural Journal/March-April 2014
most apparent weakness is the lack of any treatment of the depth effect in the shear resistance from the concrete. EC2 is only slightly more complicated, but reduces the coefficient of variation of Vu/Vcalc by 0.026. The mean is also reduced, and there are four unsafe predictions for slabs with and four for slabs without shear reinforcement. The simplest way to obtain a characteristic level of safety would be to reduce the constant in the expression for the concrete component of resistance and extend the range of slab depths affected by the depth factor. The CSCT is considerably more complex, and reduces the mean and coefficient of variation of Vu/Vcalc, by a further 0.015. There are unsafe predictions for four slabs with and one without shear reinforcement. The CSCT goes further than the other two approaches in attempting to model the slab behavior. Although its expression for total slab rotation seems good, the assumption that half of this rotation occurs in the critical shear crack is incorrect, as nearly all of it is at the column face. The assumption that all critical cracks are at 45 degrees to the slab plane is also incorrect. The relationship assumed between the concrete component of punching resistance and slab rotation is not confirmed by the test data, and the determination of the area of active shear reinforcement as that crossed by a particular 45 degree surface seems less satisfactory than considering d/sr perimeters. AUTHOR BIOS
ACI member Maurício P. Ferreira is a Lecturer at the Federal University of Para, Belem, Brazil. He received his PhD from the University of Brasília, Brasília, Brazil, in 2010. His research interests include ultimate shear design, strut and tie, and nonlinear finite element modeling. ACI member Guilherme S. Melo is an Associate Professor at the University of Brasilia, where he was Head of the Department of Civil and Environmental Engineering. He is a member of ACI Committees 440, Fiber-Reinforced Polymer Reinforcement; and Joint ACI-ASCE Committee 445, Shear and Torsion. His research interests include punching and post-punching of flat plates, the use of fiber-reinforced plastic (FRP) in concrete structures, and strengthening and rehabilitation of structures. ACI member Paul E. Regan is a Professor Emeritus at the University of Westminster, London, UK, where he was Head of Architecture and Engineering. He was Chair of the European Concrete Committee (CEB) commission on member design. His research interests include member design in both reinforced and prestressed concrete, with particular emphasis on problems of punching, shear, and torsion. ACI member Robert L. Vollum is a Reader in concrete structures at Imperial College London, London, UK, where he also received his MSc and PhD. His research interests include design for shear, strut-and-tie modeling, and design for the serviceability limit states of deflection and cracking.
ACKNOWLEDGMENTS
The authors are grateful to the Brazilian Research Funding Agencies CAPES (Higher Education Co-ordination Agency) and CNPq (National Council for Scientific and Technological Development) for their support throughout this research and to RFA-Tech for their permission to include test results from Reference 7.
Asw =
NOTATION
area of shear reinforcement in one perimeter
ACI Structural Journal/March-April 2014
side length of square column or diameter of circular column mean effective depth maximum size of aggregate depth from tension reinforcement to compression zone anchorage of shear reinforcement Es = modulus of elasticity of reinforcement fc = cylinder compression strength of concrete fy = yield stress of flexural reinforcement so = distance from column face to first perimeter of shear reinforcement sr = radial spacing of shear reinforcement st = tangential spacing of shear reinforcement st,max = maximum value of st (general in outer perimeter of shear reinforcement) u0 = length of column perimeter u1 = length of control perimeter for calculation of VR,c and VR,cs uout = length of control perimeter for calculation of VR,out uout,ef = effective value of uout for calculations by EC2, where st,max > 2d V = applied shear force Vcalc = calculated punching resistance Vflex = flexural strength of slab calculated by yield-line theory VR,c = punching resistance of slab without shear reinforcement VR,cs = punching resistance within shear reinforced zone VR,max = maximum punching resistance for given column size, slab effective depth, and concrete strength VR,out = punching resistance outside shear reinforced zone VR,s = contribution of shear reinforcement to punching resistance VR,cs Vu = experimental punching strength ρ = ratio of flexural reinforcement ρ = ρx ρy (calculated for width of column plus 3d to either side in EC2) ψ = rotation of part of slab outside critical shear crack c d dg dv
= = = =
REFERENCES
1. Ferreira, M. P., “Punção em Lajes Lisas de Concreto Armado com Armaduras de Cisalhamento e Momentos Desbalanceados,” PhD thesis, Universidade de Brasília, Brasília, Brazil, 2010, 275 pp. (in Portuguese) available at http://repositorio.bce.unb.br/handle/10482/8965. 2. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2008, 473 pp. 3. Eurocode 2, “Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings,” CEN, EN 1992-1-1, Brussels, Belgium, 2004, 225 pp. 4. Muttoni, A., “Punching Shear Strength of Reinforced Concrete Slabs without Transverse Reinforcement,” ACI Structural Journal, V. 105, No. 4, July-Aug. 2008, pp. 440-450. 5. Fernadez-Ruiz, M., and Muttoni, A., “Applications of the Critical Shear Crack Theory to Punching of R/C Slabs with Transverse Reinforcement,” ACI Structural Journal, V. 106, No. 4, July-Aug. 2009, pp. 485-494. 6. Fédération internationale du béton, “fib Model Code 2010, First complete draft—V. 2,” Bulletin 56, fib, Lausanne, Switzerland, Apr. 2010, 288 pp. 7. Regan, P. E., unpublished tests for RFA-TECH at Cambridge University, 2009. 8. Regan, P. E., and Samadian, F., “Shear Reinforcement against Punching in Reinforced Concrete Flat Slabs,” The Structural Engineer, V. 79, No. 10, May 2001, pp. 24-31. 9. Beutel, R., “Punching of Flat Slabs with Shear Reinforcement at Inner Columns,” Rheinisch-Westfälischen Technischen Hochschule Aachen, Aachen, Germany, 2002, 267 pp. (in German) 10. Birkle, G., “Punching of Flat Slabs: The Influence of Slab Thickness and Stud Layout,” PhD thesis, Department of Civil Engineering, University of Calgary, Calgary, AB, Canada, Mar. 2004, 152 pp. 11. Gomes, R., and Regan, P. E., “Punching Strength of Slabs Reinforced for Shear with Offcuts of Rolled Steel I-Section Beams,” Magazine of Concrete Research, V. 51, No. 2, 1999, pp. 121-129. 12. Mokhtar, A. S.; Ghali, A.; and Dilger, W., “Stud Shear Reinforcement for Flat Concrete Plates,” ACI Journal, V. 82, No. 5, Sept.-Oct. 1985, pp. 676-683. 13. Carvalho, A. L.; Melo, G. S.; Gomes, R. B.; and Regan, P. E., “Punching Shear in Post-Tensioned Flat Slabs with Stud Rail Shear Reinforcement,” ACI Structural Journal, V. 108, No. 5, Sept.-Oct. 2011, pp. 523-531.
373
APPENDIX A Table A1—Comparison between theoretical and experimental results
Birkle10
Gomes and Regan11
Beutel9
Regan and Samadian8
Regan7
Ferreira1
Author
Slab No. C1
Column size, mm 270 C
d, mm 143
ρ, % 1.48
fy, MPa 540
fc, MPa 48
Shear reinforcement fyw, s o, sr, Studs MPa mm mm 10 f10.0 x 6 535 70 100
stmax, mm 436
Vu, kN 858
Failure mode In
Vu/ Vflex 0.72
Vu/Vcalc and critical strength CSCT ACI 318-08 EC2-04 average 1.34 Max 0.96 Out 1.07 In
C2
360
C
140
1.52
540
47
10 f10.0 x 6
535
70
100
464
956
In
0.78
1.27
Max
1.11
Out
1.12
In
C3
450
C
142
1.49
540
49
10 f10.0 x 6
535
70
100
491
1077
In
0.82
1.21
Out
1.20
Out
1.15
In Out
C4*
360
C
140
1.52
540
48
12 f10.0 x 6
535
70
100
900
1122
In
0.92
1.47
Max
1.69
Out
1.50
C5
360
C
140
2.00
544
50
10 f10.0 x 6
535
70
100
464
1118
In
0.88
1.44
Max
1.16
Out
1.29
In
C6
360
C
143
1.48
540
49
10 f10.0 x 6
535
70
100
464
1078
In
0.86
1.36
Max
1.19
Out
1.24
In Out
C7
360
C
144
1.47
540
49
10 f10.0 x 7
535
55
80
442
1110
In
0.88
1.39
Max
1.21
Out
1.09
C8
360
C
144
1.47
540
48
12 f10.0 x 6
535
70
100
388
1059
In
0.84
1.34
Max
1.03
Out
1.14
In
S1
300
S
145
1.46
540
48
12 f10.0 x 2
535
70
100
177
1022
Out
0.80
1.71
In
1.36
Out
1.37
Out
S2
300
S
143
1.48
540
49
12 f10.0 x 4
535
70
100
280
1128
In
0.89
1.77
Out
1.12
Out
1.24
Out
S5
300
S
143
1.48
540
50
—
—
—
—
—
779
P
0.61
1.30
P
1.20
P
1.24
P
S7
300
S
143
1.48
540
49
12 f12.5 x 4
518
70
100
280
1197
Out
0.94
1.88
Out
1.19
Out
1.32
Out
1
300
S
150
1.45
550
33
10 f10.0 x 4
550
80
120
390
881
—
0.79
1.45
Out
1.02
Out
1.06
In
2
300
S
150
1.76
550
30
12 f10.0 x 6
550
60
100
390
1141
—
0.88
1.71
Out
1.13
Out
1.11
Out
3
300
S
150
1.76
550
26
10 f12.0 x 5
550
60
120
455
1038
—
0.83
1.73
Out
1.22
Out
1.09
Out
5
240
C
160
1.65
550
62
12 f12.0 x 5
550
80
120
352
1268
—
0.88
1.61
Max
0.88
Out
1.12
In
6
240
C
150
1.75
550
42
12 f10.0 x 5
550
75
120
349
1074
—
0.83
1.81
Max
1.04
In
1.24
In
R3
200
S
160
1.26
670
33
8 f12.0 x 4
442
80
120
413
850
Out
0.63
1.44
Out
1.04
Out
0.90
Out
R4
200
S
160
1.26
670
39
8 f12.0 x 6
442
80
80
444
950
Out
0.69
1.39
Out
1.10
Out
0.93
Out
A1
200
S
160
1.64
570
37
8 f10.0 x 6
519
80
80
444
1000
Out
0.67
1.50
Out
1.08
Out
0.98
Out
A2
200
S
160
1.64
570
43
8 f10.0 x 4
519
80
120
413
950
In
0.62
1.42
Out
1.03
In
1.00
In
Z1
200
C
250
0.80
890
25
12 f14.0 x 5
580
100
200
518
1323
Max
0.41
1.50
Max
1.26
Max
0.96
In
Z2
200
C
250
0.80
890
26
12 f14.0 x 5
580
88
200
511
1442
Max
0.44
1.59
Max
1.30
Max
1.08
In
Z3
200
C
250
0.80
890
24
12 f14.0 x 5
580
95
188
487
1616
Max
0.50
1.86
Max
1.57
Max
1.20
In
Z4
200
C
250
0.80
890
32
12 f14.0 x 5
580
88
175
459
1646
Max
0.49
1.66
Max
1.27
Max
1.18
In
Z5
263
C
250
1.25
562
28
12 f16.0 x 5
544
94
188
505
2024
Max
0.41
1.90
Max
1.31
Max
1.28
In
Z6
200
C
250
1.25
562
37
12 f16.0 x 5
544
94
188
489
1954
Max
0.39
1.81
Max
1.31
Max
1.23
In P
1
200
S
159
1.27
680
40
—
—
—
—
—
560
P
0.40
1.16
P
0.94
P
1.00
1a
200
S
159
1.27
680
41
—
—
—
—
—
587
P
0.41
1.20
P
0.98
P
1.03
P
2*
200
S
153
1.32
680
34
8 f6.0 x 2
430
80
80
255
693
In
0.53
1.64
In
1.26
In
1.12
Out
3*
200
S
158
1.27
670
39
8 f6.9 x 2
430
80
80
255
773
In
0.57
1.64
In
1.21
In
1.20
Out
4*
200
S
159
1.27
670
32
8 f8.0 x 3
430
80
80
368
853
Out
0.64
1.98
In
1.27
Out
1.26
Out
5*
200
S
159
1.27
670
35
8 f10.0 x 4
430
80
80
481
853
Out
0.63
1.77
Out
1.24
Out
1.13
Out
6
200
S
159
1.27
670
37
8 f10.0 x 4
430
80
80
323
1040
Out
0.76
2.07
Out
1.23
Out
1.34
Out
7
200
S
159
1.27
670
34
8 f12.0 x 5
430
80
80
385
1120
Out
0.83
2.02
Out
1.38
Out
1.38
Out
8
200
S
159
1.27
670
34
8 f12.0 x 6
430
80
80
447
1200
Out
0.89
1.90
Out
1.48
Out
1.38
Out
9
200
S
159
1.27
670
40
8 f12.2 x 9
430
80
80
425
1227
—
0.89
1.31
Out
1.09
Out
1.26
Max
10
200
S
154
1.31
670
35
8 f6.0 x 5
430
80
80
385
800
In
0.61
1.58
In
1.28
In
1.33
In
11
200
S
154
1.31
670
35
8 f6.9 x 5
430
80
80
385
907
In
0.70
1.68
Out
1.31
In
1.42
In
1
250
S
124
1.53
488
36
—
—
—
—
—
483
P
0.56
1.30
P
1.11
P
1.10
P
2*
250
S
124
1.53
488
29
8 f9.5 x 6
393
45
90
721
574
In
0.68
1.24
Out
1.19
Out
1.08
Out
3
250
S
124
1.53
488
32
8 φ9.5 x 6
393
45
90
495
572
In
0.67
1.10
Out
1.12
Out
1.02
In
4*
250
S
124
1.53
488
38
8 φ9.5 x 5
465
30
60
403
636
Out
0.73
1.67
In
1.21
Out
1.09
Out
5*
250
S
124
1.53
488
36
8 φ9.5 x 5
465
30
60
403
624
Out
0.72
1.67
In
1.21
Out
1.09
Out
6
250
S
124
1.53
488
33
8 φ9.5 x 5
465
30
60
330
615
Out
0.72
1.67
Out
1.18
Out
1.04
Out
7
300
S
190
1.29
531
35
—
—
—
—
—
825
P
0.49
1.12
P
0.94
P
1.02
P
8*
300
S
190
1.29
531
35
8 φ9.5 x 5
460
50
100
658
1050
In
0.62
1.29
Out
0.98
Out
0.97
In
9*
300
S
190
1.29
531
35
8 φ9.5 x 6
460
75
150
1188
1091
In
0.64
1.28
In
1.06
In
1.15
In
10*
350
S
260
1.10
524
31
—
—
—
—
—
1046
P
0.40
0.88
P
0.78
P
0.86
P
11*
350
S
260
1.10
524
30
8 φ12.7 x 5
409
65
130
856
1620
In
0.63
1.24
Out
1.00
Out
1.02
In
12* 350 S 260 1.10 524 34 8 φ12.7 x 6 409 95 195 1541 1520 In 0.58 1.03 In 0.90 Out 1.08 In ACI stud layout. Notes: Vu includes self-weight; Vflex is approximate yield-line capacity from Eq. (14). Shear reinforcement: In References 1 and 7: deformed studs, 3φ heads, so as given for all lines; in Reference 8, slabs R, plain studs, 2.5φ heads, Slabs A deformed studs, 2.5φ heads, so as given for orthogonal lines, so = 40 mm for diagonal lines; in Reference 9, deformed studs, 3φ heads, so as given for all lines; in Reference 11, I-beam slices, flange breath 102 mm, web breath 4.7 mm. φ values in the table are equivalent diameters giving the same areas as the actual web sections. so as given for orthogonal lines, so = 40 mm for diagonal lines; in Reference 10, plain studs with 3.2φ heads, so as given for all lines. Birkle’s Slabs 5 and 6 had 7 perimeters of studs. The outer two, with sr = d, have been ignored. Aggregate (maximum size and type): In Reference 1, 9.5 mm crushed limestone. In References, 7, 8, 9, and 11, 20 mm gravel. In Reference 10, Slabs 1-6—14 mm; Slabs 7-12—20 mm, type unknown. Failure modes: P is punching of slabs without shear reinforcement, In = failure inside shear reinforced zone (VR,cs), Out = failure outside shear reinforced zone (VR,out); Max = inclined compression failure of concrete close to column (VR,max); in Reference 7 and Slab 9 of Reference 10, the concrete soffit around the column crushed and spalled due to tangential compression, the spalling extended and at failure there was inclined cracking starting at the end of the spalled area. 1 mm = 0.03937 in.; 1 kN = 0.225 kip; 1 MPa = 145 psi. *
374
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S33
Behavior of Concentrically Loaded Fiber-Reinforced Polymer Reinforced Concrete Columns with Varying Reinforcement Types and Ratios by Hany Tobbi, Ahmed Sabry Farghaly, and Brahim Benmokrane Fiber-reinforced polymer (FRP) materials have proven their effectiveness as an alternative reinforcement for concrete structures in severe environmental conditions. Many studies have investigated the flexural and shear behaviors of FRP-reinforced concrete beams and slabs. Limited research, however, has gone into investigating the behavior of internally reinforced FRP concrete columns. This paper reports the experimental investigation of the compressive performance of concrete columns reinforced longitudinally with FRP or steel bars and with FRP as transverse reinforcement. Twenty concrete columns measuring 350 x 350 x 1400 mm (13.8 x 13.8 x 55.1 in.) were constructed and tested under concentric compressive load. The parametric study included variables such as transverse reinforcement configuration, material type and spacing, longitudinal reinforcement ratio, and confining volumetric stiffness. Results showed that FRP bars have contribution as longitudinal reinforcement for concrete columns subjected to concentric compression and that the combination of FRP transverse reinforcement and steel longitudinal bars offers acceptable strength and ductility behavior. Keywords: column; concentric compression; confinement volumetric stiffness; failure mechanism; fiber-reinforced polymer (FRP); steel; volumetric ratio.
INTRODUCTION The deterioration of infrastructure owing to corrosion of steel reinforcement is one of the major challenges facing the construction industry. The use of reinforcement with fiberreinforced polymer (FRP) composite materials in concrete structures subjected to severe environmental exposure has been growing to overcome the common problems caused by corrosion of steel reinforcement (ACI Committee 440 2007; Federation Internationale de Béton 2007). Recent advances in polymer technology have led to the development of the latest generation FRP reinforcing bars (ACI Committee 440 2007). These corrosion-resistant bars have shown promise as a way to further protect bridges and public infrastructure from the devastating effects of corrosion. With standards ACI 440.6M (ACI Committee 440 2008) and CSA S807 (2010) and bars being produced of the highest quality, FRP bars are emerging as a realistic and cost-effective reinforcement alternative to traditional steel for concrete structures under severe environmental conditions. Steel bars cannot, however, simply be replaced with FRP bars due to various differences in the mechanical and bond properties of the two materials (Nanni 1993; ISIS Canada Research Network 2007) and the greater variation of material properties for FRP reinforcing products.
ACI Structural Journal/March-April 2014
Columns are one of several structural elements that may be exposed to severe environmental effects. The response of FRP bars in compression is affected by different modes of failure (transverse tensile failure, buckled FRP bar, or shear failure). General acceptance of FRP bars by practitioners requires that appropriate design guidelines for using FRP bars in compression members be established. Due to the lack of experimental data, the current ACI 440.1R (ACI Committee 440 2006) design guidelines do not recommend the use of FRP bars as longitudinal reinforcement in compression members, while the CSA S806 (2012) code states that the compressive contribution of FRP longitudinal reinforcement is negligible. Moreover, confined concrete behaves differently from unconfined concrete. Several studies clarified the importance of the lateral reinforcement as a confining system to the performance in terms of capacity and ultimate axial strain of axially loaded concrete members (Richart et al. 1928, 1929; Sheikh and Uzumeri 1980, 1982; Sheikh 1982; Saatcioglu and Razvi 1992; Mander et al. 1988 a,b; Teng et al. 2002; Harries and Kharel 2003). RESEARCH SIGNIFICANCE As the use of FRP reinforcement in concrete structures grows, appropriate design guidelines for axially concentric loaded concrete columns should be established. In this regard, laboratory investigations should be conducted to expand understanding of the compressive behavior of concrete columns internally reinforced with FRP, particularly given the lack of data about this application, but also to highlight the most important parameters affecting compressive performance of FRP reinforced columns. This study investigated concrete columns reinforced longitudinally with glass FRP (GFRP), carbon FRP (CFRP), and steel bars and GFRP and CFRP transverse reinforcement subjected to concentric loading. The experimental study yielded a better understanding of the mechanical behavior of FRP reinforced columns. The set of specimens is presented to enrich the literature regarding the use of FRP as internal reinforcement for compressive members in preparation for developing design models.
ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-123.R1, doi:10.14359.51686528, was received November 9, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
375
Fig. 1—(a) and (b) C-shaped; and (c) closed transverse reinforcement.
Fig. 2—Transverse reinforcement configuration: (a) 1; (b) 2; and (c) 3. EXPERIMENTAL PROGRAM The experimental study comprised 20 concrete columns measuring 350 x 350 x 1400 mm (13.8 x 13.8 x 55.1 in.) subjected to concentric compressive loading. These dimensions are representative of the columns commonly found in concrete structures. One column was kept un-reinforced (plain concrete) while the remaining 19 were internally reinforced with FRP and steel according to different parameters. All used transverse reinforcements were GFRP or CFRP, while the longitudinal reinforcement was GFRP, CFRP, or steel bars. Studied parameters included the shape of transverse reinforcement (C-shaped parts assembly or closed ties, as shown in Fig. 1), longitudinal reinforcement ratio, longitudinal reinforcement material (GFRP, CFRP, or steel), FRP-transverse reinforcement material (GFRP or CFRP), the diameter of the transverse reinforcement (No. 9.5 and 12.7 mm [No. 3 and No. 4]), transverse reinforcement spacing, and confining volumetric stiffness. Volumetric ratio is an important parameter for confinement efficiency (Sheikh and Uzumeri 1980, 1982; Sheikh 1982; Saatcioglu and Razvi 1992; Mander et al. 1988 a,b; Watson et al. 1994; Cusson and Paultre 1994; Saatcioglu et al. 1995) for passive confinement with internal reinforcement. Volumetric ratio ρv is defined as the ratio of the volume of transverse confining reinforcement to the volume of confined concrete core. FRP mechanical proprieties vary depending on fiber material and fiber content. For consistency, therefore, volumetric ratio should be multiplied by the modulus of elasticity of FRP confining material (ρv × Ef), which is the so-called confining volumetric stiffness. The same confining volumetric stiffness (ρv × Ef) can be obtained by changing at least two of the following parameters: transverse reinforcement’s configuration, spacing, material, or diameter. The GFRP transverse reinforcement diameter was 12.7 mm (No. 4). Two transverse reinforcement shapes 376
were used: the first is assembled from C-shaped parts as shown in Fig. 1(a) and (b), and the second is closed form, as shown in Fig. 1(c). The first shape was the first available product for bent bars; therefore, it has been chosen to build up the transverse reinforcement of the FRP reinforced columns. The second shape, however, has the benefit of eliminating the discontinuity of the C-shaped and reducing the assembly labor time. Generally speaking, both can be used in construction. The closed transverse reinforcements were cut from continuous square spirals, with an overlap equal to one side length. For each transverse reinforcement shape, three configurations labeled 1, 2, and 3, as shown in Fig. 2 (a), (b), and (c), were investigated in Tobbi et al. (2012), which revealed that the effect of Configuration 2 is not different from Configuration 3; therefore, only Configurations 1 and 3 will be addressed in this study. In the case of C-shaped transverse reinforcements in Configuration 1, the cross hairpins in two consecutive layers were staggered to preserve overall symmetry. In the case of the closed transverse reinforcements in Configuration 1, cross hairpins were staggered C-shaped legs. In Configuration 3, the cross ties were closed rectangular ties with one side overlap. All CFRP transverse reinforcements were closed with different diameters (No. 9.5 and 12.7 mm [No. 3 and No. 4]) to investigate their effect on the compressive performance of the columns. The test matrix is listed in Table 1. To fulfill the objectives of the parametric study, eight columns were exclusively reinforced with FRP: seven with GFRP, both longitudinal bars and transverse reinforcements (Configurations 1 and 3), and one with CFRP, also with both longitudinal bars and transverse reinforcements. Eleven columns were reinforced longitudinally with steel bars and FRP transverse reinforcements (Configurations 1 and 3): four reinforced transversally with GFRP, and seven with CFRP. One column was unreinforced (plain concrete).
ACI Structural Journal/March-April 2014
Table 1—Test matrix
Columns reinforced with steel longitudinal bars and FRP tie and cross-ties
Columns entirely reinforced with FRP bars
Group
fc′, ΜPa (ksi)
Longitudinal reinforcement
Transverse reinforcement
Ties spacing, mm (in.)
ρv x Ef, GPa
Designation
Material
Designation
Material
Ties configuration
P-0-00-0
—
—
—
—
—
—
—
G-1c-120-1.9
8 No. 6 (19 mm)
1
120 (4.7)
0.96
12 No. 5 (15.9 mm)
3
120 (4.7)
1.28
12 No. 5 (15.9 mm)
3
80 (3.2)
1.92
Specimen
G-3c-120-1.9
33 (4.8)
G-3c-80-1.9 G-1-120-1.9
8 No. 6 (19 mm)
1
120 (4.7)
1.18
G-3-120-1.9
12 No. 5 (15.9 mm)
3
120 (4.7)
1.58
G-1-120-1.0
4 No. 4 + 4 No. 5 (12.7; 15.9 mm)
1
120 (4.7)
1.18
G-1-120-0.8
35 (5.1)
2 x 8 No. 4 (12.7 mm)*
G-1-120-1.0S
4 M15 + 4 M10†
C-1-120-1.0S
4 M15 + 4 M10
No. 3C-1-67-1.0S
4 M15 + 4 M10
No. 3C-3-80-1.0S
12 M10
C-1-80-1.0S
4 M15 + 4 M10
C-1-60-1.0S
4 M15 + 4 M10
C-3-80-1.0S
27 (3.9)
No. 4 (12.7 mm)
GFRP
8 No. 4 (12.7 mm)
No. 3C-1-67-1.6
C-3-120-1.0S
GFRP
CFRP
No. 3 (9.5 mm) No. 4 (12.7 mm)
No. 3 (9.5 mm)
Steel
G-1-80-1.0S
4 M15 + 4 M10
G-3-120-1.0S
12 M10
G-3-80-1.0S
12 M10
120 (4.7)
1.18
1
67 (2.6)
2.87
GFRP
1
120 (4.7)
1.18
CFRP
1
120 (4.7)
3.04
1
67 (2.6)
2.87
3
80 (3.2)
3.20
1
80 (3.2)
4.56
1
60 (2.4)
6.08
3
120 (3.2)
4.05
3
80 (3.2)
6.08
1
80 (3.2)
1.78
3
120 (4.7)
1.58
3
80 (3.2)
2.37
CFRP
CFRP
12 M10 12 M10
1 CFRP
No. 4 (12.7 mm)
GFRP
*
Bundled bars.
†
M15 placed at corners.
Notes: P is plain concrete; G is GFRP; C is CFRP; (1; 3) = Stirrup configuration; c is «C» shaped legs assembly; (120; 80; 67; 60) is stirrup spacing, mm; (0.8; 1.0; 1.9) is longitudinal reinforcement ratio; S is steel longitudinal bars.
Materials The columns were cast vertically using normalweight ready mixed concrete with a target 28-day concrete compressive strength of 30 MPa (4.4 ksi). The columns were cured for 7 days, after which the specimens were left in the laboratory at ambient temperature for at least three more weeks before testing. The concrete compressive strength used for analysis was based on the average values of tests performed on at least five 150 x 300 mm (6 x 12 in.) cylinders for each concrete batch under displacement control standard rate of 0.01 mm/s (3.9 × 10–4 in./s) (Table 1). Grade 60 steel reinforcing bars were used as longitudinal reinforcement for specific specimens. Table 2 provided the tensile properties of Grade 60 steel bars. The longitudinal reinforcement for the exclusively FRPreinforced columns was (1) No. 12.7 mm (No. 4) straight CFRP bars, and (2) No. 15.9 mm (No. 5) and 19.1 mm (No. 6) GFRP straight bars. The tensile properties of longitudinal FRP and steel bars were determined by performing the B.2 test method according to ACI 440.3R (ACI Committee 440 2004) as reported in Table 2. Bent bars of 12.7 mm (No. 4) GFRP and 9.5 mm (No. 3) and 12.7 mm (No. 4) CFRP were used as transverse reinforcements. The ultimate tensile strength ffu and modulus of elasticity Ef for the straight portions of the transverse reinforcements were determined according ACI Structural Journal/March-April 2014
Table 2—Tensile properties of FRP and steel longitudinal reinforcement Af, mm2 (in.2)
Ef, GPa (ksi)
ffu, MPa (ksi)
12.7 (0.5)
127 (0.19)
46.3 (6715)
1040 (151)
2.25
No. 5 GFRP
15.9 (0.62)
199 (0.31)
48.2 (6990)
751 (109)
1.56
No. 6 GFRP
19.1 (0.75)
284 (0.44)
47.6 (6904)
728 (106)
1.53
No. 4 CFRP
12.7 (0.5)
127 (0.19)
137 (19,870)
1902 (276)
1.38
Steel M10
11.3 (0.44)
100 (0.15)
200 (29,000)
fy = 450 (65)
εy = 0.2
Steel M15
16.0 (0.62)
200 (0.31)
200 (29,000)
fy = 460 (66)
εy = 0.2
Bar type
db, mm (in.)
No. 4 GFRP
εf, %
Notes: db is bar diameter; Af is cross-sectional area of bar; Ef is modulus of elasticity of bar; ffu is ultimate tensile strength of bar; εf is ultimate strain of bar.
to the ACI 440.3R B.2 test method (ACI Committee 440 2004). The ultimate bent strength ffu,bend, however, was determined using the B.5 test method according to ACI 440.3R (ACI Committee 440 2004). Table 3 provides the measured 377
Fig. 3—(a) Loading machine; and (b) instrumentation. Table 3—Tensile properties of FRP transverse reinforcement Straight portion Ef, GPa (ksi)
εf, %
ffu,bend, MPa (ksi)
ffu,bend/ ffu
No. 3 CFRP 1327 (192) 126 (18,275)
1.05
614 (89)
0.46
No. 4 CFRP 1372 (198) 133 (19,290)
1.03
700 (101)
0.51
No. 4 GFRP
962 (139)
52 (7542)
1.85
500 (72)
0.52
C-shaped No. 4 GFRP
640 (92)
44 (6382)
1.45
400 (58)
0.62
Bar type
ffu, MPa (ksi)
Bend portion
Notes: Ef is modulus of elasticity of bar; ffu is ultimate tensile strength of bar; εf is ultimate strain of bar; ffu,bend is ultimate tensile strength of bar bend.
Fig. 4—Stress-strain relationship for both plain concrete cylinder and P-0-00-0 column. (Note: 1 MPa = 0.145 ksi.) tensile strength and modulus of elasticity for the straight and bent portions. The GFRP and CFRP longitudinal bars were pultruded products (Pultrall, Inc. 2009). Transverse reinforcements were fabricated with the bend process (Pultrall, Inc. 2009). Sand coating was used on the surface of the longitudinal and transverse FRP bars to improve the bond to concrete, as in standard industry practice. Instrumentation and testing procedures Reinforcement strain was measured with electrical strain gauges adhered to the bars at midheight of the column. A set of ties in each specimen was instrumented with strain gauges placed at the middle and in the corner of the outer tie and the cross hairpins. The test specimens were loaded by a rigid MTS high force load frame (Fig. 3(a)) with a maximum compressive capacity of 11,400 kN (2,560,000 lbf) having the load controlled up to 2200 kN (495,000 lbf) with a rate of 2.5 kN/s (562 lb/s). Thereafter, displacement control was used to apply the load until failure with the rate of 0.002 mm/s (7.87 × 10–5 in./s). The axial displacement of the 378
column specimens was recorded using four linear variable differential transducers (LVDTs) located at the midheight of each side of the specimens, as shown in Fig. 3(b). The top and bottom ends of the specimens were capped with a thin layer of high-strength mortar to ensure that the bearing surfaces were parallel and the load was distributed uniformly during testing. To ensure the failure would occur in the instrumented region, the ends of each specimen were further confined with bolted steel plates made from 13 mm (0.5 in.) thick steel plates (Fig. 3(b)). EXPERIMENTAL RESULTS AND DISCUSSION Overall behavior The unreinforced plain concrete column (P-0-00-0) was the first to be tested. The stress-strain behavior until peak was similar to the concrete cylinder, while peak stress was slightly lower as shown in Fig. 4. Post-peak behavior was completely different. Concrete cylinders exhibit a considerable softening branch meaning gradual damage, while P-0-00-0 failure was brittle; total loss of sustained load occurred just after reaching peak stress. This difference in post-peak behavior was due to the higher energy accumuACI Structural Journal/March-April 2014
Fig. 5—Total cross-section-based stress-strain curves for all tested columns. lated by the P-0-00-0 column compared to the small concrete cylinder. The post-peak behavior of plain concrete subjected to axial load is an important parameter for determination of cover contribution of the reinforced columns subjected to the same type of load. The stress-strain curve for confined concrete core of all reinforced columns is then obtained. Considering the total cross-sectional area for concrete columns with FRP transverse reinforcements (Fig. 5), the stress-strain curve was divided into three phases. The first phase corresponds to the behavior until the peak stress, which was similar to plain concrete column, implying that transverse reinforcement had no effect on this phase. The concrete cover was visually free of cracks (Fig. 6(a)), yet the peak stress varied depending on the longitudinal reinforcement material and ratio (Fig. 5(b) and (c)). The second phase was very short, and was characterized by a rapid drop in bearing capacity. This started once the peak stress was reached, and finished with passive-confinement activation (strain increase in the transverse reinforcements). In this phase, cracks began growing in the concrete cover, as shown in Fig. 6(b), leading to gradual spalling that reduced the load-resisting cross-sectional area and resulted in strength degradation. The third phase is characterized by activation ACI Structural Journal/March-April 2014
of transverse reinforcing associated with complete spalling of concrete cover, and ended with total failure of the column (Fig. 6(c)). This phase is clearly governed by transverse reinforcement and longitudinal bar material (Fig. 5). The following sections contain detailed discussion. Confined concrete core behavior Analyzing compressive behavior of internally confined concrete columns considering the total cross-sectional area from the starting of the elastic phase until failure is not accurate because the stress calculation does not take into account the degradation of concrete cover contribution after cracking. Nevertheless, when concrete cover is spalled off, the confined concrete core remained uncracked until a certain level, depending on the confinement effect. Therefore, studying the effect of confinement accurately requires considering the confined concrete core only. Nevertheless, the concrete cover strength should be subtracted from the total applied load based on the behavior of the plain concrete column, as shown in Fig. 4. The reduced load, divided by the concrete core area delimited by the centerlines of the outer transverse reinforcements, presents the column’s actual stress behavior. Figure 7 shows the curves representing the 379
Fig. 6—Cracking appearance of test specimens at different loading stages.
Fig. 7—Effect of concrete cover (G-3c-80-1.9). axial stress sustained by the concrete with respect to: 1) the total load divided by the total concrete area (Path 0-A-B′-C′); and 2) the total load divided by the confined concrete area delineated by the centerline of the outer transverse reinforcements (Path 0-A′-B-C). The actual response of the concrete column, represented by the bold curve (Path 0-A-B-C), is expected to be a combination of the two calculated curves. The response of the concrete column (bold curve) coincides with the ascending part of the lower curve (total concrete area) up to Point A, which corresponds to the spalling of the concrete cover. When the concrete cover no longer contributed to the axial strength, the response of the concrete column coincided with the part of the higher curve (confined concrete area) that follows Point B, when the concrete core began to gain strength due to confinement by the transverse reinforcement. The transition between Points A and B of the response of the concrete column was quantified by subtracting the contribution of the concrete cover (which decreased with increasing axial deformation) based on the stress-strain response of the plain concrete (Fig. 4). Point C corresponds to the ultimate strength of the tested columns.
380
Strength and failure mode Different failure modes were observed based on reinforcement layout. The failure mode of exclusively FRPreinforced column followed this progression: 1) crushing or buckling of the FRP longitudinal bar; and 2) transverse reinforcement rupture. Excessive buckling of the longitudinal steel bars was the failure mode of columns reinforced longitudinally with steel bars. The failure modes were governed by the shape, configuration, and diameter of the transverse reinforcements, as well as longitudinal bar material. The failure of all longitudinally and transversally FRPreinforced columns was due to longitudinal bar crushing or buckling, as shown in Fig. 8. In general, the columns with C-shaped GFRP transverse reinforcements experienced brittle failure. The failure of Column G-1c-120-1.9, which had the lowest confinement volumetric stiffness, was explosive. Column G-3c-120-1.9, which had higher confinement volumetric stiffness, showed failure starting with the longitudinal GFRP bars crushing, followed by total concrete crushing. In both columns, the slipping of the outer C-shaped transverse reinforcements at the splice location occurred due to concrete core expansion pressure, leading to degradation of sustained load until crushing of the longitudinal bars, followed instantaneously by concrete core crushing. Moreover, inclined shear sliding surfaces were observed, leading to a separation of the concrete core into two wedges, causing a sudden drop in axial strength. The failure of Column G-3c-80-1.9 was different: no transverse reinforcement slippage was observed. This might be attributed to the smaller tie spacing, which allowed the column to fail progressively in successive crushing of all longitudinal GFRP bars followed by concrete core crushing. The FRP reinforced columns with closed transverse reinforcements failed progressively due to successive crushing of the longitudinal bars before concrete core crushing. No transverse reinforcements rupture was observed, except in Column G-3-120-1.9, which was the only FRP-reinforced column with Configuration 3 transverse reinforcements. Reinforcing the columns longitudinally with steel bars instead of FRP bars changed the failure mode. The longiACI Structural Journal/March-April 2014
Fig. 8—Failure mode of columns reinforced longitudinally and transversely with FRP.
Fig. 9—Failure mode of columns reinforced longitudinally with steel and transversely with FRP. tudinal steel bars consistently buckled (Fig. 9(a) and (b)). In addition, cross-tie rupture was observed for columns with Configuration 3, (Fig. 9(c)), while failure was due to excessive bars buckling and substantial decrease in bearing capacity in columns with Configuration 1 transverse reinforcements. Moreover, excessive buckling of the longitudinal bars in columns induced openings in the GFRP transverse reinforcements, as shown in Fig. 9(b). Opening (albeit minor) was also observed with transverse CFRP reinforcement at 80 and 60 mm (3.2 and 2.4 in.) spacing. Failure due to transverse reinforcement rupture was experienced in columns transversely reinforced with CFRP No. 9.5 mm (No. 3) with both Configurations 1 and 3 (Fig. 10). Even Column No. 3C-1-67-1.6 experienced transverse reinforcement rupture after the longitudinal CFRP bars experienced crushing. Parametric investigation Parametric investigation was carried out to study the strength mechanism and performance based on stress-strain relationship for the tested columns. The investigated parameters included transverse reinforcement shape, material, spacing and diameter (No. 9.5 and 12.7 mm [No. 3 and No. 4]), longitudinal reinforcement ratio, longitudinal reinforcement material and confining volumetric stiffness. To compare the strength behavior of columns cast from different concrete batches, the stress values σc were normalized to the cylinder compressive strength fc′ of the batch. Therefore, the stress response σc along the test for each column was divided by the concrete compressive cylinder ACI Structural Journal/March-April 2014
Fig. 10—Transverse reinforcement rupture for No. 3 CFRP laterally reinforced columns. strength fc′. Columns were cast in three different groups. While the targeted concrete strength was 30 MPa (4.4 ksi), the actual concrete strength for the three groups was 33, 35, and 27 MPa (4.8, 5.1, and 3.9 ksi). Before testing the columns, actual cross-sectional area was measured to calculate the precise stress values. Effect of transverse reinforcement shape (C-shaped versus closed) Four columns were studied to investigate the effect of transverse reinforcement shape. Two columns, G-1c120-1.9 and G-3c-120-1.9, were transversely reinforced with C-shaped GFRP No.12.7 mm (No. 4). The other two columns, G-1-120-1.9 and G-3-120-1.9, were transversely 381
Fig. 11—C-shaped Vs closed transverse reinforcement normalized stress-strain relationship. reinforced with closed GFRP No.12.7 mm (No. 4). The four columns had identical longitudinal reinforcement. Figure 11 shows the normalized stress-strain response. The confined concrete strength gain (fcc′/fc′) is quite similar for the columns transversely reinforced with either transverse reinforcement type. Moreover, Configuration 3 showed a higher strength gain than Configuration 1. Nevertheless, a significant difference was noted based on transverse reinforcement type. In the columns with C-shaped transverse reinforcement (G-1c-120-1.9 and G-3c-120-1.9), the strength decreased due to leg slippage after reaching normalized confined concrete strength (fcc′/fc′). Therefore, the normalized ultimate strength (fcu′/fc′) corresponding to ultimate axial strain εcu was lower than the normalized peak strength (fcc′/fc′). Meanwhile, in the columns with closed transverse reinforcement (G-1-120-1.9 and G-3-120-1.9), no descending branch was observed. The failure of columns occurred at the maximum normalized confined concrete strength. In other words, fcc′ and fcu′ had the same value. Therefore, it can be deduced that closed transverse reinforcement yield more efficient confinement than C-shaped transverse reinforcement because of the material continuity that eliminates slippage, increasing the lateral confinement pressure rather than confinement degradation. Effect of longitudinal reinforcement The longitudinal reinforcement effect was more pronounced in the stress-strain curves based on total cross-sectional area because the contribution of the longitudinal reinforcement was more effective on the pre-peak phase before the activation of the confinement effect. Figure 12 shows that increasing the FRP longitudinalreinforcement ratio from 0.8 to 1.0 then 1.9 increased the load at the peak before activation of confinement. The stressstrain curves for these three columns had the same trend. The three columns failed when the longitudinal bars buckled at nearly the same axial strain. Figure 12 also shows the effect of longitudinal reinforcement material: Columns G-1-1201.0 and G-1-120-1.0S had GFRP and steel longitudinal reinforcement, respectively, with the same reinforcement ratio 382
Fig. 12—Effect of longitudinal reinforcement on compressive behavior of columns. (1.0%). Two main differences were observed: the peak stress for the steel longitudinally reinforced column was higher than that of GFRP-reinforced column, and the GFRP-reinforced column showed stabilization of the load-carrying capacity, represented by nearly horizontal plateau until failure, at the post-peak phase, while the load-carrying capacity of steel longitudinally reinforced column decreased after reaching the peak load. The difference in post-peak behavior is due to longitudinal reinforcement material. Indeed, the load carried by steel bars after yielding remained constant, while the load increased with axial strain with the elastic GFRP bars. This behavior is more pronounced in Column G-3c-80-1.9, which was the only column that exhibited stiffening behavior after cracking of the cover and a reduction in the load drop that ended with a second peak load higher than the first one, as shown in Fig. 5(a). The ultimate axial strain of the columns reinforced longitudinally with FRP is lower than those reinforced with steel. Columns longitudinally reinforced with FRP, however, reached axial compressive strains of 0.011 and 0.018 in G-1-120-1.9 and G-3c-80-1.9, respectively, which showed that, under good confinement conditions, the FRP bars were able to reach high compressive strains. The nominal compressive capacity of the FRP reinforced columns at peak, considering the gross cross-sectional area Pn, was defined as the sum of the forces carried by the concrete and the longitudinal reinforcement. Based on the elastic theory, the contribution of FRP longitudinal reinforcement bars in compression at peak was calculated according to the material proprieties given in Table 2. The authors proposed an equation to calculate the nominal compressive capacity of the longitudinally and transversally FRP-reinforced columns, which given as follows Pn = 0.85 × fc′ × (Ag – Afrp) + εco × Efrp × Afrp (SI) (1) where Ag is gross cross-sectional area of the column; Afrp is cross-sectional area of FRP longitudinal reinforcement; fc′ is concrete compressive strength; εco is concrete strain at peak stress; and Efrp is modulus of elasticity of FRP longitudinal reinforcement. ACI Structural Journal/March-April 2014
Table 4—Prediction of nominal compressive capacity fc′, MPa (ksi)
Ac, mm2 (in.2)
PExp, kN (lbf)
Pn, kN (lbf)
Pn/PExp
Pc, kN (lbf)
PLongi, kN (lbf)
G-1-120-0.8
127,132 (197)
3900 (876,755)
3899 (876,530)
1.00
3782 (850,227)
117 (26,303)
G-1-120-1.0
128,803 (200)
4212 (946,895)
3995 (898,111)
0.95
3832 (861,468)
163 (36,644)
Column
G-1-120-1.9
125,528 (194)
4297 (966,004)
4048 (910,027)
0.94
3734 (839,437)
314 (70,590)
G-1-120-1.0S
124,642 (193)
4272 (960,384)
4260 (957,686)
1.00
3708 (833,592)
552 (124,094)
127,688 (198)
5159 (1,159,789)
4714 (1,059,749)
0.91
3799 (854,049)
919 (206,599)
No. 3C-1-67-1.0S
125,340 (194)
4660 (1,047,610)
4281 (962,407)
0.92
3729 (838,312)
552 (124,094)
G-3-120-1.9
125,734 (195)
4615 (1,037,493)
4086 (918,569)
0.89
3741 (841,010)
345 (77,559)
C-1-120-1.0S
128,922 (200)
4584 (1,030,524)
4387 (986,237)
0.96
3835 (862,142)
552 (124,094)
No. 3C-1-67-1.6
35 (5.07)
Notes: Ac = (Ag – Afrp); Ag is actual total cross-sectional area of considered column.
Fig. 13—Transverse reinforcement layout effect on confined concrete stress-strain response. Whereas for columns with steel longitudinal reinforcement, the nominal compressive capacity at the peak is given as follows according to ACI 318 (ACI Committee 318 2008) Pn = 0.85 × fc′ × (Ag – As) + fy × As (2) where As is the cross-sectional area of longitudinal steel reinforcement; and fy is the yielding strength of steel reinforcement. The strength of full-scale plain-concrete columns tested under concentric compression load is generally lower than the concrete compressive strength measured on standard 150 x 300 mm (6 x 12 in.) cylinders. The 0.85 reduction factor suggested by ACI 318 (ACI Committee 318 2008) is mainly attributed to the differences between the reinforced concrete column and the concrete cylinder regarding concrete compressive strength, size, and shape of the element. Table 4 compares the predicted nominal compressive capacity at the peak to the experimental results for columns reinforced transversely with FRP and reinforced longitudiACI Structural Journal/March-April 2014
nally with FRP or steel bars according to Eq. (2) and (1), respectively. The results showed that nominal compressive capacity predictions Pn were conservative and very close to experimental results, with Pn/PExp ratios varying from 0.89 to 1.00. It is important to note that when Pn differs from one specimen to another, the load carried by the concrete remained similar in all the columns. In other words, the difference in Pn is primarily due to the longitudinal reinforcement ratio and material, not to concrete strength. Effect of transverse reinforcement The transverse reinforcement restrains the expansion of the concrete core in the column subjected to compressive load and delays its failure. Accordingly, the compressive performance of concrete columns depends strongly on the transverse reinforcement efficiency. Figure 13 shows the stress-strain curves of the columns reinforced with different transverse reinforcement layouts to investigate the effect of transverse reinforcement configuration, spacing, material, diameter, and confining volumetric stiffness. The stress383
strain curves based on the confined concrete core showed that, regardless the transverse reinforcement configuration or material, reducing spacing increases the nominal confined-concrete strength (fcc′/fc′) and changes the behavior after this point. With 120 mm (4.7 in.) spacing, a descending branch followed the peak stress, while for 80 mm (3.2 in.) spacing, the stress stabilized at a nearly horizontal plateau; however, stress increased with the 60 mm (2.4 in.) spacing. Configuration 3 proved to be more efficient than Configuration 1, offering higher nominal confined concrete strength (fcc′/fc′) and enhancing the peak stress. In the case of 120 mm (4.7 in.) spacing, the slope of the descending branch following the peak stress was less steep for Configuration 3 than Configuration 1, resulting in higher ultimate strain (almost double) as comparing C-3-120-1.0S and G-3-1201.0S with C-1-120-1.0S and G-1-120-1.0S, respectively (0.039 and 0.041 versus 0.019 and 0.016, respectively). For columns with 80 mm (3.2 in.) spacing, the stabilization plateau was longer in Configuration 3 than Configuration 1. The ultimate strain increased for the CFRP transversely reinforced columns from 0.026 to 0.034, corresponding to C-1-80-1.0S and C-3-80-1.0S, respectively. The increase of ultimate strain in the GFRP transversely reinforced columns, however, was more than the double comparing G-1-80-1.0S and G-3-80-1.0S (0.021 and 0.052, respectively). It is clearly shown that the transverse reinforcement spacing and configuration determined the effectively confined concrete volume, which increased with closer transverse reinforcement and a better distribution of longitudinal bars around the column concrete core. The larger the effectively confined concrete volume, the higher the confinement efficiency. In addition, transverse reinforcement spacing controlled the buckling of the longitudinal bars by reducing their slenderness ratio. The effect of transverse reinforcement material was related to columns mode of failure, which is dependent on the configuration. Figure 13(b), (c), and (d) showed that, in the case of columns with Configuration 1 (C-1-120-1.0S, G-1-120-1.0S, C-1-80-1.0S, and G-1-80-1.0S) that failed because of excessive longitudinal bars buckling, CFRP transverse reinforcement enabled the columns to attain higher nominal confined concrete strength (fcc′/fc′) than those reinforced with GFRP transverse reinforcement. The stressstrain curves of both materials, however, followed the same trend. The modulus of elasticity was determinant: given the same layout, the CFRP transverse reinforcements were stiffer than the GFRP ones. The stiffer transverse reinforcement tended to open less, thereby better limiting the buckling of longitudinal bars. Two different spacing related cases were observed in columns with Configuration 3. The first relates to 120 mm (4.7 in.) spacing, which was wide enough to enable significant bar buckling and the development of a localized plastic hinge, as illustrated in Fig. 9(a) and (b). The columns reinforced transversely with CFRP and GFRP behaved identically. In the second case, the stirrups spacing of 80 mm (3.2 in.) prevented excessive bar buckling and the development of a localized plastic hinge. In this case, the CFRP stirrups allowed the column to achieve higher nominal confined concrete strength than GFRP stirrups (1.7 versus 1.6). Conversely, the larger ultimate elongation of 384
GFRP (Table 3) allowed Column G-3-80-1.0S to reach a higher strain than C-3-80-1.0S (0.052 versus 0.034). Regarding transverse reinforcement diameter, C-3-80-1.0S outperformed 3C-3-80-1.0S in terms of nominal confined concrete strength (1.7 versus 1.4) and ultimate strain (0.034 versus 0.015). In 3C-3-80-1.0S, however, the longitudinal bars buckled outside the strain measurement zone. Analyzing the results shown in Fig. 13 illustrates the effect of the confining volumetric stiffness. Given the same transverse reinforcement layout ρv, the GFRP volumetric stiffness (ρv × Ef) was far less than that of the CFRP, yet the performances were close, which indicates that the configuration and spacing are more important parameters than modulus of elasticity. Given the same confining volumetric stiffness and transverse reinforcement material, Configuration 3 performed better than Configuration 1 in terms of ultimate strain (C-1-60-1.0S and C-3-80-1.0S, as shown in Fig. 13). CONCLUSIONS Failure mechanisms of axially loaded concrete columns reinforced longitudinally with FRP or steel bars and with FRP transverse reinforcement involving different layouts were investigated. Based on the analytical results, the following remarks can be made: 1. The confinement efficiency of closed FRP transverse reinforcements cut from continuous square spiral is higher than C-shaped type transverse reinforcements. 2. The ultimate axial strain of columns reinforced longitudinally with FRP is almost 30% lower than those reinforced with the same volume of steel. 3. The ultimate axial compressive strain for columns reinforced longitudinally and transversally with FRP can reach a value on the same order of magnitude as the FRP ultimate tensile strain of the longitudinal bars under good confinement conditions. 4. The contribution of FRP longitudinal reinforcement in concrete columns subjected to axial concentric loading should not be neglected. A proposed equation based on elastic theory yields good predictions compared with laboratory test data. 5. FRP transverse reinforcement configuration and spacing are the most important parameters (compared with confinement provided by concrete cover) affecting confining efficiency in internally reinforced concrete columns under axial loading. 6. In the case of large spacing with low volumetric ratio, CFRP transverse reinforcement performed significantly better than GFRP. Increasing the volumetric ratio while reducing spacing will eliminate the effect of material stiffness. In such cases, the GFRP transverse reinforcements are more cost effective. 7. Columns internally reinforced with a combination of steel longitudinal bars and FRP transverse reinforcements exhibit good gains in terms of compressive strength and ultimate axial strain. Nonetheless, the use of FRP transverse reinforcement should still improve corrosion resistance of a column by adding an extra 10 mm (0.4 in.) of cover to the steel. ACI Structural Journal/March-April 2014
8. The presented study showed the applicability of exclusively reinforcing the columns with FRP and subjected to concentric load. Further research elaboration is necessary to investigate the behavior of FRP reinforced columns loaded laterally or subjected to load combination (axially and laterally). AUTHOR BIOS
Hany Tobbi is a Doctoral Candidate in the Department of Civil Engineering at the University of Sherbrooke, Sherbrooke, QC, Canada. He received his BSc from the University of Mentouri, Constantine, Algeria, and his MSc from the University of Claude Bernard, Lyon, France. His research interests include structural analysis, design, and testing of concrete structures reinforced with fiber-reinforced polymers. Ahmed Sabry Farghaly is a Postdoctoral Fellow in the Department of Civil Engineering at the University of Sherbrooke, and Associate Professor in the Department of Civil Engineering, Assiut University, Assiut, Egypt. His research interests include nonlinear analysis of reinforced concrete structures, and behavior of structural concrete reinforced with fiber-reinforced polymers. Brahim Benmokrane, FACI, is an NSERC Research Chair in FRP Reinforcement for Concrete Infrastructures and Tier-1 Canada Research Chair Professor in Advanced Composite Materials for Civil Structures in the Department of Civil Engineering at the University of Sherbrooke. He is a member of ACI Committee 440, Fiber-Reinforced Polymer Reinforcement.
ACKNOWLEDGMENTS
The authors would like to express their special thanks and gratitude to the Natural Science and Engineering Research Council of Canada (NSERC), the Fonds québécois de la recherche sur la nature et les technologies (FQRNT), the Canadian Foundation for Innovation (FCI), and the technical staff of the structural lab in the Department of Civil Engineering at the University of Sherbrooke.
REFERENCES
ACI Committee 318, 2008, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 473 pp. ACI Committee 440, 2004, “Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures (ACI 440.3R-04),” American Concrete Institute, Farmington Hills, MI, 40 pp. ACI Committee 440, 2006, “Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06),” American Concrete Institute, Farmington Hills, MI, 44 pp. ACI Committee 440, 2007, “Report on Fiber-Reinforced Polymer (FRP) Reinforcement Concrete Structures (ACI 440R-07),” American Concrete Institute, Farmington Hills, MI, 100 pp. ACI Committee 440, 2008, “Specification for Carbon and Glass Fiber-Reinforced Polymer Bar Materials for Concrete Reinforcement (ACI 440.6M-08),” American Concrete Institute, Farmington Hills, MI, 6 pp. CSA S806, 2012, “Design and Construction of Building Components with Fiber-Reinforced Polymers,” Canadian Standards Association, Mississauga, ON, Canada, 177 pp.
ACI Structural Journal/March-April 2014
CSA S807, 2010, “Specification for Fibre-Reinforced Polymers,” Canadian Standards Association, Mississauga, ON, Canada, 44 pp. Cusson, D., and Paultre, P., 1994, “High Strength Concrete Columns Confined by Rectangular Ties,” Journal of Structural Engineering, ASCE, V. 120, No. 3, Mar., pp. 783-804. Federation Internationale de Béton (FIB), 2007, “FRP Reinforcement in RC Structures,” Task Group 9.3, Lausanne, Switzerland, 157 pp. Harries, K. A., and Kharel, G., 2003, “Experimental Investigation of the Behavior of Variably Confined Concrete,” Cement and Concrete Research, V. 33, pp. 873-880. ISIS Canada Research Network, 2007, “Reinforcing Concrete Structures with Fibre Reinforced Polymers,” ISIS Design Manual No. 3, ISIS Canada Research Network, 151 pp. Mander, J. B.; Preistley, M. J. N.; and Park, R., 1988a, “Theoretical Stress-Strain Model for Confined Concrete,” Journal of Structural Engineering, ASCE, V. 114, No. 8, pp. 1804-1826. Mander, J. B.; Preistley, M. J. N.; and Park, R., 1988b, “Observed Stress-Strain Behaviour of Confined Concrete,” Journal of Structural Engineering, ASCE, V. 114, No. 8, pp. 1827-1849. Nanni, A., 1993, “Flexural Behavior and Design of RC Members Using FRP Reinforcement,” Journal of Structural Engineering, ASCE, V. 119, No. 11, pp. 3344-3359. Pultrall, Inc., 2009, V-ROD Composite Reinforcing Rods Technical Data Sheet, Thetford Mines, Canada, www.pultrall.com. Richart, F. E.; Brandtzaeg, A.; and Brown, R. L., 1928, “A Study of the Failure of Concrete under Combined Compressive Stresses,” Bulletin No. 185, Engineering Experimental Station, University of Illinois, Urbana, IL, 104 pp. Richart, F. E.; Brandtzaeg, A.; and Brown, R. L., 1929, “The Failure of Plain and Spirally Reinforced Concrete in Compression,” Bulletin No. 190, Engineering Experimental Station, University of Illinois, Urbana, IL, 74 pp. Saatcioglu, M., and Razvi, S. R., 1992, “Strength and Ductility of Confined Concrete,” Journal of Structural Engineering, ASCE, V. 118, No. 6, pp. 1590-1607. Saatcioglu, M.; Salamat, A. H.; and Razvi, S. R., 1995, “Confined Columns under Eccentric Loading,” Journal of Structural Engineering, ASCE, V. 121, No. 11, pp. 1547-1556. Sheikh, S. A., 1982, “A Comparative Study of Confinement Models,” ACI Journal, V. 79, No. 4, July-Aug., pp. 296-306. Sheikh, S. A., and Uzumeri, S. M., 1980, “Strength and Ductility of Tied Concrete Columns,” Journal of the Structural Division, ASCE, V. 106, No. 5, pp. 1079-1112. Sheikh, S. A., and Uzumeri, S. M., 1982, “Analytical Model for Concrete Confinement in Tied Columns,” Journal of the Structural Division, ASCE, V. 108, No. 12, pp. 2703-2722. Teng, J. G.; Chen, J. F.; Smith, S. T.; and Lam, L., 2002, FRP Strengthened RC Structures, John Wiley & Sons, Ltd., Hoboken, NJ, 266 pp. Tobbi, H.; Farghaly, A. S.; and Benmokrane, B., 2012, “Concrete Columns Reinforced Longitudinally and Transversally with GFRP Bars,” ACI Structural Journal, V. 109, No. 4, July-Aug., pp. 551-558. Watson, S.; Zahn, F. A.; and Park, R., 1994, “Confining Reinforcement for Concrete Columns,” Journal of Structural Engineering, ASCE, V. 120, No. 6, pp. 1798-1824.
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S34
Repair of Prestressed Concrete Beams with Damaged Steel Tendons Using Post-Tensioned Carbon FiberReinforced Polymer Rods by Clayton A. Burningham, Chris P. Pantelides, and Lawrence D. Reaveley Research implementing unibody clamp anchors and a simple mechanical stressing device to post-tension external, unbonded carbon fiber-reinforced polymer (CFRP) rods is presented. The experiments described in the paper concern three prestressed concrete beams: one was used as the control beam and the other two were damaged. Damage consisted of cracked concrete that was removed and internal steel tendons that were cut to simulate vehicle collision, corrosion, or both. The repair system was then applied to the two damaged concrete beams. The CFRP repair system performed well, increasing the ultimate strength and flexural capacity of the damaged beams to meet or exceed the strength capacity of the control. An analytical model considering the tendon stress at ultimate and the distribution of internal forces was developed to explore design recommendations for the use of the unibody clamp anchors and stressing device for post-tensioning CFRP rods. Keywords: beams; carbon fiber-reinforced polymer (CFRP); post-tensioning; prestressed concrete; repair; retrofit.
INTRODUCTION Many bridges in the Unites States are approaching the end of their design life, and some bridges are showing signs of aging and damage such as corrosion of steel reinforcement, large cracks, and missing concrete cover. Damage to concrete cover and internal steel prestressing tendons can occur when large vehicles attempt to pass under a bridge without adequate clearance. Vehicular impact can fracture the concrete cover, expose the internal steel prestressing tendons, and/or sever all or part of the outer steel prestressing tendons. Even if the tendons are not severed, removal of the protective concrete cover accelerates the corrosion process. Additionally, cracking from overloading or fatigue could facilitate corrosion of internal steel prestressing tendons. Damage to internal steel prestressing tendons decreases flexural capacity, and bridges exhibiting these symptoms could be in critical need of replacement, repair, or strengthening. Typically, girder replacement is expensive, time consuming, and disruptive; therefore, repair or retrofit is often the preferred option. One system used for repair applications is external post-tensioning. This repair method not only restores flexural capacity, but can also mitigate the demands of an increase in service load and help with serviceability considerations such as deflection. Thus, external post-tensioning is an excellent option for repairing concrete bridge girders with damage to internal steel prestressing tendons. Traditionally, external post-tensioning has been implemented with high-strength steel tendons because of low material cost, material availability, and ease of installation. ACI Structural Journal/March-April 2014
Despite its historic use, however, exposed steel is susceptible to corrosion, limiting its useful lifespan and requiring extensive protection from deicing salt and moisture. The limitations of steel tendons can be overcome in external post-tensioning applications by the use of fiber-reinforced polymer (FRP) materials. FRP materials are advantageous because of their corrosion resistance and high specific strength. Additionally, the use of FRP materials is becoming increasingly attractive as the price of FRP composites decreases. Several studies have shown that post-tensioned FRP tendons can contribute to flexural strength in new construction or for strengthening (Abdel Aziz et al. 2005; El-Hacha and Elbadry 2006; Täljsten and Nordin 2007); however, few studies have shown the usefulness of post-tensioned FRP tendons in flexural repair and retrofit applications (Elrefai et al. 2007). As a result, additional research is required to investigate the suitability of post-tensioned FRP tendons for the repair of severe flexural damage. Widespread use of FRP tendons in post-tensioning applications has been slow because of the difficulty in developing an effective tendon anchor. Research has produced a unibody clamp anchor and mechanical stressing device for use in post-tensioning carbon FRP (CFRP) rods (Burningham 2011). The clamp anchors are machined from a single piece of steel, and the clamping force is provided by high-strength bolts. Further research is needed to analyze the effectiveness of the complete post-tensioning system consisting of the CFRP rods, unibody clamp anchors, and mechanical stressing device when applied to prestressed concrete members. The research in this paper is concerned with applying CFRP rods, unibody clamp anchors, and the aforementioned mechanical stressing device as a complete FRP strengthening system for the repair of damaged prestressed concrete beams. In the present research, the unibody clamp anchors were fabricated using mild steel. In actual implementation, the anchor and stressing device might need to be manufactured using stainless steel or other corrosion-resistant steel. The specific damage considered during this research was damage resulting from impact with vehicles passing underneath a bridge without adequate clearance. Such impact could result in severed internal steel prestressing tendons ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-135.R2, doi:10.14359.51686529, was received October 18, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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or removal of concrete cover and subsequent corrosion of internal steel prestressing tendons. An illustrative example of impact damage observed on an actual prestressed concrete bridge girder can be seen in Fig. 1. The paper includes details of testing methods, specimen design and fabrication, experimental design, and analysis of results. Additionally, the methods used for collecting data during laboratory testing as well as details pertaining to the performance and effectiveness of the FRP repair system and its application are provided, with specific focus on the performance of the CFRP tendons and their ability to aid in the repair of damaged beams. An analytical model considering the tendon stress at ultimate and conventional beam theory is presented to explore design recommendations for the use of the unibody clamp anchors and stressing device. RESEARCH SIGNIFICANCE Previous research on using external post-tensioned CFRP tendons for repair of damaged concrete beams has been limited. This research presents the implementation of newly developed unibody clamp anchors and a simple mechanical stressing device for the repair of damaged prestressed concrete beams with post-tensioned CFRP rods. In addition, the paper validates equations from the literature for evalu-
ating the ultimate stress of unbonded post-tensioned CFRP rods. The CFRP repair system implemented in this research could facilitate the acceptance of CFRP post-tensioning systems by the construction industry. EXPERIMENTAL INVESTIGATION Specimen fabrication Three prestressed concrete (PC) beam specimens were designed and fabricated for testing. The three beams (Specimens P2, RP1, and RP3, with “R” indicating a specimen to which the repair system was applied) were manufactured by a local PCI-certified precast/prestressed concrete company. The precast beams measured 12 in. (305 mm) wide x 20 in. (508 mm) tall x 15 ft (4.57 m) long, and each prestressed beam had three 1/2 in. (13 mm) seven-wire low-relaxation prestressing steel strands with an ultimate strength of 270 ksi (1862 MPa). The beams were also reinforced with two No. 5 (16 mm) mild steel bars in the tension zone, and two No. 5 (16 mm) mild steel bars in the compression zone. The prestressed beams had No. 3 (10 mm) stirrups placed at 12 in. (305 mm) on center. The beam dimensions and location of internal reinforcement are shown in Fig. 2. Experimental design All three beams were tested and subjected to initial damage using a four point loading system to induce tensile cracking. The same setup was used to test the beams to failure. A hydraulic actuator with a 500 kip (2220 kN) inline load cell and a steel spreader beam were used to apply a two-point load, spaced 30 in. (762 mm) apart, to the top of the specimens, as shown in Fig. 3. The specimens were tested with an unbraced length of 13 ft, 8 in. (4.17 m) and had a depth of 20 in. (508 mm), giving a shear span-depth ratio (a/d) of 3.35.
Fig. 1—Girder damage from vehicle impact.
Material properties The materials used in this research are typical of construction in the United States. All steel reinforcing bars used in the fabrication of the specimens had a nominal tensile strength
Fig. 2—Reinforcement layout for Specimens P2, RP1, and RP3. (Note: 1 in. = 25.4 mm; 1 ft = 0.305 m.) 388
ACI Structural Journal/March-April 2014
Fig. 4—Damaged outer steel tendon in Specimen RP1 (three wires cut) and RP3 (seven wires cut). Fig. 3—Test setup. (Note: 1 in. = 25.4 mm; 1 ft = 0.305 m.) of 60 ksi (414 MPa). The CFRP rods used in this research had the following properties as provided by the manufacturer: rod diameter = 3/8 in. (9.53 mm), tensile strength = 250 ksi (1724 MPa), tensile modulus = 22,500 ksi (155 GPa), and elongation at break = 1.11%. In separate tensile tests of CFRP rods from the same lot as the ones used in this research, carried out using unibody clamp anchors, the average measured tensile strength was 308 ksi (2124 MPa), and the average ultimate strain measured was 1.37%. The internal steel prestressing tendons were low relaxation 1/2 in. (13 mm) diameter seven-wire strands with a nominal ultimate strength of 270 ksi (1862 MPa). Concrete cylinder tests performed at 7 days after casting of the steam cured prestressed concrete beams gave an average compressive concrete strength of 7.0 ksi (48 MPa), and at the time of specimen testing, the concrete had an average compressive strength of 10.0 ksi (69 MPa) based on compression tests of 4 in. (102 mm) diameter by 8 in. (204 mm) high cylinders. Testing methods Load testing was carried out in three phases: damage, repair, and failure. First, loading was used to introduce tensile cracks, which could lead to accelerated corrosion of internal steel prestressing tendons. Additionally, Specimens RP1 and RP3 were damaged with respect to the internal prestressing steel—to simulate impact damage. Subsequently, Specimens RP1 and RP3 were repaired with external post-tensioned CFRP rods. Finally, all three specimens were loaded monotonically to failure. Damage loading—Damage loading applied to the specimens consisted of downward half-cycles to induce tensile cracking. The loading was displacement controlled to avoid catastrophic failure and subsequent loss of the specimens. Displacement half-cycles were applied in increments of 0.0625 in. (1.59 mm), with the amplitude of each successive half-cycle increasing by 0.0625 in. (1.59 mm).
ACI Structural Journal/March-April 2014
In addition, the rate of displacement was held constant at 0.0625 in./min (1.59 mm/min) throughout the test. All specimens were subjected to the same loading protocol, with termination of loading dependent upon the level of cracking. The vertical deflection at midspan was limited to 0.375 in. (9.5 mm), and the cracks were of a hairline width mainly in the constant moment region at a spacing of 12 in. (305 mm). Additional damage was inflicted on Specimens RP1 and RP3 to simulate damage to internal steel prestressing tendons from vehicle collision, subsequent corrosion, or both. An area approximately 8 in. (203 mm) long with a depth equal to the concrete cover of the prestressing tendons was removed from both Specimen RP1 and RP3 to expose an outer sevenwire steel prestressing strand within the constant moment region. For Specimen RP1, three of the seven wires in this strand were cut—leaving two intact seven-wire strands and one four-wire damaged strand. For Specimen RP3, all seven wires of an outer steel prestressing strand were cut to simulate severe damage, leaving two intact seven-wire strands. These cuts, seen in Fig. 4, simulated partial or complete severing of the exterior tendon on impact in an exterior girder or corrosion of an exterior tendon due to loss of concrete cover and subsequent exposure to the elements. FRP repair—After simulating damage to internal steel prestressing tendons in Specimens RP1 and RP3, the beams were repaired with external post-tensioned CFRP rods. The unibody clamp anchors and mechanical stressing device seen in Fig. 5 were used to introduce the post-tensioning force. Specimens RP1 and RP3 were repaired with two rods, one on each side of the beam along the beam length at a depth of 15 in. (381 mm) from the top compression fiber. The CFRP rods were post-tensioned to a strain of approximately 0.485% measured using strain gauges attached to the rod at midspan, producing a calculated design post-tensioning force of 12 kip (53.4 kN) in each rod. ACI 440.4R (ACI Committee 440 2004) recommends initial jacking stresses of 40 to 65% of the design ultimate tensile strength of the prestressed FRP tendon and anchorage system. In the present case, the amount of initial jacking of the CFRP 389
Fig. 5—End view of stressing system showing clamp anchors and stressing device. rods was approximately 44% of the design ultimate tensile strength based on the manufacturer’s specification. The novel mechanical stressing device implemented in this research consists of a slotted square HSS section running perpendicular to the beam length at both ends of the beam. The slots in the HSS section allow the tendons to pass through the slots such that the unibody clamp anchors make contact with the back side of the tube. On the stressing end of the beam, two sleeve nuts are positioned on top, and two on the bottom of the HSS section. The sleeve nuts run parallel with the beam, and tendon stressing occurs when 1.0 in. (25 mm) diameter bolts are screwed into the sleeve nuts; the bolts react against the beam end, moving the HSS section back to stress the tendons. Tightening the stressing bolts in an alternating star pattern ensures the tendons are stressed with controlled increments of tightening. More details of the unibody clamp anchor and stressing device are provided by Burningham (2011). Loading to failure—After repairing Specimens RP1 and RP3 with external post-tensioned CFRP rods, the specimens were loaded to failure, with Specimen P2 as the control specimen. The displacement controlled loading to failure was monotonic at a rate of 0.0625 in./min (1.59 mm/min). The test was stopped at imminent failure of the specimen, as measured by a 20% decrease from the maximum load or failure of the external CFRP rods, whichever occurred first. EXPERIMENTAL RESULTS Instrumentation and data collection methods Instrumentation consisted of strain gauges and linear variable differential transformers (LVDTs). The specimens were instrumented with three LVDTs, one 54.5 in. (1.38 m) from either end and one at midspan as shown in Fig. 3; these were attached to the bottom of the beam to measure the deflected shape under load. Concrete strain gauges placed at 69.5 in. (1.77 m) from each end and at midspan on the top face of the beams measured the concrete compressive strain. Strain gauges were also applied to each CFRP rod at midspan as shown in Fig. 3; they were used to measure strain at initial prestress and throughout the tests until failure of Specimens RP1 and RP3. All measurements were collected by an electronic data acquisition system at a sampling rate of two data points per second. All strain gauge readings were 390
Fig. 6—Control Specimen P2 at failure; grid = 4 in. (102 mm).
Fig. 7—Repaired Specimen RP1 at imminent failure: (a) front; and (b) back; grid = 4 in. (102 mm). measured in units of microstrain, and all LVDT readings were measured within 0.001 in. (0.025 mm). Specimen data analysis No anchor slippage was observed in any of the CFRP rods during testing of the specimens to failure. The lack of slip demonstrates that the anchors work as designed. This was confirmed in the laboratory in CFRP rod tensile tests using the unibody anchors according to ACI 440.3R guidelines (ACI Committee 440 2012). During testing, Specimen P2 (control) failed due to concrete compressive failure at the center, after flexural cracks had developed; crack spacing in the constant moment region was 6 in. (152 mm) and the maximum crack width was 0.08 in. (2 mm), as shown in Fig. 6. Specimen RP1 (repaired) failed due to concrete compression failure accompanied by flexural cracks, after rupture of the external CFRP rods; crack spacing in the constant moment region was 6 in. (152 mm), and the maximum crack width was 0.06 in. ACI Structural Journal/March-April 2014
Fig. 9—Concrete compressive strain at midspan versus applied load to failure.
Fig. 8—Repaired Specimen RP3 at failure: (a) front; (b) back; grid = 4 in. (102 mm). (1.5 mm), as shown in Fig. 7. Specimen RP3 (repaired) failed due to concrete compression failure at the center; flexural crack spacing in the constant moment region was 4 in. (102 mm), and the maximum crack width was 0.07 in. (1.8 mm). In addition, Specimen RP3 developed several flexural tension cracks around the area of the cut tendon, and the top compression mild steel bars buckled subsequent to concrete crushing, as shown in Fig. 8. For all three specimens, the highest compressive concrete strain was observed near midspan, as seen in Fig. 9, which shows the change in concrete compressive strain at midspan as a function of applied load. From Fig. 9 it can be seen that Specimens P2 and RP3 experienced maximum concrete strains just greater than 0.30%. Specimen RP1 also started failing in compression, but the test was terminated prematurely at a smaller deflection than the other two tests with the maximum concrete strain reaching 0.27%. These numerical data correlate well with the failure mode visually observed in Specimens P2 and RP3 and seen in Fig. 6 and 8, respectively. Figure 7 shows that Specimen RP1 experienced severe cracking damage with significant flexural cracks reaching the top of the beam, and imminent concrete compression failure, similar to Specimen P2. The change in CFRP rod strain at midspan as a function of applied load for Specimens RP1 and RP3 is shown in Fig. 10. An increase in strain of the CFRP rods for Specimens RP1 and RP3 was observed during testing of the specimens to failure. The initial strain in the rods from the post-tensioning application was 0.485%. At failure of the external CFRP tendons, the average maximum strain in the CFRP rods was 0.750 and 0.814% for Specimens RP1 and RP3, respecACI Structural Journal/March-April 2014
Fig. 10—CFRP rod strain at midspan versus applied load to failure. tively. Because the measured ultimate strain of the rods in axial tension is 1.37, the most likely explanation for rupture of the rods at lower strains is eccentric bending due to lack of rotation of the anchor at the supports; this caused stress concentrations at a point other than where the strain gauges were located at midspan. One location of stress concentrations is near the clamp anchors at the beam ends due to rotation of the latter at large deflections. Figure 11 shows the two modes of failure observed: straw broom and splitting failure; the former failure was observed near the clamp anchors, and the latter near midspan. In actual applications, the use of a rotating rocker at both anchorage devices is desirable to keep the rod from experiencing flexural bending stresses. The CFRP repair system was successful—both Specimens RP1 and RP3 exhibited an increase in ultimate capacity and benefited from application of the CFRP repair system. The ultimate load for Specimens P2 (control), RP1 (repaired), and RP3 (repaired) was 104, 112, and 102 kip (463, 498, and 454 kN), respectively. For Specimen RP1, the ultimate load corresponds to an increase of approximately 7.7% in ultimate capacity from the use of external post-tensioned CFRP rods. It should be remembered, however, that Specimen RP1 (repaired) had two intact seven-wire strands and one four-wire strand (three wires were cut), whereas Specimen P2 (control) had three intact seven-wire strands. Therefore, application of the theoretical capacity of Specimen RP1 (repaired) based on the cut wires produces an effec391
Fig. 12—Applied load versus midspan deflection to failure.
Fig. 11—Failure of CFRP rods: (a) straw broom; and (b) splitting. tive increase in ultimate capacity of 20.6% from the use of external post-tensioned CFRP rods. In addition, although a third of the prestressing force was removed from Specimen RP3, the repair with the external post-tensioned CFRP rods produced load-deflection behavior virtually identical to that of the control specimen. This identical behavior implies restoration of the girder and an effective increase in ultimate capacity of 31.1% from the use of external post-tensioned CFRP rods. Deformability and ductility—The similarities in the performance of Specimens P2 (control) and RP3 (repaired) are shown in Fig. 12. From Fig. 12, it can be seen that failure of the CFRP rods for Specimen RP1 occurred at a deflection about eight times greater than L/800 (0.21 in. or 5.21 mm), the maximum allowable design deflection under service live loads for concrete bridge construction (AASHTO 2009). Therefore, although failure of the post-tensioned CFRP rods was brittle, failure of the beams occurred at a deflection much greater than any expected service load deflections. After failure of the CFRP rods, Specimen RP1 (repaired) exhibited a residual strength of approximately 97 kip (431 kN). This residual strength is evidence that complete catastrophic failure of the beam did not occur because of the reserve capacity and ductility of the original system. Additionally, it can be concluded from Fig. 12 that the residual strength in Specimen RP1 (repaired) after failure of the CFRP rods suggests that at large deflections, it would fail similarly to Specimen P2 (control)—from concrete compressive failure; the test for Specimen RP1 was terminated prematurely at a smaller deflection. Another measure of performance is the ductility of the repaired beams compared with the control beam. Ductility is provided by the mild steel present in the tension and compression zone of all three beams, as shown in Fig. 2. CFRP rods are brittle, and even though the amount of mild steel was the same, the amount of prestressing steel was less for the repaired beams; therefore, it is interesting to compare the ductility of the three beams. One definition of 392
Fig. 13—Member ductility of concrete beams prestressed by FRP by Abdelrahman et al. (1995). ductility for FRP reinforced beams is the method developed by Abdelrahman et al. (1995). As shown in Fig. 13, ductility is defined in terms of the equivalent displacement of the uncracked section and the displacement at ultimate and is given by the following expression
µ∆ =
∆2 ∆1
(1)
where Δ1 is the displacement of the uncracked section at a load equal to the ultimate load; and Δ2 is the displacement at failure. Using Eq. (1) and Fig. 12, the ductility of the control beam Specimen P2 is obtained as 8.1, and that of the repaired beams as 7.7 for RP3 and 7.3 for RP1. It is observed that the repaired beams are practically as ductile as the control beam. It should be noted that Specimen RP1 would have achieved greater ductility if the test had not been terminated. ANALYTICAL INVESTIGATION Conventional beam theory can be used to predict the ultimate load of the specimens tested in this research. The nominal theoretical capacity of control Specimen P2 was calculated to be 73 kip (330 kN). Compared with the actual ultimate load of 104 kip (463 kN), the ratio of actual to theoretical ultimate load is 1.42, indicating that the theoretical prediction is in good agreement with the actual value, and the ACI Structural Journal/March-April 2014
Table 1—Data for calculation of theoretical values at ultimate Specimen
fp_CFRP, ksi (MPa)
cu, in. (mm)
Aps, in.2 (mm2)
a, in. (mm)
Mu, kip-ft (kN-m)
RP1 (repaired)
155 (1069)
2.51 (63.8)
0.393 (254)
1.63 (41.4)
220 (298)
PR3 (repaired)
162 (1117)
2.22 (56.4)
0.306 (197)
1.44 (36.6)
196 (266)
design is conservative. To determine the theoretical capacity of Specimens RP1 and RP3, the stress in the CFRP rods at ultimate should first be determined. Previous research for unbonded steel tendons has shown that strain compatibility can be used to analyze the tendons as if they were bonded, and then apply a strain reduction factor to account for the tendons being unbonded (Naaman and Alkhairi 1991). It has been suggested that this method of using a strain reduction factor could also be applied to FRP tendons (Naaman et al. 2002; ACI Committee 440 2004); the stress at ultimate in unbonded FRP tendons is given as
d f p _ CFRP = f pe _ CFRP + Ωu ECFRP e cu CFRP − 1 cu
(2)
where cu is the depth to the neutral axis at ultimate; dCFRP is the depth to the CFRP rods, 15 in. (381 mm); ECFRP is the modulus of elasticity of the CFRP rods, 22,500 ksi (155 GPa); fp_CFRP is the stress in the CFRP rods at ultimate; fpe_CFRP is the effective prestress in the CFRP rods, 109 ksi (752 MPa); Ωu is the strain reduction factor; and εcu is the failure strain of concrete in compression, 0.003 in./in. (mm/mm). Suggested values for the strain reduction factor depend on the type of loading. The research presented in this paper is best described as center point loading because the distance between loading points was only 30 in. (762 mm) compared with an unbraced length of 13ft, 8 in. (4.17 m). The strain reduction factor—standardized to likely produce a conservative predicted value—for center point loading is given as 1.5 Ωu = L / dCFRP
(3)
− B + B2 − 4 AC 2A
A = 0.85 fc′bb1
(
(4a)
)
B = ACFRP ECFRP e cu Ωu − f pe _ CFRP − As f y − Aps f ps (4b)
Ωu =
C = − ACFRP ECFRP e cu Ωu dCFRP
In the aforementioned expressions, ACFRP is the area of CFRP rods, 0.22 in.2 (142 mm2); Aps is the area of internal ACI Structural Journal/March-April 2014
A 0.21 + 0.04 CFRP int + 0.04 L / dCFRP ACFRP tot
(5)
where ACFRP int is the area of internal CFRP tendons; and ACFRP tot is the total area of CFRP tendons. Additionally, to account for the change in an external tendon’s eccentricity, the effective CFRP tendon depth can be found using
where L is the unbraced length of the beam, 13 ft, 8 in. (4.17 m) (Naaman et al. 2002; ACI Committee 440 2004). The use of Eq. (3) for specimens in this research results in a strain reduction factor of 0.137. Additionally, appropriate values of cu can be calculated from the following equation cu =
steel prestressing strands; As is the area of tensile mild steel reinforcement, 0.62 in.2 (400 mm2); b is the beam width, 12 in. (305 mm); fc′ is the compressive strength of concrete, 10.0 ksi (69 MPa); fps is the prestressing force in the internal steel strands, 243 ksi (1.68 GPa); fy is the yield stress of mild steel reinforcement, 60 ksi (414 MPa); and β1 is 0.65. The use of Eq. (4) produces cu values of 2.51 and 2.22 in. (63.8 and 56.4 mm) for Specimens RP1 and RP3, respectively. The resulting CFRP rod ultimate stresses predicted by Eq. (2) are 155 ksi (1069 MPa) for Specimen RP1, and 162 ksi (1120 MPa) for Specimen RP3, which are conservative compared with the actual values of measured ultimate CFRP rod stress (from strain gauges on the rods) of 169 and 183 ksi (1163 and 1263 MPa), respectively. The analytical results for ultimate stress are summarized in Table 1. An alternative strain reduction factor for external, unbonded steel tendons has also been developed, and it had been recommended for FRP tendons (Aravinthan et al. 1997; ACI Committee 440 2004). This alternative strain reduction factor is given as
de _ CFRP = dCFRP Rd
(6)
where Rd is the depth reduction factor given as
L S − 0.19 d ≤ 1.0 Rd = 1.14 − 0.005 L dCFRP
(7)
with the deviator spacing Sd equal to the span L for specimens in this research because no deviators were used. For the case of specimens in this research, the value of Rd is 0.895. The predicted ultimate CFRP tendon stresses from Eq. (2) using the alternative strain reduction factor from Eq. (5) are 135 and 138 ksi (931 and 951 MPa) for Specimens RP1 and RP3, respectively. Similar to the results from the application of the strain reduction factor of Eq. (3), these predictions are conservative. A comparison of the applicability of the two strain reduction factors can be made when considering the actual and predicted ultimate CFRP tendon stresses for Specimens RP1 and RP3. The measured CFRP tendon stresses, the predicted, and the error are shown in Table 2. Although both strain reduction factors produced 393
Table 2—Measured and predicted ultimate tendon stresses
Specimen
Measured CFRP tendon stress at ultimate, ksi (MPa)
Predicted CFRP tendon stress at ultimate from Eq. (3), ksi (MPa)
Error in prediction from Eq. (3), %
Predicted CFRP tendon stress at ultimate from Eq. (5), ksi (MPa)
Error in prediction from Eq. (5), %
RP1 (repaired)
169 (1163)
155 (1069)
8
135 (931)
18
PR3 (repaired)
183 (1263)
162 (1120)
11
138 (951)
24
conservative ultimate stress predictions, the strain reduction factor from Eq. (3) results in the smallest error, indicating that it works best for specimens in this research. Conventional beam theory leads to the following equation for ultimate moment capacity a a Mu = Aps f ps d ps − + As f y d − 2 2
a + ACFRP f p _ CFRP dCFRP − 2
(8)
where Mu is the ultimate moment capacity; a is the depth of the equivalent compression stress block equal to β1cu; and d is the depth to the mild steel reinforcement, 15 in. (381 mm). Next, from the ultimate moment capacity, the ultimate load Pu can be found from the following equation Pu =
4 Mu
(L − s)
(9)
where s is the spacing between load points, 30 in. (762 mm), as shown in Fig. 3. From Eq. (9), the theoretical ultimate capacity is 79 kip (351 kN) for Specimen RP1 and 70 kip (311 kN) for Specimen RP3 when implementing the predicted CFRP tendon stresses at ultimate from the use of Eq. (3). Consequently, the corresponding ratios of actual to theoretical ultimate load are 1.42 and 1.46 for Specimens RP1 and RP3, respectively. Similar to the ratio of 1.42 found for control Specimen P2, these ratios show that theoretical ultimate loads are in good agreement with actual measured ultimate loads, and that the design is conservative. A summary of the experimental and theoretical ultimate loads is given in Table 3. Furthermore, the ratios of actual to theoretical ultimate load and the percentage of error between the actual and theoretical stress in the CFRP rods at ultimate indicate that Eq. (2) and (3) are appropriate for predicting the stress in the CFRP rods at ultimate when calculating the theoretical ultimate capacity of prestressed concrete members repaired with the system of unibody clamp anchors, mechanical stressing device, and CFRP rods used in the current research. CONCLUSIONS Based on the experiments carried out in this research, it can be concluded that Specimens RP1 and RP3 were successfully repaired using an external post-tensioning system consisting of CFRP rods, unibody clamp anchors, and a mechanical stressing device. Repaired Specimens RP1 394
Table 3—Experimental and theoretical ultimate loads
Specimen
Experimental ultimate load, kip (kN)
Theoretical ultimate load from Eq. (3), kip (kN)
Ratio of experimental to theoretical ultimate load
P2 (control)
104 (463)
73 (325)
1.42
RP1 (repaired)
112 (498)
79 (351)
1.42
PR3 (repaired)
102 (454)
70 (311)
1.46
and RP3 showed an effective increase in ultimate strength of 20.6 and 31.1%, respectively, with respect to the damaged condition. This increase in ultimate strength of Specimens RP1 (repaired) and RP3 (repaired) compared with Specimen P2 (control) demonstrate that external post-tensioned CFRP rods are able to compensate for partial or complete removal of a prestressing strand. Although the repaired Specimen RP1 failed as a result of rupture of the external post-tensioned CFRP rods, this rupture occurred at deflections much greater than those expected from service loads. Additionally, residual capacity was present after CFRP rod rupture. This is significant in that catastrophic beam failure did not occur even though the CFRP rods failed in tension. The repaired beams were essentially as ductile as the control beam, because the mild steel and the remaining prestressing steel dominated the ductility of the damaged beams. It was found that theoretical expressions from the literature may be used to predict the stress at ultimate in the CFRP tendons used in this research as well as the ultimate capacity of the beams, with Eq. (3) being the preferred strain reduction factor even though it was originally developed for steel tendons. Post-tensioning CFRP rods using unibody clamp anchors and a mechanical stressing device is a viable technique for the repair of concrete beams with severe damage to internal steel prestressing tendons. It is recommended that further studies be carried out to assess the system and its feasibility for general use. It is also recommended that further studies be carried out to test unibody clamp anchors made of stainless steel and to determine the suitability of unibody clamp anchors for use as a coupling device for CFRP rods. The successful implementation of the anchors and CFRP rods in this research suggests that the anchors could potentially be used to join two sections of CFRP rod, facilitating post-tensioning of longer spans that are typical of actual bridges. Although the repair system investigated in this paper was successful, it requires access to the end of the beam, which is not always available in field applications. For use of the CFRP repair ACI Structural Journal/March-April 2014
system implemented in this research, however, only 18 in. (0.46 m) of free space is required behind the beams. ACKNOWLEDGMENTS
The authors wish to acknowledge the financial support of the Utah Department of Transportation and the University of Utah. The authors would also like to acknowledge the contributions of Hanson Structural Precast and Sika, Inc. In addition, the authors would like to thank M. Bryant and R. Liu for their assistance in specimen fabrication and testing.
NOTATION
ACFRP = area of post-tensioned CFRP rods ACFRP int = area of internal post-tensioned CFRP rods ACFRP tot = total area of post-tensioned CFRP rods Aps = area of internal steel prestressing strands A s = area of tensile mild steel reinforcement a = depth of equivalent compression block cu = depth to neutral axis at ultimate d = depth of mild steel reinforcement dCFRP = depth to CFRP rods de_CFRP = effective depth to CFRP rods ECFRP = modulus of elasticity of CFRP rods fc′ = compressive strength of concrete fp_CFRP = stress in CFRP rods at ultimate fpe_CFRP = effective prestress in CFRP rods fps = prestressing force in internal steel strands fy = yield stress of mild steel reinforcement L = unbraced length of beam Mu = ultimate moment capacity Rd = depth reduction factor Sd = deviator spacing s = spacing between load points on top of beam β1 = factor relating depth of equivalent compression block to depth of neutral axis Δ1 = displacement of uncracked section at load equal to ultimate load Δ2 = displacement at failure εcu = failure strain of concrete in compression Ωu = strain reduction factor
AUTHOR BIOS
Clayton A. Burningham is a PhD Candidate in the Department of Civil and Environmental Engineering at the University of Utah, Salt Lake City, UT. He received his bachelor’s and MS degrees from the University of Utah. His research interests include repair of reinforced and prestressed concrete structures and post-tensioning carbon fiber-reinforced polymer materials. ACI member Chris P. Pantelides is a Professor in the Civil and Environmental Engineering Department at the University of Utah. His research interests include seismic design and rehabilitation of reinforced concrete,
ACI Structural Journal/March-April 2014
precast and prestressed concrete buildings and bridges, and the application of fiber-reinforced polymer composites. Lawrence D. Reaveley is a Professor and former Department Chair of Civil and Environmental Engineering at the University of Utah. He received his bachelor’s and MS degrees from the University of Utah, and his PhD from the University of New Mexico, Albuquerque, NM. His research interests include structural dynamics, with an emphasis on earthquake engineering and seismic rehabilitation.
REFERENCES
AASHTO, 2009, “AASHTO LRFD Bridge Design Specifications,” fourth edition, American Association of State Highway and Transportation Officials, Washington, DC, 1518 pp. Abdel Aziz, M.; Abdel-Sayed, G.; Ghrib, F.; Grace, N.; and Madugula, M., 2005, “Analysis of Concrete Beams Prestressed and Post-Tensioned with Externally Unbonded Carbon Fiber Reinforced Polymer Tendons,” Canadian Journal of Civil Engineering, V. 31, pp. 1138-1151. Abdelrahman, A. A.; Tadros, G.; and Rizkalla, S. H., 1995, “Test Model for the First Canadian Smart Highway Bridge,” ACI Structural Journal, V. 92, No. 4, July-Aug., pp. 451-458. ACI Committee 440, 2004, “Prestressing Concrete Structures with FRP Tendons (ACI 440.4R-04) (Reapproved 2011),” American Concrete Institute, Farmington Hills, MI, 35 pp. ACI Committee 440, 2012, “Guide Test Methods for Fiber-Reinforced Polymer (FRP) Composites for Reinforcing or Strengthening Concrete and Masonry Structures (ACI 440.3R-12),” American Concrete Institute, Farmington Hills, MI, 23 pp. Aravinthan, T.; Mutsuyoshi, H.; Fujioka, A.; and Hishiki, Y., 1997, “Prediction of the Ultimate Flexural Strength of Externally Prestressed PC Beams,” Transactions of the Japan Concrete Institute, V. 19, pp. 225-230. Burningham, C., 2011, “Development of a Carbon Fiber Reinforced Polymer Prestressing System for Structural Applications,” PhD dissertation, University of Utah, Salt Lake City, UT, 103 pp. El-Hacha, R., and Elbadry, M., 2006, “Strengthening Concrete Beams with Externally Prestressed Carbon Fiber Composite Cables: Experimental Investigation,” PTI Journal, V. 4, No. 2, pp. 53-70. Elrefai, A.; West, J.; and Soudki, K., 2007, “Strengthening of RC Beams with External Post-Tensioned CFRP Tendons,” Case Histories and Use of FRP for Prestressing Applications, SP-245, R. El-Hacha and S. H. Rizkalla, eds., American Concrete Institute, Farmington Hills, MI, pp. 123-142. Naaman, A., and Alkhairi, F., 1991, “Stress at Ultimate in Unbonded Post-Tensioning Tendons: Part 2—Proposed Methodology,” ACI Structural Journal, V. 88, No. 6, Nov.-Dec., pp. 683-692. Naaman, A.; Burns, N.; French, C.; Gamble, W.; and Mattock, A., 2002, “Stresses in Unbonded Prestressing Tendons at Ultimate: Recommendation,” ACI Structural Journal, V. 99, No. 4, July-Aug., pp. 518-529. Täljsten, B., and Nordin, H., 2007, “Concrete Beams Strengthened with External Prestressing Using External Tendons and Near-Surface-Mounted Reinforcement,” Case Histories and Use of FRP for Prestressing Applications, ACI SP-245, R. El-Hacha and S. H. Rizkalla, eds., American Concrete Institute, Farmington Hills, MI, pp. 143-164.
395
NOTES:
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S35
Study of Composite Behavior of Reinforcement and Concrete in Tension by John P. Forth and Andrew W. Beeby This paper aims to further the understanding of the interaction between reinforcement in tension and the surrounding cracked concrete. This is achieved using the elastic analysis of axisymmetric prisms reinforced with a single central bar. As a preliminary to the analyses, the behavior of axially reinforced prisms is described based on previous experiments. This preliminary analysis confirms that the elastic analysis adopted in this investigation is reasonable. Two analytical exercises are described: the first assumes no slip, plasticity, or internal cracking at the interface between the steel and the concrete; the second introduces internal cracking and debonding between ribs. The first analysis indicates that shear deformation of the surrounding concrete accounts for a substantial proportion of the surface crack width, and therefore that this form of deformation cannot be ignored in crack prediction formulae. The second analytical exercise shows that the internal cracking model described by Goto is appropriate. Keywords: axisymmetric tension specimens; cover; crack width calculations; cracking mechanisms; finite element modeling; shear distortions.
INTRODUCTION The objective of this study is to gain greater understanding of the interaction of reinforcement and concrete in tension. The analysis models used have been kept as simple as possible; the approach has been limited to pure elastic behavior, and an assumed internal cracking pattern, based on the work by Goto,1 has been adopted (rather than use a nonlinear finite analysis software based on, for instance, a smeared cracking approach where cracks are predicted regions of damaged material with degraded properties). This keeps difficulties in interpretation to a minimum, though it is recognized that concrete does not necessarily behave in a perfectly elastic manner. Use of elastic modeling, where the cracks being studied are open, is not so unreasonable as might be thought by some. Extensive data obtained by Scott and Gill2 and Beeby and Scott3-5 suggest that much of the behavior revealed during tension tests is close to what would be expected from an assumption of elastic-brittle behavior for concrete in tension. This is effectively what will be assumed in the study. RESEARCH SIGNIFICANCE In reinforced concrete, the interaction between reinforcement in tension and the surrounding concrete is still not fully understood. Two internal failure mechanisms, pure slip and internal cracking, form the basis of three approaches that exist in the codes to model the tension zone behavior under service loads. The models presented in this investigation are based only on Goto’s internal cracking mechanism. These models predict the experimental behavior of tension ACI Structural Journal/March-April 2014
Fig. 1—Load-deformation response of Specimen 10T12 (figure taken from Reference 4). members quite effectively. The simpler model proposed herein further confirms the concept that crack width is a function of the shear deformation of the concrete cover. BASIC BEHAVIOR AS REVEALED BY TESTS The information used herein is taken from Reference 4. Initially, strain data for Specimen 100T12 will be presented, as this gives a convenient illustration of a number of aspects of behavior. Figure 1 shows the load-average reinforcement strain response for this specimen. It should be noted that the response is not a continuous smooth curve as is commonly plotted, but is made up of a series of linear segments separated by a sudden increase in strain on the occurrence of each crack. Up to a load of approximately 7.868 kip (35 kN), these linear segments, extrapolated backwards, can be seen to pass through the origin. The behavior of the tension specimen with a given number of cracks is thus elastic. Using the computer to produce best fit lines for each segment enables the stiffness of the specimen to be established for each crack configuration. Figure 2 shows this compliance plotted against the number of cracks. There is a linear relationship between stiffness and number of cracks. This implies that the formation of each crack reduces the stiffness of the element by a constant amount. The final point for four cracks does not quite fit the linear relationship. This point is obtained from the behavior immediately after formation of the fourth crack. Figure 1 shows that, at higher loads, there are two further sudden increases in strain. These increases were not related to the formation ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-148, doi:10.14359.51686564, was received May 10, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
397
Fig. 2—Stiffness of element as function of number of cracks for Specimen 100T12. Fig. 4—Concrete stresses at right end of Specimen T16B1. (Note: 1 MPa = 145 psi; 1 kN = 0.225 kip; 1 mm = 0.0394 in.)
Fig. 3—Specimen T16B1: reinforcement strains along bar at various loads. (Note: 1 kN = 0.225 kip; 1 mm = 0.0394 in.) of visible surface cracks, and it may be speculated that they arise from some form of internal failure. It should be noted that both these increases in strain occurred only at very high levels of stress in the reinforcement (>58.02 ksi [400 MPa]). Figures 1 and 2 show that the behavior between cracking events is generally elastic, and this is the assumption that will effectively be made in the finite element analyses. The next aspect of behavior to be considered is the variation of steel stress or concrete stress with distance from a crack. Figure 3 shows the variation of strain along a reinforcing bar for various levels of axial load. Various pieces of information can be gleaned from this figure. First, over a considerable part of the distance from a crack or the free end of the specimen, the variation in strain is very close to linear. This can possibly be seen better from Fig. 4, which shows the variation in concrete stress over the end 11.81 in. (300 mm), enlarged for two levels of load. At the lower load level, there is a clear curve over the part of the bar where the stress is close to that for uncracked concrete. This is not clear for the higher load, where it would not be unreasonable to consider the relationship to be linear over the whole distance to midway between cracks. Secondly, even at the low level of load, which is below the cracking load for the specimen, the strain in the reinforcement over most of the length affected by the end of the specimen So is considerably greater than the cracking strain of the concrete, which can be assumed to be in the range of 100 to 150 × 10–6. This implies that some form of internal failure occurs over the whole length So as soon as cracking occurs. 398
Fig. 5—Relationship between So and cover. (Note: 1 mm = 0.0394 in.) A critical factor in crack prediction theories is the definition of the transfer length. This is the distance on one side of a crack over which the stress in the reinforcement is affected by the crack. In References 3 through 5, this is represented by the symbol So. In some papers, the symbol ltr is used. There are various ways of estimating So from experimental results. Most of these are indirect and assume a relationship, for example, between So and crack width. The work reported in References 3 through 5, however, recorded the variation in strain at closely spaced intervals along the reinforcing bar, permitting the direct measurement of So. Even with these tests there are difficulties, as can be seen from the strain variation for the 4.496 kip (20 kN) level of load shown in Fig. 4. It is difficult to define exactly the point where the crack no longer influences the strain. The method used to establish a value for So is illustrated in Fig. 4, where So is defined as the distance from the crack (or free end of the bar) and the point where a best fit line through the strains intersects the strain in the uncracked concrete. This is clearly an imperfect procedure, but it is consistent and seems to agree well with the calculation of So by indirect means. A good, straight line relationship was found between So and cover. This is illustrated in Fig. 5, which also includes the equation for the straight line. An issue that has been studied by a number of researchers, but is generally ignored by those developing theories of ACI Structural Journal/March-April 2014
Fig. 6—Schematic illustration of situation analyzed. cracking, is the shape of the crack (that is, how the width of a crack varies between the bar surface and the surface of the concrete). An assumption generally seems implicit in cracking formulae based on the classical theory that the crack width at the concrete surface is the same as that at the bar surface. There is now ample evidence that this is not the case. The research evidence has been reviewed in Reference 6, and this shows that the cracks are tapered, being much smaller near the bar surface than at the concrete surface. Though the results are highly variable, it can be concluded that the width at the concrete surface is at least twice that near the bar surface. SIMPLE ELASTIC ANALYSIS WITHOUT INTERNAL CRACKING Initially, a simple two-dimensional analysis was performed on an axially reinforced circular cross section prism to give some idea of the stress and deformation conditions around a bar. The axial symmetry greatly simplified the analysis. A fully elastic analysis of the area surrounding a bar, assuming no slip between the bar and the concrete, was considered. The situation analyzed is illustrated in Fig. 6, in which ws is the surface crack width. Analyses were carried out using axisymmetric elements. For the initial analysis, a 0.79 in. (20 mm) diameter f bar was considered with 1.97 in. (50 mm) cover c. Square elements of 0.20 in. (5 mm) were used, and a length from the free face up to the fixed end of 5.91 in. (150 mm) was assumed. A uniform stress of 14.51 kip/in.2 (100 MPa) was applied to the free end of the bar. Figure 7 shows the stress distribution in the concrete along the specimen obtained in two ways: the stress in the concrete on the outer face (that is, the concrete surface), and the average stress in the concrete. The average stress was calculated by taking the force in the reinforcing bar at each 0.20 in. (5 mm) section, deducting this from the total applied force at the free end, and dividing this difference by the area of the concrete. In algebraic terms, if T is the tension force applied at the free end, the bar area is As, and the concrete area is Ac, the stress in the bar at any section a distance x from the crack is ssx and the average stress in the concrete is scx then, by equilibrium, because the force at section x is T, the stress in the concrete is given by
ACI Structural Journal/March-April 2014
Fig. 7—Variation in calculated stresses in concrete with distance from free end. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.; S*0s is surface spacing; S*0m is mean spacing.) scx = (T – Asssx)/Ac (1) The average stress in the concrete was calculated in this way because it corresponds to the method of concrete stress calculation used in References 3 through 5. It is also effectively what is used in many theoretical derivations of crack prediction formulas. There are several interesting points which arise from Fig. 7. First, as might be expected, the surface stress is not the same as the average stress, but is considerably lower over almost the whole of the length analyzed. So for the surface is thus different than So for the average stress, with the surface value being considerably longer. Straight lines have been drawn in passing through the origin and the point where the calculated curves reach two-thirds of the homogeneous stress. This is simply done to permit a simple visual comparison of the curves. It should also be noted that the surface is actually in compression for the area closest to the crack face. Second, the stress in the concrete does not actually reach the stress calculated for a homogeneous section. Thus, there is no absolutely clear definition of So, as is assumed in all theoretical equations for predicting cracking. This is not necessarily a critical point, but it may be worth remembering that So is an effective value rather than an absolute value. Figure 8 shows the variation in the deformed shape of the free end over the height of the crack from the bar surface to the specimen surface. Quantitative comparisons cannot directly be made in this case, as the geometries of the available experimental specimens are somewhat different from that analyzed. The deformation at the surface in Fig. 8 corresponds to a crack width of 0.0019 in. (0.047 mm). Analyses have been carried out for different covers, and Fig. 9 shows the calculated crack widths as a function of cover. Crack width decreases with a decrease in cover. The decrease is not linear as suggested from the experimental data3-5; however, certain factors should be borne in mind. The finite element analyses are elastic, and therefore, any specimen having a geometrically similar cross section to the one for which the crack width has been calculated will give a crack width that can be calculated by direct scaling from the previously calculated width. Thus, for example, the crack 399
Fig. 8—Variation in calculated crack width with distance from bar surface. (Note: 1 mm = 0.0394 in.) width for any specimen with a value of c/f of 2.5 will lie on a straight line joining the point for c/f = 2.5 to the origin. This applies for any other value of c/f. Thus, all results for any specimens with c/f in the range 1 to 2.5 will lie between the two dashed lines drawn in Fig. 9. If a relatively random set of tension specimens are analyzed, the result, when plotted on a graph such as Fig. 9 will, to the engineering eye, be accepted as giving a linear relationship between cover and crack width with some relatively small level of scatter. Figure 10 aims to make an approximate quantitative comparison between calculated and experimental crack widths. The test specimens, from Farra and Jacccoud,7 were 3.94 in. (100 mm) square and reinforced with a single axial 0.79 in. (20 mm) bar. The cover was thus 1.57 in. (40 mm), and results from an analysis for 1.57 in. (40 mm) cover have been used in the comparison. It should be remembered, however, that the experimental specimens had a square cross section, whereas this analysis considered a circular cross section. It can be seen that the analysis underestimates the maximum crack width by approximately 30%. This is to be expected, as no account has been taken in this analysis of internal failure (slip or internal cracking) which, as has been discussed previously, occurs and reduces the stiffness of the concrete in tension. This will be considered further in a following section. It seems likely that this initial simple analysis gives a lower-bound indication of the deformation of the tensile concrete, and hence, the estimate of the crack width. In reality, concrete in tension is not absolutely elastic-brittle,
400
Fig. 9—Variation in maximum surface crack width with cover. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.)
Fig. 10—Maximum crack widths from Farra and Jaccoud Specimens N-20-207 compared with finite element analysis. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) but will undergo some plastic deformation before rupture. This will result in the actual deformation of the concrete being greater than that calculated on the assumption of elasticity. Additionally, a short-term value has been used for Ec. There is likely to be some creep during the test that would result in further deformation of the concrete and steel, and hence higher calculated crack widths. Depending on the effect of these two factors, the calculated width could be closer to the experimental values. Overall, the analysis seems to have been very successful in predicting the general qualitative behavior of axially reinforced specimens.
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Fig. 11—Finite element model of axially reinforced tension specimen with internal cracks. ANALYSIS OF TENSION ZONE INCLUDING INTERNAL CRACKS As mentioned previously, some form of internal failure takes place over the whole of the length So from a very early load stage. There are two mechanisms that are commonly proposed for this internal failure: slip along the steel-concrete interface, and internal cracks forming at an angle to the axis of the bar. Slip is the most common mechanism invoked, and has been used as the basis for many crack prediction theories. The internal cracking mechanism was first illustrated by Goto,1 and was elaborated further by Beeby and Scott,4 whose model which will be investigated in this paper (it is believed that there are plenty of advocates of the slip model who can, if they wish, carry out further modeling of this option). It should be noted that the type of modeling that will be attempted herein will not prove that a particular model is the actual behavior; at best, it can simply show that the particular model gives a reasonable simulation of reality. Other models may exist that are as good or better. It could, however, show that a particular model was unreasonable. An axially symmetrical specimen was chosen for the analysis. Initially, the analysis will be carried out on a specimen the same basic size as that used to produce the results detailed in Fig. 7 and 8. It will now, however, also model a number of internal cracks. The length of the model specimen has been doubled to 11.81 in. (300 mm), partly because the length So was expected to be greater than in the case with no internal cracks, and partly because it was felt that the length used in the previous analysis may have been slightly short for the largest cover. The number of cracks, the angle of the cracks to the bar axis, and the length of the cracks is somewhat arbitrary, but is based on photographs from Goto1 and Otsuka and Ozaka,8 and the analysis presented in Beeby and Scott.4 Experimental work by Goto and others suggest that internal cracks form at each rib on the bar. The spacing used in the model analyzed herein is rather larger than the rib spacing for reasons of practicality. An angle of 60 degrees to the axis of the bar was chosen, although this angle could only be approximately maintained as the basic grid of 0.20 in. (5 mm) did not permit exactly 60 degrees to be maintained for all cracks. Furthermore, the aim was to use a linear decrease in crack height with distance from the crack face. Again, the 0.20 in. (5 mm) grid meant that this could only be achieved approximately. The elastic finite element model used is illustrated in Fig. 11 and 12. Others have carried out analyses aimed at studying internal ACI Structural Journal/March-April 2014
Fig. 12—Axisymmetric model created using OASYS-GSA software.
Fig. 13—Axisymmetric model: detail of assumed crack pattern. cracking (for example, Gerstle and Ingraffea9). The difference between those analyses and this analysis is that most of the other analyses have attempted to study the development of the internal cracking as a function of applied load, whereas in this study, to study a larger range of variables, a crack pattern has been assumed. The results from the analysis are shown in Fig. 13 to 18. Figure 15 shows a number of interesting changes from the stress results shown in Fig. 7 resulting from the element without internal cracks. First, the relationship between the average stress and distance from the crack is much closer to linear. It now models more closely the experimental result shown in Fig. 4. The deformed shape of the free end (Fig. 16), which is actually a tracing of the finite element analysis graphical output (Fig. 14) with the elements and nodes removed for clarity, is now possibly less similar to that obtained for the specimen without internal cracks and to that of the experimental specimen, but it is still reasonable. The surface 401
Fig. 16—Calculated deformation of specimen with seven internal cracks. (Note: Dimensions in mm; 1 mm = 0.0394 in.) Fig. 14—Axisymmetric model: deformed state. (Note: 1 MPa = 145 psi.)
Fig. 15—Concrete stresses calculated by finite element analysis for specimen with seven internal cracks. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) deformation corresponds to a crack width of 0.0031 in. (0.08 mm), 60% greater than that obtained for the specimen without internal cracks. This agrees closely with the experimental results, as can be seen from Fig. 17, which shows the same data as used for Fig. 10, but with the calculated line shown for the analysis with internal cracks. The predicted effect of cover is shown in Fig. 18, where it can be seen that a reasonably linear relationship is predicted between cover and surface crack width. There is, however, some scatter in these results, possibly due to the difficulty of modeling absolutely geometrically similar internal cracks in the analyses for the various covers. A further assessment of the performance of the model can be performed by considering the work by Broms10 and Beeby.11 Broms10 carried out a series of tests on short prisms and measured the longitudinal extension at various stress levels in the reinforcement. Results are presented in Reference 10 for a circular cross section specimen, 6 in. (152 mm) in diameter and 8 in. (203 mm) long with a central 1 in. (25 mm) diameter bar. An elastic analysis has been carried out for this specimen, and Fig. 19 shows the experimental 402
Fig. 17—Maximum crack widths from Farra and Jaccoud Specimen N-20-207 compared with finite element analysis, with and without internal cracks. (Note: 1 mm = 0.0394 in.; 1 MPa = 145 psi.)
Fig. 18—Predicted maximum crack width as function of cover for analyses including internal cracks. (Note: 1 mm = 0.0394 in.) and calculated results for two levels of stress. The experimental results have been scaled from a figure in Broms’ paper.10 It can be seen that, in this case, the experimental results exceed the calculated results by approximately 20%. The general trend of the results, however, is well reflected by the calculations. This is not in absolute agreement, but it is ACI Structural Journal/March-April 2014
Fig. 19—Comparison of calculated and measured crack widths for Brom’s Specimen T-C-5.10 (Note: 1 mm = 0.0394 in.; 1 MPa = 145 psi.)
Fig. 20—Comparison of calculated and measured overall extension for specimen reported in Reference 11. (Note: 1 mm = 0.0394 in.; 1 MPa = 145 psi.)
probably within the range that could be covered by judicious adjustment of the model. A cylindrical specimen was tested by Beeby11 where the overall extension of a 5.91 in. (150 mm) diameter specimen with an axial 0.87 in. (22 mm) bar at various distances from the bar surface were measured. This has been analysed, and the extensions scaled off the figure presented in Reference 11. Figure 20 shows the measured extensions compared with the finite element calculations for two levels of steel stress. Agreement between experiment and calculation is slightly better than for Broms10 in Fig. 19, though the calculation, again, tends to underestimate the measured results. The introduction of the internal cracks (Fig. 12 to 14) has, in general, resulted in an improved agreement with the experimental behavior, and does suggest that the internal cracking model is a reasonable model for the behavior of tension zones. The analysis is clearly capable of further refinement, and has only been carried far enough to demonstrate its inherent reasonableness.
tions implicitly assume that this shear deformation is negligible. The analyses show that this is not so; the elastic shear deformation of the concrete in the analyses reported herein accounts for around two thirds of the crack width. Had other material factors, such as creep or inelasticity of the concrete in tension, been taken into account in the analyses, the shear deformations and their contribution to the crack widths would have been even greater. This substantial contribution of the shear deformation of the cover concrete seems inescapable, and suggests that any approach to the prediction of crack widths that ignore this are fundamentally flawed. In the second analysis, the output from the model with internal cracks generally agreed with the experimental data, where comparisons could be made. This suggests that the internal cracking model of behavior can provide a good model of cracking behavior. It does not prove that the mechanism accommodating excess tensile strains above those which the concrete can support in tension is internal cracking; it shows that it is a viable alternative to the bondslip model, and should not be dismissed. The analyses carried out are somewhat limited, and can be considered to make a prima facie case for the reasonableness of the internal cracking model rather than a fully developed analytical study. Some of the more obvious limitations of the model are given as follows. • Circular cross sections are analysed, not square or rectangular ones. Due to difficulties in manufacture, very few circular specimens have been made and tested; thus, it is not possible to compare the analytical results rigorously with test results that are almost all from specimens with square or rectangular cross sections. • Location and size of internal cracks is somewhat arbitrary. As mentioned in a previous section, no attempt has been made to refine the form of the internal cracking. From the existing experimental evidence, the pattern assumed seems reasonable, but it cannot be said to be rigorously justified. • Rib pattern. By its nature, the axisymmetric analysis assumes that the ribs are perpendicular to the bar axis and extend round the full circumference of the bar. This is not normally so for modern ribbed bars, where the ribs tend to be staggered. There is also frequently
DISCUSSION Elastic analyses Two basic analyses have been described in this paper. In the first, the concrete is considered to remain elastic and uncracked, and complete bond is assumed between the reinforcement and the concrete. In the second, a pattern of internal cracking has been assumed, based on the findings of Goto.1 In neither of the analyses is any form of bond-slip relationship assumed; thus, bond-slip can have no influence on the results obtained. In the first analysis (without internal cracking), it was expected that the predicted crack widths would be less than obtained experimentally, and this proved to be the case. Nevertheless, the analyses were not trivial, and the results illustrate a significant point that has commonly been ignored. If a shear stress is applied to a material, then shear strains and displacements occur. Bond stress is simply a shear stress, and therefore, the concrete surrounding a bar in the region of a crack undergoes shear deformations. Though this has not been shown to be explicitly stated, the classical theories of cracking that lie behind many crack prediction equaACI Structural Journal/March-April 2014
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Table 1—Comparison of crack widths at center and near corner of axially reinforced tension specimens (from Reference 12)
Mean values of w/e
5% values of w/e
Specimen
B
a
b
b/a
a
b
b/a
Z2
80
76
113
1.48
174
203
1.17
Z6
130
104
171
1.64
253
354
1.40
Z7
180
91
254
2.79
231
535
2.32
Z9
230
101
259
2.56
282
580
2.06
analysis of three-dimensional specimens (with the exception of axisymmetric situations). Issues relating to development of valid design formulae for crack width prediction It would be helpful for further discussion if a brief outline is given of the development of crack theories and code provisions. The earliest developed theory of cracking assumed that the widths of cracks accommodated slip between the bar and the concrete. The theory ignored any contribution to the crack width from the shear deformation of the cover concrete. To develop equations, it required assumptions be made about the development of the bond stresses as a function of slip. Many different assumptions were considered, but all resulted in a basic equation of the form
Notes: B, a, and b, are in mm; 1 mm = 0.0394 in.; w/e is average crack width/average surface strain.
w = kffcte/tr (2)
a longitudinal rib. The result of this is that, in reality, the pattern of internal cracks may be considerably more complicated than is modeled in this analysis. The spacing of the internal cracks, which would be expected to follow the spacing of the ribs, is too large in the model.
where w is crack width (variously defined); k is a constant; fct is the tensile strength of the concrete; e is strain (variously defined); f is the bar diameter; r is reinforcement ratio (variously defined); and t is bond strength. Many design provisions have been based directly on this equation, including those in the CEB-FIP Model Code 1990.18 In 1965, Broms19 and Broms and Lutz20 published a radically different theory which assumed that the crack width arose entirely from the shear deformation of the cover concrete. The following formula was developed
•
Issues requiring further study What is measured when crack widths are being investigated is the crack width on the surface. It is found that the surface crack width is strongly dependent on where the cracks are measured relative to the position of the reinforcement. If the cracks are measured at points on the surface directly over the bar, they are found to be substantially smaller than if they were measured, for example, close to the corner of an axially reinforced prism. The variation is less in situations where there are multiple bars and the crack width over the bars is compared with that at mid-spacing. This behavior is illustrated in Table 1, containing data from Reference 12. This effect seems perfectly rational for crack widths resulting from shear deformation of the concrete; the shear displacement will increase with increasing distance from the bar in any direction. Because the corner of the specimens used in Table 1 are further from the bar than a point directly over the bar, the deformation will be greater, and the crack width larger. This effect was recognized by Broms10 and in the work carried out at the Cement and Concrete Association.12,13 It is implicitly included in the ACI code14 formula and taken into account directly in the UK code.15 The analyses performed herein have been exclusively concerned with members subjected to pure tension. There is evidence that flexural members behave rather differently. Studies by Beeby16 showed that, in shallow members, such as slabs, the depth of the tension zone has a significant effect on the crack width. This is explicitly taken into account in the UK code,15 and is also recognized in Eurocode 2.17 These effects have not been investigated in this study because the finite element package used did not permit the
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wav = 2tes (3) or wmax = 4tes where wav is the average crack width; wmax is the maximum crack width; t is distance from the center of the bar to the point on the surface where the crack width is considered; and es is average strain of the steel. For multiple bars, t was modified to te, an effective distance, which is defined, for bottom cracks, as 3 (tb A), where tb is the distance from the bottom of the beam to the center of the lowest layer of bars, and A is the area of concrete immediately surrounding the tension reinforcement. This formula, along with many others, was tested against the available crack width data by Gergely and Lutz21 and shown to be the best available at the time. The formula has formed the basis of the ACI code14 crack width control provisions ever since. At the same time as the work being carried out at by Broms, Lutz and Gergely,19-21 a major series of tests were carried out at the Cement and Concrete Association in the UK.13 The first series of tests consisted of 105 beams, and the results were with the publishers at the time that Broms’19 paper appeared. The paper13 concluded that crack width could be predicted by the formula
ACI Structural Journal/March-April 2014
wmax = 3.3acrem (4)
where wmax is the maximum crack width; acr is the distance from the point where the crack width is being considered to the surface of the nearest bar; and em is the average strain at the level where the width is considered. It can be seen that, while acr is slightly larger than t in Broms’19 equation and that the equation aims to predict the maximum width rather than the average, the Cement and Concrete Association13 and Broms’19 basic formula are almost the same. Like Broms’19 theoretical approach, the formula assumes that there is no bond failure or slip at the bar-concrete interface, and that the crack width results entirely from the deformation of the cover concrete. The Cement and Concrete Association13 work was extended over the following few years by Beeby,22-24 resulting in modifications to deal with bar spacing and the effect of the depth of the tension zone. It was recognized that some mechanism was necessary to accommodate the strains in the concrete in excess of the tensile strain capacity of the concrete, and it was proposed that the form of cracking identified by Goto1 provided that mechanism. The resulting formula was simplified somewhat, and has been used in UK codes15 since 1972. This formula is w = 3acrem/{1 + 2(acr – c)/(h – x)} (5) where c is the cover to the face of the member where the crack width is being considered; h is the overall depth of the section; and x is the neutral axis depth (depth of the compression zone). During the same time, Ferry-Borges25 developed a formula that combines the theoretical ideas behind the classical bond-slip model and the shear deformation models. His formula is sav = k1c + k2f/r (6) wav = savem where sav is the average crack spacing. The term k1c is justified in Reference 25 by the following statement: “The need to consider the influence of the thickness of the cover, c, is easy to understand. In fact, even if perfect bonding between concrete and steel existed, the mean distance between cracks would not be zero but proportional to c.” This formula was adopted in the CEB Model Code 1978,26 and also in Eurocode 2.17 The object of this survey of approaches to crack width calculation is to point out that there are three basic approaches used in codes: 1. The assumption that the crack width arises purely from slip. This is used in a number of codes and, notably, in CEB-FIB Model Code 199018; 2. The assumption that there is no significant slip and that the crack width arises entirely from the deformation of the concrete around the bar. Bond and slip do not feature
ACI Structural Journal/March-April 2014
in formulae derived on this basis. Strains beyond those supportable by concrete in tension are accommodated by a reduction in the stiffness of the cover concrete by internal cracking. This is the case for the UK15 and ACI codes14 and the codes of any country that basically follow either British or American practice; and 3. The assumption that the crack width arises from a combination of slip and deformation of the concrete. This is true of CEB-FIB Model Code 197824 and Eurocode 2,17 and will become the case for all countries which either adopt Eurocode 2 or base their national codes on Eurocode 2. From this investigation, it is apparent that a significant proportion of the crack width is due to the deformation of the concrete surrounding the bar. Therefore, Item 1 mentioned previously is not tenable as a basis for a rational crack prediction formula; Items 2 and 3 are tenable depending on whether or not slip plays a significant role. The paper does not aim to show which of these possibilities is closest to the truth, merely that the concept of crack width being a function of the deformation of the cover concrete is reasonable. CONCLUSIONS In this paper, a number of simple elastic finite element analyses of the concrete in tension surrounding tensile reinforcement, in members subject to pure tension, are described and the results compared with the behavior of actual tension specimens, as revealed by experiment. The study leads to the following conclusions. 1. The analyses show clearly that cover should be an important factor in any approach to the calculation of crack widths. This effect arises from the shear distortion of the concrete between the bar surface and the concrete surface. 2. Experimental results show clearly that there should be some form of internal failure in the region of the bar over the whole length over which the crack influences the stress distribution. Two mechanisms have been proposed for this internal failure: slip along the bar-concrete interface, and internal cracks of the form proposed by Goto1 and elaborated by Beeby and Scott.4 In this paper, Beeby and Scott’s model is analyzed and is shown to describe the experimental behavior of tension members effectively. 3. The results from this study and those described in References 2 through 5 suggest the possibility of a model for tension zone behavior under service loads which is, in principle, simpler and more all-embracing than current models. This can be described by the following two assumptions: a) Concrete in tension behaves in an elastic-brittle manner; and b) Force is transferred between ribbed reinforcing bars and concrete by the mechanical action of the ribs. It is assumed that there is no bond between the ribs and no slip past the ribs. AUTHOR BIOS
John P. Forth is a Senior Lecturer in the School of Civil Engineering at the University of Leeds, Leeds, UK. He received his BEng in civil and structural engineering from the University of Sheffield, Sheffield, UK. He received his PhD from the University of Leeds. His research interests include serviceability and durability performance of reinforced concrete and masonry structures.
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The late Andrew W. Beeby was Emeritus Professor of Structural Design in the School of Civil Engineering at the University of Leeds. He received both his first degree and his PhD from London University, London, UK. He research interests included the serviceability behavior of concrete structures.
REFERENCES
1. Goto, Y., “Cracks Formed in Concrete around Deformed Tension Bars,” ACI Journal, V. 68, No. 4, Apr. 1972, pp. 224-251. 2. Scott, R. H., and Gill, P. A. T., “Short Term Distributions of Strain and Bond Stress along Tension Reinforcement,” The Structural Engineer, V. 65B, No. 2, June 1987, pp. 29-43. 3. Beeby, A. W., and Scott, R. H., “Insights into the Cracking and Tension Stiffening Behavior of Reinforced Concrete Tension Members Revealed by Computer Modeling,” Magazine of Concrete Research, V. 56, No. 3, Apr. 2004, pp. 179-190. 4. Beeby, A. W., and Scott, R. H., “Cracking and Deformation of Axially Reinforced Members Subjected to Pure Tension,” Magazine of Concrete Research, V. 57, No. 10, Dec. 2005, pp. 611-621. 5. Beeby, A. W., and Scott, R. H., “Mechanisms of Long-Term Decay of Tension Stiffening,” Magazine of Concrete Research, V. 58, No. 5, June 2006, pp. 255-266. 6. Beeby, A. W., “The Influence of the Parameter f/reff on Crack Widths,” Structural Concrete, V. 5, No. 2, 2004, pp. 71-83. 7. Farra, B., and Jaccoud, J.-P., “Influence du beton et de l”armature sur la fissuration des structures en beton,” Publication No. 140, Rapport des essais de tirants sous deformation impose de court duree, Department de Genie Civil, Ecole Polytechnique Federale de Lausanne, Nov. 1993. 8. Otsuka, K., and Ozaka, Y., “Group Effects on Anchorage Strength of Deformed Bars Embedded in Massive Concrete Block,” Proceedings of International Conference on Bond in Concrete—From Research to Practice, V. 1, Riga Technical University, Riga, Latvia, Oct. 1992, pp. 1.38-1.47. 9. Gerstle, W., and Ingraffea, A. R., “Does Bond-Slip Exist?” Concrete International, V. 13, No. 1, Jan. 1991, pp. 44-48. 10. Broms, B., “Theory of the Calculation of Crack Width and Crack Spacing in Reinforced Concrete Members,” Cement och Betong, No. 1, 1968, pp. 52-64. 11. Beeby, A. W., Concrete in the Oceans: Cracking and Corrosion, CIRIA/UEG, Cement and Concrete Association, Department of Energy, 1978, 77 pp. 12. Beeby, A. W., “A Study of Cracking in Reinforced Concrete Members Subjected to Pure Tension,” Technical Report No. 42.468, Cement and Concrete Association, June 1972, 25 pp.
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13. Base, G. D.; Beeby, A. W.; Read, J. B.; and Taylor, H. P. J., “An Investigation of the Crack Control Characteristics of Various Types of Bar in Reinforced Concrete Beams,” Research Report 18, Cement and Concrete Association, London, UK, Dec. 1966, 31 pp. 14. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp. 15. BS8110-2, “Structural Use of Concrete—Part 2: Code of Practice for Special Circumstances,” British Standards Institution, BSI Milton Keynes, London, UK, 1985, 62 pp. 16. Beeby, A. W., “An Investigation of Cracking in Slabs Spanning One Way,” Technical Report TRA 433, Cement and Concrete Association, Apr. 1970. 17. Eurocode 2, “Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings,” CEN, EN 1992-1-1, Brussels, Belgium, 2004, 225 pp. 18. CEB-FIP, “CEB-FIP Model Code (1990),” Bulletin d’information No. 213/214, Comité Euro-Internationale du Béton (CEB), Lausanne, Switzerland, 1993, 437 pp. 19. Broms, B. B., “Crack Width and Crack Spacing in Reinforced Concrete Members,” ACI Journal, V. 62, No. 10, Oct. 1965, pp. 1237-1256. 20. Broms, B. B., and Lutz, L. A., “Effects of Arrangement of Reinforcement on Crack Width and Spacing of Reinforced Concrete Members,” ACI Journal, V. 62, No. 11, Nov. 1965, pp. 1395-1410. 21. Gergely, P., and Lutz, L. A., “Maximum Crack Width in Reinforced Concrete Flexural Members,” Causes, Mechanism, and Control of Cracking in Concrete, SP-20, R. E. Philleo, ed., American Concrete Institute, Farmington Hills, MI, 1968, pp. 87-117. 22. Beeby, A. W., “An Investigation of Cracking in the Side Faces of Beams,” Technical Report 42.466, Cement and Concrete Association, Dec. 1971, 11 pp. 23. Beeby, A. W., “A Study of Cracking in Reinforced Concrete Members Subjected to Pure Tension,” Technical Report 42.468, Cement and Concrete Association, June 1972, 25 pp. 24. Beeby, A. W., “The Prediction of Crack Widths in Hardened Concrete,” The Structural Engineer, V. 57A, No. 1. Jan. 1979, pp. 9-17. 25. Ferry-Borges, J., “Cracking and Deformability of Reinforced Concrete Beams,” V. 26, International Association for Bridge and Structural Engineering. Zurich, Switzerland, 1966, pp. 75-95. 26. “CEB-FIP Model Code for Concrete Structures,” Bulletin d’information No. 125, Comité Euro-International du Beton, Paris, France, Apr. 1978, 460 pp.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S36
Flexural Capacity of Fiber-Reinforced Polymer Strengthened Unbonded Post-Tensioned Members by Fatima El Meski and Mohamed Harajli Experimental and analytical investigations were carried out for evaluating the nominal moment capacity of unbonded posttensioned members when strengthened using external fiberreinforced polymer (FRP) composites. In the experimental part of the study, 36 simply supported specimens were tested to failure. The main test parameters included area of internal tension reinforcement, area of external FRP reinforcement, span-depth ratio of the member, profile of the prestressing tendons, and type of concrete structural system. In the analytical part of the study, a designoriented procedure for evaluating the nominal moment capacity of FRP-strengthened post-tensioned members with internal or external unbonded tendon systems is developed. The procedure is consistent with the approach proposed in ACI Committee 440 report for reinforced concrete or bonded prestressed concrete members, and is applicable for both simply supported and continuous members. The accuracy of the design approach was verified by comparing it with the test results of the experimental part of this investigation. Keywords: fiber-reinforced polymer; flexure; prestressing; post-tensioning; strengthening; unbonded tendons.
INTRODUCTION AND BACKGROUND LITERATURE The flexural capacity of bonded prestressed concrete members can be evaluated in accordance with the general ACI Building Code1 approach and the guidelines recommended by ACI Committee 4402 by accounting for the effect of fiber-reinforced polymer (FRP) reinforcement as follows
(
)
(
M n = Aps f ps d p − b1c / 2 + As fs ( d − b1c / 2 ) + ψ f A f E f e f d f − b1c / 2
) (1)
where
fps = F(eps) (2)
fs = Eses ≤ fy (3)
dp − c e ps = e pe + e ce + e cu c
e ce =
(4)
2 1 Aps fse Aps fse e + Ec Ac Ig
ACI Structural Journal/March-April 2014
(5)
d − c e s = e cu c
(6)
d f −c − e bi ≤ e fd e f = e cu c
(7)
fc′ ≤ 0.9e fu nf Ef t f
(8)
e fd = 0.41
c=
Aps f ps + As fs + A f ( f f = E f e f ) a1 fc′ b1b
(9)
in which c is the neutral axis depth of the section at nominal flexural strength; Aps and dp are area and depth of the unbonded prestressing steel (PS); Af is area and df is depth of the FRP reinforcement; and As is area of bonded ordinary reinforcing steel (RS) at the section under consideration. For slabs, the areas Aps, As, and Af are per unit width b of the slab section. εce is precompression strain in concrete at the level of the prestressed tendons; Ac and Ig are area and moment of inertia of the gross section, respectively; e is eccentricity of the tendons; Ec, Es, and Ef are modulus of elasticity of concrete, steel, and FRP reinforcement, respectively; εf and ff are strain and stress in the FRP reinforcement, respectively; εfu is rupture strain of the FRP reinforcement; F is the material stress-strain relationship of the prestressing reinforcement; εpe, fse, εps, and fps are effective strain, effective stress, strain, and stress at ultimate, respectively, in the prestressing steel (εpe = fse/Eps, where Eps is the modulus of elasticity of the prestressing steel); εs, fs, and fy are strain, stress, and yield stress, respectively, for the ordinary RS; fc′ is concrete cylindrical compressive strength; εcu is usable concrete strain at compression failure (equal to 0.003 in accordance with ACI 318-111); α1 = 0.85 corresponding to a concrete strain in the outermost compression fiber equal to εcu; β1 is concrete strength factor defined in section 10.2.7.3 of the ACI Building Code1; εbi is initial substrate strain at which the FRP was applied for strengthening (ACI Committee ACI Structural Journal, Vol. 111, No. 2, March-April 2014. MS No. S-2012-168.R2, doi:10.14359.51686565, was received January 10, 2013, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
407
4402), determined using elastic cracked section analysis, considering all loads that will be on the member during the FRP installation; εfd is strain in the FRP reinforcement at which FRP debonding failure occurs; nf and tf are number of FRP layers and thickness per one layer, respectively; and ψf is the FRP strength-reduction factor recommended by ACI Committee 440,2 which is taken equal to 0.85 for flexure. To calculate the nominal moment capacity of FRP-strengthened reinforced concrete (RC) or bonded PC members, ACI Committee 4402 recommends using a trialand-error procedure for estimating the neutral axis depth c until the requirements of strain compatibility and force equilibrium across the depth of the critical section are satisfied (Eq. (9)). Also, two modes of flexural failure are recognized by ACI Committee 440: 1) concrete crushing—that is, when the strain in the outermost concrete compression fiber reaches εcu before FRP failure; and 2) FRP failure before concrete crushing. FRP failure could occur either by FRP rupture, cover delamination, or FRP debonding. Accordingly, ACI Committee 4402 limits, conservatively, the strain in the FRP reinforcement at which FRP failure takes place to the debonding strain εfd (Eq. (8)). When the strain in the FRP reaches its limiting strain εfd before the concrete compression strain reaches εcu, the concrete compression strain εcu in Eq. (2) through (9) should be replaced by its actual value expressed as a function of εfd as follows
c e c = e fd + e bi df − c
(
)
(10)
The values of α1 and β1, which are now different from their values when εc = εcu, can be estimated with reasonable accuracy using the following expressions recommended by ACI Committee 440,2 which were derived assuming a parabolic relationship for the stress-strain curve of concrete in compression
4 e c′ − e c 6 e c′ − 2 e c
(11)
3e c′ e c − (e c )2 3b1 (e c′ )2
(12)
b1 =
a1 =
where εc′ is the strain corresponding to fc′, which can either be taken equal to 0.002 or calculated more accurately as εc′ = 1.7fc′/Ec. RESEARCH SIGNIFICANCE An experimental study was carried out and a designoriented approach was developed for evaluating the nominal flexural capacity Mn of unbonded PC members when strengthened using external FRP composites. The design approach builds on a previous model generated for evaluating the stress in unbonded tendons at ultimate in simply supported or continuous members, and is consistent with the
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Fig. 1— FRP-strengthened continuous unbonded member with multi-collapse mechanisms. ACI Committee 4402 guidelines for calculating Mn for FRP strengthened bonded PC or RC members. The approach is validated for simply supported members by comparing with the test results generated in the experimental part of this investigation. STRESS IN UNBONDED TENDONS AT ULTIMATE While the approach recommended by ACI Committee 4402 for estimating Mn for FRP strengthened RC or bonded PC members is simple because it relies on commonly adopted and familiar principles, it is not as straightforward for PC members with unbonded tendons. In PC members with internal or external unbonded tendons, because the unbonded steel slips relative to the surrounding concrete, the strain or stress fps in the prestressing steel that develops at nominal flexural strength relies on the deformation of the member as a whole. This makes the evaluation of the corresponding strain and stress member, rather than section, dependent. Several design approaches are available for predicting the stress in unbonded tendons at ultimate.1,3,4 A comparative evaluation of these approaches has been discussed in detail elsewhere.5 Using plastic analysis and the concept of collapse mechanism in continuous members, as well as idealization of the curvature distribution along the span lengths at nominal flexural strength as shown in Fig. 1 (for εc = εcu, and Af = 0.0) and further incorporating an empirically derived expression for the equivalent plastic hinge length for unbonded members given as5 lp = (20.7/f + 10.5)c, Harajli6 developed the following general and yet elegant expression for calculating the strain εps in unbonded tendons at ultimate
dp c e ps = e pe + f ps N p e cu − N p (e cu − e ce ) (13) La La
where ACI Structural Journal/March-April 2014
20.7 Np = + 10.5 n p + + 10.5n p − f
(14)
in which c is the neutral axis depth at the section under consideration; εce is calculated using Eq. (5) by neglecting the effect of the secondary moment due to prestressing in continuous members; La is the total length of tendons between anchorages; Np (Eq. (14)) is a parameter that combines the effect of member continuity and type of applied load; f = ∞ for a single concentrated load, 3.0 for two-third point loads, and 6.0 for uniform load application, respectively; np+, np– are the number of positive and negative plastic hinges, respectively, that develop in the process of forming a collapse mechanism; and φps is a stress-reduction factor taken equal to 0.7. Note that because the live load in buildings and bridges is seldom a concentrated load, and also because the dead load is uniformly distributed, the multiplier (20.7/f + 10.5) of the positive number of plastic hinge(s) np+ can always be set equal to 14.0 to correspond to uniform load application.6 Equations (13) and (14) were developed with the perspective that the calculation of the stress in unbonded tendons at ultimate in continuous members differs from one critical section to another. That is, the stress at a critical section depends on the pattern of applied load and the consequent collapse mechanism that would potentially develop for producing the maximum factored design moment at that section. For the hypothetical case of Fig. 1, in which collapse mechanisms are assumed to form in all spans: np1+ = 2.0, np2– = 2.0, and np3+ = 2.0. In actual design, however, the numbers of plastic hinges np+ and np– are obtained from the collapse mechanisms that develop when loading the minimum number of spans for producing maximum moment at the section under consideration. For instance, in simply supported members, one span is loaded, and hence np+ = 1.0, np– = 0.0, and Np = 14.0. For continuous members, collapse mechanisms (a), (b), (c), (d), and (e) in Fig. 2, and corresponding values of Np are recommended6 for computing the tendon stress fps and the nominal moment capacity at the maximum positive moment section in exterior spans; negative moment section at the interior support of a two-span member; maximum positive moment section in interior spans; negative moment section at the first interior support; and negative moment section at the remaining interior supports of members with more than two spans, respectively. PROPOSED APPROACH FOR COMPUTING MN IN FRP STRENGTHENED UNBONDED MEMBERS Using Eq. (13) but neglecting the precompression strain εce due to its minor effect on the tendon stress in unbonded members, particularly when compared with bonded members, and considering that the flexural strength may be controlled by FRP failure at which εc ≤ εcu (Fig. 1), the following expression is recommended for computing the strain εps in unbonded tendons of FRP-strengthened simply
ACI Structural Journal/March-April 2014
Fig. 2—Loading pattern and corresponding values of continuity parameter Np for continuous members. supported or continuous members at nominal flexural strength
dp − c e ps = e pe + f ps N p e c La
(15)
Recognizing that the stress in the prestressing steel seldom exceeds yield and limiting the corresponding stress to 0.95fpy6 allows the use of a linear relationship between the stress and strain in the prestressing steel, that is, fps = Epsεps, leading to
f ps = fse +
f ps N p E ps e c c 1 − ≤ 0.95 f py La / d p d p
(16)
The force equilibrium across the depth of the critical section, assuming rectangular section or rectangular section behavior, is expressed as
Apsfps + Asfs + AfEfef = a1fc′bb1c (17)
It should be noted that for unbonded members without FRP reinforcement (that is, Af = 0.0 and α1 = 0.85), the value of c from Eq. (17) can be integrated in Eq. (16) to produce a direct expression for computing fps in unbonded members at ultimate.6 Using Eq. (15), (16), and (17), the following step-by-step procedure can be adopted for evaluating the nominal moment capacity Mn of FRP strengthened unbonded post-tensioned members.
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Case I—Flexural capacity controlled by concrete crushing Step 1—Assume that the nominal flexural strength at a critical section is controlled by concrete crushing—that is, εf calculated using Eq. (7) is less than or equal to εfd (Eq. (8)). This implies that εc = εcu, α1 = 0.85, and β1is as defined in section 10.2.7.3 of the ACI Building Code.1 Replacing fps from Eq. (16) into Eq. (17) and assuming that the RS yields, that is, fs = fy, leads to the following quadratic equation for calculating the neutral axis depth at nominal flexural strength at the section under consideration c=
B + B2 + 4 AC 2A
(18)
where
A = 0.85b1 fc′b +
f ps N p Aps E ps e cu La
(19a)
f ps N p E ps e cu d p B = Aps fse + + As f y − A f E f (e cu + e bi ) La
(19b)
C = Af Ef ecudf (19c)
in which Np is as defined previously (Fig. 2). For simply supported members, Np = 14.0. Step 2—Check if εf (Eq. (7)) is indeed ≤ εfd. Also check if the strain εs in the RS is larger than the yield strain εy. If εf ≤ εfd while εs is less than εy, repeat Step 1 for recalculating more accurately the neutral axis depth using Eq. (18) in which the coefficients A, B, and C are revised by substi
d − c
tuting fs = Es e s = e cu c for fy in Eq. (17). Step 3—Calculate fps from Eq. (16) corresponding to εc = εcu, and fs from Eq. (3), and hence calculate the nominal moment capacity Mn from Eq. (1). Case II—Flexural capacity controlled by FRP failure Step 4—If εf calculated from Step 2 is greater than εfd (Eq. (8)), then FRP failure occurs before the strain εc reaches εcu. In this case, the strain εf in the FRP reinforcement is equal to εfd, and hence, a trial-and-error procedure for calculating c, as described in the next steps, becomes more appropriate. Step 5— Using the value of εf = εfd, together with an initial assumed value of c, calculate the concrete strain εc at the top concrete compression fiber from Eq. (10) and calculate the stress in the prestressing steel (Eq. (16)) and the stress in the RS from Eq. (3) and (6) by replacing εc for εcu. Step 6—Check equilibrium of forces using Eq. (17) in which εf = εfd, and α1 and β1 are as calculated from Eq. (11) and (12).
410
Step 7—Repeat Steps 5 and 6 by revising the neutral axis depth c until the requirement of force equilibrium in Eq. (17) is satisfied within some degree of tolerance. Step 8—Calculate the nominal moment capacity Mn at the section under consideration using Eq. (1) in which εf = εfd. Step 9—Check if φMn ≥ Mu, where Mu is the load-factored applied moment at the section under consideration obtained by loading the spans (pattern loading) for producing maximum moment at the section under consideration. The strength-reduction factor φ is taken in accordance with the ACI Building Code1 approach using the relationship between the net tensile strain in the tension reinforcement and the neutral axis depth c at nominal flexural strength as follows
φ = 0.90 for c/de ≤ 0.38
(20a)
φ = 0.65 for c/de ≤ 0.6
(20b)
c f = 0.65 + 0.25 2.73 − 4.55 for de
(20c)
0.38 ≤ c / de ≤ 0.6
where de is the equivalent depth of the tension reinforcement (PS, RS, and FRP laminates) expressed as de =
( Aps f ps d p + As fs d + A f E f e f d f ) Aps f ps + As fs + A f E f e f
(21)
EXPERIMENTAL STUDY Twenty-four unbonded post-tensioned specimens were tested to evaluate their nominal flexural strength before and after FRP strengthening. An additional six bonded posttensioned and six RC specimens were also tested for comparison. All 36 specimens were simply supported over a 3.0 m (9.84 ft) span. Dimensions and reinforcement layout are given in Fig. 3. Eighteen of the specimens had a 150 mm (5.9 in.) wide by 250 mm (9.8 in.) deep cross section and a span-depth ratio (depth to center of tension steel) of 15, representing beam members, and the remaining 18 had a 360 mm (14.2 in.) wide by 120 mm (4.7 in.) deep cross section and a span-depth ratio of 35, simulating one-way slab members. The specimen designation, along with areas and depths of reinforcement and other pertinent details and design properties, are summarized in Table 1. The test parameters included, in addition to the span-depth ratio of the member, area of internal prestressed reinforcement for the PC specimens or area of ordinary tension reinforcement for the RC specimens; area of external FRP reinforcement; and tendon profile. Two tendon profiles were selected for each set of specimens: one horizontal and one parabolic. In the specimens designation provided in Table 1, the first letter U stands for unbounded, B for bonded, and R for reinforced. The second letter B stands for beam, while S stands ACI Structural Journal/March-April 2014
Fig. 3—Typical dimensions and reinforcement details of the beam and slab specimens. (Note: dimensions in mm; 1 mm = 0.039 in.) for slab. The numbers 1 and 2 following the second letter designate two different levels of PS or RS areas or ratios. Letters H and P designate horizontal and parabolic tendon profile, respectively, and F1 and F2 denote two different levels (areas or layers) of external FRP reinforcement. The parabolic tendon profile in all beam and slab specimens had zero eccentricity at the support. The prestressing reinforcement consisted of seven-wire strands having 7.9 and 9.5 mm (5/16 and 3/8 in.) diameter, with an area of 37.5 and 52.0 mm2 (0.058 and 0.08 in.2), and actual ultimate strength fpu of 1958 and 1978 MPa (284 and 287 ksi), respectively. Generated from coupon tests, the actual stress-strain (fps – εps) behavior of the two sizes of the prestressing steel were best reproduced using the following relationship7
f ps = E ps e ps Q +
1−Q 1/ N E e N 1 + ps ps Kf py
ACI Structural Journal/March-April 2014
(22)
where fpy = 1670 MPa (242 ksi), Eps = 195,130 MPa (28,400 ksi), N = 14.84, K = 1.0, and Q = 0.0357 for the 7.9 mm (5/16 in.) strands; and fpy = 1690 MPa (245 ksi), Eps = 194,440 MPa (28,200 ksi), N = 12.1, K = 1.011, and Q = 0.0301 for the 9.5 mm (3/8 in.) strands. All ordinary reinforcing bars (except the 6 mm [0.25 in.] bars) were deformed Grade 60 steel with actual yield strength as given in Table 1. The FRP composite used for strengthening consisted of carbon fiber-reinforced polymer (CFRP) flexible sheets having unidirectional carbon fabric with glass cross-fiber for added strength and fabric stability during installation. The design thickness, the modulus of elasticity, and the ultimate tensile strain of the fibers are 1 mm (0.039 in.), 95,800 MPa (13,895 ksi), and 1%, respectively. Before casting the specimens, the steel cages were instrumented with electric strain gauges and then placed in plywood formwork ready for concrete casting. The ducts for the post-tensioned steel consisted of galvanized flexible tubes 20 mm (0.79 in.) in diameter. One strand was placed in each duct. For the bonded post-tensioned slab and beam specimens, cement-based grout was injected inside the ducts after the tendons were stressed to provide bond between the strands and concrete. The grout mixture was prepared using Type I portland cement, and proportioned in accordance 411
Table 1—Summary of test parameters Prestressing steel Concrete system
Reinforcing steel
FRP
Beam Unbonded post-tensioned
Av
fy, MPa
Af, mm2 (nf)
fc′, MPa
—
φ8 at 150
560
—
42
220
—
φ8 at 150
612
150 (1)
36
2 (8 mm)
220
—
φ8 at 150
612
300 (2)
36
815
2 (8 mm)
220
—
φ8 at 150
560
—
42
200
971
2 (8 mm)
220
—
φ8 at 150
612
150 (1)
36
1 (5/16 in.)
200
781
2 (8 mm)
220
—
φ8 at 150
612
300 (2)
37
Horizontal
2 (3/8 in.)
200
778
2 (8 mm)
220
2 (8 mm)
φ8 at 150
560
—
42
UB2-H-F1
Horizontal
2 (3/8 in.)
200
924
2 (8 mm)
220
2 (8 mm)
φ8 at 150
612
150 (1)
36
UB2-H-F2
Horizontal
2 (3/8 in.)
200
896
2 (8 mm)
220
2 (8 mm)
φ8 at 150
612
300 (2)
37
UB2-P
Parabolic
2 (3/8 in.)
200
836
2 (8 mm)
220
2 (8 mm)
φ8 at 150
560
—
42
UB2-P-F1
Parabolic
2 (3/8 in.)
200
936
2 (8 mm)
220
2 (8 mm)
φ8 at 150
612
150 (1)
36
UB2-P-F2
Parabolic
2 (3/8 in.)
200
923
2 (8 mm)
220
2 (8 mm)
φ8 at 150
612
300 (2)
37
US1-H
Horizontal
2 (5/16 in.)
85
927
2 (8 mm)
92.5
—
—
560
—
42
US1-H-F1
Horizontal
2 (5/16 in.)
85
917
2 (8 mm)
92.5
—
—
612
150 (1)
36
US1-H-F2
Horizontal
2 (5/16 in.)
85
964
2 (8 mm)
92.5
—
—
612
300 (1)
36
d,mm
As′, top
2 (8 mm)
220
962
2 (8 mm)
200
963
1 (5/16 in.)
200
Parabolic
1 (5/16 in.)
UB1-P-F2
Parabolic
UB2-H
Specimen label
Tendon profile
Aps
UB1-H
Horizontal
UB1-H-F1
dp, mm
fse, MPa
As, bottom
1 (5/16 in.)
200
813
Horizontal
1 (5/16 in.)
200
UB1-H-F2
Horizontal
1 (5/16 in.)
UB1-P
Parabolic
UB1-P-F1
Slab Beam Slab
Bonded post-tensioned
Beam Slab
Reinforced concrete
US1-P
Parabolic
2 (5/16 in.)
85
886
2 (8 mm)
98.5
—
—
560
—
42
US1-P-F1
Parabolic
2 (5/16 in.)
85
949
2 (8 mm)
98.5
—
—
612
150 (1)
36
US1-P-F2
Parabolic
2 (5/16 in.)
85
971
2 (8 mm)
98.5
—
—
612
300 (1)
37
US2-H
Horizontal
3 (3/8 in.)
85
804
2 (8 mm)
92.5
—
—
560
—
42
US2-H-F1
Horizontal
3 (3/8 in.)
85
912
2 (8 mm)
92.5
—
—
612
150 (1)
36
US2-H-F2
Horizontal
3 (3/8 in.)
85
858
2 (8 mm)
92.5
—
—
612
300 (1)
37
US2-P
Parabolic
3 (3/8 in.)
85
831
2 (8 mm)
98.5
—
—
560
—
42
US2-P-F1
Parabolic
3 (3/8 in.)
85
921
2 (8 mm)
98.5
—
—
612
150 (1)
36
US2-P-F2
Parabolic
3 (3/8 in.)
85
916
2 (8 mm)
98.5
—
—
612
300 (1)
37
BB2-P
Parabolic
2 (3/8 in.)
200
884
2 (6 mm)
220
2 (6 mm)
φ8 at 150
0
—
37
BB2-P-F1
Parabolic
2 (3/8 in.)
200
894
2 (6 mm)
220
2 (6 mm)
φ8 at 150
0
150 (1)
37
BB2-P-F2
Parabolic
2 (3/8 in.)
200
885
2 (6 mm)
220
2 (6 mm)
φ8 at 150
0
300 (2)
37
BS2-P
Parabolic
3 (3/8 in.)
85
970
2 (8 mm)
98.5
—
—
0
—
37
BS2-P-F1
Parabolic
3 (3/8 in.)
85
915
2 (8 mm)
98.5
—
—
0
150 (1)
37
BS2-P-F2
Parabolic
3 (3/8 in.)
85
892
2 (8 mm)
98.5
—
—
0
300 (1)
37
RB2
—
—
—
—
2 (16 mm)
220
—
φ8 at 100
530
—
37
RB2-F1
—
—
—
—
2 (16 mm)
220
—
φ8 at 100
530
150 (1)
37
RB2-F2
—
—
—
—
2 (16 mm)
220
—
φ8 at 100
674
300 (2)
37
RS2
—
—
—
—
4 (12 mm)
100
—
—
555
—
37
RS2-F1
—
—
—
—
4 (12 mm)
100
—
—
555
150 (1)
37
RS2-F2
—
—
—
—
4 (12 mm)
100
—
—
624
300 (1)
37
Note: 1 in. = 25.4 mm; 1 MPa = 0.145 ksi; 1 mm2 = 0.0016 in.2.
with the ACI Building Code1 with a water-cement ratio of 0.40. The CFRP sheets were attached to the bottom tension face of the beam and slab specimens in accordance with 412
the manufacturer’s recommendations and in compliance with the ACI Committee 4402 recommendation for securing proper development length. No particular measures were taken to improve bond strength between the FRP and the ACI Structural Journal/March-April 2014
substrate. One or two layers of 150 mm (5.9 in.) wide FRP sheets were applied for the beam specimens, while only one layer of 150 or 300 mm (5.9 or 11.8 in.) wide sheets was applied for the slab specimens (Table 1). All specimens were tested in four-point bending using two symmetrical concentrated loads spaced a distance equal to 1/6 the span length, or 500 mm (19.7 in.) apart (Fig. 3). It should be noted that because the increase in tendon strain/ stress (above effective prestrain/prestress) of unbonded members due to increase in applied load depends on the overall deformation of the member or elongation of the tendon between the anchorages, the ultimate tendon stress and flexural capacity of unbonded members are influenced by the geometry of applied load.8 Two-point loads spaced at 1/6 the span length were found analytically8,9 to be equivalent to uniform load application for predicting the ultimate tendon stress and moment capacity of unbonded post-tensioned members. To replicate actual conditions of concrete flexural members that require strengthening or repair, all control and strengthened specimens were first subjected to cyclic loading consisting of six cycles before the FRP application, and another six cycles after FRP application, ranging between a minimum load Pmin and a maximum load Pmax, simulating dead load and dead plus live load, respectively. The loads Pmin and Pmax were set at 30 and 70%, respectively, of the calculated nominal load capacity of the specimens. For the control or unstrengthened specimens, the cyclic loading stage was followed immediately by a stage of monotonically increasing load until complete flexural failure of the specimens. The specimens that were strengthened using CFRP were first subjected to the same cyclic loading protocol as the control specimens, and then unloaded to prepare them for CFRP application. Following at least 7 days of CFRP application, the strengthened specimens were subjected to a loading protocol consisting of cyclic loading and monotonically increasing load to failure, similar to the control specimens. Test measurements included strains and stresses in the prestressing strands, CFRP laminates, and reinforcing bars of the RC specimens within the constant moment region close to midspan; applied load; and deflection. Crack patterns were also monitored throughout the test for each specimen. The strains were measured using electric strain gauges, while deflection was measured using a linear voltage differential transformer (LVDT). The test results were automatically collected and recorded using a data acquisition and control system. DISCUSSION OF RELEVANT TEST RESULTS Typical photos of the specimens at the conclusion of the test are shown in Fig. 4. Representative modes of failure and cracking patterns at nominal strength for the unbonded PC beam specimens in comparison with the bonded PC and RC beam specimens are provided in Fig. 5. Flexural failure for the various beam and slab specimens occurred either by concrete crushing or by FRP debonding or fracturing. Relevant experimental results at nominal flexural strength including load capacity, deflection, stress in the prestressing ACI Structural Journal/March-April 2014
Fig. 4—Typical photos of specimens at conclusion of test. steel, strain in the CFRP reinforcement, and mode of failure are all summarized in Table 2. Representative variations of deflection, FRP strain, and stress increase in the prestressing steel above effective prestress fse with applied load are shown in Fig. (6) through (9), respectively. The crack patterns for the unbonded beam specimens (Fig. 5) and the slab specimens (not shown for brevity) were similar to those developed in the companion bonded specimens. The spreading of cracks outside the constant moment region increased with the use of FRP reinforcement and as the area of FRP reinforcement increased, and was most significant for the RC specimens (Fig. 5). It is clear from the test data summarized in Table 2 that the use of FRP reinforcement significantly increased the moment capacity of unbonded post-tensioned members. The corresponding increase grew higher as the area of FRP reinforcement increased, and varied between 24 and 105% for the beam specimens and between 21 and 126% for the slab specimens of the current investigation. As would be expected, however, the increases in load capacities were accompanied with reductions in ductility or ultimate deformation capacities, which were most notable for the beam specimens. The reductions in deformation capacity, which are attributed in 413
were significantly larger than the stresses developed in the unbonded specimens. Based on the experimental results and observations of the current investigation, it was obvious that the cracking and crack patterns, increase in load capacities, reduction in deformation capacities, and modes of flexural failure of the unbonded PC specimens as a result of FRP strengthening were quite similar to those of the bonded PC and RC specimens. More test data and a detailed discussion of test results are reported elsewhere.10
Fig. 5—Typical comparison of crack pattern for unbonded PC, bonded PC, and RC beam specimens. part to the FRP debonding mode of flexural failure, were almost identical for the slab or beam specimens reinforced with Level F1 and F2 FRP reinforcement (Table 2). The FRP strain/stress developed at flexural failure (Fig. 8 and Table 2) generally decreased as the area of FRP reinforcement increased within the specimens of the same test series, or as the area of prestressing reinforcement increased. The overall average FRP strains at ultimate for the combined beam and slab specimens strengthened using the two different areas or levels (F1 and F2) of FRP reinforcement were 6260 to 5400 με for the unbonded PC, 6875 to 4970 με for the bonded PC, and 7608 to 5419 με for the RC specimens, respectively. Being unbonded, the stress in the prestressing steel at nominal flexural strength was below yield for all specimens. The corresponding strain (Table 2) decreased as the area of FRP reinforcement increased. On the other hand, the strains and stresses in the prestressing steel for all companion bonded PC beam and slab specimens exceeded yield and
414
COMPARISON OF ANALYTICAL PREDICTIONS WITH TEST DATA Table 2 shows comparisons of the predictions of the proposed design-oriented approach developed in this study for FRP-strengthened unbonded PC members together with the predictions of the ACI Committee 4402 approach for bonded PC and RC members against the test results generated in the experimental part of this investigation. These include stress fps in the prestressing steel, strain εf in the FRP reinforcement, mode of flexural failure, and nominal moment capacity Mn. In calculating the stress in the prestressing steel and the nominal moment capacity, the reduction factors φps and ψf were both set equal to 1.0. Also, because the load at which the FRP was applied was very small (equal to the selfweight of the specimen), the initial substrate strain εbi was taken equal to zero. Figure 10 shows predicted stress increase Δfps (Δfps = fps – fse) and total stress fps in the prestressing steel at ultimate versus test results for the unbonded prestressed beams and slab specimens of the current investigation. The data are superimposed on predicted versus test results of a collection of unbonded members (without FRP reinforcement) compiled and reported previously.5,6 The compiled data correspond to internally or externally post-tensioned simply supported members, and continuous members having two or three spans, and loaded with two-point or single-point loads, respectively. Figure 11 shows predicted versus measured nominal moment capacities for the 36 beam and slab specimens tested in this investigation. Given the inevitable scatter associated with the prediction of the stress in unbonded tendons at ultimate, it can be seen from Fig. 10 that the proposed analytical approach predicted the test data with reasonable accuracy. More conservative predictions can be obtained by using the stress reduction parameter φps = 0.7 proposed for design purposes. As expected, the stress predictions for the bonded members were more accurate than the unbonded members. The average ratio of the test-to-predicted tendon stress were 1.10 (standard deviation [SD] = 0.12) for the unbonded specimens, and 1.02 (SD = 0.04) for the bonded specimens. It should be noted that due to the presence of 2φ8 mm ordinary steel bars, which are required as minimum bonded reinforcement in accordance with the ACI Building Code,1 the control unbonded PC specimens developed well-distributed cracks along their length as opposed to the development of few cracks or concentration of deformation at a single crack that normally occurs in members with an unbonded tendon system.5 In other words, the equivalent plastic hinge length ACI Structural Journal/March-April 2014
Table 2—Summary of test results and analytic predictions Δu Pu (kN) (mm)
FRP Strain εf
fps (MPa)
Mode of failure
Exp./ Exp./ Exp. Analysis Analysis Exp. Analysis Analysis
Specimen
Exp.
Exp.
UB1-H
42.3
64
1567
1253
1.25
—
—
UB1-H-F1
66.9
31
1303
1250
1.04
7122
UB1-H-F2
86.9
33
1223
1290
0.95
UB1-P
46.8
81
1669
1255
UB1-P-F1
66.3
35
1413
1259
Nominal moment Mn (kN-m) Exp./ Analysis Analysis
Experiment
Analysis
Exp.
—
Concrete crushing
Concrete crushing
26.4
20.8
1.27
7948*
0.90
FRP debonding
FRP debonding
41.8
46.5
0.90
5378
5620*
0.96
FRP debonding
FRP debonding
54.3
55.6
0.98
1.33
—
—
—
Concrete crushing
Concrete crushing
29.3
20.8
1.41
1.12
4556
7948*
0.57
FRP debonding
FRP debonding
41.4
46.5
0.89
*
UB1-P-F2
89.0
36
1102
1098
1.00
5604
5698
0.98
FRP debonding
FRP debonding
55.6
55.2
1.01
UB2-H
63.6
43
1246
1205
1.03
—
—
—
Concrete crushing
Concrete crushing
39.8
35.3
1.13
UB2-H-F1
80.8
26
1163
1230
0.95
6934
7949*
0.87
Partial rupture + partial debonding
FRP debonding
50.5
60.4
0.84
UB2-H-F2 104.8
31
1122
1239
0.91
5329
5698*
0.94
FRP debonding
FRP debonding
65.5
68.9
0.95
UB2-P
75.2
88
1598
1260
1.27
—
—
—
Concrete crushing
Concrete crushing
47.0
36.3
1.29
UB2-P-F1
93.6
37
1339
1244
1.08
5393
7948*
0.68
FRP debonding + concrete crushing
FRP debonding
58.5
60.6
0.97
UB2-P-F2 101.2
30
1223
1270
0.96
4285
5698*
0.75
FRP debonding
FRP debonding
63.3
69.3
0.91
62
1211
1106
1.09
—
—
US1-H
22.7
—
Concrete crushing
Concrete crushing
14.2
11.5
1.23
*
1.05
FRP rupture
FRP debonding
21.4
23.3
0.92
US1-H-F1
34.3
63
1195
1033
1.16
8309
7948
US1-H-F2
43.0
66
1152
1112
1.04
6074
6490
0.94
Partial rupture + partial debonding
Concrete crushing
26.9
30.1
0.89
US1-P
21.3
100
1413
1066
1.33
—
—
—
Concrete crushing
Concrete crushing
13.3
11.6
1.15
US1-P-F1
34.5
68
1177
1065
1.11
5770
7948*
0.73
FRP debonding
FRP debonding
21.6
23.8
0.91
US1-P-F2
48.1
75
1165
1117
1.04
6280
6580
0.95
FRP rupture + concrete crushing
Concrete crushing
30.1
30.8
0.97
US2-H
35.1
87
1227
966
1.27
—
—
—
Concrete crushing
Concrete crushing
21.9
16.3
1.34
US2-H-F1
42.6
62
—
1039
—
6277
6758
0.93
Concrete crushing Concrete crushing + partial debonding
26.6
26.4
1.01
US2-H-F2
57.2
75
1065
972
1.10
5517
5551
0.99
Concrete crushing
Concrete crushing
35.8
31.6
1.13
US2-P
36.9
66
1105
992
1.11
—
—
—
Concrete crushing
Concrete crushing
23.1
17.0
1.36
US2-P-F1
47.6
68
1146
1047
1.09
7554
6731
1.12
Concrete crushing
Concrete crushing
29.8
26.9
1.11
US2-P-F2
59.8
67
1136
1029
1.10
5570
5429
1.03
Concrete crushing
Concrete crushing
37.4
32.1
1.16
BB2-P
63.4
44
1738
1737
1.00
—
—
—
Concrete crushing
Concrete crushing
39.6
34.2
1.16
BB2-P-F1
87.0
35
1710
1682
1.02
5906
7027
0.84
FRP rupture
Concrete crushing
54.4
53.6
1.01
BB2-P-F2 107.8
30
1680
1591
1.06
4781
5523*
0.87
FRP debonding
FRP debonding
67.4
63.1
1.07
BS2-P
33.9
71
1662
1687
0.99
—
—
—
Concrete crushing
Concrete crushing
21.2
21.4
0.99
BS2-P-F1
44.3
67
1702
1556
1.09
7834
6000
1.31
FRP debond. and rupture
Concrete crushing
27.7
28.1
0.98
BS2-P-F2
59.7
70
1429
1435
1.00
5701
5045
1.13
Concrete crushing
Concrete crushing
37.3
32.2
1.16
RB2
72.5
46
—
—
—
—
—
—
Concrete crushing
Concrete crushing
45.3
42.5
1.07
RB2-F1
98.6
35
—
—
—
7608
6740
1.13
FRP rupture
Concrete crushing
61.6
62.0
0.99
RB2-F2
110.8
33
—
—
—
5003
4177
1.20
Concrete crushing
Concrete crushing
69.3
73.4
0.94
RS2
37.0
77
—
—
—
—
—
—
Concrete crushing
Concrete crushing
23.1
22.7
1.02
RS2-F1
48.5
60
—
—
—
—
6863
—
FRP rupture
Concrete crushing
30.3
32.2
0.94
RS2-F2
66.7
77
—
—
—
5834
4660
1.25
FRP rupture
Concrete crushing
41.7
36.6
1.14
*
Equal to debonding strain calculated using Eq. (8). Notes: Exp. is Experiment; 1 kN = 0.224 kip; 1 mm = 0.039 in.; 1 MPa = 0.145 ksi; 1 kN-m = 8.83 k-in.)
ACI Structural Journal/March-April 2014
415
Fig. 7—Representative load-deflection response of slab specimens. (Note: 1 mm = 0.039 in.; 1 kN = 0.224 kip.)
Fig. 6—Comparison between load-deflection response of unbonded and bonded PC beam specimens. (Note: 1 mm = 0.039 in.; 1 kN = 0.224 kip.) developed in these specimens was, admittedly, larger than that predicted from lp = (20.7/f + 10.5)c, based on which Eq. (13) and (16) were developed. Consequently, the ultimate strains or stresses in the prestressing steel for the control specimens in this investigation (Table 2 and Fig. 10) were conservatively larger than those predicted by Eq. (13) or (16). Also, as can be seen from Table 2, the analytical approach predicted the experimentally measured strain in the FRP reinforcement and associated mode of flexural failure reasonably accurately for most unbonded specimens, as well as for the bonded PC and RC specimens. While the results are, to a great extent, in support of the ACI Committee 4402 guidelines for predicting modes of flexural failure in FRP-strengthened members, the experimentally measured FRP strains for the unbonded specimens were consistently slightly lower than those predicted using Eq. (8). The average ratio of test-to-predicted FRP strains is calculated at 0.9 (SD = 0.15) for the unbonded specimens, 1.1 (SD = 0.18) for the combined bonded PC and RC specimens, and 0.96 (SD = 0.18) for all unbonded, bonded, and RC specimens. Finally, from Fig. 11, Table 2, and the statistical data provided, except for the control unbonded PC specimens that developed larger than predicted moment capacities due to the development of larger-than-predicted steel stresses, 416
Fig. 8—Representative variation of FRP strain with applied load. (Note: 1 kN = 0.224 kip.)
Fig. 9—Typical variation of stress increase in unbonded prestressing steel with applied load. (Note: 1 kN = 0.224 kip.) ACI Structural Journal/March-April 2014
Fig. 11—Prediction of nominal moment capacity of combined specimens of current investigation. (Note: 1 kN-m = 8.83 k-in.)
Fig. 10—Prediction of experimental data for unbonded members6 including FRP strengthened unbonded specimens of current investigation for φps = 1.0. (Note: 1 MPa = 0.145 ksi.) as illustrated previously, the predicted nominal moment capacities Mn of the FRP-strengthened specimens (assuming ψf = 1.0) were generally in good agreement with the test results. Despite little discrepancy, the level of accuracy in predicting Mn for the unbonded specimens using the proposed design approach is consistent with the level of accuracy in predicting Mn for bonded PC and RC specimens using the ACI Committee 4402 approach. The average ratio of test-to-predicted results is calculated as 0.97 (SD = 0.09) for the FRP-strengthened unbonded specimens, and 1.05 (SD = 0.09) for the combined FRP-strengthened bonded PC and RC specimens. For the combined control and FRP-strengthened specimens, the coefficient of correlation R between the experimentally measured and the calculated nominal moment capacities is equal to 0.97 for the unbonded specimens, 0.98 for the bonded PC and RC specimens, and 0.97 for the overall unbonded PC, bonded PC, and RC specimens. Their corresponding average ratios of test-topredicted results are equal to 1.07 (SD = 0.17), 1.04 (SD = 0.08), and 1.06 (SD = 0.15). It should be noted that because the experimentally measured FRP strains of the FRP-strengthened unbonded ACI Structural Journal/March-April 2014
specimens, particularly when the mode of failure is by FRP debonding or rupture, were slightly lower than those predicted by Eq. (8), these specimens developed slightly lower moment capacities than those predicted using the proposed approach (Table 2). Consequently, although additional conservatism in predicting Mn for design purposes can be gained by setting ψf = 0.85 as recommended by ACI Committee 4402 (Eq. (1)), the FRP debonding strain in Eq. (8) may require slight modification in its application for unbonded members. Until further experimental evidence is available to support such modification, however, Eq. (8) can still be used for unbonded members without significant loss of accuracy. CONCLUSIONS A design-oriented approach for calculating the nominal moment capacity Mn of unbonded PC members when strengthened using external FRP composites is presented. The approach is applicable for simply supported and continuous members, and is consistent with the guidelines of ACI Committee 4402 for evaluating Mn of bonded PC or RC members. The accuracy of the proposed approach for simply supported members was verified by comparing with the results of a comprehensive test program designed and carried out specifically for the purpose of this study. Except for a slight discrepancy in predicting the FRP debonding strain for the unbonded specimens that encountered FRP failure before concrete crushing, the proposed approach for unbonded PC members, and the approach recommended by ACI Committee 440 for bonded PC and RC members, predicted well the test results at ultimate, including the strain/stress in the PS, strain in the FRP reinforcement, mode of flexural failure, and nominal flexural strength. The experimental results and the proposed approach for calculating Mn of FRP-strengthened unbonded PC members clearly show that the use of external FRP reinforcement is as effective in improving the nominal flexural strength of 417
unbonded PC members, as when used for strengthening bonded PC or RC members. Consequently, in designing the FRP system for flexural strengthening of unbonded PC members, no special guidelines are needed beyond those recommended in the ACI Committee 4402 report and the design-oriented approach proposed for unbonded members in this investigation. AUTHOR BIOS
Fatima El Meski is a Lecturer at the Lebanese American University, Beirut, Lebanon. She was formerly a PhD Student in the Department of Civil and Environmental Engineering at the American University of Beirut, Beirut, Lebanon. ACI member Mohamed H. Harajli is a Professor of civil engineering at the American University of Beirut. His research interests include design and behavior of reinforced, prestressed, and fiber-reinforced concrete members and strengthening and repair of concrete structures.
REFERENCES
1. ACI Committee 318, “Building Code Requirements for Reinforced Concrete and Commentary (ACI 318-11),” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp. 2. ACI Committee 440, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI
418
440.2R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 76 pp. 3. AASHTO, “LRFD Bridge Design Specifications,” American Association of State Highway and Transportation Officials, Washington, DC, 2004, 1324 pp. 4. Naaman, A. E.; Burns, N.; French, C.; Gamble, W. L.; and Mattock, A. H., “Stresses in Unbonded Prestressing Tendons at Ultimate: Recommendation,” ACI Structural Journal, V. 99, No. 4, July-Aug. 2002, pp. 518-529. 5. Harajli, M. H., “On the Stress in Unbonded Tendons at Ultimate: Critical Assessment and Proposed Changes,” ACI Structural Journal, V. 103, No. 6, Nov.-Dec. 2006, pp. 803-812. 6. Harajli, M. H., “Tendon Stress at Ultimate in Continuous Unbonded Post-Tensioned Members: Proposed Modification of ACI Eq. (18-4) and (18-5),” ACI Structural Journal, V. 109, No. 2, Mar.-Apr. 2012, pp. 183-192. 7. Menegotto, M., and Pinto, P. E., “Method of Analysis for Cyclically Loaded Reinforced Concrete Plane Frames.” IABSE Preliminary Report for Symposium on Resistance and Ultimate Deformability of Structures Acted on Well-Defined Repeated Loads, Lisbon, Portugal, 1973, pp. 15-22. 8. Harajli, M. H., and Hijazi, S., “Evaluation of the Ultimate Steel Stress in Unbonded Partially Prestressed Beams,” PCI Journal, V. 36, No. 2, Jan.-Feb. 1991, pp. 62-82. 9. Moon, J. H., and Burns, N. H., “Flexural Behavior of Members with Unbonded Tendons. II: Application,” Journal of Structural Engineering, ASCE, V. 123, No. 8, Aug. 1997, pp. 1095-1101. 10. El Meski, F., “Behavior of Unbonded Post Tensioned Members Strengthened Using External FRP Composites: Experimental Evaluation and Analytic Modeling,” PhD dissertation, Department of Civil and Environmental Engineering, American University of Beirut, Beirut, Lebanon, 2012, 283 pp.
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S37
Size Effect on Strand Bond and Concrete Strains at Prestress Transfer by José R. Martí-Vargas, Libardo A. Caro, and Pedro Serna-Ros The size-effect phenomenon has been analyzed with pretensioned prestressed concrete prismatic specimens at prestress transfer. An experimental program that includes variables such as concrete mixture design, specimen cross section size, and concrete age, has been conducted. Several series of specimens with different embedment lengths have been made and tested using a testing technique based on the bond behavior analysis by measuring prestressing strand force. In addition, some specimens have been instrumented to determine longitudinal concrete strain profiles. The tests have provided data on concrete strains, transfer length, effective prestressing force, bond stress, and concrete modulus of elasticity. Relationships between measured prestressing strand forces and effective prestressing forces obtained from concrete compressive strains have been found. A coefficient to account for the specimen crosssection size-effect on the concrete modulus of elasticity has been proposed. Comparisons between test results and theoretical predictions from pre-existing equations in the codes have been made. Keywords: bond; modulus of elasticity; prestress; size-effect; strain; strand; transfer length.
INTRODUCTION Force in a prestressing strand is transferred to concrete by bond in the case of pretensioned prestressed concrete members.1 At prestress transfer, the prestressing strand tends to shorten, the concrete around the prestressing strand shortens as the prestressing force is applied to it, and the prestressing strand that is bonded to the concrete shortens with it. Consequently, prestress loss due to the elastic shortening of concrete occurs in the central zone of the member. At the member ends, the prestressing strand force varies from zero to the effective prestressing force along the distance defined as transfer length2 (Fig. 1). Both bond strength and transfer length depend on several factors, such as concrete strength at prestress transfer, initial strand stress, concrete cover, prestress transfer method, strand geometry, and strand surface condition,3 and bond strength improves when a confining stress is applied.4,5 Average bond stress along the transfer length has been characterized as being proportional to the square root of the concrete compressive strength given the influence of the elastic modulus of the concrete that surrounds the prestressing strand.6 A short transfer length results in higher stresses and risk of cracking near member ends, and a long transfer length shortens the available member length to resist the bending moment and shear.6 As the transfer length is an important parameter in the design exercise,6,7 bond performance is assumed essential for an adequate response of pretensioned prestressed concrete applications, and quality ACI Structural Journal/March-April 2014
Fig. 1—Idealized prestressing strand force diagram. assurance procedures for bonded applications should be used.2 However, neither codes2,8,9 nor standards10,11 specify minimum requirements for the bond performance of prestressing strands, and there is no consensus on the main parameters to be considered in equations to compute transfer length12,13 or on a standard test method for bond quality.3 By way of example, the ACI 318-112 code provisions for transfer length are not a function of concrete strength, while the fib Model Code 20109 includes concrete properties; moreover, several test procedures to determine bond characteristics14,15 or to measure transfer length16,17 have been proposed as alternatives to the two most widely used methods18: measuring the strand end slip or determining the longitudinal concrete surface-strain profile. At prestress transfer, variation in strand stress along the transfer length involves slips between the strand and the surrounding concrete. These slips can be used to estimate transfer length,19,20 but the results obtained from transfer length estimations vary vastly.21 After prestress transfer, the longitudinal concrete surface strain profile also follows a similar law to that of the prestressing strand force shown in Fig. 1. Transfer length can be determined directly from the concrete strain profile18,22,23 by either the Slope-Intercept Method24 (by intersecting an adjusted line to the initial branch with an adjusted line to the central branch) or the 95% Average Maximum Strain (AMS) Method7 (by intersecting the initial branch with the horizontal line corresponding to 95% of the average strains in the central branch). Based on test results obtained from a recently developed experimental methodology, the ECADA (Ensayo para ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-174.R2, doi:10.14359.51686530, was received February 19. 2013, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
419
Table 1—Concrete mixture designs Designation 3
3
A
B
C
Cement, lb/yd (kg/m )
843 (500)
624 (370)
674 (400)
Water-cement ratio (w/c)
0.3
0.45
0.5
Aggregate 7/12, lb/yd3 (kg/m3)
1674 (993)
1637 (971)
1645 (976)
Sand 0/4, lb/yd3 (kg/m3)
1468 (871)
1448 (859)
1443 (856)
1.7 Polycarboxylate ether polymers
1.4 Modified polycarboxylic ethers
0.1 Modified polycarboxylic ethers
High-range water-reducing admixture additive
Concrete compressive strength, ksi (MPa)
(%) Type
12 hours
5.8 (40)
—
—
24 hours
7.5 (52)
4.6 (32)
3.5 (24)
48 hours
8.4 (58)
5.2 (36)
4.2 (29)
28 days
12.3 (85)
7.3 (50)
6.3 (43)
Note: 1 mm = 0.04 in.
Caracterizar la Adherencia mediante Destesado y Arrancamiento; in English: Test to Characterize the Bond by Release and Pull-Out) test method,17 the research herein analyzes the specimen cross section size-effect on strand bond and concrete strains at prestress transfer. Three different concrete mixture designs applicable to the precast prestressed concrete members industry, in combination with three different specimen cross sections, have been tested. RESEARCH SIGNIFICANCE This research provides information on how specimen cross section size-effect influences strand bond behavior and concrete strains at prestress transfer. This paper analyzes series of tests conducted on pretensioned prestressed concrete prismatic specimens using a testing technique based on bond behavior analysis by measuring prestressing strand force. The tests provide data on concrete strains, transfer length, effective prestressing force, bond stress, and concrete modulus of elasticity. A coefficient to account for the specimen cross section size-effect on the concrete modulus of elasticity is proposed. The experimental results have been compared with predictions from ACI 318-112 and fib Model Code 2010.9 EXPERIMENTAL RESEARCH An experimental program was conducted and the ECADA test method17 was used. The method allows for the analysis of bond behavior by the sequential reproduction of the prestress transfer and the anchorage of prestressing strands on the same specimen. A series of specimens with different embedment lengths is required to determine both transfer and development lengths25,26 by means of the ECADA test method. Its feasibility has been verified for both shorttime27,28 and long-term analyses.29,30 In this work, only the transfer length test results and analyses at prestress transfer were included. Complementarily, several specimens were also instrumented to obtain longitudinal concrete surface strains. Materials Three concrete mixtures applicable for the precast prestressed concrete industry with different compressive 420
strengths at the time of testing (fci′), ranging from 24 to 55 MPa (3.5 to 8.4 ksi), were tested. For all the concretes, the components were: cement CEM I 52.5 R,31 crushed limestone aggregate 7 to 12 mm (0.275 to 0.472 in.), washed rolled limestone sand 0 to 4 mm (0 to 0.157 in.), and a highrange water-reducing admixture additive. The mixtures of the tested concretes are shown in Table 1. The prestressing strand was a low-relaxation seven-wire steel strand specificied as UNE 36094:97 Y 1860 S7 13.010 with a guaranteed ultimate strength of 1860 MPa (270 ksi). The main characteristics were those according to the manufacturer: diameter, 13 mm (0.5 in.); cross-sectional area, 100 mm2 (0.154 in.2); ultimate strength, 200.3 kN (45.1 kip); yield stress at 0.2%; 189.9 kN (42.8 kip); and the modulus of elasticity, 203,350 MPa (29,500 ksi). The prestressing strand was used under the as-received condition (rust-free and lubricant-free). The strand was not treated in any special way. The strand was stored indoors and care was taken to not drag the strand along the floor. Testing program The variables considered in the test program were concrete mixture, specimen cross section, and concrete age at prestress transfer. A series of specimens with different embedment lengths were tested for each combination of variables selected. Embedment lengths followed increments of 50 mm (2 in.) in the nearness of the transfer length for its determination and specimens with 1350 mm (53.15 in.) were included to determine profiles of longitudinal concrete surface strains. Specimens were designed as M-D-T-L, where M is the concrete mixture type (A, B, or C); D is the specimen cross section size in mm (100, 80, or 60, for a 100 x 100 mm2 [3.94 x 3.94 in.2], 80 x 80 mm2 [3.15 x 3.15 in.2], and a 60 x 60 mm2 [2.36 x 2.36 in.2] cross section, respectively); T is the concrete age at prestress transfer (12, 24, or 48 hours); and L is the specimen embedment length (in mm). The designation for a complete series included only the parameters detailing M-D-T. In two cases (A-60-48, A-80‑12), only specimens with an embedment length of 1350 mm (53.15 in.) were made.
ACI Structural Journal/March-April 2014
Table 2—Test program Age at prestress transfer, hours
12
24
48
Concrete (specimen embedment lengths, mm) A
B
C
A-80-12 (1350)
—
—
A-100-12 (300, 400, 500, 550, 600, 650, 700, 750, 900, 1350)
—
—
A-60-24 (300, 450, 600, 950, 1350)
—
—
A-80-24 (300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 1350)
B-80-24 (550, 600, 650, 700, 750, 800, 1350)
—
A-100-24 (300, 400, 450, 500, 550, 600, 650, 700, 750, 900, 1350)
B-100-24 (300, 550, 600, 650, 700, 750, 800, 850, 1350)
C-100-24 (600, 650, 700, 750, 800, 1350)
A-60-48 (1350)
B-60-48 (300, 350, 400, 450, 500, 550, 600, 650, 950, 1000, 1350)
—
—
B-80-48 (300, 450, 500, 550, 600, 650, 700, 950, 1350)
C-80-48 (550, 600, 650, 800, 850, 900, 950, 1350)
—
B-100-48 (300, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 1350)
C-100-48 (550, 600, 650, 700, 750, 1350)
Note: 1 mm = 0.04 in.
Fig. 3—General view of test equipment. Fig. 2—Pretensioning frame layout. Table 2 summarizes the test program conducted and provides the embedment lengths of tested specimens. Test equipment and instrumentation The ECADA test method is based on measuring and analyzing the prestressing strand force in a series of pretensioned prestressed concrete specimens with different embedment lengths. Specimens are made and tested using pretensioning frames, as shown in Fig. 2. In this way, each specimen has only one end zone with the corresponding transfer length. Several components were coupled at both ends of the pretensioning frames to complete the test equipment. A hollow hydraulic jack of 300 kN (67.5 kip) capacity with an end-adjustable anchorage device was placed at one end to carry out tensioning, provisional anchorage, and detensioning of prestressing strands. At the opposite end, an Anchorage-Measurement-Access (AMA) system was placed to guarantee the anchorage of the prestressing strand and to simulate the specimen’s sectional stiffness. The AMA system was made up of a sleeve of 120 mm (4.72 in.) in length in the final specimen stretch (beyond the specimen embedment length), the end frame plate and an anchorage plate supported on the frame by two separators. Figure 3 shows a general view of the test equipment, which includes a pretensioning frame (blue components) of ACI Structural Journal/March-April 2014
2000 mm (78.74 in.) in length and both end frame plates of 320 x 320 x 50 mm (12.60 x 12.60 x 1.97 in.), and an anchorage plate of 320 x 200 x 60 mm (12.60 x 12.60 x 2.36 in.) supported by both 250 x 120 x 20 mm (9.84 x 9.84 x 0.79 in.) welded elements 250 mm (9.84 in.) in length (white components). The instrumentation used included a hydraulic jack pressure transducer to control the tensioning and detensioning operations; the AMA system included a hollow force transducer to measure the prestressing strand force; and in the specimens with an embedment length of 1350 mm (53.15 in.), detachable mechanical strain gauges were used to obtain the longitudinal concrete surface strain profile at the prestressing strand level. The gauge points were uniformly spaced at 50 mm (2 in.) intervals and were placed on two opposite specimen faces. No internal measuring devices were used in the test specimens to not distort the bond phenomenon. Test procedure Each ECADA test series included a variable number of specimens (usually 6 to 12). The step-by-step test procedure for each specimen is described in detail in Martí-Vargas et al.17 and may be summarized as follows (steps marked by “opt” have been included only for any specimens additionally instrumented to obtain the longitudinal concrete surface strains): a) Fabrication stage: 421
1. The strand is placed in the frame with both anchorage devices at the ends. 2. Strand tensioning is done using the hydraulic jack. 3. Provisional strand anchorage is done by the end-adjustable device. 4. The concrete is mixed, placed into the formwork in the frame, and consolidated. 5. The specimen is cured to achieve the desired concrete properties at the time of testing. b) Preparation stage: 1. The formwork is removed from the frame. 2. (opt) Attaching gauge points by epoxy glue along both the lateral sides of the specimen at the prestressing strand level. 3. (opt) Reading the initial set of distances between gauge points. 4. The end-adjustable strand anchorage is relieved using the hydraulic jack. c) Prestress transfer. Strand detensioning is produced by unloading the hydraulic jack. The specimen is supported on the end frame plate. d) Stabilization period. The prestressing strand force depends on not only the strain compatibility with the concrete specimen but also on its action in the AMA system. This force requires a stabilization period to guarantee its measurement. e) Measurement: 1. Measuring the prestressing strand force achieved (Pi) in the AMA system. 2. (opt) Rereading the set of distances between gauge points (after prestress transfer). Test parameters All the specimens were prestressed by a concentrically located single strand at a prestress level before releasing 75% of the guaranteed ultimate strength. Specimens were subjected to the same consolidation and curing conditions. The prestress transfer was gradually performed in each specimen at a controlled speed of 0.80 kN/s (0.18 kip/s). A 2-hour stabilization period after detensioning was established. DATA PROVIDED FROM TESTS The measured prestressing strand forces and sets of distances between gauge points were the direct data collected from the specimen test. Based on these direct data from a specimen or from complete series of specimens, and by means of back-calculations using theory of mechanics concepts, parameters such as concrete strains, transfer length, effective prestressing force, bond stress, and concrete modulus of elasticity can be obtained. Concrete strains Concrete strains can be obtained from the changes in distances between gauge points before and after the prestress transfer by dividing them by gauge length. The strain change for each gauge length was assigned to its center point. From the specimen free end, a profile with an ascendent branch, followed by a practically horizontal branch, was depicted
422
Fig. 4—Transfer length determination according to ECADA test method. when these strains were plotted according to specimen embedment length. Transfer length Approximation to transfer length determination can be obtained directly from the longitudinal concrete strain profile of a specimen with a long embedment length (1350 mm [53.15 in.] in this research), such as ascendent branch length. In this work, the 95% Average AMS Method7 was used. On the other hand, for a complete series of specimens tested with the ECADA test method, the measured Pi forces can be ordered according to specimen embedment lengths (Fig. 4). The obtained curve presented a bilinear tendency, with an ascendent initial branch and horizontal branch corresponding to effective prestressing force Pe. Transfer length Lt corresponded to the embedment length that marked the beginning of the horizontal branch—that is, it corresponded to the shorter specimen embedment length, where Pi = Pe. Effective prestressing force Beyond transfer length, compatibility of the strains between the prestressing strand and the concrete exists: the prestressing strand strain change Δεp accounted for just before the prestress transfer is equal to the concrete strain change Δεc. Therefore, effective prestressing strand force can be obtained from the concrete strains according to Eq. (1)
Pes = P0 – ΔP = P0 – Δεp · Ep · Ap (1)
where Pes is the effective prestressing strand force obtained from the measured specimen strains; P0 is the prestressing strand force just before the prestress transfer; ΔP is the prestress loss due to elastic concrete shortening (ΔP = Δεp · Ep · Ap); Δεp is the prestressing strand strain change beyond the transfer length, accounted for just before the prestress transfer (Δεp = Δεc); Ep is the modulus of elasticity of the prestressing strand; and Ap is the prestressing strand area. In addition, effective prestressing strand force can be measured directly from the AMA system on specimens with an embedment length equal to or longer than the transfer length. An ideal AMA system must have the same sectional stiffness as the specimen,17 which depends on the concrete ACI Structural Journal/March-April 2014
Fig. 6—Concrete strain profile for Specimen B-100-48-1350.
Fig. 5—End-discontinuity effect. properties and the specimen cross section. Different AMA system designs should be devised for different test conditions. However, it would not be feasible to design a system for each specific test condition. For this reason, the stiffness of the designed AMA system was greater than the specimen’s sectional stiffness. Consequently, the prestressing strand force measured in the AMA system after the prestress transfer was greater than the effective prestressing force in the specimen. This difference of forces caused an enddiscontinuity effect and gave rise to a slight overestimation of the real transfer length (Fig. 5). Bond stress Based on the equilibrium of the effective prestressing strand force achieved, the average bond stress along the tranfer length can be obtained according to Eq. (2) ut =
Pe 4 3 πf Lt
(2)
where ut is the average bond stress along the transfer length; Pe is the effective prestressing force; (4πφ/3) is the actual seven-wire strand perimeter; φ is the nominal diameter of prestressing strand; and Lt is the transfer length. Concrete modulus of elasticity An early concrete modulus of elasticity at prestress transfer for each specimen can be obtained from prestress loss due to elastic concrete shortening and the transformed cross-section properties according to Eq. (3)
P0 1 ∆e ci = ⋅ 1 + nρ Eci Ac
P0 − E p Ap ∆e ci or Eci = (3) Ac
where Δεci is the elastic shortening strain of concrete due to the prestress transfer; P0 is the prestressing strand force
ACI Structural Journal/March-April 2014
just before prestress transfer; n is the initial steel modular ratio (n = Ep/Eci, where Ep is the modulus of elasticity of the prestressing strand and Eci is the concrete modulus of elasticity at prestress transfer); ρ is the geometric ratio (ρ = Ap/Ac, where Ap is the prestressing strand area and Ac is the net cross-sectional area of the specimen). EXPERIMENTAL RESULTS AND DISCUSSION Concrete strains By way of example based on the collected test data, Fig. 6 provides the concrete strain profile for Specimen B-100-48-1350. The results are obtained by averaging the readings from the two opposite specimen faces. Three regions can be distinguished: initial branch, plateau, and end-discontinuity. In this case, a transfer length of 600 mm (23.6 in.) is observed directly from the curve, and another of 575 mm (22.6 in.) is determined from the 95% AMS. Beyond the transfer length, greater concrete strains— Δεci = 0.00075—result because of the early age of concrete at prestress transfer. The influence of specimen cross section size-effect on the average concrete strains beyond the transfer length is depicted in Fig. 7. A strong influence is observed and explained because of the combined effects of the different concrete stress levels and the deformability behavior related to the specimens’ cross sections. The concrete stress level can be obtained by dividing the effective prestressing force, transferred according to Eq. (1), between the specimen’s net cross-sectional area and the concrete compressive strength at prestress transfer. As Fig. 8 depicts, for the same concrete type and concrete age at prestress transfer, the concrete stress level and concrete strains evidently increase when the specimen cross section decreases. Besides, the specimens with different concrete stress levels present similar concrete strains when specimens are of the same cross section size: approximately 0.0008 for specimens with a larger cross section, between 0.0012 and 0.0016 for specimens with an intermediate cross section, and approximately 0.0020 for specimens with a smaller cross section. However, for the same concrete stress level, concrete strains significantly increase when the cross section size reduces. This implies that a significant deformability behavior relating to the specimen cross section exists. This fact will be analyzed later by considering the concrete modulus of elasticity. 423
Fig. 7—Concrete strain versus specimen side cross section.
Fig. 9—Prestressing strand forces for Series B-100-48.
Fig. 8—Concrete strain versus concrete stress level.
Fig. 10—Measured and predicted transfer length.
Transfer length Figure 9 provides the transferred prestressing forces versus the embedment lengths for the complete B-100-48 series. All the test specimens with embedment lengths equal to or longer than 650 mm (25.6 in.) present similar Pi values and are, therefore, equal to the effective prestressing force Pe. In contrast, all the test specimens with embedment lengths shorter than 650 mm (25.6 in.) present lower Pi values. Therefore, the transfer length determined by the ECADA test method can be affirmed as 650 mm (25.6 in.) in this case. Figure 10 shows the transfer length obtained from concrete strains (directly [two values are depicted when the ascendent branch length is unclear] and by 95% AMS) and from prestressing strand forces. Specimens have been ordered by concrete mixture by increasing cross section size and concrete age at prestress transfer. As observed in Fig. 10, the transfer lengths in the specimens made with Concrete C are longer than those in the specimens made with Concrete B which, in turn, are longer than the transfer lengths in the specimens made with Concrete A: C-100-48/B-100-48, C-100-24/B-100-24/A-100-24, C-80-48/B-80-48, B-80-24/A-80-24, and B-60-48/A-60-48. Generally, transfer length values also reduce when concrete age at prestress transfer increases: A-60-24/A-60-48, A-80-12/A-80-24, A-100-12/A-100-24, B-80-24/B-80-48, and C-100-24/C-100-48, except for B-100-24/B-100-48. Besides, similar transfer lengths are obtained for the 100 x
100 mm2 (3.94 x 3.94 in.2) and the 80 x 80 mm2 (3.15 x 3.15 in.2) specimen cross sections. However, A-60-48 and B-60-48 show the shortest transfer lengths, while A-60-24 presents a high value. The transfer lengths predicted according to ACI 318-112 and fib Model Code 20109 from the measured parameters are included in Fig. 10. As observed, the predictions from ACI 318-112 have similar values, as only strand parameters are considered. However, the predictions from fib Model Code 20109 vary vastly as concrete properties are also considered. ACI 318-112 overestimates transfer length, except for Concrete Mixture C, while fib Model Code 20109 generally overestimates it (only case A-60-24 is underestimated).
424
Effective prestressing force Figure 11 shows the measured prestressing strand forces in the AMA system (P0, Pe), and the effective prestressing forces (Pes) obtained according to Eq. (1). For each complete series, P0 and Pe are obtained by averaging the corresponding prestressing strand forces P0 and Pi from those specimens with an embedment length equal to or longer than the transfer length. Due to the end-discontinuity effect, overestimation of the effective prestressing strand force is observed; Pe is always greater than Pes for all the specimens. Effective prestressing force increases within the same concrete mixture when the specimen cross section and the concrete age at prestress transfer increase. These tendencies are seen more clearly by the specimen strains.
ACI Structural Journal/March-April 2014
Fig. 11—Effective prestressing force. Bond stress According to Eq. (2), Fig. 12 shows the average bond stress along the measured transfer lengths from the two techniques, based on strains or forces. Predicted bond stress values from ACI 318-112 and fib Model Code 20109 have been included for comparison purposes: a constant value of 2.76 MPa (0.4 ksi)32 results from ACI 318-11,2 and 3.2fctdi (0.464fctdi)12—where fctdi is the specified tensile strength at prestress transfer—results from fib Model Code 2010.9 Besides, a corrected value has been obtained from fib Model Code 20109 by applying a 0.75 factor based on the ratio between nominal and actual strand perimeter (πφ in fib Model Code 20109 and 4πφ/3 in ACI 318-112 and Eq. (2), respectively).33 As observed in Fig. 12, the predictions from fib Model Code 20109 are of the measured values order and follow the logical sequence for the different concrete types and within the same concrete type by varying specimen cross-section size and concrete age at prestress transfer, except for A-60-24 and A-60-48. The predictions from ACI 318-112 and the corrected predictions from fib Model Code 20109 show global tendencies in accordance with the transfer lengths depicted in Fig. 10; but inversely, however, in this case, transfer length increases when bond stress decreases. As observed in Fig. 12, the bond stresses in the specimens made with Concrete A are greater than those in the specimens made with Concrete B which, in turn, are greater than the bond stresses in the specimens made with Concrete C. The specimen cross section size-effect on the average bond stresses can be analyzed from Fig. 13: a) greater bond stress values for larger specimen cross sections are observed in some cases (A-24h, B-24h, and C-48h); b) similar bond stress values are obtained for A-12h irrespectively of the specimen cross sections; and c) bond stress values decrease for B-48h when the specimen cross section increases. Some authors have found these tendencies: examples of reported increases in bond strength with increases of concrete cover thickness (or specimen cross section) can be found in the literature34,35 and also examples of a size effect on bond strength, which reduces as concrete cover thickness increases.36 Finally, Fig. 13 also shows that, for the same
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Fig. 12—Average bond stress along transfer length.
Fig. 13—Average bond stress versus specimen side cross section. cross-section size, the bond stress values rise when concrete age at prestress transfer increases (except for Concrete B and side 100 mm [3.94 in.]). Concrete modulus of elasticity: cross section size-effect Figure 14 shows the experimental Eci value according to Eq. (3) for each specimen with an embedment length of 1350 mm (53.15 in.). As seen, higher Eci values are obtained when concrete compressive strength increases, when specimen cross section increases, and when concrete age at prestress transfer increases. The early concrete modulus of elasticity is commonly only obtained from the concrete compressive strength at 28 days. To this end, as ACI 318-112 overestimates the concrete modulus of elasticity for very early-age and concrete compressive strengths above 50 MPa (7.25 ksi),37 the fib Model Code 20109 provisions (Eq. (4) to Eq. (6)) are taken as a reference Ec 28
f = 19, 400 cm 10
1/ 3
(Eq. 5.1 − 21)9 (4)
Ec(t) = [βcc(t)]0.5 · Ec28 (Eq. 5.1-56)9 (5)
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Fig. 14—Experimental concrete modulus of elasticity at prestress transfer.
28 0.5 bcc (t ) = exp s ⋅ 1 − (Eq. 5.1 − 51)9 (6) t
where Ec28 is the concrete modulus of elasticity at 28 days (MPa); fcm is the concrete compressive strength at 28 days (MPa); Ec(t) is the concrete modulus of elasticity at age t; βcc(t) is a coefficient to describe development with time; s is a coefficient to account for the strength class of cement (s = 0.2 for Class 52.5 R); and t is concrete age (days). To analyze the specimen cross section size-effect on the concrete modulus of elasticity from the obtained test results, several adjustments of the experimental Eci values (Eq. (3)) and the expected Ec(t) values at prestress transfer (Eq. (5)) are made as shown in Fig. 15. Therefore, the following equation is proposed Eci = λ · Ec(t) (7) where λ is a coefficient to account for the cross-section size-effect: 0.721 for 100 x 100 mm2 (3.94 x 3.94 in.2) specimen cross section, 0.612 for 80 x 80 mm2 (3.15 x 3.15 in.2), and 0.523 for 60 x 60 mm2 (2.36 x 2.36 in.2). The concrete modulus of elasticity for each specimen at 28 days (Ec28_s) can be obtained as follows: 1. Determination of Eci (Eq. (3)). 2. Computation of a concrete modulus of elasticity at 28 days (Ec28_s) using Eq. (5) with Ec(t) = Eci. 3. Application of the λ coefficient (Eq. (7)), as follows: Ec28_s = λ· Ec28_ref. 4. The Ec28_ref values are obtained. These values have good agreement with the fib Model Code 20109 provisions (Eq. (4)) for each concrete mixture, as shown in Fig. 16. Therefore, the λ coefficient—initially obtained at prestress transfer—is also applicable at 28 days. 5. An Ec28_m value is computed for each concrete mixture by averaging the Ec28_ref values from the specimens made with the same concrete mixture. 6. The Ec28_s values are obtained using Eq. (7): Ec28_s = λ· Ec28_m.
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Fig. 15—Comparison of concrete modulus of elasticity at prestress transfer.
Fig. 16—Comparison of concrete modulus of elasticity at 28 days. The results of this process are presented in Table 3. Also, the Ec28_s values can be obtained approximately from the concrete compressive strength through Ec28 (Eq. (4)) using Eq. (7): Ec28_s = λ· Ec28; and an expected Eci can be computed using Eq. (5), by substituting Ec(t) for Eci and Ec28 for Ec28_s. Concrete modulus of elasticity: influence of concrete stress A normalized concrete modulus of elasticity Eci* = Eci/λ (Eci from Eq. (3) and λ from Eq. (7)) is obtained to avoid the cross section size-effect. Figure 17 depicts the obtained Eci* relating to the concrete stress level. As observed, for the same concrete type and concrete age at prestress transfer, the tendencies when the concrete stress level increases are as follows: Eci* decreases for Series A-12 h and B-24 h and Eci* increases for Series C-48 h, with Eci* practically nothing varies for Series A-24 h and B-48 h. Besides, a general tendency showing similar Eci* values for different concrete stress levels (refer to the horizontal line) is observed when considering all the series. Therefore, the concrete modulus of elasticity seems to be practically independent of concrete stress, and the main influence is based on the specimen cross section size-effect.
ACI Structural Journal/March-April 2014
Table 3—Concrete modulus of elasticity, MPa Modulus of elasticity of concrete, MPa fib Model Code 20109
Experimental Specimen
Eci
Ec28_s
Ec28_ref
Ec28_s
Eci
A-60-24
13,790
21,180
40,498
20,848
20,707
13,481
A-60-48
16,205
21,317
40,759
20,848
20,707
15,741
A-80-12
11,221
21,458
35,062
24,230
12,670
A-80-24
15,820
24,299
39,703
24,230
15,775
A-100-12
16,718
31,971
44,342
28,741
28,546
14,927
A-100-24
18,219
27,984
38,812
28,741
28,546
18,585
B-60-48
12,296
16,175
30,927
17,190
17,350
13,189
B-80-24
13,146
20,191
32,992
20,116
20,302
13,218
Ec28_m
39,863
Ec28_s
24,396 24,396
39,592
B-80-48
16,037
21,095
34,470
20,302
15,434
B-100-24
16,002
24,578
34,088
23,698
23,918
15,572
B-100-48
17,465
22,975
31,865
23,698
23,918
18,183
C-80-48
15,366
20,213
33,027
19,320
19,307
14,677
C-100-24
14,742
22,643
31,405
22,745
14,809
C-100-48
16,594
21,828
30,275
22,745
17,291
32,868
31,569
20,116
Ec28
22,761 22,761
33,174
31,547
Note: 1 MPa = 145 psi.
Fig. 17—Concrete modulus of elasticity versus concrete stress level.
Fig. 18—Comparison of elastic shortening losses.
Concrete modulus of elasticity: elastic shortening prestress loss Finally, to verify the applicability of the obtained λ coefficients to account for the cross section size-effect, predicted prestress losses due to the elastic shortening of concrete from the measured and theoretical parameters are estimated using preexisting equations. According to the ACI 318-11 Commentary,2 prestress losses can be calculated in accordance with several procedures.38,39 Figure 18 shows the measured and predicted prestress losses due to the elastic shortening of concrete for all the specimens with an embedment length of 1350 mm (53.15 in.). The λ coefficient has been applied in all cases. As observed in Fig. 18, the predicted prestress losses follow the tendencies of measured prestress losses. The prestress loss ranges with values of 10% for those specimens with a larger cross section, with values of 15 to 20% for those with an intermediate cross section, and of 25 to 30%
for those specimens with a smaller cross section. This fact can be explained by the different concrete stress levels and the deformability behavior relating to cross sections of specimens. Therefore, a clear effect of specimen cross section size on prestress loss cannot be ruled out. Moreover, Fig. 18 shows that the tendencies of the measured prestress losses according to the variable’s concrete mixture, specimen cross section size, and concrete age at prestress transfer are followed by the prestress losses predicted by all the methods: prestress losses disminish in the same concrete mixture when the specimen cross section increases and when the concrete age at prestress transfer increases, and prestress losses in the specimens made with Concrete C are greater than those in the specimens made with Concrete B, which are also greater than the prestress losses in the specimens made with Concrete A. The PCI CPL39 predictions made with experimental Eci (Eq. (3)) and fib Model Code 20109 practically coincide with the measured
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prestress losses. However, the PCI CPL39 predictions made with Eci according to ACI 318-112 underestimate prestress losses as the concrete modulus of elasticity is overestimated. For Zia et al.38 predictions, which consider gross section properties, an overestimation trend of prestress losses for cases with smaller specimen cross section sizes is observed. CONCLUSIONS Based on the results of this experimental research, the following main conclusions can be drawn: • Transfer lengths have been determined by two techniques: the longitudinal concrete strain profile and prestressing strand forces. Based on both techniques, transfer length values are higher when concrete quality diminishes. • The transfer lengths predicted from ACI 318-112 have similar values, irrespectively of concrete quality, as only strand parameters are considered. However, the fib Model Code 20109 predictions vary considerably as concrete properties are also considered. ACI 318-112 overestimates transfer length when concrete quality is good, while fib Model Code 2010 overestimates in general. • A strong influence of specimen cross section size-effect on average concrete strains beyond transfer length has been observed. This fact can be explained by the combined effects of different concrete stress levels and deformability behavior in relation to the cross sections of specimens. • The effective prestressing force increases in the same concrete mixture when specimen cross section and concrete age at prestress transfer increase. These tendencies are seen more clearly with the specimen strains technique rather than with the strand forces technique. • Higher bond stress values for larger specimen cross sections have been observed in most cases. For the same cross section size, bond stress values are greater when the concrete age at prestress transfer increases and when concrete quality increases. • The concrete modulus of elasticity at prestress transfer has been obtained from the experimental data of prestressed specimens. Higher concrete modulus of elasticity values result from greater concrete compressive strength, larger specimen cross section, and older concrete age at prestress transfer. • A coefficient to account for the specimen cross section size-effect on the concrete modulus of elasticity is proposed. • fib Model Code 2010 predictions for transfer length, average bond stress, concrete modulus of elasticity at prestress transfer, and elastic shortening prestress loss have showed a best agreement to the experimental results than the ACI 318-112 predictions. AUTHOR BIOS
José R. Martí-Vargas is an Associate Professor of civil engineering at the Universitat Politècnica de València (UPV), València, Spain, where he received his MEng in civil engineering and his PhD. His research interests include the bond behavior of reinforced and prestressed concrete structural
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elements, fiber-reinforced concrete, durability of concrete structures, and strut-and-tie models. Libardo A. Caro is an Assistant Researcher and PhD Candidate in the Department of Construction Engineering and Civil Engineering Projects at UPV. He received his civil engineering degree from the Universidad Santo Tomás, Bogotá, Colombia. His research interests include bond properties of prestressed concrete structures and the use of advanced cement-based materials in structural applications. Pedro Serna-Ros is a Professor of civil engineering at UPV, where he received his MEng in civil engineering; he received his PhD from École Nationale des Ponts et Chaussées, Paris, France. His research interests include self-consolidating concrete, fiber-reinforced concrete, and the bond behavior of reinforced and prestressed concrete.
ACKNOWLEDGMENTS
Funding for this research has been provided by the Spanish Ministry of Education and Science, the Ministry of Science and Innovation, and ERDF (Projects BIA2006-05521 and BIA2009-12722).
REFERENCES
1. Janney, J., “Nature of Bond in Pretensioned Prestressed Concrete,” ACI Journal, V. 51, No. 5, May 1954, pp. 717-737. 2. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 473 pp. 3. fib, “Bond of Reinforcement in Concrete. State-of-Art Report,” Fédération Internationale du Béton, Bulletin d’Information No. 10, Lausanne, Switzerland, 2000, 427 pp. 4. ElBatanouny, M. K.; Ziehl, P. H.; Larosche, A.; Mays, T.; and Caicedo, J. M., “Bent-Cap Confining Stress Effect on the Slip of Prestressing Strands,” ACI Structural Journal, V. 109, No. 4, July-Aug. 2012, pp. 487-496. 5. ElBatanouny, M. K., and Ziehl, P. H., “Determining Slipping Stress of Prestressing Strands in Confined Sections,” ACI Structural Journal, V. 109, No. 6, Nov.-Dec. 2012, pp. 767-776. 6. Barnes, R. W.; Grove, J. W.; and Burns, N. H., “Experimental Assessment of Factors Affecting Transfer Length,” ACI Structural Journal, V. 100, No. 6, Nov.-Dec. 2003, pp. 740-748. 7. Russell, B. W., and Burns, N. H., “Measured Transfer Lengths of 0.5 and 0.6 in. Strands in Pretensioned Concrete,” PCI Journal, V. 44, No. 5, Sept.-Oct. 1996, pp. 44-65. 8. CEN, “Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings,” European Standard EN 1992-1-1:2004:E, Comité Européen de Normalisation, Brussels, Belgium, 2004, 225 pp. 9. fib, “Model Code 2010. First complete draft—Volume 1,” Fib Bulletin No. 55, International Federation for Structural Concrete, Lausanne, Switzerland, 2010, 292 pp. 10. AENOR, “UNE 36094: Alambres y Cordones de Acero para Armaduras de Hormigón Pretensado,” Asociación Española de Normalización y Certificación, Madrid, Spain, 1997, 21 pp. 11. ASTM A416/A416M-10, “Standard Specification for Steel Strand, Uncoated Seven-Wire for Prestressed Concrete,” ASTM International, West Conshohocken, PA, 2010, 5 pp. 12. Martí-Vargas, J. R.; Arbeláez, C. A.; Serna-Ros, P.; Navarro-Gregori, J.; and Pallarés-Rubio, L., “Analytical Model for Transfer Length Prediction of 13 mm Prestressing Strand,” Structural Engineering & Mechanics, V. 26, No. 2, 2007, pp. 211-229. 13. Martí-Vargas, J. R.; Serna, P.; Navarro-Gregori, J.; and Pallarés, L., “Bond of 13 mm Prestressing Steel Strands in Pretensioned Concrete Members,” Engineering Structures, V. 41, 2012, pp. 403-412. 14. Moustafa, S., “Pull-out Strength of Strand and Lifting Loops,” Technical Bulletin 74-B5, Concrete Technology Associates, Tacoma, WA, 1974, 34 pp. 15. Cousins, T. E.; Badeaux, M. H.; and Moustafa, S., “Proposed Test for Determining Bond Characteristics of Prestressing Strand,” PCI Journal, V. 37, No. 1, Jan.-Feb. 1992, pp. 66-73. 16. Peterman, R. J., “A Simple Quality Assurance Test for Strand Bond,” PCI Journal, V. 54, No. 2, 2009, pp. 143-161. 17. Martí-Vargas, J. R.; Serna-Ros, P.; Fernández-Prada, M. A.; MiguelSosa, P. F.; and Arbeláez, C. A., “Test Method for Determination of the Transmission and Anchorage Lengths in Prestressed Reinforcement,” Magazine of Concrete Research, V. 58, No. 1, Feb. 2006, pp. 21-29. 18. Thorsen, N., “Use of Large Tendons in Pretensioned Concrete,” ACI Journal, V. 52, No. 2, Feb. 1956, pp. 649-659.
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19. Guyon, Y., “Béton Précontrainte. Étude Théorique et Expérimentale,” Ed. Eyrolles, Paris, France, 1953, 711 pp. 20. Balázs, G., “Transfer Length of Prestressing Strand as a Function of Draw-in and Inicial Prestress,” PCI Journal, V. 38, No. 2, Mar.-Apr. 1993, pp. 86-93. 21. Martí-Vargas, J. R.; Arbeláez, C. A.; Serna-Ros, P.; and Castro-Bugallo, C., “Reliability of Transfer Length Estimation from Strand End Slip,” ACI Structural Journal, V. 104, No. 4, July-Aug. 2007, pp. 487-494. 22. Mahmoud, Z. I.; Rizkalla, S. H.; and Zaghloul, E. R., “Transfer and Development Lengths of Carbon Fiber Reinforcement Polymers Prestressing Reinforcement,” ACI Structural Journal, V. 96, No. 4, July-Aug. 1999, pp. 594-602. 23. Caro, L. A.; Martí-Vargas, J. R.; and Serna, P., “Prestress Losses Evaluation in Prestressed Concrete Prismatic Specimens,” Engineering Structures, V. 48, 2013, pp. 704-715. 24. Deatherage, J. H.; Burdette, E.; and Chew, C. K., “Development Length and Lateral Spacing Requirements of Prestressing Strand for Prestressed Concrete Bridge Girders,” PCI Journal, V. 39, No. 1, Jan.-Feb. 1994, pp. 70-83. 25. Martí-Vargas, J. R.; Arbeláez, C. A.; Serna-Ros, P.; Fernández-Prada, M. A.; and Miguel-Sosa, P. F., “Transfer and Development Lengths of Concentrically Prestressed Concrete,” PCI Journal, V. 51, No. 5, Sept.-Oct. 2006, pp. 74-85. 26. Martí-Vargas, J. R.; Serna, P.; and Hale, W. M., “Strand Bond Performance in Prestressed Concrete Accounting for Bond Slip,” Engineering Structures, V. 51, 2013, pp. 236-244. 27. Martí-Vargas, J. R.; Serna-Ros, P.; Arbeláez, C. A.; and Rigueira-Victor, J. W., “Bond Behaviour of Self-Compacting Concrete in Transmission and Anchorage,” Materiales de Construcción, V. 56, No. 284, 2006, pp. 27-42. 28. Martí-Vargas, J. R.; Serna, P.; Navarro-Gregori, J.; and Bonet, J. L., “Effects of Concrete Composition on Transmission Length of Prestressing Strands,” Construction & Building Materials, V. 27, 2012, pp. 350-356. 29. Martí-Vargas, J. R.; Caro, L.; and Serna, P., “Experimental Technique for Measuring the Long-Term Transfer Length in Prestressed Concrete,” Strain, V. 49, 2013, pp. 125-134.
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30. Caro, L. A.; Martí-Vargas, J. R.; and Serna, P., “Time-Dependent Evolution of Strand Transfer Length in Pretensioned Prestressed Concrete Members,” Mechanics of Time-Dependent Materials, V. 17, No. 4, Nov. 2013, pp. 501-527. 31. EN 197-1:2000, “Cement. Part 1: Compositions, Specifications and Conformity Criteria for Common Cements,” Comité Européen de Normalisation, Brussels, Belgium, 2000, 30 pp. 32. Tabatabai, H., and Dickson, T., “The History of the Prestressing Strand Development Length Equation,” PCI Journal, V. 38, No. 5, Sept.-Oct. 1993, pp. 64-75. 33. Martí-Vargas, J. R., and Hale, W. M., “Predicting Strand Transfer Length in Pretensioned Concrete: Eurocode versus North American Practice,” Journal of Bridge Engineering, ASCE, V. 18, No. 12, Dec. 2013, pp. 1270-1280. 34. Yerlici, V. A., and Özturan, T., “Factors Affecting Anchorage Bond Strength in High-Performance Concrete,” ACI Structural Journal, V. 97, No. 3, May-June 2000, pp. 499-507. 35. García-Taengua, E.; Martí-Vargas, J. R.; and Serna-Ros, P., “Statistical Approach to Effect of Factors Involved in Bond Performance of Steel Fiber-Reinforced Concrete,” ACI Structural Journal, V. 108, No. 4, July-Aug. 2011, pp. 461-468. 36. Ichinose, T.; Kanayama, Y.; Inoue, Y.; and Bolander, J. E., “Size Effect on Bond Strength of Deformed Bars,” Construction & Building Materials, V. 18, 2004, pp. 549-558. 37. Khan, A. A.; Cook, W. D.; and Mitchell, D., “Early Age Compressive Stress-Strain Properties of Low-, Medium-, and High-Strength Concretes,” ACI Materials Journal, V. 92, No. 6, Nov.-Dec. 1995, pp. 617-624. 38. Zia, P.; Preston, H. K.; Scott, N. L.; and Workman, E. B., “Estimating Prestress Losses,” Concrete International, V. 1, No. 6, June 1979, pp. 32-38. 39. PCI Commitee on Prestress Losses, “Recommendations for Estimating Prestress Losses,” PCI Journal, V. 20, No. 4, July-Aug. 1975, pp. 43-75.
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NOTES:
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ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S38
Proposed Minimum Steel Provisions for Prestressed and Nonprestressed Reinforced Sections by Natassia R. Brenkus and H. R. Hamilton The current ACI code includes two separate provisions for minimum steel reinforcement: one for nonprestressed reinforced sections, and another for prestressed sections. For nonprestressed reinforced sections, the current minimum steel requirement is written in terms of geometric and material properties of the section. For prestressed concrete, the current provision is written in terms of the cracking moment of the section. Prestressed concrete only cracks when the applied flexural tensile stress exceeds both the tensile strength of the concrete and the net compressive stress from the prestressing force in the steel. Consequently, when bonded prestressing steel quantities are increased, the cracking moment of the section increases. Depending on the shape of the cross section and ultimate strength requirements, in certain instances it is possible that a section can contain a large volume of bonded prestressing steel and yet not meet the minimum reinforcement requirement. A parametric study of several cross sections was performed to investigate this behavior. This paper describes an exact and unified solution approach for specifying minimum reinforcement for both nonprestressed and prestressed sections. A second parametric study to validate the proposed minimum steel provisions is also presented. Keywords: ductile design; flexure; minimum reinforcement; prestressed concrete.
INTRODUCTION Reinforced and prestressed concrete members are typically designed with a minimum quantity of flexural reinforcement. Steel reinforcement ensures that the postcracking flexural capacity of the section is greater than the cracking moment Mcr, which is typically defined as the moment necessary to cause the maximum flexural tensile stress to exceed the modulus of rupture of the concrete. If a beam with insufficient reinforcement cracks, then the reinforcement will rupture immediately following crack formation; the resulting failure mode, being sudden and brittle, is undesirable and dangerous. Consequently, minimum reinforcement requirements have life-safety implications. Both AASHTO LRFD (AASHTO 2007) and ACI 318-11 (ACI Committee 318 2011) design specifications have minimum reinforcement requirements. ACI 318-11 has separate provisions for nonprestressed and prestressed concrete. The current nonprestressed provisions do not explicitly consider cracking moment, while the prestressed provisions require the direct calculation of cracking moment. This is true in the AASHTO LRFD as well. The AASHTO LRFD, however, applies to both prestressed and nonprestressed concrete. Although both design specifications aim to ensure that flexural members contain a sufficient quantity of reinforcement so that the post-cracking flexural capacity is at least equal to the cracking moment of the concrete section, the method of implementation has been somewhat different. ACI Structural Journal/March-April 2014
Explicit consideration of the cracking moment when determining minimum reinforcement leads to an iterative problem, sometimes without solution. Prestressed concrete only cracks when the applied flexural tensile stress exceeds both the net compressive stress from the prestressing force in the steel and the tensile strength of the concrete. Consequently, when bonded prestressing steel quantities are increased, the cracking moment of the section increases. In certain instances, depending on the shape of the cross section and ultimate strength requirements, it is possible for a section to contain a large volume of bonded prestressing steel yet fail to meet the minimum reinforcement requirement. This issue has been raised by others (Kleymann et al. 2006; Freyermuth and Aalami 1997; Ghosh 1986). To address this issue and the inherent problem of separate provisions for prestressed and nonprestressed concrete, a unified approach for determining minimum reinforcement for both nonprestressed and prestressed sections was derived, and is presented in this paper. The proposed provisions are based on minimum steel concepts for prestressed concrete introduced by Leonhardt (1964), avoid the explicit consideration of cracking moment, and are applicable to both prestressed and nonprestressed concrete. The parametric studies presented in this paper compare the proposed provisions with current provisions and detailed calculations of moment capacity using a direct tensile concrete behavior approach rather than the modulus of rupture. Simplified forms of the provisions are presented for rectangular and T-shaped members. RESEARCH SIGNIFICANCE ACI 318-11 has different minimum reinforcement requirements for prestressed and nonprestressed reinforcement. Furthermore, the current method of calculating the minimum steel requirements for prestressed members results in a variable quantity of minimum reinforcement, which depends on the prestress level. Such an approach can result in an inefficient use of reinforcing steel or even, in some circumstances, the inability to satisfy the minimum reinforcement requirements. The derivation and parametric studies described in this paper provide a direct and unified method of determining minimum steel requirements for both nonprestressed reinforced and prestressed sections. ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-175.R1, doi:10.14359.51686531, was received July 17, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
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CURRENT PROVISIONS: HISTORICAL PERSPECTIVE The earliest known minimum reinforcement requirement appeared in a 1936 ACI committee document. A minimum area of steel satisfying Eq. (1) was required for nonprestressed concrete (ACI Committee 501 1936)
AASHTO LRFD PROVISIONS AASHTO LRFD specifications (2007) have unified provisions that apply to sections containing either prestressed or nonprestressed reinforcement, or both. To meet the minimum reinforcement requirements, the flexural resistance Mr should satisfy Eq. (3) or (4)
As,min = 0.0005b′d (1)
Mr ≥ 1.2Mcr (3)
where b′ is the width of web in I- or T-beam sections, and d is the depth from the compression face to the center of the longitudinal tensile reinforcement. In 1954, the Bureau of Public Roads issued design requirements for prestressed concrete bridges (Bureau of Public Roads 1954) and, in 1958, general recommendations were published for the design of prestressed concrete (ACI-ASCE Committee 323 2004). Neither of these documents, however, contained minimum reinforcement requirements for prestressed concrete. In 1963, prestressed concrete was incorporated within the scope of ACI 318-63 (ACI Committee 318 1963); the committee reasoned that combined discussion of the nonprestressed and prestressed reinforced concrete was less confusing than their separate consideration. To this end, ACI 318-63 combined nonprestressed reinforced and prestressed concrete under the generic term “reinforced concrete”; it included, however, two separate requirements for minimum tensile reinforcement. During this code cycle, the minimum reinforcement provision for nonprestressed concrete was rewritten in terms of p, the ratio of the area of the tension reinforcement to the effective area of the concrete. As a lower limit, an area of steel satisfying 200bd/fy was required; this absolute minimum was derived by equating the ultimate strength of the section without reinforcement to the ultimate strength of the section with reinforcement and solving for p (ACI Committee 318 1963). In cases where the provided area of reinforcement was one-third greater than that required by analysis, the minimum reinforcement requirement was considered satisfied—an exception included to ensure that the minimum reinforcement required for large members was not excessive. The separate prestressed concrete design chapter added to the ACI code during this cycle introduced minimum reinforcement requirements for prestressed concrete: the provided area of steel was required to be adequate to develop an ultimate load capacity greater than 1.2 times the cracking load. The cracking load was based on a modulus of rupture of 7.5√fc′ psi (0.62√fc′ MPa). In 1995, the minimum reinforcement requirements for nonprestressed concrete were revised to explicitly account for concrete and reinforcement tensile strengths (ACI Committee 318 1995). Equation (2) gives the typical requirement
where Mcr is the cracking moment
As,min =
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3 fc′ fy
bw d ≥ 200bw d / f y (2)
Mr ≥ 1.33Mu (4) where Mu is the factored moment of the applicable load combination. The cracking moment is determined using Eq. (5)
S M cr = Sc ( fr + fcpe ) − M dnc c − 1 ≥ Sc fr (5) S nc
where fr is the modulus of rupture of the concrete; fcpe is the compressive stress in the concrete due to effective prestress forces (after allowance for all prestress losses) at the extreme fiber of the section where tensile stress is caused by externally applied loads; Sc is the section modulus with respect to the extreme tensile fiber of the composite section; Snc is the section modulus with respect to the extreme tensile fiber of the monolithic or noncomposite section; and Mdnc is the total unfactored dead load moment acting on the monolithic or noncomposite section. When monolithic or noncomposite sections are designed to resist all loads, the designer is directed to substitute Snc for Sc in Eq. (5) for the calculation of Mcr. The modulus of rupture fr used depends on the limit state being checked and the specified concrete strength. Literature is cited in which the modulus of rupture values typically range between 7.5√fc′ psi (0.62√fc′ MPa) and 11.7√fc′ psi (0.97√fc′ MPa) (ACI Committee 318 1992; Walker and Bloem 1960; Khan et al. 1996). For determining minimum steel requirements using the AASHTO LRFD provisions, the cracking moment is calculated using an estimated modulus of rupture equal to 11.7√fc′ psi (0.97√fc′ MPa). The AASHTO LRFD rationale for using a higher modulus of rupture value for minimum steel requirements is that it is a strength limit state, so the use of the upper bound value is justified; the 20% margin provided by Eq. (3) could be lost by using a lower modulus-of-rupture value. These provisions are valid for specified concrete strengths up to 15,000 psi (100 MPa). ACI PROVISIONS ACI 318-11, Section 18.8.2, specifies the following for minimum reinforcement: “Total amount of prestressed and nonprestressed reinforcement in members with bonded prestressed reinforcement shall be adequate to develop a factored load at least 1.2 times the cracking load computed on the basis of the modulus of rupture fr specified in 9.5.2.3.”
ACI Structural Journal/March-April 2014
The cracking load, however, is not explicitly defined in ACI 318-11 as it is in AASHTO LRFD. In general, it is implicitly understood that the cracking load is the force required such that the stress in the extreme tension fiber is equal to the modulus of rupture, which is defined as 7.5√fc′ psi (0.62√fc′ MPa). EFFECT OF PRESTRESSING ON MINIMUM STEEL REQUIREMENTS As described previously, the current AASHTO LRFD and ACI 318-11 minimum steel requirements are based on cracking moment, either implicitly or explicitly. The consequence of this dependence is that the quantity of minimum reinforcement for a given cross section varies with the prestressing force, and thus, the quantity of bonded prestressing steel. Oladapo (1968) noted this peculiarity in a parametric study that compared the moment capacity for varying levels of prestress, eccentricity, and tensile strength of the concrete. He found that, after a certain level of prestress, continuing to increase the amount of prestressing steel moved the section further away from meeting the minimum requirements. O’Neill and Hamilton (2009) conducted a similar parametric study on a Florida bulb tee 78, a 4 ft (1.22 m) wide by 8 in. (20.3 cm) deep hollow core slab, and a segmental box girder, verifying Oladapo’s findings. Figure 1 shows the results of the study. The variation of the design moment capacity φMn of each section was calculated using strain compatibility and normalized by the cracking moment; cracking moment was calculated using Eq. (5). The moment capacity varies as a result of the increase in area of bonded prestressing steel Aps from zero to an arbitrary maximum; Aps was normalized by the area of the concrete cross section between the flexural tension face and the center of gravity of the gross section Act. The Florida bulb tee and hollow core were investigated for positive bending, and the segmental box girder was investigated for negative bending. The graph contains two curves for each section, which correspond to the ACI 318-11 modulus of rupture estimate of 7.5√fc′ psi (0.62√fc′ MPa) and AASHTO LRFD estimate of 11.7√fc′ psi (0.97√fc′ MPa). All three sections exhibit a similar trend: as bonded prestressing steel is added, the curves quickly rise above the minimum steel required to reach 1.2Mcr. Because the cracking moment increases at a slightly greater rate than that of the moment capacity, each curve eventually declines as more prestressing steel is added. In general, the large quantities of prestressing steel required to cause a decrease in the moment ratio are likely beyond typical strength and serviceability needs. In the case of the box girder in negative bending, however, the addition of bonded prestressing steel of approximately 1.4% beyond an Aps/Act ratio results in a section that does not meet AASHTO LRFD minimum reinforcement requirements. Beyond this point, unnecessary bonded prestressing steel should be added to satisfy Eq. (3). The precompression force in a section has less effect than the concrete tensile strength on the section’s overall strength when the compression zone is smaller than tension zone, as in the case of the box girder (SB). This is seen in the plot ACI Structural Journal/March-April 2014
Fig. 1—Results from parametric study of current ACI provisions (O’Neill and Hamilton 2009). where the difference between the two curves for SB in negative bending is much greater than that between the hollow core curves or the Florida bulb-tee curves. Consequently, as the amount of prestressing steel increases, the cracking moment increases at a faster rate than the moment capacity due to the overriding effect of the relatively large tension zone in sections such as the SB. The use of 7.5√fc′ psi (0.62√fc′ MPa) versus 11.7√fc′ psi (0.97√fc′ MPa) was also investigated by O’Neill and Hamilton (2009) in a series of prestressed girder and pile laboratory tests. It was found that the girder cracking stresses ranged from approximately 6√fc′ psi (0.5√fc′ MPa) to 14√fc′ psi (1.2√fc′ MPa). In cases with low amounts of prestressing steel, however, the cracking stress ranged from 6.1√fc′ psi (0.5√fc′ MPa) to 7.6√fc′ psi (0.63√fc′ MPa). As the minimum steel requirement usually controls the steel quantity when the section is larger than required for strength, and the amount of prestressing steel required is similarly small, the use of 7.5√fc′ psi (0.62√fc′ MPa) as an estimate of the modulus of rupture is justified. Minimum reinforcement requirements for nonprestressed sections do not change with the selected quantity of reinforcement. The authors believe that a more rational approach would be for nonprestressed and prestressed concrete to have a single unique minimum reinforcement requirement for each section. This requires direct calculation of the cracking moment using only section and material properties, as will be shown in the following section with the derivation of a minimum reinforcement equation. PROPOSED MINIMUM REINFORCEMENT PROVISIONS Leonhardt (1964) proposed a minimum steel requirement for prestressed concrete based on providing sufficient steel area to resist net tensile concrete stresses that occur just before cracking. His approach takes advantage of the prestressing steel’s tensile capacity between the effective prestressed state (State I) and the ultimate state at flexural capacity (State II) without explicit consideration of the cracking moment to determine the minimum prestressing steel required. It is applicable to both nonprestressed and 433
Fig. 2—Concrete and reinforcement forces at State I and State II (Leonhardt 1964).
Fig. 3—Stress state of section at decompression.
prestressed concrete. A representation of the concept is shown in Fig. 2. The method ensures sufficient area of reinforcement such that the tensile force associated with the incremental change in steel stress from the effective prestress fse to the stress associated with ultimate flexural capacity fps, combined with the nonprestressed reinforcement yield strength fy, is greater than the tensile force generated in the concrete just before cracking Tcr. This relationship can be expressed as Apsfps ≥ Tcr + Apsfse + Asfy (6) Leonhardt’s proposed method made several assumptions: the tensile zone is rectangular, the resultant of the tension block is at the same elevation as the prestressing steel, and the section is noncomposite. These assumptions are probably conservative in most cases; however, to accurately model real sections without requiring excessive steel area, it is important to account for the variation of the steel location, the section shape, and the effects of composite construction. The following derivation takes all of these variations into account by resolving the forces into the internal and external moments acting on a section. To illustrate the proposed method, consider a rectangular section with nonprestressed steel and prestressing steel reinforcement as shown in Fig. 3. The left stress profile shows the section under effective prestress after time-dependent losses have occurred; fse is the effective prestress in the tendon, and fpe is the compressive stress in concrete at the extreme fiber of section where tensile stress is caused by externally applied loads. The center stress profile shows an externally applied moment causing the concrete tensile stress at the bottom of the section to be exactly equal in magnitude to fpe. Superimposing the two stress profiles results in a net stress at the extreme fiber of zero. The applied moment required to cause this stress state is defined as the decompression moment Mdec. While this moment will cause an increase in prestressing steel stress, in typical prestressed concrete members, this increase is not considered significant. As moment is applied beyond the decompression moment, the net stress in the bottom of the section becomes tensile. The point at which the tensile stress at the extreme fiber is equal to the modulus of rupture defines cracking; this applied moment is shown as the right stress profile and is referred to as Mncr, or the net cracking moment. The moment applied to 434
Fig. 4—External and internal forces diagram. achieve zero stress at the extreme tensile fiber is differentiated herein from the moment subsequently applied to achieve the rupture stress at the extreme tensile fiber. The cracking moment Mcr is then defined as the sum of the decompression and net cracking moment, Mdec + Mncr, and is used to determine the minimum quantity of prestressing steel necessary to ensure a ductile failure mode. This difference in definition is illustrated in Fig. 3. Leonhardt (1964) reasoned (reframed herein in terms of moment rather than force) that because the prestressing steel necessary to resist in Mdec is already present, then additional reinforcement or prestressing steel is needed only to ensure minimum strength to support Mncr. To ensure that the structure remains stable after cracking, sufficient reinforcement should be present such that the moment capacity is greater than the cumulative applied moment Mdec + Mncr ≤ Mn. Figure 4 shows these external and internal moments acting on a rectangular section. The left side of Fig. 4 illustrates the stress distribution in a concrete section just before cracking. If the stress at the extreme fiber of the concrete is equal to the rupture strength, then the net cracking moment can be defined as M ncr =
fr I (7) yt
ACI Structural Journal/March-April 2014
which ACI currently employs as an estimate of concrete tensile strength when determining minimum reinforcement. Further, as discussed previously, additional investigations by O’Neill and Hamilton (2009) justify the use of this estimate for the calculation of minimum steel. The net cracking moment described in Eq. (7) can then be written M ncr = 7.5 fc′
I (8) yt
The force coupled on the right side of the figure represents the internal forces immediately after cracking, in which the reinforcement resists the tensile force carried by the concrete before cracking. If the reinforcement volume is sufficiently low, then the section will reach its nominal moment capacity immediately after cracking; low volumes of reinforcement will ensure the section is tension-controlled. Defining the internal moment arms of the nonprestressed and prestressed steel reinforcement for this condition as jd and jdp, respectively, the moment capacity can then be defined as Mn = Ts(jd) + Tps(jdp) (9) If the extreme tension fiber stresses caused by the prestress force and decompression moment shown in Fig. 5 are summed, the result is the following equation
I yt 1 M dec = Aps fse A + e I (10) Ay t final transfer
This approach results in the self-weight moment being carried by the composite section, which results in a conservative minimum steel requirement. The transfer term should incorporate the section properties at the time of prestress transfer, and the final term should incorporate the section properties of the element after construction is complete. For composite construction, the transfer term will typically be the noncomposite section properties, and the final term will be the composite section properties. For noncomposite sections, these terms are simply the noncomposite section properties. To ensure sufficient flexural capacity immediately after cracking, the resisting moment should be greater than or equal to the total applied moment. By Leonhardt’s reasoning, the decompression moment is resisted by the already-present prestressing steel; the 1.2 (included to ensure ductility) need only be considered for Mncr. Further, when the safety factor of 1.2 used by ACI 318-11 and the strength reduction factor φ are included, the relationship can be written as
φMn ≥ 1.2Mncr + Mdec (11)
Using Leonhardt’s approach and the strength capacity of the prestressing steel beyond the effective prestress to resist the tensile force in the concrete, the relationship described in Eq. (11) may be rewritten as
ACI Structural Journal/March-April 2014
Fig. 5—Stress states under decompression moment. fAps f ps jd p + fjdAs f y ≥ 1.2
7.5 fc′I yt
I yt 1 + Aps fse + e I (12) Ayt final A transfer
As tension failure is the intended failure mode φ = 0.9. Assuming that j = 0.9 9 fc′I I yt 1 + 0.8dAs f y ≥ Aps 0.8 f ps d p − fse + e I yt Ayt final A transfer
(13)
When the member contains only prestressing steel, then the minimum requirement for bonded prestressed reinforcement is simplified as Aps,min =
9 fc′ y y 1 (14) 0.8 t +e t f d −f I final ps p se A I transfer
When the member contains only nonprestressed steel, then the minimum requirement is simplified as As,min ≥
11.25 fc′I df y yt
(15)
To illustrate the implementation of Eq. (14), consider a typical precast bridge with a cast-in-place topping. To calculate the minimum reinforcement using the proposed minimum, the designer would use the moment of inertia, area, and yt of the precast section for the transfer terms, as these were the section properties during the prestress transfer. For the final terms, the designer would consider the section properties of the completed structure: the composite moment of inertia, area, and yt, all considering the cast-inplace deck. The proposed provisions are in agreement with the fundamental approach of providing a moment capacity that is greater than Mcr to ensure a ductile failure—a provision that has been in the code either explicitly or implicitly for many years, and has empirically shown itself to be a successful design practice. The proposed provisions provide two things: unification of the minimum reinforcement provisions to include both prestressed and nonprestressed concrete sections (to provide less confusion and a more uniform level of safety) and revision of the provisions to eliminate the explicit consideration of the cracking moment 435
for prestressed sections (as such, avoiding the problem that arises in the case of prestressed concrete systems in which the minimum prestressing cannot be reached.) PARAMETRIC STUDY: COMPARISON OF CURRENT AND PROPOSED PROVISIONS A parametric study was conducted to compare the minimum area of steel and the subsequent provided capacity as calculated using the proposed provisions against those calculated using the ACI 318-11 minimum reinforcement provisions. A wide range of geometries was chosen for investigation: standard precast sections (single tees, double tees, inverted tees, and hollow core slabs), a Florida bulb tee, a box girder, and an AASHTO girder. Sections were selected to include geometries commonly used in construction, as well as both top-heavy and bottom-heavy sections, as the proposed provisions are dependent on the centroid of the gross area relative to the centroid of the tension area. Both nonprestressed and prestressed sections were investigated. For each cross section, the minimum required area of steel was calculated according to ACI 318-11 and the proposed provisions. The cracking moment of the geometry was calculated by assuming the concrete tensile strength based on a modulus of rupture of 7.5√fc′ psi (0.62√fc′ MPa). The ultimate design strength was calculated using strain compatibility. The ultimate flexural capacity and the theoretical cracking moment were then compared to determine the margin between cracking and flexural failure. PRESTRESSED CONCRETE: NONCOMPOSITE AND COMPOSITE SECTIONS Comparison of the current and proposed provisions is awkward because ACI 318-11 minimum reinforcement provisions (hereafter referred to as ACI minimum) depend on a moving target—that is, the cracking moment that changes as the amount of bonded prestressing steel changes. On the contrary, the proposed minimum reinforcement provision (hereafter referred to as proposed minimum) does not depend directly on the cracking moment; it depends, instead, on only the material and geometric properties of the section. Defined as such, the proposed minimum is like the AASHTO LRFD minimum reinforcement requirement, encompassing both types of reinforced sections while basing the minimum steel requirement on the concrete section properties rather than the cracking moment. A wide variety of prestressed sections was investigated in this parametric study. A table showing the ACI and proposed minimums for all geometric sections investigated by this parametric study is included as Appendix A. Prestressing strand was assumed to be Grade 270. Prestress losses due to elastic shortening and time-dependent losses were assumed to be 20% after an initial strand stress of 0.74fpu. The sections in the following discussion were chosen as representative of the range of all standard geometries analyzed in the study and include a 12 ft (3.66 m) wide by 30 in. (76.2 cm) deep double-tee (12DT30), a 28 in. (71.1 cm) wide by 24 in. (61 cm) deep inverted tee (28IT24), a 4 ft (1.22 m) wide by 12 in. (30.5 cm) deep hollow core (12HC), an AASHTO IV girder (AIV), a 78 in. (1.98 m) deep Florida 436
Fig. 6—Prestressed noncomposite sections: proposed and ACI minimums. bulb tee (FBT78), and a segmental box girder (SB). The SB was considered under negative bending (tension at the top of section). All other sections were considered under positive bending. The nominal moment capacity was calculated using strain compatibility, and the cracking moment was calculated using Eq. (5). Nonprestressed steel was not considered in these calculations. Appendix A tabulates data for all investigated sections. A comparison of the ACI minimum and proposed minimum (from Eq. (14)) reinforcement quantities for noncomposite sections is shown in Fig. 6. The sections were also evaluated by calculating the ratio of the design strength φMn to the cracking moment Mcr; this relation is shown in Fig. 7. For noncomposite sections, the computed minimum area of prestressing steel is within approximately 10% of the area currently required by the ACI minimum. It can be observed that for all sections, the proposed minimum area of steel results in a φMn/Mcr ratio greater than 1, and is close to the 1.2Mcr limit. Notably, comparison of the design moment strength across a variety of sections indicates a nearly constant excess of moment strength (around 17%) beyond the cracking limit of each section, ensuring a ductile failure mode for each section as is intended by the ACI minimum. Use of the proposed method eliminates the issue that as a section increases in depth, the moment capacity increases at a faster rate than the cracking moment. As Fig. 8 illustrates, a series of varying depth noncomposite hollow core slabs were examined, including a 6 in. (15.2 cm) deep (6HC), an 8 in. (20.3 cm) deep (8HC), a 10 in. (25.4 cm) deep (10HC), and a 12 in. (30.5 cm) deep (12HC) slab. Appendix A tabulates these data for all investigated sections. Figure 8 also shows that as the section depth increases, the ratio of the provided moment capacity to the cracking moment remains constant. Furthermore, the proposed minimum provides adequate reinforcement to ensure ductile failure mode in every case. A deck was added to each of the noncomposite sections evaluated previously (with the exception of the SB) to investigate the results of the proposed minimum reinforceACI Structural Journal/March-April 2014
Fig. 7—Prestressed noncomposite capacity versus cracking moment.
sections:
moment Fig. 9—Prestressed composite sections: proposed and ACI minimums.
Fig. 8—Prestressed noncomposite hollow core slabs with proposed minimum. ment provisions for composite sections. Figure 9 shows the proposed minimum reinforcement quantity normalized by the ACI minimum. The proposed minimum was compared against the ACI minimum calculated for both shored and unshored construction to demonstrate the full range of expected discrepancies between the two methods. The sections shown in Fig. 9 were also evaluated by calculating the ratio of the design moment strength φMn to the cracking moment Mcr using the minimum area of steel prescribed by the proposed method. The results are shown in Fig. 10. For composite sections, with the exception of the inverted tee, a 15 to 61% increase in minimum reinforcement over the ACI minimum was found. The inverted tee is even larger, with a 94 to 112% increase. Furthermore, the difference is greatest when comparing the proposed minimum to ACI minimum for an unshored condition. This is, in part, due to the conservative assumption made in the derivation in which the self-weight of the section is assumed to be carried by the composite section. To evaluate the impact of this increase,
ACI Structural Journal/March-April 2014
Fig. 10—Prestressed composite sections: moment capacity versus cracking moment. typical design volumes of prestressing steel were determined for each of the sections considered in the parametric study. Typical design loads were taken from load tables (if appropriate), or actual highway designs. Figure 11 shows how the proposed minimum reinforcement compares to the volume of reinforcement required by the design. In most cases, the differences between the current ACI minimum and the proposed minimum are minor. In general, as can be observed in Fig. 11, the proposed minimum area of steel is always less than, and usually much less than, that of a typical design. Only in the hollow core slab case does the proposed minimum approach the typical design value. As Fig. 11 demonstrates, the area of steel is usually controlled by either stress or strength limits, and the proposed minimum provisions will not affect most designs.
437
Fig. 11—Proposed area of steel versus typical design. NONPRESTRESSED CONCRETE: CURRENT VERSUS PROPOSED The current ACI minimum for concrete reinforced with nonprestressed steel requires a minimum area of steel, as prescribed by Eq. (2). In general, minimum steel requirements are usually invoked when sections are larger than required for strength, such as for architectural or other reasons. To evaluate the effect the proposed provisions would have in these instances, the minimum steel requirement was allowed to control the quantity of steel in the section. The steel quantity was then compared with the current ACI minimum. Two standard reinforced geometries were analyzed as nonprestressed concrete, a 10 ft (3.05 m) wide top flange by 48 in. (1.22 m) deep single-tee with an 8 in. (20.32 cm) web (MS10ST48) and a 28 in. (71.1 cm) wide by 60 in. (1.52 m) deep inverted tee (MS28IT60), as well as three rectangular sections of varying depth: 12 x 12 in. (30.5 x 30.5 cm), 12 x 36 in. (30.5 x 91.4 cm), and 12 x 72 in. (30.5 x 182.9 cm). All sections were assumed to be under positive bending (compression in the top of the section). A comparison of ACI and proposed minimums is shown in Fig. 12. Appendix B tabulates these data for all investigated sections. The sections were also evaluated by calculating the ratio of the design moment capacity φMn to the cracking moment Mcr; these ratios are shown in Fig. 13. The nominal moment capacity was calculated using strain compatibility, and the cracking moment was calculated using Eq. (5). Figure 12 highlights the conservative nature of the current ACI minimum. In the sections selected for this parametric study, the ACI minimum for nonprestressed members provide between 1.25 and 2.0 safety margins, growing excessively conservative in sections with tensile zones relatively larger than their compressive zones. Parametric studies completed by Seguirant et al. (2010) demonstrated the variability of the safety margin provided by the ACI minimum for nonprestressed sections from slightly under-conservative to extremely over-conservative (up to 4.43 margin of safety). In most cases, the ACI minimum requires more steel than the proposed provisions. Despite the general reduction in
438
Fig. 12—Nonprestressed sections: proposed and ACI minimums.
Fig. 13—Nonprestressed sections: moment capacity versus cracking moment using proposed provision and ACI 318-11 (ACI Committee 318 2011) Eq. (10-5). steel quantity, as inspection of the section’s moment capacity and cracking moment reveals, the proposed method still ensures a ductile failure mode. The rectangular sections and the inverted tee reveal the consistent level of conservatism achieved by the proposed method with less steel. As calculated using the proposed provisions, these sections require approximately 15 to 30% less steel than the ACI minimum, and yet provide a uniform moment capacity near 1.6Mcr. In fact, an inspection of all of the nonprestressed sections reveals that the proposed method, unlike ACI, provides a consistently conservative design with ductile failure mode— the proposed minimum requirement for each section type, regardless of the section geometry, provides a capacity equal to approximately 1.6Mcr. Considering this, the proposed provisions, although requiring less steel in some cases, provide a more reliable estimate of minimum reinforcement required, and one that is independent of cracking moment. ACI Structural Journal/March-April 2014
SUMMARY The derivation and parametric studies described in this paper provide a direct and unified method of determining minimum steel requirements for both nonprestressed reinforced and prestressed sections. For composite prestressed sections, the moment capacity provided by the area of steel determined with the proposed minimum always exceeds 1.2Mcr. While the proposed method requires more steel for composite prestressed sections than the ACI 318-11 minimum reinforcement provision, the difference is negligible when considering the steel typically provided for design. For nonprestressed sections, the proposed method results in a consistent moment capacity of 1.6Mcr, regardless of the section shape. Noncomposite prestressed sections have a consistent moment capacity of 1.17Mcr. The proposed method has several advantages for a designer; it is independent of the cracking moment and explicitly calculated. AUTHOR BIOS
ACI member Natassia R. Brenkus is a Graduate Research Assistant at the University of Florida, Gainesville, FL, where she received her BS in 2006 and her ME in 2012. H. R. Hamilton, FACI, is the Byron D. Spangler Professor of Civil Engineering at the University of Florida. He is past Chair of Joint ACI-ASCE Committee 423, Prestressed Concrete, and a member of ACI Subcommittee 318-6, Precast and Prestressed Concrete (Structural Concrete Building Code).
ACKNOWLEDGMENTS
The authors would like to thank C. O’Neill for her contributions to this paper and the Florida Department of Transportation for providing funding that supported this work.
= = = = = = =
NOTATION
area of concrete cross section area of concrete in flexural tension area of prestressing steel in flexural tension zone area of nonprestressed longitudinal tension reinforcement web width, or diameter of circular section width of web in I- or T-beam sections depth from compression face to center of nonprestressed tensile reinforcement dp = depth from compression face to center of prestressed tensile reinforcement e = distance between prestressed reinforcement and centroidal axis fc′ = specified compressive strength of concrete fcpe = compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads fpe = compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is cause by externally applied loads fps = stress in prestressing steel at nominal flexural strength fr = modulus of rupture of concrete fse = effective stress in prestressing steel (after allowance for all prestress losses) fy = specified yield strength of reinforcement I = moment of inertia of section about centroidal axis j = distance between compressive resultant force and tensile resultant force Mcr = cracking moment, computed as sum of decompression and net cracking moment, Mdec + Mncr Mdec = applied moment causing the net stress at bottom of section to be zero A Act Aps A s bw b′ d
ACI Structural Journal/March-April 2014
Mdnc =
unfactored dead load moment acting on monolithic or noncomposite section Mn = nominal flexural strength at section Mncr = moment applied beyond decompression moment to reach rupture stress in extreme tensile fiber; net cracking moment Mr = flexural resistance Mu = factored moment at section p = ratio of area of tension reinforcement to effective area of concrete Sc = section modulus with respect to extreme tensile fiber of composite section Snc = section modulus with respect to extreme tensile fiber of monolithic or noncomposite section Tps = tensile force in prestressed steel Ts = tensile force in nonprestressed steel yt = distance from centroidal axis of gross section, neglecting reinforcement, to tension face φ = strength reduction factor
REFERENCES
AASHTO, 2007, “AASHTO LRFD Bridge Design Specifications,” 4th edition with 2007 interim revisions, American Association of State Highway and Transportation Officials, Washington, DC, pp. 5-44 through 5-45. ACI-ASCE Committee 323, 2004, “Landmark Series: Tentative Recommendations for Prestressed Concrete,” Concrete International, V. 26, No. 3, Mar., pp. 95-131. ACI Committee 318, 1963, “Building Code Requirements for Reinforced Concrete (ACI 318-63),” American Concrete Institute, Farmington Hills, MI, 144 pp. ACI Committee 318, 1986, “Building Code Requirements for Reinforced Concrete (ACI 318-83) (Revised 1986),” American Concrete Institute, Farmington Hills, MI, 114 pp. ACI Committee 318, 1992, “Building Code Requirements for Structural Concrete (ACI 318-92) and Commentary (ACI 318R-92),” American Concrete Institute, Farmington Hills, MI, 347 pp. ACI Committee 318, 1995, “Building Code Requirements for Structural Concrete (ACI 318-95) and Commentary (ACI 318R-95),” American Concrete Institute, Farmington Hills, MI, 373 pp. ACI Committee 318, 2008, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 473 pp. ACI Committee 318, 2011, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 503 pp. ACI Committee 501, 1936, “Building Regulations for Reinforced Concrete,” ACI Journal, V. 32, No. 3, Mar., pp. 407-444. Bureau of Public Roads, 1954, “Criteria for Prestressed Concrete Bridges,” U. S. Government Printing Office, Washington, DC, 25 pp. Freyermuth, C. L., and Aalami, B. O., 1997, “Unified Minimum Flexural Reinforcement Requirements for Reinforced and Prestressed Concrete Members,” ACI Structural Journal, V. 94, No. 4, July-Aug., pp. 409-420. Ghosh, S. K., 1986, “Exceptions of Precast Prestressed Concrete Members to Minimum Reinforcement Requirements,” PCI Journal, V. 31, No. 6, pp. 74-91. Khan, A. A.; Cook, W. D.; and Mitchell, D., 1996, “Tensile Strength of Low, Medium, and High-Strength Concretes at Early Ages,” ACI Materials Journal, V. 93, No. 5, Sept.-Oct., pp. 487-493. Kleymann, M.; Girgis, A.; Tadros, M. K.; and Vranek, C. J., 2006, “Open Forum Problems and Solutions—Minimum Reinforcement in Flexural Members,” PCI Journal, V. 51, No. 5, Sept.-Oct., pp. 146-148. Leonhardt, F., 1964, Prestressed Concrete Design and Construction, Wilhelm Ernst & Sohn, Germany, 677 pp. O’Neill, C. M., and Hamilton, H. R., 2009, “Determination of Service Stresses in Pretensioned Beams,” No. BD 545-78, Florida Department of Transportation. Oladapo, I. O., 1968, “Relationship between Moment Capacity at Flexural Cracking and at Ultimate in Prestressed Concrete Beams,” ACI Journal, V. 65, No. 10, Oct., pp. 863-875. Seguirant, S. J.; Brice, R. B.; and Khaleghi, B., 2010, “Making Sense of Minimum Flexural Reinforcement Requirements for Reinforced Concrete Members,” PCI Journal, V. 55, No. 3, Summer, pp. 64-85. Walker, S., and Bloem, D. L., 1960, “Effects of Aggregate Size on Properties of Concrete,” ACI Journal, V. 32, No. 3, Mar., pp. 283-298.
439
APPENDIX A f = 0.9
Area, in.2
Mn, kip-ft
Mcr, kip-ft
fMn/Mcr
2.448
1067.9
629.4
1.53
0.924
411.0
309.5
1.20
ACI min
0.931
414.1
311.0
1.20
Table 18X8
2.750
532.4
506.4
0.95
0.481
214.6
165.6
1.17
0.520
230.3
171.3
1.21
0.510
47.2
30.7
1.39
0.314
30.1
23.2
1.17
ACI min
0.339
32.3
24.2
1.20
Table 6X6
0.510
70.2
48.6
1.30
e, in. Table 8X16
12DT30
28IT24
Prop min
Prop min
10
2.73
ACI min Table 6X6 6 in. hollow core
8 in. hollow core
10 in. hollow core
12 in. hollow core
Prop min
Prop min
1.5
0.382
53.6
41.1
1.17
ACI min
0.405
56.4
42.3
1.20
Table 4X8
0.612
110.7
77.3
1.29
0.467
85.7
65.8
1.17
Prop min
1.5
1.5
ACI min
0.499
91.2
68.3
1.20
Table 7X6
0.595
135.1
97.1
1.25
0.502
114.2
87.6
1.17
0.535
121.1
90.8
1.20
7.350
3157.8
4162.0
0.68
1.309
1284.4
990.0
1.17
ACI min
1.405
1373.1
1028.7
1.20
Typical
7.490
11403.3
6704.2
1.53
Prop min
1.5
ACI min Typical AASHTO Type IV
FBT78
Box girder
Prop min
8
Prop min
2.237
3453.8
2611.8
1.19
ACI min
2.290
3533.6
2649.7
1.20
Typical
65.290
209444.4
173166.7
1.09
45.148
147777.8
115096.7
1.16
51.100
166235.6
124574.2
1.20
Prop min
8
6.75
ACI min Notes: 1 in. = 2.54 cm; 1 in.2 = 6.45 cm2; 1 kip-ft = 1.36 kN-m.
APPENDIX B f = 0.9 MS 10ST48
MS 28IT60
MS 12X12
MS 12X36
MS 12X72
Area, in.2
Mn, kip-ft
Mcr, kip-ft
fMn/Mcr
1.2Mcr
1.310
281.1
210.8
1.20
prop min
1.838
393.3
210.8
1.68
ACI Sect 10-5 min
1.358
291.4
210.8
1.24
1.2Mcr
2.895
763.2
570.7
1.20
prop min
3.932
1024.4
570.7
1.62
ACI Sect 10-5 min
4.619
1194.4
570.7
1.88
1.2Mcr
0.310
15.2
11.4
1.20
prop min
0.416
20.7
11.4
1.63
ACI Sect 10-5 min
0.389
18.8
11.4
1.48
1.2Mcr
0.820
138.0
102.4
1.21
prop min
1.122
187.6
102.4
1.65
ACI Sect 10-5 min
1.300
215.6
102.4
1.89
1.2Mcr
1.580
544.4
409.8
1.20
prop min
2.188
750.9
409.8
1.65
ACI Sect 10-5 min
2.666
911.7
409.8
2.00
Notes: 1 in. = 2.54 cm; 1 in.2 = 6.45 cm2; 1 kip-ft = 1.36 kN-m.
440
ACI Structural Journal/March-April 2014
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title No. 111-S39
Lateral Strain Model for Concrete under Compression by Ali Khajeh Samani and Mario M. Attard The relationship between the lateral and axial strain is important when predicting the confinement stresses within reinforced concrete or fiber-reinforced polymer confined columns. Difficulties in measuring reliable lateral strains in triaxial compressive experiments mean that there is a scarcity of lateral strain experimental results. Two recent lateral strain models will be compared with available experimental results. Discussed in this paper is the transition point in the lateral and axial strain relationship at which the volumetric strain changes sign, and how this transition point is related to the peak stress. A lateral strain-versus-axial strain model is proposed based on the supposition that the concrete behaves linear elastically in the early stages of loading. Once microcracks form, nonlinear hardening occurs up to the peak stress. After the peak stress, the inelastic lateral strain varies linearly with the inelastic axial strain. The lateral-to-axial inelastic strain ratio is shown to be a function of the lateral confinement level and the failure mechanism. Moreover, the shear band and tensile crackinginduced size effect is also discussed from the lateral strain versus axial strain perspective. Keywords: confined concrete; fracture energy; lateral strain; size effect; volumetric strain.
INTRODUCTION There are many design formulas for predicting the behavior of reinforced concrete column behavior. Many of these formulas depend on estimating the lateral confinement. The lateral ties providing confinement are usually assumed to be at yield when a column reaches its peak load-carrying capacity. For reinforced high-strength concrete columns, the confinement ties are generally not at yield at the peak column load-carrying capacity. Therefore, this implies that formulas which rely on the confining ties to be at yield are not applicable. To overcome this problem, the lateral expansion of the confined column core can be related to the stress in the confining ties, which can then be used to predict the core confinement. The reinforcing ties are assumed to be fully bonded to the concrete, with no sliding or slippage occurring during the loading of the column. The lateral deformation of the concrete and the confining reinforcement cage or fiber-reinforced polymer (FRP) wrap is then taken as equal and related to axial strain in the column core. The lateral strain relationship has been used in the prediction of the confinement level for columns confined by reinforcement cages by Cusson and Paultre1 and Ahmad and Shah,2 and FRP wraps by Talaat and Mosalam3 and Lokuge et al.4 RESEARCH SIGNIFICANCE To predict the lateral expansion of axially loaded concrete, a lateral strain-versus-axial strain relationship is needed. Baseline experimental data on measured lateral strain from uniaxial and triaxial loaded concrete are limited to a few research publications such as Candappa et al.,5 Hurlbut,6 ACI Structural Journal/March-April 2014
Imran and Pantazopoulou,7 Jamet et al.,8 Lee and Willam,9 Lu and Hsu,10 Newman,11 and Smith et al.12 The major focus of this paper is to establish an analytical relationship between lateral and axial strain for concrete under uniaxial compression or compression under confinement. Such a model is important when determining the confinement and ductility of reinforced and FRP confined concrete columns. Furthermore, specimen size effects associated with the formation of a shear band and tensile cracking during softening are also incorporated into the model. LATERAL CONCRETE STRAIN UNDER COMPRESSION The lateral strain behavior of concrete under compression is a key aspect of concrete behavior. Studies on the lateral strain behavior under axial compression are conducted under various loading regimes. The loading conditions referenced herein are mainly uniaxial and triaxial tests conducted on cylindrical specimens. Triaxial testing of concrete is usually conducted in Hoek cells or triaxial cells. In a Hoek cell, the loading path begins with a sitting or locking axial load. After securing the specimen, the lateral confinement is enforced up to the desired confinement level. Once the confinement reaches the desired value, the axial load is then gradually applied while the confining stress is maintained. Because the lateral confining stress is applied using liquid pressure and the axial strain is externally applied, it is very difficult to enforce a hydrostatic load state without the use of complicated computerized devices. The triaxial cell used on concrete specimens is similar to those used for triaxial testing of soils. It is important to note the limitations of the various techniques used to extract or estimate the lateral strain. Lateral strains can be measured by utilizing strain gauges on the specimens or measuring the deformation of the circumference via a lateral ring. Strain gauges can show some inaccuracy under high confining pressures inside the test cell. Moreover, the lateral strain can be drastically different at different locations on the specimen. The change in the volume of oil used to apply the confinement can also be used to measure the volumetric strain, which can then be used to estimate an average lateral strain. For an intact specimen, the lateral strain obtained from the volumetric changes in the specimen correlates well with the lateral strain measured from strain gauges and linear variable displacement transducers (LVDTs) placed at several locations on the surface of the specimen. If ACI Structural Journal, V. 111, No. 2, March-April 2014. MS No. S-2012-177.R3, doi:10.14359.51686532, was received March 27, 2013, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
441
Fig. 1—Typical: (a) lateral strain; and (b) volumetric strain diagrams for concrete subjected to increasing levels of confinement. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) localization is present, however, the lateral strains obtained from the changes in oil volume and the strains obtained from strain measurement devices are drastically different. Lateral strain results are presented as either a set of axial stress-versus-axial strain and axial stress-versus-lateral strain or volumetric strain-versus-axial strain diagrams (Fig. 1). If volumetric strains are used to obtain the lateral strain, the obtained lateral strain is an average strain for the whole specimen. Consider, for example, the situation where a specimen under confinement and axial compression is loaded past the peak and reaches a residual axial load level after softening. If a localized shear band has formed, the applied axial displacements from the loading machine only impose a sliding displacement on the specimen. This displacement does not represent any change of specimen volume, but corresponds to sliding across the shear band. In this case, the actual change in volume is zero, but the plastic strain or permanent displacement across the whole specimen is not zero. If LVDTs are used across the fractured zone, a displacement will be measured, and a plastic or irrecoverable strain estimated. Analytical models by Lokuge et al.4 and Binici13 Lateral strain versus axial strain models developed by Lokuge et al.4 and Binici13 are presented as follows, and are later compared with some experimental results. These two models are analytical models for the total lateral strain, and are functions of the axial strain. The model proposed by Lokuge et al.4 is defined by
a e vi e ≤ e1 e ′ e0 = (1) e 0′ e a > e e 1 e 0
equal to 0.5ε0. The strain ε0 corresponding to the peak stress is given by Eq. (3), and fc′ is the uniaxial compressive strength of concrete in MPa. f e 0 = e c × 1 + (17 − 0.06 fc′) r (fc′ in MPa; 1 MP Pa = 145 psi) (3) fc′
In the previous equation, fr is the lateral confinement on the specimen. The strain at the peak stress for uniaxial compression, εc, is taken as 0.002 for all concrete grades. In the model proposed by Binici,13 the secant ratio νs is used to correlate the lateral deformation with the axial deformation. The concrete behavior in the lateral direction is divided into three regions: the elastic region, inelastic hardening region, and softening region. The model is defined by
ε′ = νsε
in which, ε′ is the lateral strain, ε is the axial strain, and νs is the secant ratio, defined by ν s = νe
e − ee 2 νs = νl − ( νl − νe ) exp − ∆
ee =
–6
2
(fc′ in MPa, 1 MPa = 145 psi) and ε is the axial strain, ε′ is the lateral strain, ε1 can be obtained by equating the two right hand side expressions in Eq. (1), and ε0′ is the lateral strain at the peak axial stress
e > ee
(5)
2 f f f fc′ 0.1 1 + 9.9 r − 0.9 r + r fc′ fc′ fc′
4750 fc′
νl = ν p +
a = 0.0177fc′ + 1.2818; vi = 8 × 10 (fc′) + 0.0002fc′ + 0.138 (2)
442
e ≤ ee
In the previous equation, νe is the Poisson’s ratio of the concrete, which varies between 0.15 to 0.2; εe, νl, and Δ are defined by
where a
(4)
∆=
1 fr f ′ + 0.85 c
4
(6)
e0 − ee νl − ν p − ln νl − ν0
ACI Structural Journal/March-April 2014
Fig. 2—Comparison of Jamet et al.8 test results with: (a) Binici13; and (b) Lokuge et al.4 models. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) Herein, νp is the ratio of lateral strain to the axial strain at the peak stress and assumed to be 0.5, νl is the largest secant ratio, and ε0 is the axial strain at the peak stress defined by
(
e 0 = 5 × −0.067 fc′ 2 + 29.9 fc′ + 1053
)
f f × 1 + 9.9 r + r − 0.8 × 10 −6 fc′ fc′
(7)
Comparing existing models with experimental results for confined concrete In this section, the two analytical models described previously are compared with available experimental results. In the following comparisons, the elastic moduli and the value of the axial strain at the peak stress used in the analytical models is adopted from the experimental results. The first set of results are from Jamet et al.,8 who tested microconcrete in triaxial and uniaxial compression. The results of Jamet et al.8 for lateral strain were extracted from measurements of the volumetric strain rather than from LVDTs, strain gauges, or both. The cylindrical specimens had a diameter of 110 mm (4.3 in.) and height of 220 mm (8.7 in.). The uniaxial compression strength was approximately 26 MPa (3.8 ksi). The applied confinement levels were 0, 3, 10, 25, 50, and 100 MPa (0, 0.4, 1.5, 3.6, 7.3, and 14.5 ksi). Jamet et al.8 presented results using true strain rather than engineering or simple strain values. It can be shown that for the magnitudes of strains measured, the true strain and the corresponding engineering strain are virtually indistinguishable. All results presented herein are based on engineering strains rather than true strains. The lateral strain results are compared with the models proposed by Binici13 and Lokuge et al.4 in Fig. 2. Hurlbut6 and Willam et al.14 tested normal strength concrete in direct tensile and uniaxial compression, as well as triaxial compression. The ultimate uniaxial compressive strength was 22 MPa (3.2 ksi). The size of the cylindrical specimens in the uniaxial compression tests had a diameter of 76 mm (3 in.) and a height of 152 mm (6 in.), while in the triaxial tests, the specimens were 54 mm (2.125 in.) in diameter by 108 mm (4.25 in.) in height. A modified Hoek cell ACI Structural Journal/March-April 2014
was used to impose the desired confinement pressure on the triaxial test specimens. The confining pressures ranged from 0.69 to 13.79 MPa (0.1 to 2 ksi). The axial displacements were transmitted to the specimens via steel rams without any friction-reduction measures. Hurlbut6 observed that the unconfined compression test exhibited the largest dilatant behavior in the post-peak regime, with the radial displacement three times greater than the applied axial displacements. The results showed a large volumetric expansion in the post-peak region. In agreement with the observations by Imran and Pantazopoulou,7 the results of Hurlbut6 showed that as the level of confinement was increased, the dilatancy rapidly decreased while exhibiting a transition from large volumetric expansions under low confinement to an elastic volumetric compaction for high confinement. The results of Hurlbut6 and Willam et al.14 are compared with the models of both Binici13 and Lokuge et al.4 in Fig. 3. Smith et al.12 and Smith15 tested 51 cylindrical samples with dimensions of 54 x 108 mm (2.125 x 4.25 in.), which were tested either in an unconfined or confined state using a Hoek cell. The compressive strength was either 34.5 or 44.2 MPa (5.0 or 6.4 ksi). No friction-reducing layer was used between the steel rams and the specimen ends. The confinement applied to the specimens varied with a maximum of 34.5 MPa (5.0 ksi). The test results on 34.5 MPa (5.0 ksi) concrete specimens are compared with Binici13 and Lokuge et al.4 models in Fig. 4. The analytical models proposed by Binici13 and Lokuge et al.4 give a reasonable fit to the trend of the results in Fig. 2 to 4, but not a good match to the lateral strain quantities. Moreover, one can see that neither of the models predicts the initial compaction in the lateral direction under high confinement before the specimen starts to expand. The test results of Lee and Willam,9 who tested cylindrical specimens with three different heights in uniaxial compression, are also compared in Fig. 5. All the specimens had a diameter of 76.2 mm (3 in.). The heights were 137.2, 91.44, or 45.72 mm (5.4, 3.6, and 1.8 in.). The peak concrete strength was 30.7 MPa (4.5 ksi) for the specimens with heights of 137.2 and 91.44 mm (5.4 and 3.6 in.), and 32 MPa (4.6 ksi) for the specimen with a height of 45.72 mm (1.8 in.). The results obtained by Lee and Willam9 are shown in Fig. 5, and demonstrate the effects of different specimen 443
Fig. 3—Comparison of Willam et al.14 test results with: (a) Binici13; and (b) Lokuge et al.4 models. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.)
Fig. 4—Comparison of Smith15 test results with: (a) Binici13; and (b) Lokuge et al.4 models. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) levels and concrete strengths, and to incorporate size effect issues. PROPOSED LATERAL STRAIN MODEL
Fig. 5—Comparison of Lee and Willam9 test results compared with Binici13 model and Lokuge et al.4 model. (Note: 1 mm = 0.0394 in.) height on the measured lateral strains. Figure 5 also shows the comparison with the models of Binici13 and Lokuge et al.4 The lateral strain size effect was not considered in the model of Lokuge et al.4 Binici13 did consider specimen size effect on the axial strain-versus-axial stress relationship, but not on the lateral strain, as the model of Binici13 considers the lateral strain as a direct function of the axial strain. A new model for predicting the lateral strain is developed in the following section, which attempts to give a better predictor of the lateral strain for a broad spectrum of confinement 444
Lateral strain at peak axial stress Kotsovos and Newman16 proposed that the point where the volume expansion begins is at the onset of unstable fracture propagation (OUFP), and that this should be considered as the true strength indicator of concrete. The load at OUFP is usually very close to the peak load (approximately 90%), and it is observed that deformations increase significantly between the OUFP and the peak. Based on experimental results, Nielsen17 suggested that the axial strain at the peak stress is 2.2 times greater than the absolute value of the lateral strain at peak stress. Imran18 studied the effect of water-cement ratio, concrete strength, and confinement level on the lateral strain of concrete. Figure 6 shows the relationship between the axial compressive strain at the peak stress ε0, and the axial compressive strain at the instant of zero volumetric strain. A similar figure was originally presented by Imran.18 Herein, results from the experimental studies of Candappa et al.,5 Jamet et al.,8 Newman,11 and Smith15 have been augmented to Imran’s results. The diagonal line in Fig. 6 would correspond to a situation where the volumetric strain is zero at the instance of the peak load. Imran and Pantazopoulou7 concluded that the axial compressive strain ACI Structural Journal/March-April 2014
Fig. 6—Axial strain at zero volumetric change versus axial strain at peak stress. (Note: 1 mm = 0.0394 in.) at the instant of zero volumetric strain is approximately equal to the axial compressive strain at which the concrete reaches its peak compressive axial stress. The volumetric strain εv at the peak axial stress can be written as
ev
e = e0
= e 0 + 2 e 0′ = 0 (8)
where ε0′ is the lateral strain at the peak axial stress. Hence, the ratio of the lateral strain ε0′ to the axial strain at the peak stress μ0 can be taken as
μ0 = ε0′/ε0 = –0.5
Post-peak plastic lateral strain Vonk19 observed that in the first stage of loading, the average lateral deformation versus average axial deformation is governed by Poisson’s ratio, which results in a decrease of the volume of the specimen. In the second stage, macrocracks are formed, causing dilatant behavior. After a gradual change, a more-or-less constant dilatant behavior was observed, which indicated that the process of macrocrack formation had stopped, and the final crack pattern had been developed. The behavior of concrete after the peak stress can be quantified by looking at the plastic or inelastic deformations after the peak. Figure 7 plots the plastic lateral strain minus the plastic lateral strain at the peak stress against the plastic axial strain minus the plastic axial strain at the peak stress based on the test results of Candappa et al.1 The results show an almost linear relationship. For relatively low levels of confinement associated with the results in Fig. 7, a shear band has probably formed with the deformations in the axial and lateral directions concentrated on the deformations within the shear band. The slope of the linear trends in Fig. 7 are associated with differing levels of confinement. As the confinement level increases, the lateral deformation rate decreases. An equation for this approximate linear trend is therefore εp′ – εp′(at peak) = β[εp – εp(at peak)] (10)
ACI Structural Journal/March-April 2014
in which εp is the plastic axial strain, and εp′ is the plastic lateral strain. The quantities εp(at peak) and εp′(at peak) are the axial and lateral plastic strain at the peak stress level, respectively. If it is assumed that the elastic part of the strains can be calculated using Hooke’s law, then Eq. (10) becomes f f f f e ′ − r − µ e . − e 0′ − r − µ e . 0 Ec Ec Ec Ec
(9)
This assumption will be used in this study.
Fig. 7—Plastic lateral strain minus plastic lateral strain at the peak stress versus the plastic axial strain minus the plastic axial strain at the peak stress for a 40 MPa concrete specimens tested by Candappa et al.5 (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.)
f f f f = b e − − µe . r − e0 − 0 − µe . r Ec Ec Ec Ec
(11)
Using Eq. (9), the previous equation becomes f f e ′ + µ e ⋅ − µ 0 e 0 + µ e ⋅ 0 Ec Ec
f f = b e − − e0 − 0 Ec Ec
(12)
In the previous equation, f is the stress level at a strain of ε; f0 is the peak stress, and Ec is the elastic modulus of concrete. The axial strain versus axial stress model for confined concrete proposed by Samani and Attard20 will be used for the relationship between the axial strain and axial stress. Experimental estimates for the parameter β as a function of the confinement ratio, obtained from the tests of Candappa et al.,5 Hurlbut,6 Jamet et al.,8 Lu and Hsu,10 Newman,11 and Smith15 are shown in Fig. 8. The experimental data used in Fig. 8 are for specimens with a height-diameter or heightwidth ratio of h/D or h/w = 2. The experimental results in Fig. 8 show a large scatter, particularly for the uniaxial compression state. The β parameter varies from approximately –2.5 (for h/D or w/h = 2) at the uniaxial state, to an upper limit of –0.5 for high confinement. To gain an understanding of the numerical range for the parameter β, consider a simple Mohr Coulomb nonassoci445
residual level under confinement, the dilatancy angle would be zero if a shear band forms and there is purely friction type sliding across the shear band. When the dilatancy angle is zero, Eq. (15) would give b≈
Fig. 8—Variation of parameter β with confinement. (Note: 1 MPa = 145 psi.) ated plasticity model. The model has an initial failure angle φf, and a plastic strain dilatancy angle ψ. Assuming there is a shear failure plane with an inclination angle θ measured from the horizontal, the inclination of the failure shear plane can be related to the Mohr Coulomb failure surface by
θ=
π ff + (13) 4 2
The plastic strain rate acting on the shear failure plane can be decomposed vectorially into a plastic normal strain rate, and a plastic shear strain rate. Incorporating a nonassociated flow rule, the relationship between the normal and shear plastic strain rates is
tan ( ψ ) =
e np e sp
(14)
The relationship between the plastic axial strain rate and plastic lateral strain rate is then defined by
e ′p tan ( ψ − θ) = e p tan (θ)
(15)
For concrete, the value of the dilatancy angle is approximately 13 degrees.21 The Mohr Coulomb failure surface angle (before softening) is usually approximately 30 degrees, which results in a shear plane failure angle of approximately 60 degrees. Using Eq. (15), the ratio of the plastic lateral strain rate to the plastic axial strain rate is then roughly –0.58. The ratio of the plastic lateral strain rate to the plastic axial strain rate approximates the definition of the parameter β defined by Eq. (10). The experimentally measured expansion rate, as reflected by the parameter β shown in Fig. 8, for the uniaxial, low confinement case, or both, is much greater than predicted by assuming a shear plane failure and a Mohr Coulomb failure surface. The estimate based on Eq. (15) assumed the plastic strain dilatancy angle and the friction angle to be constant during softening, while it is known that these parameters change. When the load reduces to a 446
e ′p = −1 e p
(16)
Referring to Fig. 8, the β parameter is approximately –1 when the confinement ratio is approximately 10 to 20%. In the study by Samani and Attard,20 it was observed that the post-peak compressive fracture energy is not constant, but varies with the level of confinement. The compressive fracture energy increases with increasing confinement and reaches a limit at a confinement ratio of approximately 10 to 20%. The compressive fracture energy then decreases for increasing confinement until the compressive fracture energy becomes zero after the transition from brittle to hardening failure. It was suggested by Samani and Attard20 that for uniaxial compressive and triaxial compression with low levels of confinement, tensile cracking exists along with the formation of a shear band during failure (Fig. 9). In Fig. 9, hd is the damage zone height taken to be between 2 to 2.5 times the width or diameter of the specimen. With increasing levels of confinement, eventually tensile splitting is nullified, and the compressive fracture energy increases above the uniaxial level. As the confinement is further increased, the mode of failure changes, and is dominated by barreling dispersed cracking and the compressive fracture energy decreases to zero. Applying these observations to the lateral strain phenomenon, the presence of tensile splitting coupled with a shear band failure under uniaxial and low confinement could explain why the measured β parameter is much greater than predicted using Eq. (15) based on a simple Mohr Coulomb failure criterion and the assumption of a single shear band. Tensile splitting increases the magnitude of the relative lateral dilation. Vonk19 observed that “the formation of a larger number of splitting cracks causes larger lateral deformations.” The plotted data for the parameter β in Fig. 8 is categorized in Fig. 10 to reflect the failure mode. When the confinement ratio is less than 10 to 20%, the failure and fracture is due to tensile splitting and shear failure, with the associated β less than –1. As the confinement increases, tensile splitting is nullified, and failure is predominately a shear band failure with an associated β of between –1 to –0.5. Increasing the lateral confinement beyond the brittle continuous hardening transition point (confinement ratio of approximately 30 to 50%), the concrete behavior changes from shear failure to ductile behavior. When ductile, the β parameter is –0.5. Figure 11 plots experimental estimates for the parameter β for uniaxial compression as a function of the aspect ratio D/h or w/h, where D is the diameter for a cylindrical specimen, w is the width for a prism, and h is the specimen height. The experimental results are from the work of Lee and Willam,9 Van Mier,22 Hurlbut,6 Lu and Hsu,10 Newman,11 and Smith.15 As mentioned previsously, Lee and Willam9 tested cylindrical specimens in uniaxial compression with ACI Structural Journal/March-April 2014
Fig. 10—Concrete behavior based on β equation.
Fig. 9—Shear band failure plane and tensile splitting under uniaxial compression. three different heights of 137.2, 91.44, and 45.72 mm (5.4, 3.6, and 1.8 in.), and a diameter of 76.2 mm (3 in.). Results by Van Mier22 are also shown. Van Mier22 tested prisms with a cross section of 100 x 100 mm (4 x 4 in.) and varying heights of 50, 100, and 200 mm (2, 4, and 8 in.). Both Lee and Willam9 and Van Mier22 measured the axial and lateral strain for specimens with aspect ratios h/D or h/w less than or equal to 2. The results show a large scatter, which could be attributed to the increasing dominance of tensile cracking for specimens with aspect ratios less than 2. An equation for the parameter β defined by Eq. (12) is estimated using an analysis of the experimental results by Candappa et al.,5 Hurlbut,6 Jamet et al.,8 Lee and Willam,9 Lu and Hsu,10 Newman,11 Smith et al.,12 Smith,15 and Van Mier22 (Fig. 8 and 11). The parameter β is taken as a function of the specimen aspect ratio, concrete strength, and the confinement ratio, but independent of axial strain. The proposed expression is written as b=
c b
f a × r’ + 1 fc
a = 65e
−0.015 fc′
− 0.5;
; b = 1.5 − e
−0.02 fc′
D c = −4 h ≤ hd ; c = −2 h
( fc′ in MPa, 1 MPa = 145 psi) (17) h > hd
Lateral strain model A model for the lateral strain versus axial strain is proposed herein based on the assumption that the concrete behavior is firstly linear elastic. Once the microcracks form, the behavior becomes nonlinear hardening up to the peak stress. After the peak stress, volumetric expansion starts with plastic/inelastic lateral strain varying linearly with ACI Structural Journal/March-April 2014
Fig. 11—Variation of parameter β for uniaxial compression with varying aspect ratio. (Note: 1 MPa = 145 psi.) the plastic/inelastic axial strain. A preliminary and primitive version of the model presented herein was presented in Samani and Attard.23 The model described herein is a refined version based on comprehensive research on reinforced concrete columns, and also includes size effect issues. The equations for the lateral strains in the three phases are f µ f e ′ = pr − e E Ec c f pr µ e f − e ′ = + A1 ( e ) Ec Ec e ′ = −µ f + b e − f − e − f0 + µ e + µ f0 e 0 0 0 e Ec Ec Ec Ec
e ≤ e pr e pr < e ≤ e 0
(18)
e > e0
in which ε is the axial strain and ε′ is the lateral strain; μe is the elastic Poisson’s ratio that normally varies between 0.15 and 0.25; fpr and εpr are the axial stress and strain at the proportional limit in concrete (this is usually taken at 45% of the peak stress f0); and Ec is the elastic modulus. ε0 is the axial strain at the peak stress; μ0 is the ratio of the lateral strain to the axial strain at the peak stress; β is defined by Eq. (17); and A1(ε) is a function describing the dilation 447
during the nonlinear hardening phase up to the peak stress. The Appendix contains the detailed derivation for A1(ε), which is determined to ensure continuity between the three phases in Eq. (18). The lateral strain axial strain model is then given by f pr µ e f − e ′ = Ec Ec 2 e − e pr e − e pr exp a e e − f pr µ e . f f pr µ e f0 o e o − e pr pr − − e ′ = + µ 0 e 0 − Ec Ec exp(a ) Ec Ec e ′ = − µ e f + b e − f − e − f0 + µ e + µ e f0 0 0 0 Ec Ec Ec Ec
e pr < e ≤ e 0 e > e0
The parameter α is given by h b h r a= e − e pr − 2 (20) e ′po o
)
where hr is the reference cylinder height. To adjust the stress strain model to incorporate size effects, Samani and Attard20 divided the total axial strain ε into its inelastic and elastic components, such that
f w pc + e d hd f e = e0 − 0 + + E Ec h c
h > hd
f f w pc + ed + e = e0 − 0 + Ec h Ec
h ≤ hd
(21)
Herein, wpc is the localized inelastic axial displacement due to shear band fracture; hd is the damage zone height; and εd is the additional inelastic axial strain in the damaged zone associated with longitudinal tensile cracking given in Samani and Attard20 by ed =
f0 − f r (1 + k ) f0 f0 − fresidual 2 kG ft
0.8
fresidual ≤ f ≤ f0 (22)
where Gft is the tensile fracture energy; r is a parameter with the dimension of length proportional to the average distance between successive longitudinal cracks; k is a material constant; and fresidual is the residual axial stress level. The value of r was estimated by Markeset and Hillerborg24 to be approximately 1.25 mm (0.05 in.) for a maximum aggregate size of 16 mm (0.6 in.), with r increasing with increasing maximum aggregate size. The value of k suggested by Markeset and Hillerborg24 was approximately 3 for normal density concrete and 1 for lightweight aggregate concrete. An expression for the tensile fracture energy as a function of the uniaxial compressive proposed by Van Mier25 can be used 448
Samani and Attard20 back-calculated an expression for the localized inelastic displacement using the results of Attard and Setunge26 for a reference cylinder height of hr = 200 mm (8 in.), that is
e ≤ e pr
(19)
(
Gft = 0.00097fc′ + 0.0418 N/mm (N/mm = 5.71 lpf/in.) (23)
w pc = ( e − e 0 ) hr +
( f0 − f ) h Ec
r
− e d hr (24)
Substituting Eq. (21) into (19) for the case of ε > ε0, one obtains e ′ = −µ e .
w pc + e d hd f0 f + b. + µ 0 e 0 + µ e ⋅ E Ec h c
w pc f f e ′ = −µ e . + b. + ed + µ0 e0 + µe ⋅ 0 Ec Ec h
h > hd (25) h ≤ hd
Using Eq. (24), Eq. (25) can be rewritten to give the lateral strain for the post-peak region as: e ′ = −µ e
h ( f − f ) hr f h h + b (e − e0 ) r + 0 − ed r − d h h Ec h Ec h
+µ0 e0 + µe
f0 Ec
h > hd and e > e 0
f0 Ec
h ≤ hd and e > e 0
(26) hr ( f0 − f ) hr f hr − e d − 1 e ′ = −µ e + b (e − e0 ) + h Ec h Ec h +µ0 e0 + µe
Figures 12 to 15 show a comparison of the proposed model with test results presented in Candappa et al.,5 Hurlbut,6 Imran and Pantazopoulou,7 Jamet et al.,8 and Smith.15 Generally, the proposed model makes very good predictions giving the correct trends, and, in most cases, reasonable estimates of the lateral strain. These comparisons demonstrate the capability of the proposed model in modelling a wide range of compressive strengths and confining pressures. Figures 16 and 17 show comparisons of the new analytical model with uniaxial compression tests involving specimens of different dimensional aspect ratios. The tests of Lee and Willam,9 who tested cylindrical specimens in uniaxial condition with different heights of 137.2, 91.44, and 45.72 mm (5.4, 3.6, and 1.8 in.) and a diameter of 76.2 mm (3 in.), have already been mentioned. Figure 16 shows the comparison with Lee and Willam9 results. Although the match is only fair, the new model has the correct trend that shows larger lateral strains for the specimens with the smallest height. Van Mier,27 a pioneer in the work of strain softening and size effect issues, also presented experimental lateral strain versus axial strain results for prisms with a square cross section of 100 x 100 mm (4 x 4 in.) and heights of 50, 100, and 200 mm (2, 4, ACI Structural Journal/March-April 2014
Fig. 12—Comparison of lateral strain versus axial strain for Candappa et al.5 test results (fc′ = 100 MPa) with proposed model. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.)
Fig. 15—Comparison of lateral strain versus axial strain for Smith15 test results (fc′ = 34.5 MPa) with proposed model. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.)
Fig. 13—Comparison of lateral strain-versus-axial strain test results of Willam et al.14 with proposed model. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.)
Fig. 14—Comparison of lateral strain versus axial strain for Jamet et al.8 test results with proposed model. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) and 8 in.) under uniaxial compression. Comparisons with the results of Van Mier27 are shown in Fig. 17. Van Mier27 tested several specimens, and presented a range of results for each specimen height. There is a wide scatter in the test results indicative of the dominance of tensile splitting with speci-
ACI Structural Journal/March-April 2014
Fig. 16—Comparison of lateral strain versus axial strain for Lee and Willam9 test results with proposed model. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) mens having aspect ratios less than 2. The proposed model gives quantitatively good results. CONCLUSIONS Two analytical models for the lateral strain versus axial strain proposed by Binici13 and Lokuge et al.4 were reviewed and compared with test results. The correlation between 449
Fig. 17—Comparison of lateral strain versus axial strain for Van Mier24 test results with proposed model. (Note: 1 MPa = 145 psi; 1 mm = 0.0394 in.) the test results and the analytical model predictions was reasonable, but not for high confinement levels. The initial compaction under high confinement was not predicted, and the models did not incorporate size effects associated with varying specimen aspect ratios. A new model for the lateral strain-versus-axial strain relationship has been proposed based on the assumption that the concrete behavior could be classified into three phases. It was assumed that the concrete responds to loads linearly elastically up to a proportional limit, and then its response changes to a nonlinear hardening up to the peak stress. From previous studies, the point at which the volumetric strain becomes zero was taken to be the same as the peak stress point; therefore, the lateral strain at the peak axial stress was half that of the axial strain at the peak axial stress. In the post-peak phase, a linear relationship between the plastic lateral strain and the plastic axial strain was observed. The total lateral strain was calculated by adding the elastic and estimated plastic components of the lateral axial. The parameters affecting the relationship between the plastic lateral and axial strain was shown to be the confinement level and the specimen aspect ratio. To show the model’s accuracy, the proposed model predictions were compared with a vast range of results in which the concrete strengths varied from low to high strength, and differing levels of confinement were applied. The model showed a realistic match with similar trends to experimental results. The model also compared reasonably well for uniaxial specimens of different aspect ratios, although the experimental results showed a large scatter because of the effects of tensile splitting. AUTHOR BIOS
Ali Khajeh Samani is currently a Post-Graduate Fellow at the School of Civil and Environmental Engineering, the University of New South Wales, Sydney, Australia. His research interests include modeling of confined concrete. Mario M. Attard is an Associate Professor at the School of Civil and Environmental Engineering, the University of New South Wales. His research interests include buckling analysis, hyperelastic constitutive modeling, finite strain continuum mechanics, and softening and constitutive modeling of concrete.
450
A1(ε) a b c D Ec f f0 fc′ fpr fr fresidual Gft h hd hr k r
NOTATION
= function in proposed model = parameter in proposed model = parameter in proposed model = parameter in proposed model = diameter of specimen = elastic modulus of concrete = stress level at a strain of ε = peak stress = uniaxial compressive strength of concrete, in MPa = axial stress and strain at proportional limit in concrete = lateral confinement on specimen, in MPa = residual axial stress level = tensile fracture energy = height of specimen = damage zone height = reference cylinder height = material constant = parameter with dimension of length proportional to average distance between successive longitudinal cracks wpc = localized inelastic axial displacement due to shear band fracture α = parameter in proposed model β = parameter defining the relationship of plastic lateral and axial strain Δ = scaling parameter in Binici13 ε = axial strain = strain at peak stress for uniaxial compression tests εc εe = elastic limit strain εe = additional inelastic axial strain in the damaged zone εp = plastic axial strain εpr = axial strain at proportional limit in concrete εp(at peak) = axial plastic strain at peak stress level ε0 = strain corresponding to peak stress ε0′ = lateral strain at peak axial stress equal ε1 = transition point in Lokuge et al.4 ε′ = lateral strain εp′ = plastic lateral strain ε′p(at peak) = lateral plastic strain at peak stress level e np = plastic normal strain rate e sp = plastic shear strain rate φf = initial failure angle μ0 = ratio of lateral strain to axial strain at peak stress μe = elastic Poisson’s ratio νe = Poisson’s ratio of concrete varying between 0.15 to 0.2 νl = largest secant ratio νp = ratio of lateral strain to axial strain at the peak stress νs = secant Poisson’s ratio θ = shear failure plane ψ = plastic strain dilatancy angle
REFERENCES
1. Cusson, D., and Paultre, P., “Stress-Strain Model for Confined HighStrength Concrete,” Journal of Structural Engineering, ASCE, V. 121, 1995, p. 468. 2. Ahmad, S., and Shah, S., “Stress-Strain Curves of Concrete Confined by Spiral Reinforcement,” ACI Journal, V. 79, No. 6, Nov.-Dec. 1982, pp. 484-490. 3. Talaat, M., and Mosalam, K., “Computational Modeling of Progressive Collapse in Reinforced Concrete Frame Structures,” PEER Report 2007/10, Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, 2008, 308 pp. 4. Lokuge, W.; Sanjayan, J.; and Setunge, S., “Stress-Strain Model for Laterally Confined Concrete,” Journal of Materials in Civil Engineering, V. 17, No. 6, 2005, pp. 607-616. 5. Candappa, D.; Sanjayan, J.; and Setunge, S., “Complete Triaxial Stress-Strain Curves of High-Strength Concrete,” Journal of Materials in Civil Engineering, V. 13, No. 3, 2001, pp. 209-215. 6. Hurlbut, B., Experimental and Computational Investigation of Strain-Softening in Concrete, University of Colorado, Boulder, CO, 1985, 256 pp. 7. Imran, I., and Pantazopoulou, S., “Experimental Study of Plain Concrete under Triaxial Stress,” ACI Materials Journal, V. 93, No. 6, Nov.-Dec. 1996, pp. 589-601. 8. Jamet, P.; Millard, A.; and Nahas, G., “Triaxial Behaviour of Micro-Concrete Complete Stress-Strain Curves for Confining Pressures Ranging from 0 to 100 MPa,” RILEM-CEB International Conference: Concrete under Multiaxial Conditions, V. 1, May 1984, pp. 133-140.
ACI Structural Journal/March-April 2014
9. Lee, Y., and Willam, K., “Mechanical Properties of Concrete in Uniaxial Compression,” ACI Materials Journal, V. 94, No. 6, Nov.-Dec. 1997, pp. 457-471. 10. Lu, X., and Hsu, C., “Stress-Strain Relations of High-Strength Concrete under Triaxial Compression,” Journal of Materials in Civil Engineering, V. 19, No. 3, 2007, pp. 261-268. 11. Newman, J., “Concrete under Complex Stress,” Developments in Concrete Technology—I, F. Lydon, ed., Applied Science Publishers, London, 1979, pp. 151-219. 12. Smith, S.; Willam, K.; Gerstle, K.; and Sture, S., “Concrete Over the Top—Or, is there Life After Peak?” ACI Materials Journal, V. 86, No. 5, Sept.-Oct. 1989, pp. 491-497. 13. Binici, B., “An Analytical Model for Stress-Strain Behavior of Confined Concrete,” Engineering Structures, V. 27, No. 7, 2005, pp. 1040-1051. 14. Willam, K.; Hurlbut, B.; and Sture, S., “Experimental and Constitutive Aspects of Concrete Failure,” Finite Element Analysis of Reinforced Concrete Structures, (Proceedings of seminar sponsored by Japan Society for the Promotion of Science and the U.S. National Science Foundation), 1986, pp. 226-254. 15. Smith, S. H., “On Fundamental Aspects of Concrete Behavior,” MS thesis, CEAE Department, University of Colorado Boulder, Boulder, CO, 1987. 16. Kotsovos, M., and Newman, J., “A Mathematical Description of the Deformational Behavior of Concrete under Complex Loading,” Magazine of Concrete Research, V. 31, No. 107, 1979, pp. 77-90. 17. Nielsen, C., “Triaxial Behavior of High-Strength Concrete and Mortar,” ACI Materials Journal, V. 95, No. 2, Mar.-Apr. 1998, pp. 144-151. 18. Imran, I., “Applications of Non-Associated Plasticity in Modeling the Mechanical Response of Concrete,” PhD thesis, University of Toronto, Toronto, ON, 1994. 19. Vonk, R., “Softening of Concrete Loaded in Compression,” thesis, 1992. 20. Samani, A., and Attard, M., “A Stress-Strain Model for Uniaxial and Confined Concrete under Compression,” Engineering Structures, V. 41, 2012, pp. 335-349. 21. Vermeer, P. A., and De Borst, R., “Non-Associated Plasticity for Soils, Concrete and Rock,” Technical University of Delft, Delft, Netherlands, 1984. 22. Van Mier, J., “Strain-Softening of Concrete under Multiaxial Loading Conditions,” Dissertation, 1984, 349 pp. 23. Samani, A., and Attard, M., “Lateral Behaviour of Concrete,” International Conference on Earthquake and Structural Engineering (ICESE 2011), Venice, Italy, 2011, pp. 940-945. 24. Markeset, G., and Hillerborg, A., “Softening of Concrete in Compression—Localization and Size Effects,” Cement and Concrete Research, V. 25, No. 4, 1995, pp. 702-708. 25. Van Mier, J., Fracture Processes of Concrete, CRC Press, Boca Raton, FL, 1996, 464 pp. 26. Attard, M., and Setunge, S., “Stress-Strain Relationship of Confined and Unconfined Concrete,” ACI Materials Journal, V. 93, No. 5, Sept.-Oct. 1996, pp. 432-442. 27. Van Mier, J., “Multiaxial Strain-Softening of Concrete,” Materials and Structures, V. 19, No. 3, 1986, pp. 179-190.
APPENDIX A The proposed lateral strain model continuity and boundary conditions are detailed here. To define A1(ε) used in Eq. (18), the following continuity conditions need to be satisfied. The lateral strains at the transition points between the elastic phase and the nonlinear hardening phase, and the nonlinear hardening phase and at the peak stress, need to be equal, hence:
f pr µ e f0 − e ′ = + A1 ( e 0 ) Ec Ec e = e0 ⇒ ⇒ A1 ( e 0 ) = e ′p0 f µ e f0 f0 f0 pr + + = − e b e − − e − e ′ ′ p 0 0 0 Ec Ec Ec Ec
(A2) The slopes at these transition points also need to be equal, therefore de′ µ =− e e d Ec e = e pr ⇒ de ′ = − µe de Ec
dA1 ( e ) =0 → d e e = e pr dA1 ( e ) + d e e = e pr
df = −µ e d e e = e pr df d e e = e pr
(A3) 0 dA1 ( e ) de′ µ e df =− + e e e d E d d e = e0 e = e0 c dA ( e ) 1 = d e e = e0 dA1 ( e ) h 0 0 e = e0 ⇒ =b ⇒ d e e = e0 hr µ e df df − + b 1 − Ec d e e = e 0 Ec d e e = e 0 h e d ′ =b = de hr hr hr df + 1 − e h h E d c e = e0 0
(A4) A form for the function A1(ε), which allows the continuity conditions to be satisfied, is 2
e − e pr e − e pr e − e exp a e − e o o pr pr (A5) A1 ( e ) = e ′p = e ′p0 exp(a ) with α defined as h b h r a= e − e pr − 2 (A6) e ′p0 o
(
)
µ e ⋅ f pr f e ′ = r − Ec Ec e = e pr ⇒ → A1 (e pr ) = 0 ⋅ f µ f e pr r e ′ = E − E + A1 (e pr ) c c (A1)
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451
NOTES:
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ACI Structural Journal/March-April 2014
DISCUSSION Disc. 110-S31/From the May-June 2013 ACI Structural Journal, p. 404.
Cyclic Loading Test for Beam-Column Connection with Prefabricated Reinforcing Bar Details. Paper by Tae-Sung Eom, Jin-Aha Song, Hong-Gun Park, Hyoung-Seop Kim, and Chang-Nam Lee Discussion by Yun Liu and Dun Wang Lecturer, College of Architecture and Civil Engineering, Zinjiang University, Urumqi, China; ACI member, PhD candidate, Research Institute of Structural Engineering and Disaster Reduction, School of Civil Engineering, Tongji University, Shanghai, China.
The subject of precast concrete systems has been a promising research field since the PRESSS (Precast Seismic Structural System Program) was initiated by the U.S. and Japan in the 1990s.16 Numerous research activities have been conducted and many novel structural systems, such as hybrid frame systems, rocking frame systems, and rocking wall systems, have been developed and applied to practical projects. The major features of precast concrete systems are the fast speed of construction, the high quality of precast and prestressed concrete units, durability improvements, and superior performance during earthquakes.17 To improve the speed of construction and ensure the seismic performance of precast systems, various techniques and construction methods have been developed, such as the welded reinforcement grid (WRG) and the SEN Steel Concrete Construction method, as mentioned in the paper. The discussed paper presents a prefabricated reinforcing bar connection method for the earthquake design of beamcolumn connections using the techniques of reinforcing bar welding, coupler splicing, and headed-bar anchorage. Test results of four test specimens under cyclic loading are given to elaborate on the effectiveness of this construction method, which could be an alternative for the application of precast concrete frame systems. Some topics in the paper are interesting and the discussers would like to comment on them as follows: • Welding stress, cracks, pores, and slags in the weld zone are complex phenomena for steel bars with welding during loading, which have an adverse effect on the behavior of reinforcement. Therefore, as mentioned in the paper, according to Saatcioglu and Grira1, to secure the ductile behavior of a column under lateral loading, the grid bar with a welded joint should have at least 4% elongation capacity in tension. However, as observed in Table 2 of the paper, no such information is present. Moreover, mechanical properties of coupler splices and headed bars should be also included in the paper. • It is indicated in the paper that axial load was not applied to columns and that the performance of such reinforcing bar details is not affected by the axial load of columns. The discussers do not agree with the authors on this point. As is well known, the behavior of the beam-column connection is more complicated with the existence of axial load than with no axial load, and the steel band plates would expand around the column, which may have an unexpectedly adverse effect on the reinforcing bar couplers. In addition, with the slenderness ratio of the column not exceeding 3 (2100/700 equates to 3), it can be defined as a short column; the existence of axial load can cause compression failure to the column and make the behavior of the connection more complex. Moreover, as mentioned in the recently pubished ACI Structural Journal/March-April 2014
•
•
•
374.2R-13,18 gravity loads should be simulated during testing, whether their effects are deemed important or not, because there is an important aspect of the application of gravity loads on a column, resulting in a fast rate of lateral force strength degradation. Therefore, it is best to include the axial load’s effect into the test of columns to get a more realistic behavior. In the “Test Program” section of the paper, it can be seen in Table 1 that there are more bottom reinforcing bars than top reinforcing bars in the beam, which may not be the case in practice. What is the consideration of such an arrangement by the authors? A second question regards the setup of the test. It is indicated that the ends of the beam cannot move upward and downward; instead, it allows the beam end to move horizontally. Does such a test setup conform to the true situation? What is the consideration for such a test setup? Please clarify. Moreover, it is mentioned in the paper that D25 bars used for the beam bottom bars had a relatively small fracture strain—5.36%—which was less than the minimum requirement specified in the Korean Industrial Standard. Strictly speaking, it is forbidden to use unqualified material in tests and in the practical project. However, such steel bars are still in use for the test specimens, which may be caused by the sequence of the test specimens’ construction—that is, the test specimens were constructed before the material properties test finished. Although there are requirements for steel bars before entering into the laboratory, it is a good choice to do material properties tests early, before the test specimens are constructed. As seen in Fig. 2 of the paper, diagonal bars are used along the entire length of the beam and in the transverse hoops in the beam, which is more than the conventional cast-in-place specimen. Undoubtedly, such an arrangement of shear reinforcement would change the behavior of the column—that is, the diagonal bars along the length of the beam strengthen the fixing of bottom reinforcing bars, resulting in minimizing the slip at the joint, as described in Fig. 2. Maybe it would be better to use a specimen with only diagonal bars in the beam to make comparisons between behaviors of test specimens. In the paper, techniques of reinforcing bar welding, coupler splicing, and headed-bar anchorage are used for the beam-column connection; however, not much more information is presented on the headed-bar anchorage and reinforcing bar welding. In addition, when constructing the specimens, how are the couplers constructed to connect the reinforcing bars from the beam and from the connection? It can be seen in Fig. 8(b) that reinforcing-bar slip occurred due to the loosened thread of the couplers, which indicated that there is a 453
possibility of the couplers not working in practice. Perhaps an alternative is to place the couplers outside the beam-column connection to connect the reinforcing bars of the beam, not in the connection region. To sum up, the construction method of a prefabricated reinforcing bar for beam-column connection by reinforcing-bar welding, coupler splicing, and headed-bar anchorage helps to accelerate the construction speed and is a good choice for a precast concrete frame system. Because the behavior of the beam-column connection is vital to the entire structural system, much more experimental research on such connections and structural frame systems with such connections should be conducted to obtain enough reliable proof for the proposed construction method, especially focusing on welding reinforcement, which has been pointed out by the authors. The discussers are waiting with great interest for the discussions in the announced follow-up paper.
Fig. 15—Direct tension tests on three D25 bars with tag welding joint.
REFERENCES
16. Priestley, M. J. N., “Overview of PRESSS Research Program,” PCI Journal, July-Aug. 1991, pp. 50-57. 17. fib Bulletin 27, “Seismic Design of Precast Concrete Building Structures, ” fib, Lausanne, Switzerland, 2003, pp. 1-2. 18. ACI Committee 374, “Guide for Testing Reinforced Concrete Structural Elements under Slowly Applied Simulated Seismic Loads (ACI 374.2R-13),” American Concrete Institute, Farmington Hills, MI, 2013, 18 pp.
AUTHORS’ CLOSURE The authors would like to thank the discussers for their interest in the paper and the informative discussion. The authors’ response to the five comments is presented as follows. 1. In the proposed prefabricated reinforcing bar construction method (PRC method), tag welding is used for the connection between the transverse D13 bars and longitudinal D25 and D22 bars. However, as shown in Fig. 5, the amount of tag welding is relatively small, when compared to the area of the longitudinal bars. Thus, the adverse effect of tag welding on the longitudinal bars was expected to be minimal. As presented in the conclusion No. 5 of the paper, in this test, the bar tag welding did not have detrimental effects on the structural performance of the specimens. The authors performed direct tension tests on the D25 bars that had a tag welding joint to a transverse D13 bar at the center (refer to Fig. 15). The results showed that two D25 bars were fractured away from the weld joints, but the third specimen failed near the weld joint. Note that the elongation capacities at rupture were much greater than 4%. A material test for the steel used in the bar couplers was not performed. The yield and tensile strengths provided by the manufacturer were fy = 751 MPa (109 ksi) and fu = 760 MPa (110 ksi), which were much greater than those of the D22 and D25 bars. The couplers used in this test are commercial products, and the mechanical properties were proved elsewhere. However, in this test, reinforcing bar slip occurred due to the loosened threads of the coupler in Specimens PRC1. Thus, attention should be paid to the coupler splice. The headed bars used in the test were different from the conventional one specified in the design code. As shown in Fig. 4, the beam flexural bars in the exterior joint were anchored to the steel band plate by nuts and washers. Because the steel band plate provides additional bearing capacity for bar anchorage, the headed bars were expected to be safe. In this test, failure did not occur in the headed bars. 454
Fig. 16—Simplified models for beam-column connections subjected to seismic loading. 2. As the discusser commented, when columns are subjected to high axial load, the axial load effect on the connection behavior may be undesirable and even critical. Thus, the overall behaviors of the beam-column connection specimens would be more realistic if axial load was applied to the columns. However, this test was performed to investigate the effect of the reinforcing bar details (such as the couplers, headed bars, band plates, and bar welding) rather than the behavior of beam-column connections itself. In the test specimens, the reinforcing bar details, except the proposed details, are the same as the conventional ones. Thus, if the proposed details do not affect the overall behavior of the specimens, the axial load effect on the overall behavior of the specimens should be the same as the effect on beam-column connections with conventional reinforcing bar details. The steel band plates are used to connect the beam reinforcing bars to the column reinforcing bars for reinforcing bar fabrication and erection, and to provide additional bearing resistance for bar anchorage. Furthermore, as shown in Fig. 3, conventional ties or hoops specified in current design codes are used in the beam-column joints. Thus, the use of the steel band plates in addition to the conventional ties is not likely to affect the overall behavior of the beam-column connections. Thus, the axial load effect on the proposed connection method is expected to be the same as the effect on conventional beam-column connections. 3. There is a misunderstanding. As shown in Table 1 and Fig. 3, the number of the top flexural bars was greater than the number of the bottom bars. The test setup was planned to simulate the lateral movements of the interior and exterior beam-column connections under seismic loading, as presented in Fig. 16. The test ACI Structural Journal/March-April 2014
setup has been used in many previous tests of beam-column connections. The material tests on the reinforcing bars used in the test program were conducted after the cyclic load tests. Because the D25 bars used in this test are commercial products and the mechanical properties were originally guaranteed by the manufacturer, material tests were not performed before testing. However, in the material tests, the elongation at failure was proven to be unqualified. As the discussers commented, a reinforcing bar tension test before the connection test is desirable and appropriate. 4. The diagonal D13 bars in the beam are nonstructural elements that are used only for reinforcing bar fabrication. Therefore, conventional vertical stirrups are required for the shear capacity of the beam. Further, as shown in Fig. 3, the number of the diagonal bars is significantly less than that of the vertical stirrups. Thus, the effect of the diagonal bars on the overall behavior of the specimens was expected to be minimal. As shown in Fig. 7, no notable difference in the
cyclic behaviors of RC1 and PRC1 was observed (compare the pinching in the cyclic curves presented in Fig. 7). 5. Please refer to the authors’ reply No. 1 regarding the bar welding, coupler splice, and headed bar anchorage. In the proposed method, the reinforcing bar cages of columns and beams are fabricated in a fabrication shop separately. In the construction field, the column bar cage is erected first. Then beam bar cage is connected to the column bar cage using the bar couplers, which are located at the column face. The location of the couplers was determined considering the efficiency and economy in fabrication and shipping. In a mockup test, the reinforcing bar fabrication of the PRC connection specimens was conducted without difficulty. In real construction fields, however, the PRC method may be a challenging construction method. Although the present study focused on verifying the structural performance of the proposed beam-column connection method, further improvement in the construction technique is required for the practical use of the proposed method.
Disc. 110-S32/From the May-June 2013 ACI Structural Journal, p. 415.
Shear Strength of Reinforced Concrete Walls for Seismic Design of Low-Rise Housing. Paper by Julian Carrillo and Sergio M. Alcocer Discussion by Dun Wang and Xilin Lu ACI member, PhD candidate, Research Institute of Structural Engineering and Disaster Reduction, School of Civil Engineering, Tongji University, Shanghi China; Professor, Research Institute of Structural Engineering and Disaster Reduction, School of Civil Engineering, Tongji University.
It is known that various models have been proposed to estimate the shear strength of shear walls, such as those based on the softened truss model initially developed by Mau and Hsu (1987) and later modified by Guta (1996), the softened strut-and-tie model proposed by Hwang et al. (2001), and the UCSD shear model by Kowasky and Priestley (2000), which was later modified by Krolicki (2011). The discussed paper presents a set of semi-empirical design equations that are capable of estimating the shear strength of walls for low-rise housing, based on an experimental program of 39 isolated walls in cantilever, and discussion of previous experimental studies by other researchers. As seen in the conclusions of this paper, the proposed equations qualify the efficiency factor of horizontal reinforcements by their contributions to the shear strength of walls in one- to two-story concrete buildings in Latin America. The discussers would like to raise the following significant issues and suggestions: • As seen in Eq. (2), the concrete contribution to the shear strength of walls is associated to a1 and fc′, and a1 is related to the shear span ratio from Eq. (7), all of which are constant because the wall specimen is cast. However, with the increase of displacement, the cracks appear and widen in concrete, resulting in reducing the effectiveness of the aggregate interlock shear resistance along the crack surface. Moreover, vertical reinforcements in the web wall may also contribute to the shear resistance, but none of these are included in the proposed model by the authors. The UCSD shear model seems to give a relatively reasonable mechanism for the concrete contribution, which takes into account the effective shear area, the degradation of the shear resistance of concrete, the volumetric ratio of longitudinal reinforcement, and the effect of the shear-span ratio. ACI Structural Journal/March-April 2014
•
•
As noted by the authors, several existing proposed models for estimating the shear strength of concrete walls have limitations, which are described in the paper. Special attention should be paid to the fact that most of these proposed shear models are based on their individual experimental research and have their own limitations to particular scopes, with different influencing factors, loading protocols, and dataprocessing methods. Therefore, there is a need for a unified experimental research activity on shear strength of walls to be launched worldwide due to the complex mechanism of shear phenomena. In addition, research on the shear strength of walls should also focus on a model based on theoretic analysis and then be verified by experimental results, such as the softened truss model theory proposed by Mau and Hsu (1987) and modified by Guta (1996), or the softened strut-and-tie model by Hwang et al. (2001); it should not be based merely on experimental results. The paper includes wall specimens with web reinforcement made of welded-wire mesh. As mentioned by the authors, displacement ductility of such a wall type may be limited by the small elongation capacity of cold-drawn wire reinforcement; it can be seen from Table 2 that the elongation is only 1.4% to 1.9%. The discussers wonder whether it is allowed by design codes to use such cold-drawn wire reinforcement with low elongation for web reinforcement of walls, especially for seismic design. In addition, Saatcioglu and Grira (1999) recommended that, to secure the ductile behavior of a column under lateral loading, the grid bar with a welded joint should have at least a 4% elongation capacity in tension. Moreover, it can be seen 455
•
•
•
•
from Table 2 that the ratio of ultimate strength to yield strength for welded-wire mesh used in the paper is, at most, 1.16, which does not seem to have enough margin of strength for seismic design. It is mentioned in the paper that wall reinforcement of specimens was placed in a single layer at wall midthickness due to the thickness of 100 mm (4 in.) for one- and two-story buildings. However, no information on the diameter of welded-wire mesh is provided in the paper, and it is not clear whether the concrete cover is too large to have a durability problem in practical projects with only one layer of reinforcement. That is to say, it is prone to cracks or shrinkage with single-layer welded-wire mesh. In addition, in practice with a thicker wall section, there would be more than one layer of reinforcement in the wall where tie bars for connecting the layers of reinforcement would be essential. So the contribution of tie bars to the shear strength of the wall should also be taken into account. In Eq. (1) and (2), Aw is the area of wall concrete section used to calculate the shear strength. In Eq. (6) and (8), lwtw is used. It is not mentioned whether the two indexes, Aw and lwtw, are equal to each other. What is the value for Aw if they are not the same? Maybe the calculation of Aw should be clarified because there are different values used in different models, such as those by Kassem (2010) and Krolicki (2011). As seen in Eq. (2), the web steel contribution to the shear strength of walls is limited to horizontal reinforcement and is associated with the yield strength of reinforcement, fyh, the volumetric ratios rh and hh, as well as Aw, which has nothing to do with the longitudinal steel reinforcement. However, as referred to by the authors in the paper, according to Barda et al. (1977), for a wall with hw/tw < 1 and with boundary elements, horizontal reinforcement becomes less effective as compared to vertical reinforcement, particularly for walls with M/Vlw < 0.5, which indicates that vertical reinforcement contributes to the shear strength of the wall. Both of the cases— hw/tw < 1 and M/Vlw < 0.5—are all included in the scope of the proposed shear-strength equations by the authors; that is, the proposed equations best predict peak shear strength of walls with M/Vlw ratios less than or equal to 2.0. In addition, what is the mechanism of the web horizontal reinforcement for the contribution to shear resistance? Because it is calculated as the products of fyh, rh, hh, and Aw, which is not similar to that mentioned in Krolicki (2011)—that is, VS = rttwhcrfy (as seen in detail in the reference). Moreover, the factor hh used for considering the yielding extent of horizontal web reinforcement is constant (0.8 for deformed bars and 0.7 for welded-wire mesh), which does not reflect the effects of other influences such as the imposed lateral drift, volumetric ratio of horizontal reinforcement, axial loading, and yielding strength. An assumption that the contribution of vertical axial stress to the shear strength of squat walls is unimportant is made in the paper by the authors. Therefore, there is no contribution of vertical axial loading effect in Eq. (2). However, as a matter of fact, axial stresses always exist whether it is increased or decreased by vertical acceleration or coupling between walls. In addition, whether it is conservative, and to what extent, is not clear without the contribution of vertical axial
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load. Therefore, it is better to make out the condition for not considering the axial loading effect by quantitative values. Moreover, as mentioned in the newly published ACI 374.2R-13 (ACI Committee 374 2013), gravity loads should be simulated during testing, whether their effects are deemed important or not, because it would result in a fast rate of lateral force strength degradation with the existence of vertical loadings. Therefore, the contribution of vertical axial loads to the shear strength of walls should be included in Eq. (2), just like those proposed by Krolicki (2011). Lastly, a clear definition for the squat wall needs to be made, and consensus should be reached on issues such as the influencing factors, the expression equation, and the mechanisms of each contribution to shear strength. After that, comparisons between the previous proposal models can be made to get a conclusive judgment for the shear strength of the shear wall. Maybe there is still a long way to go to determine the mechanisms of each contribution to the shear strength of walls based on theoretic analysis, not merely on the experimental research, whether the shear wall is a squat wall or flexural wall. REFERENCES
ACI Committee 374, 2013, “Guide for Testing Reinforced Concrete Structural Elements under Slowly Applied Simulated Seismic Loads (ACI 374.2R-13),” American Concrete Institute, Farmington Hills, MI, 18 pp. Gupta, A., 1996, “Behavior of High Strength Concrete Structural Walls,” PhD thesis, Curtin University of Technology, Perth, Australia. Hwang, S. J.; Fang, W. H., Lee, H. J.; and Yu, H. W., 2001, “Analytical Model for Predicting Shear Strength of Squat Walls,” Journal of Structural Engineering, ASCE, V. 127, No. 1, pp. 43-50. Kassem, W., and Elsheikh, A., 2010, “Estimation of Shear Strength of Structural Shear Walls,” Journal of Structural Engineering, ASCE, V. 136, No. 10, Oct., pp. 1215-1224. Kowalsky, M. J., and Priestley, M. J. N., 2000, “Improved Analytical Model for Shear Strength of Circular Reinforced Concrete Columns in Seismic Regions,” ACI Structural Journal, V. 97, No. 3, May-June, pp. 388396. Krolicki, J.; Maffei, J. G.; and Calvi, M., 2011, “Shear Strength of Reinforced Concrete Walls Subjected to Cyclic Loading,” Journal of Earthquake Engineering, V. 15, No. S1, pp. 30-71. Mau, S. T., and Hsu, T. C., 1987, “Shear Behavior of Reinforced Concrete Framed Wall Panels with Vertical Loads,” ACI Structural Journal, V. 84, No. 3, May-June, pp. 228-234. Saatcioglu, M., and Grira, M., 1999, “Confinement of Reinforced Concrete Columns with Welded Reinforcement Grids,” ACI Structural Journal, V. 96, No. 1, Jan.-Feb., pp. 29-39.
AUTHORS’ CLOSURE The authors acknowledge the interest of discussers in the paper. Indeed, shear strength of concrete members is still an issue where the development of a unified approach is needed. Studies, both experimental and analytical, contribute to providing data, evidence, and reflections on the phenomenon. Our research was aimed at developing simple design tools that could be used in practice. The following are comments based on discussers’ items: 1. The model developed in our research recognizes that factors hh,v, a1, and a2 do depend on wall ductility or wall drift. The model discussed in the paper is applicable to drifts associated with peak strength (pp. 418 and 422). The model developed also recognizes the contribution of vertical web reinforcement to wall shear strength (pp. 420-422). In fact, strains measured in the vertical web bars or steel wires during tests were mainly associated to the uniform distribution of inclined cracks on the wall web. It was confirmed that, as specified by ACI 318,1 a minimum amount of web vertical ACI Structural Journal/March-April 2014
steel should be computed using Eq. (5). On the other hand, the accuracy and variables included in the UCSD shear model are not within the scope of the paper. 2. The authors of the paper agree with the discussers that there is a need for a unified approach for experimental research on shear strength of walls to be launched worldwide due to the lack of a consistent trend of the contribution of horizontal and vertical web reinforcement to wall peak shear strength (p. 418). As the discussers indicate, other methodologies for assessing shear behavior have been developed, such as truss models and softened strut-and-tie models. Such models were not discussed in the paper and, therefore, should be studied in future research. 3. The authors agree with the discussers that steel reinforcement to be used in seismic design applications must exhibit minimum elongation capacity. The purpose of using the welded-wire mesh available was to assess its adequacy as reinforcement for seismic design applications (p. 415). The authors have recommended that welded-wire mesh with low elongation capacity should not be used for shear resistance. 4. Space limitations in the paper hindered the possibility of including details of the experimental program such as the diameter of the bars and wires. Discussers are invited to revisit the recommended references (Carrillo and Alcocer 2012, 2013). Regarding the use of one curtain of reinforcement within the wall web, Section 21.9.2.2 of ACI 318-11 also allows its use when the factored shear force is lower than a predefined value, as is the common case in lowrise concrete housing. 5. The calculation of Aw is clearly specified after Eq. (2) as the gross area of wall concrete bounded by wall thickness and wall length (Aw = twlw). 6. As indicated above, the model reported in the paper considers the contribution of vertical web reinforcement to
wall shear strength. An equation to compute the vertical web steel ratio is included. The equation to calculate the wall shear strength explicitly includes the horizontal web steel ratio only. However, for this equation to be applicable, the vertical web steel ratio should be placed in the wall and computed using the proposed Eq. (5). Differences between the proposed model and Krolicki model are not within the scope of the paper and, therefore, should be studied in future research. In the case of the so-called “efficiency factor of horizontal web steel ratio,” as argued in Note 1, the model acknowledges that hh depends on wall drift. The model proposed in the paper is applicable to calculation of maximum load-carrying capacity and, thus, the proposed equation is applicable to drifts associated with peak strength. In addition, as discussed on p. 421 of the paper, values of hh should be used when rhfyh is lower than 1.25 MPa (181 psi). 7. The authors agree with the discussers that axial stress is important to accurately determine wall shear strength and deformation capacities. As discussed on p. 423 of the paper, for these box-type low-rise structures, axial stresses on walls typically have small values. Therefore, assuming sv ≈ 0 is conservative for low-to-medium seismic hazard areas. A detailed analysis is warranted for structures located in areas of high seismic hazard. 8. The authors agree with the discussers that more work needs to be done to better differentiate shear-dominated and flexural-governed walls, as well as on the development of a comprehensive and unified theory on shear strength and deformation capacities. These issues and the comparisons between the previous proposal models are not within the scope of the paper and should be the topic of a new study.
Disc. 110-S39/From the May-June 2013 ACI Structural Journal, p. 491.
Performance of AASHTO-Type Bridge Model Prestressed with Carbon Fiber-Reinforced Polymer Reinforcement. Paper by Nabil Grace, Kenichi Ushijima, Vasant Matsagar, and Chenglin Wu Discussion by José R. Martí-Vargas Associate Professor, ICITECH, Institute of Concrete Science and Technology, Universitat Politècnica de València, Valencia, Spain.
The discussed paper presents an interesting experimental study on the design philosophy, construction techniques employed, and flexural performance of both an AASHTO I-beam and a bridge model reinforced and prestressed with carbon fiber composite cable (CFCC) strands. The authors should be complimented for producing a detailed paper with comprehensive information. This is acknowledged by the discusser, who would like to offer the following comments and questions for their consideration and response: 1. A scale factor of 1:3.6 was used for both the AASHTOType control I-beam with a span of 12,141 mm (39 ft 10 in.) and 502 mm (19.75 in.) deep and the 2500 mm (98.75 in.) width bridge model made up of five such beams. Regarding the cross section of the beam, it seems that the scale factor was taken in relation to the AASHTO Type V or Type VI I-beam when based on the 203 mm (8 in.) width of the bottom flange; –3.6 × 203 = 731 mm (28.77 in.) is next to 712 mm (28 in.), which is the actual bottom flange of AASHTO Type V and Type VI I-beam. In addition, and according to Gerges and Gergess,14 if the 502 mm (19.75 in.) depth or ACI Structural Journal/March-April 2014
the 12,141 mm (39 ft 10 in.) span length are considered, the beam is related to the AASHTO Type VI I-beam, which is 1830 mm (72 in.) depth and is often used for span lengths ranging from 36 to 45 m (118 ft 1.32 in. to 147 ft 7.65 in.) from the corresponding width and span length obtained as 3.6 × 502 mm = 1807 mm (71.14 in.) and 3.6 × 12.141 m = 43.7 m (143 ft 4.77 in.), respectively. On the other hand, the 95 mm (3.75 in.) width of the beam web results in 3.6 × 95 mm = 342 mm (13.5 in.), which seems to be a broad width to be related to the 205 mm (8.1 in.) width of the AASHTO Type V and Type VI I-beams. What were the criteria applied to choose the scale factor of 1:3.6 and the width of the beam web? It is worth noting that different effects on length, cross section, and second area moment can result in an identical scale factor. 2. Beam spacing in a bridge depends on several factors such as span length, concrete strength, loads, and environment, among others. What was the criterion used to establish a beam spacing of 502 mm (19.75 in.) in the bridge model? Regarding the average 28-day concrete compressive strength in the six AASHTO I-beams of 44.82 MPa (6500 psi), 457
502 mm beam spacing is approximately 1.13 to 1.45— obtained as (3.6 × 502)/1600 and (3.6 × 502)/1250—times the maximum beam spacing for 43.7 m (143 ft 4.5 in.) span length when taking as a reference the charts provided by Gerges and Gergess14 for optimizing girder size and spacing. 3. Based on the allowable concrete stresses at prestress transfer, the maximum number of 15.2 mm (0.6 in.) diameter 7-wire steel strands that can be accommodated in an AASHTO Type VI I-beam with a 43.7 m (143 ft 4.5 in.) span length is 45 to 55.14 The authors used 10 longitudinal CFCC strands per beam: seven non-prestressed and three prestressed at 30% of their average breaking load. It seems the concrete stresses after prestress transfer were too small to be representative of pretensioned concrete structures when compared with current practice (prestressing steel strands prestressed at 75%). This can explain the fewer prestress losses obtained as compared with conventional steel prestressed members.15,16 4. Apart from the prestressing force being small according to the number of CFCC prestressed strands and the used prestress level, a shorter transfer length is obtained. Transfer length can be measured17,18 and/or predicted from different equations based on equilibrium of forces19,20 or strand slips.21,22 As transfer length provisions differ for distinct codes and researchers,19,23 and no consensus has been reached as to the main parameters to be considered,24-26 it would be interesting to detail the transfer length provisions used by the authors to design the prestressed beams. Do the authors have any information on measured transfer length? 5. The concrete stresses at prestress transfer can be assumed with a linear distribution beyond the dispersion length,27 which is longer than transfer length and depends on beam depth and tendon position, among other factors. According to the scale factor and the beam depth, what were both the dispersion and transfer lengths in relation to the beam length? In addition, transfer length remains within the development length of prestressing strands.12,28,29 It is worth remarking that the development length equation in AASHTO1 includes a 1.6 multiplier factor that is used to avoid bond failure caused by inadequately developed lengths in structural members whose depth is greater than 610 mm (24 in.) because of high shear effects. The tested beams were 502 mm in depth (19.75 in.)—lesser than 610 mm (24 in.)—but the loading conditions regarding strand development length would differ in the full-scale member, as the resulting depth of 3.6 × 502 mm = 1807 mm (71.14 in.) is greater than 610 mm (24 in.). REFERENCES
14. Gerges, N., and Gergess, A. N., “Implication of Increased Live Loads on the Design of Precast Concrete Bridge Girders,” PCI Journal, V. 57, No. 4, Fall 2012, pp. 78-95. 15. Caro, L. A.; Martí-Vargas, J. R.; and Serna, P., “Prestress Losses Evaluation in Prestressed Concrete Prismatic Specimens,” Engineering Structures, V. 48, 2013, pp. 704-715. 16. Martí-Vargas, J. R.; Serna-Ros, P.; Arbeláez, C. A.; and RigueiraVictor, J. W., “Bond Behaviour of Self-Compacting Concrete in Transmission and Anchorage,” Materiales de Construcción, V. 56, No. 284, 2006, pp. 27-42. 17. Martí-Vargas, J. R.; Serna-Ros, P.; Fernández-Prada, M. A.; MiguelSosa, P. F.; and Arbeláez, C. A., “Test Method for Determination of the Transmission and Anchorage Lengths in Prestressed Reinforcement,” Magazine of Concrete Research, V. 58, No. 1, 2006, pp. 21-29. 18. Martí-Vargas, J. R.; Caro, L.; and Serna, P., “Experimental Technique for Measuring the Long-Term Transfer Length in Prestressed Concrete,” Strain, V. 49, 2013, pp. 125-134. 19. Martí-Vargas, J. R.; Arbeláez, C. A.; Serna-Ros, P.; Navarro-Gregori, J.; and Pallarés-Rubio, L., “Analytical Model for Transfer Length Prediction
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of 13 mm Prestressing Strand,” Structural Engineering and Mechanics, V. 26, No. 2, 2007, pp. 211-229. 20. Martí-Vargas, J. R.; Serna, P.; Navarro-Gregori, J.; and Pallarés, L., “Bond of 13 mm Prestressing Steel Strands in Pretensioned Concrete Members,” Engineering Structures, V. 41, 2012, pp. 403-412. 21. Martí-Vargas, J. R.; Arbeláez, C. A.; Serna-Ros, P; and CastroBugallo, C., “Reliability of Transfer Length Estimation from Strand End Slip,” ACI Structural Journal, V. 104, No. 4, July-Aug. 2007, pp. 487-494. 22. Martí-Vargas, J. R.; Serna, P.; and Hale W. M., “Strand Bond Performance in Prestressed Concrete Accounting for Bond Slip,” Engineering Structures, V. 51, 2013, pp. 236-244. 23. Martí-Vargas, J. R., and Hale, W. M., “Predicting Strand Transfer Length in Pretensioned Concrete: Eurocode versus North American Practice,” Journal of Bridge Engineering, ASCE, 2012, DOI:10.1061/ (ASCE)BE.1943-5592.0000456. 24. Martí-Vargas, J. R.; Serna, P.; Navarro-Gregori, J.; and Bonet, J. L., “Effects of Concrete Composition on Transmission Length of Prestressing Strands,” Construction and Buiding Materials, V. 27, 2012, pp. 350-356. 25. Caro, L. A.; Martí-Vargas, J. R.; and Serna, P., “Time-Dependent Evolution of Strand Transfer Length in Pretensioned Prestressed Concrete Members,” Mechanics of Time-Dependent Materials, V. 17, No. 4, Nov. 2013, pp. 501-527, DOI: 10.1007/s11043-012-9200-2. 26. Martí-Vargas, J. R.; Ferri, F. J.; and Yepes, V., “Prediction of the Transfer Length of Prestressing Strands with Neural Networks,” Computers and Concrete, V. 2, No. 2, 2013, pp. 187-209. 27. CEN, “Eurocode 2: Design of Concrete Structures — Part 1-1: General Rules and Rules for Buildings,” European standard EN 1992-11:2004:E, Comité Européen de Normalisation, Brussels, Belgium, 2004. 28. Martí-Vargas, J. R.; Arbeláez, C. A.; Serna-Ros, P.; Fernández-Prada, M. A.; and Miguel-Sosa, P. F., “Transfer and Development Lengths of Concentrically Prestressed Concrete,” PCI Journal, V. 51, No. 5, Sept.-Oct. 2006, pp. 74-85. 29. Martí-Vargas, J. R.; García-Taengua, E.; and Serna, P., “Influence of Concrete Composition on Anchorage Bond Behavior of Prestressing Reinforcement,” Construction and Buiding Materials, V. 48, 2013, pp. 1156-1164.
AUTHORS’ CLOSURE The authors would like to thank the discusser for his interest, insightful discussion, and thoughtful observations on the presented research paper. The beam cross section of the bridge model was inspired by the Taylor Bridge built over Assiniboine River in the Parish of Headingley, Manitoba, Canada. The five-span AASHTO-type bridge with fiber-reinforced polymer (FRP) was built in 1997 and has a span length of 31.25 m (102.53 ft) with a depth of 1.8 m (5.9 ft) and a 200 mm (7.87 in.) thick composite deck.3 The prestressed beams for the Taylor Bridge are spaced at 1.8 m (5.9 ft) with a bottom flange width of 660 mm (25.98 in.). The span-depth ratio of the tested control beam and bridge model beams were based on the AASHTO1 Table 2.5.2.6.3.1 traditional minimum depths. For a simple span length of 12.141 m (39.833 ft), the composite depth required for a prestressed concrete precast I-beam is 0.045 times the span’s length— that is, 0.045 × 12.5 m = 0.563 m (1.847 ft). The modeled beam cross section had an approximate scale factor of 1/3.6 for an AASHTO Type IV beam. The true scale model of the AASHTO Type IV beam has narrower web and depth and it would have posed difficulties in placing concrete, vibrating, and compacting; therefore, the web width and depth were adjusted for the beam models based on the constructibility in the laboratory setting.30 A similar adjustment was made in bottom flange width to accommodate minimum spacing of the carbon fiber-reinforced polymer (CFRP) reinforcement and clear cover requirements. All such modifications done in the AASHTO Type IV beam for suiting laboratory setup are clear from the dimensions given in Fig. 1 to 3. Because of these modifications, the presented beam cross section is not exactly a true scaled version of the AASHTO Type IV beam in terms of geometric properties; nevertheless, the cross section does closely represent it. ACI Structural Journal/March-April 2014
Also, it is worth mentioning that the State Departments of Transportation (DOTs) do modify, to certain extent, the standard AASHTO type prestressing beam shapes depending on the local needs (Michigan 1800 girder, Wisconsin type 70”, PennDOT 28” beams, and so on).31 Similarly, the scaled spacing of the bridge model was based on the AASHTO1 Table 4.6.2.2.2.b.1 limitations to validate load distribution factors. In the traditional design approach of the prestressed concrete bridges, the emphasis is given more on cost optimization, and hence the designers try to use the full capacity of the prestressed concrete beams. The mentioned reinforcement ratio of 0.46% is based on the strain compatibility design approach for bonded prestressed and nonprestressed CFRP tendons arranged vertically.6 It may be noted that, unlike the balanced ratio for steel, the balanced ratio for FRP bars/tendons does not signify yielding; rather, it signifies failure/rupture of the bars. Also, substantial research has been accomplished on the use of steel wire strands for the prestressing operations; therefore, the process has been industrialized with a higher level of confidence and duly specified guidelines. However, no such guidelines have yet been evolved on the use of CFRP reinforcements as prestressing strands while conducting this research. Therefore, suitably, the prestressing force level was chosen as 30% of the average measured breaking load of strands. Grace32 and Grace et al.33 investigated transfer length of the CFRP reinforcement used in prestressed concrete box beams
ACI Structural Journal/March-April 2014
and developed new equations to predict transfer length. However, for the investigation reported in the manuscript, the authors emphasized the flexural behavior of the AASHTO Type IV beams prestressed with the CFRP tendons. The significance of the presented experimental study has been to explain the design philosophy as per the ACI 440.4R-047 design guidelines and the Unified Design Approach,6 the construction techniques employed, and the flexural performance of an AASHTO I-beam and bridge model reinforced and prestressed with the CFRP strands. Moreover, the test results reported herein also aid in validation of the results of analytical and numerical studies subsequently undertaken in the future, with lucidly provided geometric and material details along with various response quantities. REFERENCES
30. Wu, C., “Performance of Concrete I-Beam Bridge Prestressed with CFCC Reinforcement,” master’s thesis, Lawrence Technological University (LTU), Southfield, MI, 2009. 31. Pennsylvania Department of Transportation (PennDOT), Bridge Design Drawings, http://www.dot.state.pa.us/Internet/BQADStandards. nsf/home. 32. Grace, N. F., “Transfer Length of CFRP/CFCC Strands for Double-T Girders.” PCI Journal, V. 45, No. 5, 2000, pp. 110-126. 33. Grace, N. F.; Enomoto, T.; Abdel-Mohti, A.; Tokal, Y.; and Puravankara, S., “Flexural Behavior of Precast Concrete Box Beams PostTensioned with Unbonded, Carbon-Fiber-Composite Cables,” PCI Journal, V. 53, No. 4, 2008, pp. 62-82.
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IN ACI MATERIALS JOURNAL The American Concrete Institute also publishes the ACI Materials Journal. This section presents brief synopses of papers appearing in the current issue.
PDF versions of these papers are available for download at the ACI website, www.concrete.org, for a nominal fee.
From the March-April 2014 issue
111-M11—Practical Approach for Assessing Lightweight Aggregate Potential for Concrete Performance by Daniel Moreno, Patricia Martinez, and Mauricio Lopez The properties and amount of lightweight aggregates used in a concrete mixture can significantly influence its mechanical properties and density. Nevertheless, such influence cannot be accurately described and used in practical application without an extensive experimental work. A practical evaluation method for assessing the influence of lightweight aggregate on concrete properties is required to anticipate the performance of concrete in advance and choose the most suitable lightweight aggregate for a certain structural application. In this paper, existing models are reviewed, generalized, and validated to obtain a methodology for assessing the potential of the lightweight aggregates to provide a specified concrete density, modulus of elasticity, and compressive strength. A practical evaluation methodology is proposed and validated with four different lightweight aggregates, obtaining correlations between measured and estimated density; modulus of elasticity; and compressive strengths of 93.4, 84.8, and 91.7%, respectively. Therefore, this methodology allows practical and reliable comparison and selection of lightweight aggregates based on only one trial mixture. 111-M12—Axisymmetric Fiber Orientation Distribution of Short Straight Fiber in Fiber-Reinforced Concrete by Jun Xia and Kevin Mackie The anisotropic orientation distribution of short fibers in fiber-reinforced concrete and the impact on mechanical properties have been established in past research. In this paper, the cast-flow induced anisotropic fiber distribution was categorized as axisymmetric with respect to the cement paste flow direction. The probabilistic spatial orientation for fibers is introduced using the beta distribution and uniformity parameters. Either theoretical or approximate equations for the orientation factor and the probability density function of the crossing angle were derived for any arbitrary cut plane. The derived orientation factor equation can be used to quantify the degree of anisotropy via image analysis. This process is easier and more accurate because instead of detailed orientation information for every single fiber, only total fiber counts on the cut sections are needed. The probabilistic macromechanical properties, such as ultimate tensile strength, are estimated based on the selected micromechanical model that defines the single fibermatrix interactions. 111-M13—Mixture Design and Testing of Fiber-Reinforced Self‑Consolidating Concrete by Kamal H. Khayat, Fodhil Kassimi, and Parviz Ghoddousi An extensive testing program was undertaken to evaluate the applicability of a mixture-proportioning method proposed for shrinkage control in fiber-reinforced concrete (FRC) in proportioning fiber-reinforced selfconsolidating concrete (FR-SCC). The study also proposed test methods to evaluate workability of FR-SCC. The investigated fibers included polypropylene, steel, and hybrid fibers of different properties with fiber lengths of 5 to 50 mm (0.20 to 1.97 in.). Fiber volume Vf ranged between 0.25 and 0.75%. The study also aimed to determine the impact of fiber type and addition on key properties of the fresh and hardened concrete. Hardened properties included compressive, splitting tensile, and average residual strengths. Test results indicate that the proposed methodology to maintain constant mortar thickness over coarse aggregate and fibers can reduce any significant drop in workability of FR-SCC, resulting from an increase in fiber
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factor. In general, a Vf of 0.5% is found to be an upper limit for the production of SCC. A greater Vf can hinder the self-consolidating characteristics. For the assessment of the passing ability of FR-SCC, a modified J-ring setup containing six or eight bars instead of 16 bars is proposed. The passing ability of FR-SCC can be expressed as the ratio of diameter:height at the center of the J-ring test. The passing ability can also be evaluated using the L-box with a single bar instead of three bars. A superworkable concrete (SWC) requiring low consolidation energy can still be produced with a Vf of 0.75% when a viscosity-modifying admixture is incorporated to prevent segregation and blockage. For the tested fiber types, the average residual strength (ARS) in flexure is shown to increase with Vf. Steel fibers exhibited the highest ARS value. 111-M14—Effect of Misalignment on Pulloff Test Results: Numerical and Experimental Assessments by Luc Courard, Benoît Bissonnette, Andrzej Garbacz, Alexander Vaysburd, Kurt von Fay, Grzegorj Moczulski, and Maxim Morency The successful application of a concrete repair system is often evaluated through pulloff testing. For such in-place quality control (QC) testing, the inherent risk of misalignment might affect the recorded value and eventually make a difference in the acceptance of the work. The issue of eccentricity in pulloff testing has been ignored in field practice because it is seen as an academic issue. This paper presents the results of a project intended to quantify the effect of misalignment on pulloff tensile strength evaluation and provide a basis for improving QC specifications if necessary. The test program consisted first of an analytical evaluation of the problem through two-dimensional finite element modeling simulations and, in a second phase, in laboratory experiments in which the test variables were the misalignment angle (0, 2, and 4 degrees) and the coring depth (15 and 30 mm [0.6 and 1.2 in.]). It was found that calculations provide a conservative but realistic lower bound limit for evaluating the influence of misalignment upon pulloff test results: a 2-degree misalignment can be expected to yield a pulloff strength reduction of 7 to 9%, respectively, for 15 and 30 mm (0.6 and 1.2 in.) coring depths, and the corresponding decrease resulting from a 4-degree misalignment reaches between 13 and 16%. From a practical standpoint, the results generated in this study indicate that when specifying a pulloff strength limit in the field, the value should be increased (probable order of magnitude: 15%) to take into account the potential reduction due to testing misalignment. 111-M15—Strength and Microstructure of Mortar Containing Nanosilica at High Temperature by Rahel Kh. Ibrahim, R. Hamid, and M. R. Taha The effect of high temperature on the mechanical properties and microstructure of nanosilica-incorporated mortars has been studied. Results show that the incorporation of nanosilica increases both compressive and flexural strengths significantly at both ambient and after a 2-hour exposure to 752°F (400°C) temperatures; the strengths increase with the increase of nanosilica content. A significant decrease in strength was recorded for all control and nanosilica-incorporated mortar specimens after a 2-hour exposure to 1292°F (700°C) heat; however, nanosilica-incorporated specimens show higher residual strength than those without nanosilica. Microstructural analysis shows that nanosilica reduces the calcium hydroxide crystals to produce more calcium silicate hydrate, the process that contributes to the strength and the residual strength of the material. In addition, the material exhibits a stable structure state up to 842°F (450°C), while exposure to higher temperatures results in a decomposition of hydration products.
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111-M16—Prediction of Strength, Permeability, and Hydraulic Diffusivity of Ordinary Portland Cement Paste by B. Kondraivendhan and B. Bhattacharjee In this investigation, the compressive strength, permeability, and hydraulic diffusivity of ordinary portland cement (OPC) paste have been predicted from the knowledge of mixture factors, such as water-cement ratio (w/c) and curing ages. The relationships for pore size distribution (PSD) parameters, such as mean distribution radius r0.5, dispersion coefficient d, and permeable porosity P, are functions of the w/c and curing ages, and are readily available in the literature. By using these relationships, the compressive strength, permeability, and hydraulic diffusivity can be estimated from the w/c and curing age information. It is observed that the predicted compressive strength closely matches the reported experimental compressive strength. It is also observed that the estimated permeability data also closely matches the reported experimental permeability data. The predicted hydraulic diffusivity follows a similar trend, as reported in the literature. 111-M17—Cracking Tendency of Lightweight Aggregate Bridge Deck Concrete by Benjamin E. Byard, Anton K. Schindler, and Robert W. Barnes Early-age cracking in bridge decks is a severe problem that may reduce the functional life of the structure. In this project, the effect of using lightweight aggregate on the cracking tendency of bridge deck concrete was evaluated using testing frames that restrain movement due to volume change effects from placement to cracking. Expanded shale, clay, and slate lightweight coarse and fine aggregates were used to produce internal curing, sand-lightweight, and all-lightweight concretes to compare their behavior relative to a normalweight concrete in bridge deck applications. Specimens were tested under temperature conditions that simulate summer and fall placement scenarios. Increasing the amount of pre-wetted lightweight aggregate in the concrete systematically decreased the density, modulus of elasticity, and coefficient of thermal expansion of the concrete. When compared to a normalweight concrete, the use of lightweight aggregates in concrete effectively delays the occurrence of early-age cracking in bridge deck applications. 111-M18—Multi-Aggregate Approach for Modeling Interfacial Transition Zone in Concrete by Hongyan Ma and Zongjin Li Interfacial transition zone (ITZ) has long been of particular interest in concrete technology. The limited sensitivity of experimental techniques makes it attractive to study ITZ using computer simulations. In this paper, a multi-aggregate approach is proposed to simulate the formation of ITZ in concrete. In light of a modified status-oriented computer model for
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simulating cement hydration, the evolution of ITZ is also simulated in this approach. Through simulations, the influences of several factors related to concrete mixture proportion on ITZ are investigated. It is found that ITZ thickness, as defined by the overall average porosity, can be reduced by using finer aggregate, increasing aggregate volume fraction, reducing water-cement ratio (w/c), or making the binder system finer. Following hydration, the ITZ thickness decreases continuously, but the difference of porosity between ITZ and bulk paste keeps almost constant at mature ages. 111-M19—C4AF Reactivity—Chemistry and Hydration of Industrial Cement by Hugh Wang, Delia De Leon, and Hamid Farzam The study described in this paper involved a close examination of one of the least-researched cement phases, 4CaO·Al2O3·Fe2O3 (C4AF or ferrite). The two ferrite materials used in this program were: 1) extracted from an industrial clinker free of 3CaO·Al2O3 (C3A or aluminate); and 2) a laboratory-synthesized C4AF compound. Both ferrite materials were initially characterized using optical microscopy, X-ray diffraction (XRD), and Raman spectroscopy. The hydration kinetics and reactivity of both materials were studied with a calorimetric technique. Similar to aluminate, ferrite also demonstrated a strong early hydration rate. An adequate amount of sulfate (SO3) was needed to regulate the ferrite hydration rate. Based on this work, an equivalent aluminate content, C3Aeq, is proposed. The hydration of C3Aeq needs to be properly controlled with the appropriate amount of sulfate. The concept, based on equivalent aluminate content for cement sulfate optimization, ensures proper early hydration behavior from both C3A and C4AF and avoids potential cement-admixture incompatibility problems, especially for cements containing little or no C3A content. 111-M20—Tailoring Hybrid Strain-Hardening Cementitious Composites by Alessandro P. Fantilli, Hirozo Mihashi, and Tomoya Nishiwaki A class of fiber-reinforced concrete, commonly called strain-hardening cementitious composite (SHCC), can show very ductile behavior under tension. In the post-cracking stage, several cracks develop before complete failure, which occurs when tensile strains finally localize in one of the formed cracks. To predict the mechanical performances of monofiber SHCC, a cohesive model has been proposed. Such a model is used herein to tailor hybrid SHCC, made with long and short fibers. By combining uniaxial tensile tests and the theoretical results of the model, the critical value of the fiber-volume fraction can be evaluated. It should be considered as the minimum amount of long fibers that can lead to the formation of multiple cracking and strain hardening under tensile actions. The aim of the present research is to reduce such volume as much as possible, to improve the workability, and to reduce the final cost of SHCC.
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REVIEWERS IN 2013 In 2013, the individuals listed on these pages served as technical reviewers of papers offered for publication in ACI periodicals. A special “thank you” to them for their voluntary assistance in helping ACI maintain the high quality of its publication program. £az´niewska-Piekarczyk, Beata Silesian University of Technology Rybnik, Poland Aamidala, Hari Shankar Parsons Brinckerhoff Herndon, VA Abdalla, Hany College of Technological Studies Shuwaikh, Kuwait Abdel-Fattah, Hisham University of Sharjah Sharjah, United Arab Emirates Abdelgader, Hakim Tripoli University Tripoli, Libyan Arab Jamahiriya Abdelrahman, Amr Heliopolis, Egypt Abo-Shadi, Nagi Robert Englekirk, Inc. Santa Ana, CA Abou-Zeid, Mohamed American University in Cairo Cairo, Egypt Abu Yosef, Ali University of Texas at Austin Austin, TX Achillopoulou, Dimitra Democritus University of Thrace Xanthi, Greece Acun, Bora University of Houston Houston, TX Adebar, Perry University of British Columbia Vancouver, BC, Canada Adhikary, Bimal Austin, TX Agarwal, Pankaj Indian Institute of Technology Roorkee Roorkee, Uttarakhand, India Aggelis, Dimitrios University of Ioannina Ioannina, Ioannina, Greece Agustiningtyas, Rudi Ministry of Public Works Bandung, Indonesia Ahmadi, Jamal University of Science and Technology Tehran, Tehran, Islamic Republic of Iran Ahmadi Nedushan, Behrooz Yazd University Yazd, Yazd, Islamic Republic of Iran Ahmed, Ayub Birla Institute of Technology and Science, Pilani Pilani, Rajasthan, India
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Ahmed, Ehab University of Sherbrooke Sherbrooke, QC, Canada Aidoo, John Rose-Hulman Institute of Technology Terre Haute, IN Aire, Carlos National Autonomous University of Mexico Mexico City, DF, Mexico Akakin, Tumer Turkish Ready Mixed Concrete Association Istanbul, Turkey Akbari, Reza University of Tehran Tehran, Tehran, Islamic Republic of Iran Akcay, Burcu Kocaeli University Kocaeli, Turkey Akiyama, Mitsuyoshi Waseda University Tokyo, Japan Akkaya, Yilmaz Istanbul Technical University Maslak, Istanbul, Turkey Alam, A.K.M. Jahangir Dhaka, Bangladesh Alam, M. Shahria The University of British Columbia Kelowna, BC, Canada Alam, Mahbub Stamford University Bangladesh Dhaka, Bangladesh Al-Attar, Tareq University of Technology Baghdad, Iraq Al-Azzawi, Adel Nahrain University Baghdad, Iraq Albahttiti, Mohammed Kansas State University Manhattan, KS Albuquerque, Albéria Federal Center of Technological Education of Mato Grosso Cuiabá, Mato Grosso, Brazil Al-Chaar, Ghassan U.S. Army Engineer Research and Development Center Champaign, IL Alcocer, Sergio Institute of Engineering, UNAM Mexico City, DF, Mexico Aldajah, Saud United Arab Emirates University Al-Ain, United Arab Emirates Aldea, Corina-Maria St. Catharines, ON, Canada
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Alexander, Scott UMA Engineering, Ltd. Edmonton, AB, Canada Ali, Nisreen Universiti Putra Malaysia Serdang, Selangor, Malaysia Ali, Samia University of Engineering and Technology, Lahore Lahore, Punjab, Pakistan Aljewifi, Hana The University of Cergy-Pontoise Cergy-Pontosie Cedex, France Alkhairi, Fadi Arabtech Jardaneh Amman, Jordan Alkhrdaji, Tarek Structural Group Hanover, MD Allahdadi, Hamidreza Bangalore, India Al-Manaseer, Akthem San Jose State University San Jose, CA Al-Martini, Samer University of Western Ontario London, ON, Canada Al-Qaisy, Wissam Safe Mix Ready Concrete Sharjah, United Arab Emirates Alqam, Maha The University of Jordan Amman, Jordan Alsiwat, Jaber Saudi Consulting Services Riyadh, Saudi Arabia Aly, Aly Mousaad Louisiana State University Baton Rouge, LA Amani Dashlejeh, Asghar Tehran, Tehran, Islamic Republic of Iran Anania, Laura University of Catania Catania, Italy Andersson, Ronny Hollviken, Sweden Andrade, Jairo Pontifical Catholic University of Rio Grande do Sul Porto Alegre, RS, Brazil Andriolo, Francisco Andriolo Ito Engenharia SC Ltda São Carlos, São Paulo, Brazil Ansari, Abdul Aziz Quaid-e-Awam Engineering University Nawabshah, Sindh, Pakistan Aqel, Mohammad King Saud University Riyadh, Saudi Arabia Aragón, Sergio Holcim (Costa Rica) San Rafael, Alajuela, Costa Rica
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REVIEWERS IN 2013 Aravinthan, Thiru University of Southern Queensland Toowoomba, Queensland, Australia Arisoy, Bengi Ege University Izmir, Turkey Aristizabal-Ochoa, Jose National University Medellin, Antioquia, Colombia Armwood, Catherine University of Nebraska Omaha, NE Asaad, Diler Gaziantep University Gaziantep, Turkey Asamoto, Shingo Saitama University Saitama, Saitama, Japan Aslani, Farhad University of Technology, Sydney Sydney, New South Wales, Australia Assaad, Joseph Notre Dame University Beirut, Lebanon Atamturktur, Sez Clemson University Clemson, SC Athanasopoulou, Adamantia AKMI Metropolitan College Xalandri, Greece Attaalla, Sayed ADR Engineering, Inc. Mission Hills, CA Aviram, Ady Simpson Gumpertz & Heger, Inc. San Francisco, CA Awati, Mahesh B.L.D.E.A.’s College of Engineering & Technology, Bijapur Bijapur, Karnataka, India Awida, Tarek KEO International Consultants Kuwait Ayano, Toshiki Okayama University Okayama, Japan Aydin, Abdulkadir Cuneyt Ataturk University Erzurum, Turkey Aydin, Ertug European University of Lefke Nicosia, Turkey Aydın, Serdar Dokuz Eylul University I˙zmir, Turkey Aykac, Sabahattin Gazi University, Faculty of Engineering and Architecture Ankara, Turkey Azad, Abul King Fahd University of Petroleum & Minerals Dhahran, Saudi Arabia
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REVIEWERS IN 2013 Aziz, Omar University of Salahaddin Erbil, Iraq Babafemi, Adewumi Obafemi Awolowo University Ile-ife, Nigeria Bacinskas, Darius Vilnius Gediminas Technical University Vilnius, Lithuania Badger, Christian Bates Engineering, Inc. Lakewood, CO Bae, Sungjin Bechtel Corporation Frederick, MD Bai, Shaoliang Chongqing University Chonqqing, China Bai, Yongtao Kyoto University Kyoto, Japan Bakhshi, Mehdi Arizona State University Tempe, AZ Balaguru, P. Rutgers, the State University of New Jersey Piscataway, NJ Balouch, Sana University of Dundee Dundee, UK Banibayat, Pouya New York, NY Banic´, Davor Civil Engineering Institute of Croatia Zagreb, Croatia Baran, Eray Atilim University Ankara, Turkey Barbosa, Maria Federal University of Juiz de Fora Juiz De Fora, Brazil Barroso de Aguiar, Jose University of Minho Guimaraes, Portugal Bartos, Peter University of the West of Scotland - Paisley Paisley, Scotland, UK Bashandy, Alaa Menofiya University Shibin El-Kom, Egypt Batson, Gordon Clarkson University Potsdam, NY Bayrak, Oguzhan University of Texas at Austin Austin, TX Bayraktar, Alemdar Trabzon, Turkey
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Bayuaji, Ridho Universiti Teknologi PETRONAS Perak, Malaysia Beddar, Miloud M’sila University M’sila, Algeria Bediako, Mark CSIR - Building and Road Research Institute Kumasi, Ghana Bedirhanoglu, Idris Dicle University Diyarbakir, Turkey Behnoud, Ali Iran University of Science and Technology Tehran, Islamic Republic of Iran Belleri, Andrea University of Bergamo Dalmine, Italy Benboudjema, Farid Ecole normale supérieure de Cachan Cachan, France Benliang, Liang Shanghai, China Bennett, Richard The University of Tennessee Knoxville, TN Bentz, Dale National Institute of Standards and Technology Gaithersburg, MD Berry, Michael Montana State University Bozeman, MT Beygi, Morteza Mazandaran University Babol, Mazandaran, Islamic Republic of Iran Bharati, Raj National Institute of Technology Calicut Calicut, Kerala, India Bhargava, Kapilesh Bhabha Atomic Research Centre Mumbai, Maharashtra, India Bhattacharjee, Bishwajit Indian Institute Of Technology, Delhi New Delhi, India Bhatti, Abdul National University of Sciences and Technology Islamabad, Pakistan Bilcik, Juraj Slovak University of Technology in Bratislava Bratislava, Slovakia Bilek, Vlastimil ZPSV a.s. Brno, Czech Republic Bilir, Turhan Bülent Ecevit University Zonguldak, Turkey Billah, Abu Hena The University of British Columbia Kelowna, BC, Canada
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Bimschas, Martin Regensdorf, Switzerland Bindiganavile, Vivek University of Alberta Edmonton, AB, Canada Biolzi, Luigi Politecnico di Milano Milan, Italy Birely, Anna Texas A&M University College Station, TX Birkle, Gerd Stantec Consulting Ltd. Calgary, AB, Canada Bisschop, Jan University of Oslo Oslo, Norway Blair, Bruce Lafarge North America Herndon, VA Bobko, Christopher North Carolina State University Raleigh, NC Bochicchio, Victor Hamon Custodis Somerville, NJ Bondar, Dali Tehran, Islamic Republic of Iran Bondy, Kenneth Consulting Structural Engineer West Hills, CA Boshoff, William Stellenbosch University Stellenbosch, Western Cape, South Africa Boulfiza, Moh University of Saskatchewan Saskatoon, SK, Canada Bousias, Stathis University of Patras Patras, Greece Bradberry, Timothy TxDOT Bridge Division Austin, TX Braestrup, Mikael Ramboll Hannemann and Hojlund A/S Virum, Denmark Brand, Alexander University of Illinois at Urbana-Champaign Urbana, IL Brena, Sergio University of Massachusetts Amherst, MA Brewe, Jared CTLGroup Skokie, IL Bui, Van BASF Admixtures, Inc. Cleveland, OH
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REVIEWERS IN 2013 Burak, Burcu Orta Dogu Teknik Universitesi Ankara, Turkey Burdette, Edwin University Of Tennessee Knoxville, TN Byard, Benjamin University of Tennessee at Chattanooga Chattanooga, TN Calixto, José Universidade Federal de Minas Gerais (UFMG) Belo Horizonte, Brazil Campione, Giuseppe Universita Palermo Palermo, Italy Canbay, Erdem Middle East Technical University Ankara, Cankaya, Turkey Cano Barrita, Prisciliano Instituto Politécnico Nacional/CIIDIR Unidad Oaxaca Oaxaca, Oaxaca, Mexico Canpolat, Fethullah Yildiz Technical University Istanbul, Turkey Capozucca, Roberto Faculty of Engineering Ancona, Italy Carino, Nicholas Chagrin Falls, OH Carreira, Domingo Chicago, IL Carrillo, Julian Universidad Militar Nueva Granada (UMNG) Bogotá, D.C., Colombia Carvalho, Alessandra Pontifical Catholic University of Goiás (PUC-Goiás) Goiânia, Goiás, Brazil Castles, Bryan Western Technologies, Inc. Phoenix, AZ Castro, Javier Pontificia Universidad Catolica de Chile Santiago, Chile Catoia, Bruna Federal University of São Carlos (UFSCar) São Carlos, São Paulo, Brazil Cattaneo, Sara Politecnico di Milano Milan, Italy Cedolin, Luigi Politecnico di Milano Milano, Italy Cetisli, Fatih Firat University Elazig, Turkey Chai, Hwa Kian Tobishima Corporation Noda, Chiba, Japan
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REVIEWERS IN 2013 Chakraborty, Arun Bengal Engineering and Science University Howrah, West Bengal, India Chang, Jeremy Holmes Fire & Safety Christchurch, New Zealand Chastre, Carlos FCT/UNL Lisbon, Portugal Chaudhry, Asif Geoscience Advance Research Laboratories Islamabad, Pakistan Chawla, Komal Indian Institute of Technology Kanpur Kota, India Chen, Chun-Tao National Taiwan University of Science and Technology Taipei, Taiwan Chen, Hua-Peng The University of Greenwich Chatham, Kent, UK Chen, Qi Boral Materials Technology San Antonio, TX Chen, Shiming Tongji University Shanghai, China Chen, Wei Wuhan University of Technology Wuhan, HuBei, China Chen, Xi Shanghai, China Cheng, Min-Yuan National Taiwan University of Science and Technology Taipei, Taiwan Chi, Maochieh WuFeng University Chiayi County, Taiwan Chiaia, Bernardino Politecnico di Torino Torino, Piedmont, Italy Chiang, Chih-Hung Chaoyang University of Technology Wufong, Taichung, Taiwan Chindaprasirt, Prinya Khon Kaen University Khon Kaen, Thailand Chiorino, Mario Politecnico di Torino Torino, Italy Cho, Chang-Geun Chosun University Gwangju, Republic of Korea Cho, Jae-Yeol Seoul National University Seoul, Republic of Korea Cho, Soon-Ho Gwangju University Gwangju, Republic of Korea
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Choi, Bong-Seob Chungwoon University Hongseong-Gun, Republic of Korea Choi, Eunsoo Hongik University Seoul, Republic of Korea Choi, Kyoung-Kyu Soongsil University Seoul, Republic of Korea Choi, Sejin University of California, Berkeley Albany, CA Chompreda, Praveen Mahidol University Nakornpathom, Thailand Choong, Kokkeong Universiti Sains Malaysia Pulau Pinang, Seberang Perai Selatan, Malaysia Chorzepa, Migeum Park Ridge, IL Chowdhury, Subrato Ultra Tech Cement, Ltd. Mumbai, Maharashtra, India Chun, Sung-Chul Mokpo National University Mooan-gun, Republic of Korea Chung, Deborah State University of New York Buffalo, NY Chung, Jae University of Florida Gainesville, FL Chung, Lan Dankook University Seoul, Republic of Korea Claisse, Peter Coventry University Coventry, UK Cleary, Douglas Rowan University Glassboro, NJ Clendenen, Joseph Pleasant Hill, IL Cobo, Alfonso Polytechnic University of Madrid Madrid, Spain Coelho, Jano AltoQi Informatica Florianopolis, Santa Catarina, Brazil Colombo, Matteo Politecnico di Milano Lecco, Italy Conley, Christopher United States Military Academy West Point, NY Cordova, Carlos La Paz, Bolivia Coronelli, Dario Politecnico di Milano Milano, Italy
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Corral, Ramón Universidad Autónoma de Sinaloa Los Mochis, Sinaloa, Mexico Correal, Juan Arcon Structural Engineers, Inc. Rancho Santa Margarita, CA Cortes, Douglas New Mexico State University Las Cruces, NM Criswell, Marvin Colorado State University Fort Collins, CO Cueto, Jorge Universidad de La Salle Bogota, Colombia D. L., Venkatesh Babu Kumaraguru College of Technology Coimbatore, Tamil Nadu, India Dang, Canh University of Arkansas Fayetteville, AR Das, Sreekanta University of Windsor Windsor, ON, Canada Daye, Marwan Intima International Co., Ltd. Al-Khobar, Saudi Arabia de Brito, Jorge IST/TUL Lisbon, Portugal de Frutos, Jose Universidad Politecnica de Madrid Madrid, Spain De Rooij, Mario TNO Delft, the Netherlands Deb, Arghya Indian Institute of Technology, Kharagpur Kharagpur, West Bengal, India Degtyarev, Vitaliy Columbia, SC Dehn, Frank University of Leipzig Leipzig, Germany Delalibera, Rodrigo University of São Paulo São Carlos, São Paulo, Brazil Delatte, Norbert Cleveland State University Broadview Heights, OH Demir, Ali Celal Bayar University Manisa, Turkey Demir, Serhat Blacksea Technical University Trabzon, Turkey Den Uijl, Joop Delft University of Technology Delft, the Netherlands
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REVIEWERS IN 2013 Deng, Yaohua Iowa State University Ames, IA Detwiler, Rachel Braun Intertec Corporation Minneapolis, MN Devries, Richard Milwaukee School of Engineering Milwaukee, WI Dhanasekar, Manicka Queensland University of Technology Brisbane, Queensland, Australia Dhonde, Hemant University of Houston Houston, TX Di Ludovico, Marco University of Naples Federico II Naples, Italy Dias, WPS University of Moratuwa Moratuwa, Sri Lanka Diaz Loya, Eleazar Louisiana Tech University Ruston, LA Dilger, Walter University of Calgary Calgary, AB, Canada Ding, Yining Dalian, China Diniz, Sofia Maria Universidade Federal de Minas Gerais (UFMG) Be lo Horizonte, Brazil Do, Jeongyun Kunsan National University Kunsan, Jeonbuk, Republic of Korea Dodd, Larry Parsons Brinckerhoff Orange, CA Dogan, Unal Istanbul Technical University Istanbul, Turkey Dolan, Charles University of Wyoming Laramie, WY Dongell, Jonathan Pebble Technologies Scottsdale, AZ Dongxu, Li Nanjing University of Technology Nanjing, Jiangsu, China Dontchev, Dimitar University of Chemical Technology and Metallurgy Sofia, Bulgaria Dragunsky, Boris Universal Construction Testing, Ltd. Highland Park, IL Du, Jinsheng Beijing Jiao Tong University Beijing, China
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REVIEWERS IN 2013 Du, Lianxiang The University of Alabama at Birmingham Birmingham, AL Du, Yingang Anglia Ruskin University Chelmsford, UK Dubey, Ashish United States Gypsum Corp Libertyville, IL Dutta, Anjan Indian Institute of Technology Guwahati Guwahati, Assam, India Dutton, John Edmonton, AB, Canada Eid, Rami University of Sherbrooke Sherbrooke, QC, Canada El Ragaby, Amr University of Manitoba Winnipeg, MB, Canada Elamin, Anwar University of Nyala Khartoum, Sudan El-Ariss, Bilal United Arab Emirates University Al Ain, United Arab Emirates Elbahar, Mohamed Ken Okamoto & Associates: Structural Engineering Rancho Santa Margarita, CA ElBatanouny, Mohamed University of South Carolina West Columbia, SC Eldarwish, Aly Alexandria, Egypt El-Dash, Karim College of Technological Studies Kuwait, Kuwait El-Dieb, Amr Ain Shams University Abbasia, Cairo, Egypt El-Hawary, Moetaz Kuwait Institute for Scientific Research Safat, Kuwait Elkady, Hala National Research Centre (NRC) Giza, Egypt El-Maaddawy, Tamer United Arab Emirates University Al-Ain, Abu Dhabi, United Arab Emirates Elmenshawi, Abdelsamie University of Calgary Calgary, AB, Canada El-Metwally, Salah University of Hawaii at Manoa Honolulu, HI Elnady, Mohamed Mississauga, ON, Canada El-Refaie, Sameh El-Gama City, Mataria, Cairo, Egypt
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El-Salakawy, Ehab University of Manitoba Winnipeg, MB, Canada Elsayed, Tarek Cairo, Egypt Emamy Farvashany, Firooz Perthpolis Pty, Ltd. Perth, Western Australia, Australia Eom, Tae-Sung Catholic University of Daegu Kyeongsan-si, Republic of Korea Erdem, T. Izmir Institute of Technology Izmir, Turkey Ergün, Ali Afyon Kocatepe University Afyonkarahısar, Turkey Evangelista, Luís Instituto Superior de Engenharia de Lisboa Lisbon, Portugal Fafitis, Apostolos Arizona State University Tempe, AZ Fanella, David Klein and Hoffman Chicago, IL Fantilli, Alessandro Politecnico di Torino Torino, Italy Faraji, Mahdi Tehran, Islamic Republic of Iran Fardis, Michael Patras, Greece Farghaly, Ahmed University of Sherbrooke Sherbrooke, QC, Canada Faria, Duarte Faculdade de Ciências e Tecnologia Caparica-Lisbon, Portugal Farrow, William Lebanon, NJ Farzam, Masood Structural Engineering Tabriz, Islamic Republic of Iran Fenollera, Maria Universidade de Vigo Vigo, Spain Ferguson, Bruce University of Georgia Athens, GA Fernández Montes, David Madrid, Spain Fernández Ruiz, Miguel Ecole Polytechnique Federale De Lausanne Lausanne, Vaud, Switzerland Ferrara, Liberato Politecnico di Milano Milan, Italy
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Ferrier, E. Université Claude Bernard Lyon 1 Villerubanne, France Folino, Paula University of Buenos Aires Buenos Aires, Argentina Foster, Stephen University of New South Wales Sydney, New South Wales, Australia Fouad, Fouad University of Alabama at Birmingham Birmingham, AL Fradua, Martin Feld, Kaminetzky & Cohen, P.C. Jericho, NY Francüois, Buyle-Bodin University of Lille Villeneuve d’Ascq, France Fuchs, Werner University of Stuttgart Stuttgart, Germany Furlong, Richard Austin, TX G., Dhinakaran Sastra University Thanjavur, India Gabrijel, Ivan University of Zagreb Zagreb, Croatia Galati, Nestore Structural Group, Inc. Elkridge, MD Gallegos Mejia, Luis Fundacion Padre Arrupe de El Salvador Soyapango, San Salvador, El Salvador Gamble, William University of Illinois at Urbana-Champaign Urbana, IL Ganesan, N. National Institute of Technology Calicut, India Garboczi, Edward National Institute of Standards and Technology Gaithersburg, MD Garcez, Estela Universidade Federal de Pelotas (UFPel) Pelotas, RS, Brazil Garcia-Taengua, Emilio Universidad Politecnica de Valencia Valencia, Spain Gardoni, Paolo University of Illinois at Urbana-Champaign Urbana, IL Gayarre, Fernando Gijon, Spain Gayed, Ramez University of Calgary Calgary, AB, Canada
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REVIEWERS IN 2013 Gesund, Hans University of Kentucky Lexington, KY Ghafari, Nima Laval University Quebec, QC, Canada Giaccio, Craig AECOM Melbourne, Victoria, Australia Giancaspro, James University of Miami Coral Gables, FL Gilbert, Raymond The University of New South Wales Sydney, New South Wales, Australia Girgin, Canan Yildiz Technical University Istanbul, Turkey Gisario, Annamaria Sapienza – Università di Roma Rome, Italy Gnaedinger, John Con-Cure Corporation Chesterfield, MO Goel, Rajeev CSIR - Central Road Research Institute Delhi, India Goel, Savita Whitlock Dalrymple Poston & Associates New York, NY Gökçe, H. Süleyman Gazi University Ankara, Turkey Gongxun, Wang Hunan University of Science and Technology Xiangtan, China Gonzales Garcia, Luis Alberto Lagging SA Lima, Peru González-Valle, Enrique Madrid, Spain Grandic´, Davor University of Rijeka Rijeka, Croatia Grattan-Bellew, P. Materials & Petrographic Research G-B Inc. Ottawa, ON, Canada Greene, Thomas W. R. Grace & Co. Houston, TX Gribniak, Viktor Vilnius Gediminas Technical University Vilnius, Lithuania Gu, Xiang-Lin Tongji University Shanghai, China Guadagnini, Maurizio The University of Shefifeld Sheffield, UK
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REVIEWERS IN 2013 Guan, Garfield University of Cambridge Cambridge, UK Guimaraes, Giuseppe Pontificia Universidade Católica do Rio de Janeiro Rio de Janeiro, Brazil Güneyisi, Erhan Gaziantep University Gaziantep, Turkey Guo, Guohui Overland Park, KS Guo, Liping Southeast University Nanjing, Jiangsu Province, China Guo, Zixiong Huaqiao University Quanzhou, Fujian, China Gupta, Ajay M.B.M. Engineering College Jodhpur, Rajasthan, India Gupta, Pawan Post-Tensioning Institute Phoenix, AZ Haach, Vladimir University of São Paulo São Carlos, São Paulo, Brazil Habbaba, Ahmad Technische Universität München Garching, Germany Haddad, Gilbert SNC-Lavalin, Inc. St. Laurent, QC, Canada Haddadin, Laith United Nations New York, NY Hadi, Muhammad University of Wollongong Wollongong, New South Wales, Australia Hadje-Ghaffari, Hossain John A. Martin & Associates Los Angeles, CA Hagenberger, Michael Valparaiso University Valparaiso, IN Hamid, Roszilah Universiti Kebangsaan Malaysia Bangi, Selangor, Malaysia Hamilton, Trey University of Florida Gainesville, FL Hansen, Will Brighton, MI Harajli, Mohamed American University of Beirut Beirut, Lebanon Harbec, David University of Sherbrooke Sherbrooke, QC, Canada
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Harris, Devin University of Virginia Charlottesville, VA Harris, G Terry Green Cove Springs, FL Harris, Nathan Menlo Park, CA Hashemi, Shervin Seoul National University Seoul, Republic of Korea Hassan, Assem Toronto, ON, Canada Hassan, Maan University of Technology Baghdad, Iraq Hassan, Wael University of California, Berkeley Berkeley, CA He, Xiaobing Chongqing Jiaotong University Chongqing, China He, Zhiqi Southeast University Nanjing, Jiangsu, China Heinzmann, Daniel Lucerne University of Applied Sciences and Arts Horw, Switzerland Henry, Richard University of Auckland Auckland, New Zealand Himawan, Aris Singapore, Singapore Hindi, Riyadh Saint Louis University St. Louis, MO Hoehler, Matthew Encinitas, CA Holschemacher, Klaus HTWK Leipzig Leipzig, Germany Hong, Sung-Gul Seoul National University Seoul, Republic of Korea Hooton, R. Doug University of Toronto Toronto, ON, Canada Hossain, Khandaker Ryerson University Toronto, ON, Canada Hossain, Tanvir Louisiana State University Baton Rouge, LA Hosseini, Ardalan Isfahan University of Technology (IUT) Isfahan, Islamic Republic of Iran Hoult, Neil Toronto, ON, Canada Hover, Kenneth Cornell University Ithaca, NY
ACI Structural Journal/March-April 2014
Hrynyk, Trevor University of Toronto Toronto, ON, Canada Hsu, Thomas University of Houston Houston, TX Hu, Jiong Texas State University-San Marcos San Marcos, TX Hu, Nan Tsinghua University Beijing, China Huang, Chang-Wei Chung Yuan Christian University Chung Li, Taiwan Huang, Jianwei Southern Illinois University Edwardsville Edwardsville, IL Huang, Xiaobao GM-WFG/GM-N American Project Center Warren, MI Huang, Yishuo Chaoyang University of Technology Wufeng, Taichung, Taiwan Huang, Zhaohui Brunel University London, UK Hubbell, David Toronto, ON, Canada Hueste, Mary Beth Texas A&M University College Station, TX Hulsey, J. University of Alaska Fairbanks, AK Hung, Chung-Chan University of Michigan Ann Arbor, MI Husain, Mohamed Zagazig University Zagazig, Egypt Husem, Metin Karadeniz Technical University Trabzon, Turkey Hussain, Raja King Saud University Riyadh, Saudi Arabia Hussein, Amgad Memorial University of Newfoundland St. John’s, NL, Canada Hwang, Chao-Lung National Taiwan University of Science and Technology Taipei, Taiwan Ibell, Tim University of Bath Bath, UK Ibrahim, Amer Baquba, Iraq
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013 Ibrahim, Hisham Buckland and Taylor, Ltd. North Vancouver, BC, Canada Ichinose, Toshikatsu Nagoya Institute of Technology Nagoya, Japan Ideker, Jason Oregon State University Corvallis, OR Ince, Ragip Firat University Elazig, Turkey I˙pek, Süleyman Gaziantep University Gaziantep, Turkey Irassar, Edgardo Universidad Nacional del Centro de la Provincia de Buenos Aires (UNCPBA) Olavarria, Buenos Aires, Argentina Islam, Md. Chittagong University of Engineering & Technology (CUET) Chittagong, Bangladesh Issa, Mohsen University of Illinois at Chicago Chicago, IL Izquierdo-Encarnación, Jose Porticus San Juan, PR Jaari, Asaad Dera, Dubai, United Arab Emirates Jaeger, Thomas Baenziger Partner AG Chur, Switzerland Jain, Mohit Nirma University Ahmedabad, Gujarat, India Jain, Shashank Delhi Technological University (DTU) New Delhi, India Jamshidi, Masoud Building and Housing Research Center (BHRC) Tehran, Islamic Republic of Iran Jang, Seung Yup Korea Railroad Research Institute Uiwang, Gyongggi-do, Republic of Korea Jansen, Daniel California Polytechnic State University San Luis Obispo, CA Jau, Wen-Chen National Chiao Tung University (NCTU) Hsinchu, Taiwan Jawaheri Zadeh, Hany Miami, FL Jayapalan, Amal Georgia Institute of Technology Atlanta, GA Jeng, Chyuan-Hwan National Chi Nan University-Taiwan Puli, Nantou, Taiwan
471
REVIEWERS IN 2013 Jensen, Elin Lawrence Technological University Southfield, MI Jeon, Se-Jin Ajou University Suwon-si, Gyeonggi-do, Republic of Korea Jiang, Jiabiao W. R. Grace (Singapore) Pte. Ltd. Singapore Jirsa, James University of Texas at Austin Austin, TX Jozic´, Dražan Universty of Split Split, Croatia Kabele, Petr Czech Technical University in Prague Praha 6, Czech Republic Kagaya, Makoto Akita, Japan Kalkan, Ilker Kırıkkale University Kırıkkale, Turkey Kan, Yu-Cheng Chaoyang University of Technology Taichung County, Taiwan Kanakubo, Toshiyuki University of Tsukuba Tsukuba, Japan Kandasami, Siva Bristol, UK Kang, Thomas Seoul National University Seoul, Republic of Korea Kankam, Charles Kwame Nkrumah University of Science & Technology Kumasi, Ghana Kansara, Kunal University of Bath Bath, UK Kantarao, Velidandi Central Road Research Institute New Delhi, Delhi, India Karahan, Okan Erciyes University Erciyes, Turkey Karayannis, Christos Democritus University of Thrace Xanthi, Greece Karbasi Arani, Kamyar University of Naples Federico II Napoli, Italy Kawamura, Mitsunori Kanazawa, Ishikawa, Japan Kazemi, Mohammad Sharif University of Technology Tehran, Islamic Republic of Iran Kazemi, Sadegh University of Alberta Edmonton, AB, Canada
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Kenai, Said Université de Blida Blida, Algeria Kevern, John University of Missouri-Kansas City Kansas City, MO Khan, Mohammad King Saud University Riyadh, Saudi Arabia Kheder, Ghazi University of Al Mustansiriya Baghdad, Iraq Khennane, Amar Australian Defense Force Academy, University of New South Wales (AFDA, UNSW) Canberra, Australian Capital Territory, Australia Khuntia, Madh DuKane Precast Inc. Naperville, IL Kianoush, M. Reza Ryerson University Toronto, ON, Canada Kilic, Sami Bogazici University Istanbul, Turkey Kim, Jae Hong UNIST Ulsan, Republic of Korea Kim, Jang Hoon Ajou University Suwon, Republic of Korea Kim, Yail University of Colorado Denver Denver, CO Kirgiz, Mehmet Hacettepe University Ankara, Turkey Kishi, Norimitsu Muroran Institute of Technology Muroran, Japan Kisicek, Tomislav University of Zagreb Zagreb, Croatia Klemencic, Ronald Magnusson Klemencic Associates Seattle, WA Ko, Lesley Suz-Chung Holcim Group Support, Ltd. Holderbank, AG, Switzerland Koehler, Eric University of Texas at Austin Austin, TX Koenders, Eddy A. B. Delft University of Technology Delft, the Netherlands Kotsovos, Gerasimos National Technical University of Athens Athens, Greece Kotsovos, Michael Athens, Greece
ACI Structural Journal/March-April 2014
Krem, Slamah University of Waterloo Waterloo, ON, Canada Krstulovic-Opara, Neven ExxonMobil Development Company Houston, TX Kumar, Pardeep University of California, Berkeley Berkeley, CA Kumar, Rakesh Central Road Research Institute Delhi, India Kumar, Vinod Steel Authority of India Limited Ranchi, Jharkhand, India Kunieda, Minoru Nagoya University Nagoya, Japan Kunnath, Sashi University of California, Davis Davis, CA Kupwade-Patil, Kunal Massachusetts Institute of Technology Cambridge, MA Kurtis, Kimberly Georgia Institute of Technology Atlanta, GA Kusbiantoro, Andri Universiti Malaysia Pahang Gambang, Pahang, Malaysia Kwan, Albert The University of Hong Kong Hong Kong, China Kwan, Wai Hoe Universiti Sains Malaysia Gelugor, Penang, Malaysia La Tegola, Antonio University of Lecce Lecce, Italy LaFave, James University of Illinois at Urbana-Champaign Champaign, IL Lai, Jianzhong Nanjing University of Science and Technology Nanjing, Jiangsu, China Larbi, Kacimi University of Sciences and Technology of Oran Oran, Oran, Algeria Laskar, Aminul National Institute of Technology Silchar, Assam, India Laterza, Michelangelo University of Basilicata Potenza, Italy Law, David RMIT University Melbourne, Victoria, Australia Lawler, John Wiss, Janney, Elstner Associates, Inc. Northbrook, IL
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013 Lee, Chadon Chung-Ang University Ansung, Kyungki-do, Republic of Korea Lee, Chung-Sheng University of California, San Diego La Jolla, CA Lee, Deuck Hang University of Seoul Seoul, Republic of Korea Lee, Douglas Douglas D. Lee & Associates Fort Worth, TX Lee, Heui Hwang Arup San Francisco, CA Lee, Hung-Jen National Yunlin University of Science and Technology Douliu, Yunlin, Taiwan Lee, Jaeman Kyoto University Kyoto, Japan Lee, Jung-Yoon Sung Kyun Kwan University Suwon, Republic of Korea Lee, Nam Ho SNC-Lavalin Nuclear Inc. Oakville, ON, Canada Lee, Seong-Cheol KEPCO International Graduate School (KINGS) Ulsan, Republic of Korea Lee, Seung-Chang Samsung C&T Corporation Seoul, Republic of Korea Lee, Yoon-Si Bradley University Peoria, IL Lee, Young Hak Seoul, Republic of Korea Leiva Fernández, Carlos University of Seville Seville, Andalucia, Spain Leo Braxtan, Nicole New York, NY Lequesne, Remy University of Kansas Madison, KS Leutbecher, Torsten Universität Kassel Kassel, Germany Li, Fumin China University of Mining and Technology Xuzhou, Jiangsu, China Li, Wei Wenzhou University Wenzhou, Zhejiang, China Lignola, Gian Piero University of Naples Naples, Italy
473
REVIEWERS IN 2013 Lima, Maria Cristina Federal University of Uberlândia Uberlandia, Minas Gerais, Brazil Lin, Wei-Ting Institute of Nuclear Energy Research Taoyuan, Taiwan Lin, Yiching National Chung-Hsing Univ Taichung, Taiwan Liu, Shuhua Wuhan University Wuhan, HuBei, China Liu, Yanbo Florida Department of Transportation-State Materials Office Gainesville, FL Lizarazo Marriaga, Juan Coventry University Coventry, UK Londhe, Rajesh Government College of Engineering Aurangabad Aurangabad, Maharashtra, India Long, Adrian Queens University Belfast, Ireland Loo, Yew-Chaye Gold Coast, Australia Loper, James Jacobs Facilities, Inc. Arlington, VA Lopes, Anne Furnas Centrais Elétricas S/A Aparecida De Goiania, Goias, Brazil Lopes, Sergio University of Coimbra Coimbra, Portugal López-Almansa, Francisco Technical University of Catalonia Barcelona, Spain Lounis, Zoubir National Research Council Ottawa, ON, Canada Lubell, Adam Read Jones Christoffersen, Ltd. Vancouver, BC, Canada Ludovit, Nad Alfa 04 Kosice, Slovakia Luo, Baifu Harbin, China Lushnikova, Nataliya National University of Water Management and Nature Resources Use Rivne, Ukraine Ma, Zhongguo University of Tennessee Knoxville, TN MacDougall, Colin Kingston, ON, Canada
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Machida, Atsuhiko Saitama University Saitama, Japan Macht, Jürgen Kirchdorf, Austria Maekawa, Koichi University of Tokyo Tokyo, Japan Magliulo, Gennaro University of Naples Federico II Naples, Italy Magureanu, Cornelia Technical University of Cluj Napoca Cluj Napoca, Cluj, Romania Mahboub, Kamyar University of Kentucky Lexington, KY Mahfouz, Ibrahim Cairo, Egypt Malik, Adnan University of New South Wales Sydney, Australia Mancio, Mauricio University of California, Berkeley Berkeley, CA Mander, John Texas A&M University College Station, TX Manso, Juan University of Burgos Burgos, Castilla-León, Spain Marikunte, Shashi Southern Illinois University Carbondale, IL Martinelli, Enzo University of Salerno Fisciano, Italy Martí-Vargas, José Universitat Politècnica de València Valencia, Valencia, Spain Maruyama, Ippei Nagoya University Nagoya, Aichi, Japan Maslehuddin, Mohammed King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia Matamoros, Adolfo University of Kansas Lawrence, KS Mathew, George Cochin University of Science and Technology Cochin, Kerala, India Matsagar, Vasant Lawrence Technological University Southfield, MI Matta, Fabio University of South Carolina Columbia, SC
ACI Structural Journal/March-April 2014
Maximos, Hany Pharos University in Alexandria Alexandria, Egypt Mbessa, Michel University of Yaoundé I - ENSP Yaoundé, Center, Cameroon McCabe, Steven Lawrence, KS McCall, W. Concrete Engineering Consultants Charlotte, NC McCarter, John Heriot Watt University Edinburgh, UK McDonald, David USG Corporation Libertyville, IL McLeod, Heather Kansas Department of Transportation Topeka, KS Meda, Alberto University of Bergamo Bergamo, Italy Medallah, Khaled Saudi Aramco IKPMS Al Khobar, Saudi Arabia Meddah, Seddik Kingston University London Kingston, London, UK Mehanny, Sameh Cairo University Cairo, Egypt Meinheit, Donald Wiss, Janney, Elstner Associates, Inc. Chicago, IL Meininger, Richard Turner-Fairbank Highway Research Center-FHWA Columbia, MD Mejia, Luis Gonzalo LGM & Cia Medellin, Colombia Melchers, Robert The University of Newcastle Newcastle, New South Wales, Australia Melo, José University of Aveiro Aveiro, Portugal Meng, Tao Institution of Building Materials Hangzhou, Zhejiang, China Menon, Devdas Indian Institute of Technology Chennai, Tamilnadu, India Mermerdas¸ , Kasım Hasan Kalyoncu University Gaziantep, Turkey Meshgin, Pania University of Colorado Boulder Boulder, CO
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013 Mezhov, Alexander Moscow State University of Civil Engineering Moscow, Russian Federation Milestone, Neil Callaghan Innovation Lower Hutt, New Zealand Minelli, Fausto University of Brescia Brescia, Brescia, Italy Mishra, Laxmi Motilal Nehru National Institute of Technology Allahabad Allahabad, Uttar Pradesh, India Mlynarczyk, Alexandar Wiss, Janney, Elstner Associates, Inc. Princeton Junction, NJ Mohamad, Gihad University of Extremo Sul Catarinense - UNESC Alegrete, Rio Grande do Sul, Brazil Mohamed, Ashraf Alexandria University Alexandria, Egypt Mohamed, Nayera Assiut University Assiut, Egypt Mohammed, Tarek University of Asia Pacific Dhaka, Bangladesh Montejo, Luis North Carolina State University Raleigh, NC Moradian, Masoud Oklahoma State University Stillwater, OK Moreno Júnior, Armando Unicamp Campinas, São Paulo, Brazil Moretti, Marina University of Thessaly Athens, Greece Moriconi, Giacomo Technical University of Marche Ancona, Italy Morley, Christopher Cambridge University Cambridge, UK Moser, Robert US Army Engineer Research and Development Center Vicksburg, MS Mostofinejad, Davood Isfahan University of Technology Isfahan, Isfahan, Islamic Republic of Iran Motaref, Sarira University of Connecticut Storrs, CT Mubin, Sajjad University of Engineering and Technology Lahore, Punjab, Pakistan Mulaveesala, Ravibabu Indian Institute of Information Technology Jabalpur, India
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REVIEWERS IN 2013 Munoz, Jose Federal Highway Administration McLean, VA Muttoni, Aurelio Swiss Federal Institute of Technology Lausanne, Switzerland Nabavi, Esrafil Rezvanshahr, Guilan, Islamic Republic of Iran Nafie, Amr Cairo, Egypt Naish, David California State University, Fullerton Fullerton, CA Najimi, Meysam University of Nevada, Las Vegas Las Vegas, NV Nakamura, Hikaru Nagoya University Nagoya, Aichi, Japan Narayanan, Pannirselvam VIT University Vellore, Tamilnadu, India Narayanan, Subramanian Gaithersburg, MD Nassif, Hani Rutgers, The State University of New Jersey Piscataway, NJ Negrutiu, Camelia Technical University of Cluj Napoca Cluj Napoca, Cluj, Romania Neves, Luís University of Coimbra Coimbra, Portugal Ng, Ernesto Maveang, S.A. Panama, Panama Ng, Pui Lam The University of Hong Kong Hong Kong Nichols, John Texas A&M University College Station, TX Nimityongskul, Pichai Asian Institute of Technology Pathumthani, Thailand Nkinamubanzi, Pierre-Claver Institute for Research in Construction Ottawa, ON, Canada Nokken, Michelle Concordia University Montreal, QC, Canada Noor, Munaz Bangladesh University of Engineering and Technology Dhaka, Bangladesh Noshiravani, Talayeh École polytechnique fédérale de Lausanne (EPFL) Lausanne, Switzerland Novak, Lawrence Portland Cement Association Skokie, IL
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Nowak, Andrzej University of Nebraska-Lincoln Lincoln, NE Nwaubani, Sunny Onyebuchi Anglia Ruskin University Chelmsford, UK O’Connor, Arthur O C Engineering Reno, NV Offenberg, Matthew Rinker Materials Orlando, FL Oh, Byung Seoul National University Seoul, Republic of Korea Okeil, Ayman Louisiana State University Baton Rouge, LA Olanitori, Lekan The Federal University of Technology Akure Akure, Ondo State, Nigeria Orakcal, Kutay Bogazici University Istanbul, Turkey Orr, John University of Bath Bath, UK Orta, Luis Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM) Zapopan, Jalisco, Mexico Ortega, J. University of Alacant Alacant, Alicante, Spain Otieno, Mike University of Cape Town Cape Town, Western Cape, South Africa Otsuki, Nobuaki Tokyo Institute of Technology Tokyo, Japan Ousalem, Hassane Takenaka Corporation - Research and Development Institute Inzai, Chiba, Japan Ozbay, Erdogan Iskenderun, Hatay, Turkey Ozden, Sevket Kocaeli Universitesi Kocaeli, Turkey Ozturan, Turan Bogazici University Istanbul, Turkey Ozturk, Ali Dokuz Eylul University Izmir, Buca, Turkey P S, Ambily Council of Scientific & Industrial Research (CSIR) Chennai, Tamilnadu, India Pacheco, Alexandre Universidade Federal do Rio Grande do Sul (UFRGS) Porto Alegre, Rio Grande do Sul, Brazil
ACI Structural Journal/March-April 2014
Page, Adrian University of Newcastle Newcastle, New South Wales, Australia Palmisano, Fabrizio Politecnico di Bari Bari, Italy Pan, Wang Fook SEGi University Petaling Jaya, Selangor, Malaysia Pantazopoulou, Stavroula Demokritus University of Thrace Xanthi, Greece Pape, Torill University of Newcastle Callaghan, New South Wales, Australia Parghi, Anant The University of British Columbia Kelowna, BC, Canada Park, Honggun Seoul National University Seoul, Republic of Korea Parsekian, Guilherme Federal University of São Carlos São Carlos, São Paulo, Brazil Patel, Raj CeraTech, Inc. Baltimore, MD Pauletta, Margherita University of Udine Tavagnacco, Udine, Italy Paulotto, Carlo Acciona S.A. Alcobendas, Spain Pavlikova, Milena CTU in Prague Prague, Czech Republic Pellegrino, Carlo University of Padova Padova, Italy Peng, Cao Harbin Institute of Technology Harbin, Heilongjiang, China Peng, Jianxin Institute of Bridge Engineering Changsha, Hunan, China Perez, Gustavo Universidad Nacional de Tucumán Yerba Buena, Tucumán, Argentina Perez Caldentey, Alejandro Universidad Politécnica de Madrid Madrid, Madrid, Spain Persson, Bertil Bara, Sweden Pessiki, Stephen Lehigh University Bethlehem, PA Phillippi, Don Diamond Pacific Rancho Cucamonga, CA
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013 Pirayeh Gar, Shobeir Houston, TX Polak, Marianna University of Waterloo Waterloo, ON, Canada Potter, William Florida Department of Transportation Tallahassee, FL Pourazin, Khashaiar International Institute of Earthquake Engineering Seismology (IIEES) Tehran, Islamic Republic of Iran Prakash, M. N. J.N.N. College of Engineering Shimoga, Karnataka, India Prasittisopin, Lapyote Oregon State University Corvallis, OR Proske, Tilo Technische Universität Darmstadt Darmstadt, Germany Prota, Andrea University of Naples Naples, Italy Provis, John University of Melbourne Victoria, Australia Prusinski, Jan Slag Cement Association Sugar Land, TX Pujol, Santiago Berkeley, CA Puthenpurayil Thankappan, Santhosh Granite Construction Company Abu Dhabi, United Arab Emirates Putra Jaya, Ramadhansyah Universiti Teknologi Malaysia Skudai, Malaysia Qasrawi, Hisham The Hashemite University Zarqa, Jordan Qiu, Bin Xi’an University of Architecture & Technology Xi’an, China Rafi, Muhammad NED University of Engineering and Technology Karachi, Sindh, Pakistan Ragueneau, Frederic Ecole normale supérieure de Cachan (ENS Cachan) Cachan, France Rahal, Khaldoun Kuwait University Safat, Kuwait Rajamane, N. P. SRM University Kattankulathur, Tamil Nadu, India Ramamurthy, K. Indian Institute of Technology Madras Chennai, Tamilnadu, India
and
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REVIEWERS IN 2013 Ramaswamy, Ananth Indian Institute of Science Bangalore, Karnataka, India Ramos, António Faculdade de Ciências e Tecnologia Monte de Caparica, Portugal Rangan, Vijaya Curtin University of Technology Perth, Western Australia, Australia Rao, Hanchate Jawaharlal Nehru Technological University Engineering Anantapur, India Rao, Sarella National Institute of Technology Warangal, Andhra Pradesh, India Raoof, Mohammed Loughborough University Loughborough, UK Rautenberg, Jeffrey Wiss, Janney, Elstner Associates, Inc. Emeryville, CA Ray, Indrajit Purdue University Calumet Hammond, IN Razaqpur, A. Ghani McMaster University Hamilton, ON, Canada Regan, Paul Trigram London, UK Reiterman, Roy Roy H. Reiterman, P.E., and Associates Troy, MI Ren, Xiaodan Shanghai, China Richardson, James University of Alabama Tuscaloosa, AL Riding, Kyle Kansas State University Manhattan, KS Rinaldi, Zila University of Rome Tor Vergata Rome, Italy Rizk, Emad Memorial University of Newfoundland St. John’s, NL, Canada Rizwan, Syed Ali University of Engineering and Technology Lahore, Punjab, Pakistan Roberts, Lawrence Grace Construction Products Cambridge, MA Robery, Peter Halcrow Group Ltd. Solihull, West Midlands, UK
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Rodrigues, Conrado Federal Centre for Technological Education in Minas Gerais (CEFET-MG) Belo Horizonte, Minas Gerais, Brazil Rodrigues, Publio LPE Engenharia e Consultoria São Paulo, Brazil Rodriguez, Mario National University of Mexico Mexico City, DF, Mexico Roh, Hwasung Chonbuk National University Jeonju, Republic of Korea Rosenboom, Owen Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong Rteil, Ahmad University of British Columbia Kelowna, BC, Canada Russell, Henry Henry G. Russell, Inc. Glenview, IL S. A., Jaffer Sathik CSIR-Structural Engineering Research Center Chennai, Tamilnadu, India Saatci, Selcuk Izmir Institute of Technology Izmir, Turkey Sabouni, Faisal Architectural Consulting Group Abu Dhabi, United Arab Emirates Sadeghi Pouya, Homayoon Coventry University Coventry, UK Saedi, Houman Tabiat Modares University Tehran, Islamic Republic of Iran Safan, Mohamed Menoufia University Shebeen El-Koom, Menoufia, Egypt Safi, Brahim University of Boumerdes Boumerdes, Algeria Sagaseta, Juan University of Surrey Guildford, Surrey, UK Sagues, Alberto University of South Florida Tampa, FL Sahamitmongkol, Raktipong CONTEC; Sirindhorn International Institute of Technology, Thammasat University; MTEC Pathumthani, Thailand Sahmaran, Mustafa Gazi University Ankara, Turkey Sahoo, Dipak Cochin University of Science and Technology Cochin, Kerala, India
ACI Structural Journal/March-April 2014
Saito, Shigehiko University of Yamanashi Kofu, Japan Sajedi, Fathollah Universiti Malaya Kuala Lumpur, Selangor, Malaysia Saka, Mehmet Middle East Technical University Ankara, Turkey Sakai, Etsuo Tokyo Institute of Technology Ichikawa-shi, Japan Saleem, Muhammad Florida International University Miami, FL Salem, Hamed Cairo University Giza, Egypt Sallam, Hossam El-Din Zagazig University Zagazig, Sharkia, Egypt Sánchez, Isidro University of Alicante Alicante, Alicante, Spain Sanchez, Leandro São Paulo, Brazil Sant, Gaurav University of California, Los Angeles Los Angeles, CA Saqan, Elias American University in Dubai Dubai, United Arab Emirates Sarker, Prabir Curtin University of Technology Bentley, Western Australia, Australia Sato, Ryoichi Hiroshima University Higashi-Hiroshima, Japan Sato, Yuichi Kyoto University Kyoto, Japan Scanlon, Andrew The Pennsylvania State University University Park, PA Schindler, Anton Auburn University Auburn, AL Schwetz, Paulete Universidade Federal do Rio Grande do Sul Porto Alegre, Rio Grande do Sul, Brazil Semaan, Hassnaa Ottawa Hills, OH Sener, Siddik Gazi University Ankara, Turkey Sengul, Ozkan Istanbul Technical University Istanbul, Turkey
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013 Sennour, Larbi Consulting Engineers Group San Antonio, TX Serna-Ros, Pedro Universitat Politècnica de València Valencia, Spain Serrano, Miguel University of Oviedo Gijon, Spain Shafigh, Payam Kuala Lumpur, Malaysia Shafiq, Nasir Universiti Teknologi Petronas Tronoh, Perak, Malaysia Shah, Santosh Dharmsinh Desai University Nadiad, Gujarat, India Shah, Surendra Northwestern University Evanston, IL Shahnewaz, Md University of British Columbia Okanagan Kelowna, BC, Canada Shannag, M. Jamal King Saud University Riyadh, Saudi Arabia Shao, Yixin McGill University Montreal, QC, Canada Shariq, Mohd Civil Engineering Aligarh, Uttar Pradesh, India Sharma, Akanshu Bhabha Atomic Research Centre Mumbai, Maharashtra, India Shayan, Ahmad ARRB Group Vermont South, Victoria, Australia Shehata, Medhat Ryerson University Toronto, ON, Canada Sheikh, Shamim University of Toronto Toronto, ON, Canada Sherman, Matthew Simpson Gumpertz & Heger Melrose, MA Sherwood, Edward Carleton University Ottawa, ON, Canada Shi, Xianming Bozeman, MT Shi, Xudong Tsinghua University Beijing, China Shield, Carol University of Minnesota Minneapolis, MN
479
REVIEWERS IN 2013 Shing, Pui-Shum University of California, San Diego La Jolla, CA Shivali, Ram Central Soil and Materials Research Station New Delhi, India Shrive, Nigel University of Calgary Calgary, AB, Canada Shukla, Abhilash Jaypee University of Information Technology Waknaghat, Himachal Pradesh, India Sideris, Kosmas Democritus University of Thrace Xanthi, Greece Sigrist, Viktor Hamburg University of Technology Hamburg, Germany Sihotang, Fransiscus National Taiwan University of Science and Technology (NTUST) Taipei City, Taiwan Silfwerbrand, Johan Swedish Cement and Concrete Research Institute Stockholm, Sweden Singh, Harvinder Guru Nanak Dev Engineering College Ludhiana, Punjab, India Sivey, Paul Sivey Enterprises Hilliard, OH Skazlic, Marijan University of Zagreb Zagreb, Croatia Smith, Scott Southern Cross University Lismore, New South Wales, Australia Smyl, Danny United States Marine Corps Quantico, VA Sneed, Lesley Missouri University of Science and Technology Rolla, MO So, Hyoung-Seok Seonam University Namwon, Republic of Korea Soejoso, Mia Hiroshima University Saijo, Japan Soltani, Amir Purdue University Calumet Hammond, IN Soltanzadeh, Fatemeh Engineering and Technology Aligarh, Uttar Pradesh, India Sonebi, Mohammed Queens University Belfast Belfast, UK
480
Song, Kai Building Materials Dalian, China Sossou, Gnida Kwame Nkrumah University of Science and Technology (KNUST) Kumasi, Ghana Souza, Rafael Universidade Estadual de Maringá Maringá, Paraná, Brazil Söylev, Altug Yeditepe University Istanbul, Turkey Sozen, Mete Purdue University West Lafayette, IN Spadea, Giuseppe University of Calabria Arcavacata di Rende, Cosenza, Italy Spinella, Nino University of Messina Messina, Italy Spyridis, Panagiotis Institute for Structural Engineering Vienna, Austria Sreekala, R. Structural Engineering Research Centre Chennai, Tamilnadu, India Stanton, John University of Washington Seattle, WA Stein, Boris Twining Laboratories Long Beach, CA Steuck, Kyle University of Washington Seattle, WA Sudhahar, Sridevi United Institute of Technology Coimbatore, Tamil Nadu, India Sujjavanich, Suvimol Kasetsart University Bangkok, Thailand Sullivan, Patrick Sullivan and Associates Rickmansworth, UK Sun, Shaoyun University of Illinois at Urbana-Champaign Urbana, IL Ta, Binh University of Civil Engineering Melbourne, Victoria, Australia Tabatabai, Habib University of Wisconsin-Milwaukee Milwaukee, WI Tadayon, Mohammad Hosein University of Tehran Tehran, Islamic Republic of Iran Tadayon, Mohsen Iranian Concrete Institute Tehran, Islamic Republic of Iran
ACI Structural Journal/March-April 2014
Tadros, Maher e.construct.USA, LLC Omaha, NE Tae, Ghi ho Leader Industrial Co. Seoul, Republic of Korea Taghaddos, Hosein PCL Industrial Management Inc. Edmonton, AB, Canada Tahmasebinia, Faham University of Wollongong Wollongong, New South Wales, Australia Takahashi, Susumu Nagoya Institute of Technology Nagoya, Japan Tan, Kefeng Southwest University of Science and Technology Sichuan, China Tan, Kiang Hwee National University of Singapore Singapore, Singapore Tanacan, Leyla Istanbul, Yesilkoy, Turkey Tanesi, Jussara Federal Highway Administration-SaLUT Vienna, VA Tang, Chao-Wei Cheng-Shiu University Niaosong District, Kaohsiung City, Taiwan Tangtermsirikul, Somnuk Sirindhorn International Institute of Technology Patumthani, Thailand Tank, Tejenadr Pandit Deendayal Petroleum University Gandhinagar, Gujarat, India Tankut, Tugrul Middle East Technical University Ankara, Turkey Tanner, Jennifer University of Wyoming Laramie, WY Tantary, Manzoor Indian Institute of Technology Roorkee Roorkee, Uttarakhand, India Tapan, Mücip Yuzuncu Yil University Van, Turkey Tasdemir, Mehmet Istanbul Technical University Istanbul, Turkey Tassios, Theodosios Athens, Greece Tastani, S.P Demokritus University of Thrace Xanthi, Greece Tavares, Maria State University of Rio de Janeiro (UERJ) Rio de Janeiro, Brazil
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013 Tavio Sepuluh Nopember Institute of Technology (ITS) Surabaya, East Java, Indonesia Tegos, Ioannis Salonica, Greece Tehrani, Fariborz California State University, Fresno Fresno, CA Thermou, Georgia Aristotle University of Thessaloniki Thessaloniki, Greece Thiagarajan, Ganesh University of Missouri-Kansas City Kansas City, MO Thokchom, Suresh Manipur Institute of Technology Imphal, India Thomas, Adam Europoles GmbH & Co. Neumarkt, Germany Thompson, Phillip Palm Desert, CA Thorne, A. Center of Engineering Materials and Structures Guilford, Surrey, UK Tian, Ying University of Nevada, Las Vegas Las Vegas, NV Tiberti, Giuseppe University of Brescia Brescia, Italy Tito, Jorge University of Houston-Downtown Houston, TX Tixier, Raphael Western Technologies Inc. Phoenix, AZ Tjhin, Tjen Buckland & Taylor Ltd North Vancouver, BC, Canada Tobolski, Matthew San Diego, CA Tokgoz, Serkan Mersin University Mersin, Turkey Tolentino, Evandro Centro Federal de Educação Tecnológica de Minas Gerais Timóteo, Minas Gerais, Brazil Topçu, I˙lker Eskis¸ehir Osmangazi University Eskis¸ehir, Turkey Torrenti, Jean-Michel Chevilly Larue, France Torres-Acosta, Andres Universidad Marista de Querétaro Querétaro, Mexico Tosun, Kamile Dokuz Eylül University Izmir, Turkey
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REVIEWERS IN 2013 Toufigh, Vahab University of Arizona Tucson, AZ Trautwein, Leandro Federal University of ABC São Paulo, Brazil Triantafillou, Thanasis University of Patras Patras, Greece Tsonos, Alexander Aristotle University of Thessaloniki Thessaloniki, Greece Tsubaki, Tatsuya Yokohama National University Yokohama, Japan Tuchscherer, Robin Northern Arizona University Flagstaff, AZ Tureyen, Ahmet Wiss, Janney, Elstner Associates, Inc. Birmingham, MI Turgut, Paki Harran University Sanliurfa, Turkey Turk, A. Murat Istanbul Kultur University Istanbul, Turkey Tutikian, Bernardo Unisinos Porto Alegre, Rio Grande do Sul, Brazil Unterweger, Andreas Institute for Structural Engineering Vienna, Austria Uygunoglu, Tayfun Afyon Kocatepe University Afyonkarahisar, Turkey Vakilly, Sedigheh Isfahan, Islamic Republic of Iran Varum, Humberto University of Aveiro Aveiro, Portugal Vaz Rodrigues, Rui École Polytechnique Fédérale de Lausanne (EPFL) Lausanne, VD, Switzerland Vazquez-Herrero, Cristina Universidade da Coruña La Coruña, Spain Veen, Cornelis Delft University of Technology Delft, the Netherlands Velázquez Rodríguez, Sergio Universidad Panamericana Zapopan, Jalisco, Mexico Velu, Saraswathy Central Electro Chemical Research Institute Karaikudi, Tamil Nadu, India Vichit-Vadakan, Wilasa CTLGroup Skokie, IL
482
Vimonsatit, Vanissorn Curtin University Perth, Western Australia, Australia Vintzileou, Elizabeth National Technical University of Athens Athens, Greece Vitaliani, Renato University of Padua Padua, Italy Viviani, Marco Haute Ecole d’Ingénierie et de Gestion du Canton de Vaud (HEIG-VD) Yverdon les Bains, Switzerland Vogel, Thomas Institute of Structural Engineering Zurich, Switzerland Vollum, Robert Imperial College London London, UK Volz, Jeffery The Pennsylvania State University University Park, PA Vosooghi, Ashkan AECOM Sacramento, CA Wagh, Prabhanjan College of Engineering, Pune Satara, Maharashtra, India Waldron, Christopher University of Alabama at Birmingham Birmingham, AL Wan, David Old Castle Precast, Inc. South Bethlehem, NY Wang, Chang-Qing Tongji University Shanghai, China Wang, Chong Brisbane, Queensland, Australia Wang, Huanzi San Jose, CA Wang, Junyan National University of Singapore Singapore Wang, Kejin Iowa State University Ames, IA Wehbe, Nadim South Dakota State University Brookings, SD Wei, Ya University of Michigan Ann Arbor, MI Wei-Jian, Yi Changsha, China Weiss, Charles U.S. Army Corps of Engineers Engineer Research and Development Center Vicksburg, MS
ACI Structural Journal/March-April 2014
REVIEWERS IN 2013
Weiss, Jason Purdue University West Lafayette, IN Wen, Ziyun South China University of Technology Guangzhou, Guangdong, China Werner, Anne Southern Illinois University Edwardsville Edwardsville, IL Weyers, Richard Blacksburg, VA Wheat, Harovel University of Texas at Austin Austin, TX Wheeler, Andrew University Of Western Sydney Sydney, New South Wales, Australia Wilson, William Université de Sherbrooke Sherbrooke, QC, Canada Windisch, Andor Karlsfeld, Germany Won, Moon Texas Tech University Lubbock, TX Wong, Hong Imperial College London London, UK Wong, Sook-Fun Nanyang Technological University Singapore Wood, Richard University of California, San Diego La Jolla, CA Woyciechowski, Piotr Warsaw University of Technology Warsaw, Poland Wu, Chenglin Missouri University of Science and Technology Rolla, MO Wu, Hui Beijing, China Wu, Hwai-Chung Wayne State University Detroit, MI Xia, Zuming Grand Prairie, TX Xiang, Tianyu Chengdu, Sichuan, China Xiangguo, Wu Harbin Institute of Technology Harbin, Heilongjiang, China Xiao, Feipeng Clemson University Clemson, SC Xiao, Yan Hunan University Changsha, Hunan, China Xingyi, Zhu Hangzhou, China
Xin-hua, Cai Wuhan University Wuhan, HuBei, China Xu, Aimin ARRB Group Melbourne, Victoria, Australia Xuan, D.X. Delft University of Technology Delft, the Netherlands Yahia, Ammar Université de Sherbrooke Sherbrooke, QC, Canada Yakoub, Haisam Ottawa, ON, Canada Yan, Libo University of Auckland Auckland, New Zealand Yang, KuoChen National Kaohsiung First University of Science and Technology Kaohsiung, Taiwan Yang, Xinbao Olathe, KS Yang, Yanan Pitt & Sherry South Melbourne, Victoria, Australia Yang, Zhifu Middle Tennessee State University Murfreesboro, TN Yassein, Mohamed Doha, Qatar Yatagan, Serkan Istanbul Technical University Istanbul, Turkey Yazıcı, S¸emsi Ege University I˙zmir, Turkey Yehia, Sherif American University of Sharjah Sharjah, United Arab Emirates Yen, Peter Bechtel National, Inc. San Francisco, CA Yerramala, Amarnath Dundee University Dundee, Scotland, UK Yigiter, Huseyin Dokuz Eylül University I˙zmir, Turkey Yildirim, Hakki Istanbul, Turkey Yoon, Young-Soo Korea University Seoul, Republic of Korea Yost, Joseph Villanova University Villanova, PA Youkhanna, Kanaan University of Dohuk Duhok, Iraq
ACI Structural Journal/March-April 2014
483
REVIEWERS IN 2013 Young-sun, Kim Tokyo University of Science Noda-Shi, Chiba, Japan Youssef, Maged University of Western Ontario London, ON, Canada Yu, Baolin Michigan State University East Lansing, MI Yuan, Jiqiu PSI; Federal Highway Administration Turner-Fairbank Highway Research Center McLean, VA Yüksel, Isa Bursa Technical University Bursa, Turkey Zahedi, Farshad Babol Noshirvani University of Technology Babol, Mazandaran, Islamic Republic of Iran Zaki, Adel SNC-Lavalin Montreal, QC, Canada Zanuy, Carlos Universidad Politécnica de Madrid Madrid, Spain Zatar, Wael West Virginia University Institute of Technology Montgomery, WV Zerbino, Raul La Plata, Argentina Zeris, Christos National Technical University of Athens Zografou, Greece Zhang, Jieying National Research Council Canada Ottawa, ON, Canada
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Zhang, Jun Tsinghua University Beijing, China Zhang, Peng Karlsruhe Institute of Technology (KIT) Karlsruhe, Germany Zhang, Wei Ping Tongji University Shanghai, China Zhang, Xiaogang Shenzhen University Shenzhen, Guangdong, China Zhang, Xiaoxin Universidad de Castilla-La Mancha Ciudad Real, Spain Zhang, Yamei Southeast University Nanjing, China Zheng, Herbert Gammon Construction Limited Hong Kong Zheng, Jianjun Zhejiang University of Technology Hangzhou, China Zhou, Wei Harbin Institute of Technology Harbin, China Zhu, Han TianJin University TianJin, China Ziehl, Paul University of South Carolina Columbia, SC Zilch, Konrad Technische Universität München Munich, Germany
ACI Structural Journal/March-April 2014
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ACI Structural Journal/March-April 2014
ACI STRUCTURAL J O U R N A L J O U R N
This journal and a companion periodical, ACI Materials Journal, continue the publishing tradition the Institute started in 1904. Information published in ACI Materials Journal includes: properties of materials used in concrete; research on materials and concrete; properties, use, and handling of concrete; and related ACI standards and committee reports.
