International Association for Bridge and Structural Engineering (IABSE)
Proceedings
IABSE Conference Cable-Stayed Bridges - Past, Present and Future
The Öresund Construction Site, October 1998
Malmö, Sweden 2-4 June, 1999
Jointly organized by the Danish and Swedish Groups of IABSE
Produced by Congrex Sweden AB
Organising Committee Hans Ingvarsson Ole Damgaard Larsen Ingvar Olofsson Karl-Otto Sicking Erik Stoltzner Henrik Christensen
Chairman, Sweden Vice Chairman, Denmark Sweden Sweden Vice Secretary, Denmark Secretary, Sweden
Scientific Committee Niels J Gimsing Niels Peter Høj João Almeida-Fernandes Andrew S Beard William C Brown Kent Gylltoft Manabu Ito Aarne Jutila Jørn Lauridsen Helge Nilsson Walter Podolny Günter Ramberger Lennart Skogsberg Man Chung Tang Ton Vrouwenvelder
Chairman, Denmark Secretary, Denmark Portugal Hong Kong, China Great Britain Sweden Japan Finland Denmark Sweden USA Austria Sweden USA The Netherlands
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International Association for Bridge and Structural Engineering (IABSE): IABSE ETH Hönggerberg CH-8093 Zürich Switzerland Phone: +41 1 633 26 47 Fax: +41 1 633 12 41 E-mail:
[email protected] Information about IABSE and the Conference is available on internet: http://www.iabse.ethz.ch
Address by the President of IABSE The Swedish and Danish Groups have taken the initiative to organise this important conference on ”CableStayed Bridges - past, present and future”. This is an excellent example of a joint arrangement in keeping with the aim of IABSE to develop and exchange know-how in order to make civil and structural engineering activities contribute to the development of society. Several modern construction technologies for both the tunnel and bridge part have been introduced and set the trend for future major links crossing waterways. The tunnel was specifically dealt with at the IABSE Colloquium on Tunnel Structures in Stockholm in 1998. The 8 km bridge with a world-record combined rail and motorway cable-stayed span of 490 m will be almost completed in 1999, an excellent timing for an international conference on cable-stayed bridges to be held in Malmö in June 1999. This event will be another high-quality event in the endeavour to assemble the structural engineering profession globally with the purpose of exchanging know-how and ideas regarding trend-setting structural engineering for the future. Klaus H. Ostenfeld President of IABSE
Welcome Address The modern cable-stayed bridge has been developed during the second half of the 20th century, and is today the preferred bridge type for main spans in the range from 200 m to 500 m (and in some cases beyond). The combined bridge and tunnel project of the Öresund link for dual mode transport of high speed railway and motorway is a vital element in the formation of a Northern European financial and commercial centre, the gateway to Scandinavia and the Scandinavian peninsula. The project is an excellent example where Scandinavian bridge and tunnel engineering with international contribution is cooperating, resulting in a high quality modern structural engineering product as a symbol of this new activity for the 21st century. Most cable-stayed bridges are built to carry roads across rivers and straits, but in a few cases also railways are crossing over the bridges. Among the cable-stayed bridges carrying both road and railway traffic, the Öresund Bridge stands out as the biggest and most heavily loaded bridge of this type. It seems, therefore, to be a good opportunity to link the completion of this bridge to an international conference covering a wide variety of topics related to the static and dynamic behaviour of cable-stayed bridges. For the first time in the history of IABSE two National Groups jointly arrange an international conference. As chairmen of the Danish and Swedish Groups we cordially invite all engineers interested in cable-stayed bridges to come to Malmö, Sweden in early June 1999.
Niels J. Gimsing Chairman of the Danish Group of IABSE Chairman of the Scientific Committee
Hans Ingvarsson Chairman of the Swedish Group of IABSE Chairman of the Organising Committee
TECHNICAL PROGRAMME KEYNOTE LECTURES Wednesday 2 June, 11.20-12.00 Niels J.Gimsing, Denmark, History of Cable-Stayed Bridges Haifan Xiang, China, Retrospect & Prospect of Cable-Stayed Bridges in China
SESSION 1 - Design and Construction Wednesday 2 June, 13.30-15.30, 16.00-18.00 1:A Chairman: Aarne Jutila, Finland Co-chairman: Ingvar Olofsson, Sweden 1:B Chairman: Helge Nilsson, Sweden Co-chairman: Erik Stoltzner, Denmark Plenary session Loizias M.P. Concrete Cable-stayed Bridges in the USA Chandra, V. & Hsu, R. The Innovative William Natcher Cable-Stayed Bridge Nagai, M., Xie. X., Yamaguchi, H. & Fujino, Y. Identification of Minimum Width-to-span Ratio of Long-span Cable Stayed Bridges Based on Lateral Torsional Buckling and Flutter Analyses Pircher H., Bokan H., Bruer A. Computer Based Optimising of the Tensioning of Cable-Stayed Bridges Astiz, M.A., Fernández Troyano, L., Manterola, J. Evolution of Design Trends in Cable-Stayed Bridges Miyazki M. Aerodynamic and Structural Dynamic Control System of Cable-Stayed Bridges for Wind Induced Vibration Hague S.T. Seismic Design for the Cape Girardeau Cable-Stayed Bridge Reis A.J., Pereira A.P., Sousa D.P. & Pedr J.O. Cable-Stayed Bridges for Urban Spaces Chen D. A New Method to Assign Initial Cable Forces for Prestressed.Concrete Cable-Stayed Bridges T. Vejrum & Petersen, A. Bridges with Spatial Cable Systems - Theoretical and Experimental Studies Christoffersen J., Hauge L., Bjerrum J., Jensen H. E. Design and Construction of a CFRP Cable-Stayed Footbridge Hansvold C., Faller P., Nilsson H. & Svahn P-O Erection of the Uddevalla Bridge Bræstrup M.W. Cable Stayed GFRP Footbridge across Railway Line Bergman D.W. Ting Kau Cable Stayed Bridge: Challenges in the Construction Process Poster Presentations T. Sugiyama Seismic Response of Partially Earth-anchored Cable-Stayed Bridge V. Chandra, Ricci A., Menn C. & McCabe R. Charles River Crossing; A Gateway to Boston Firth I. The Design and Construction of the Lockmeadow Footbridge, Maidstone Cruz J.S. & Almeida, J. F. A New Model for Cable-Stayed Bridges Control and Adjustment Auperin M. & Dumoulin, C. Cable Finite Element of High Accuracy Baumann, K. & Däniker J. Sunniberg Bridge, Klosters, Switzerland Maeda K., Nakamura H., Konno M., Moroyama Y., Abe M. Structural Countermeasures for Design of a Very Long-Span Cable-Stayed Bridge under Wind Loads Larsen S. V. Aerodynamic Performance of Cable-Supported Bridges with Large Span-to-Width Ratios Sharpe A., Yeoward A.J., & Buckby R. J. Cable Stayed Bridge in Bandung, Indonesia Fan L.C., Chen D.W., Tham L.G., Au F.T.K. & Lee P.K.K. New Developments of Erection Control for Prestressed Concrete Cable-Stayed Bridges Trenkler F., Skrikerud P & Voll D.M. The Lifting, Transport and Placing of the Öresund Pylon Caissons Cremer J.M. The Val-Benoit Cable-Stayed Bridge Han D. & Yan Q. Construction Control Practice for Panyu Cable-Stayed Bridge Wachalski K., Kaminski J. & Sudak M Some aspects of the design of Martwa Wisla River Bridge in Gdansk Larose G.L. & Wagner Smitt L. Rain/Wind Induced Vibrations of Parallel Stay Cables of the Öresund High Bridge Pulkkinen P. Swietokrzyski Bridge, Warsaw Sham R. & Monster A. The Design of the Zwolle Cable-Stayed Bridge - Integrating Engineering with Aesthetics Manabe Y., Hirahara N., Mukasa N. & Yabuno M. Accuracy Control on the Construction of the Tatara Bridge
KEYNOTE LECTURE Thursday 3 June, 08.30-08.50 Michel Virlogeux, France, Bridges with Multiple Cable-Stayed Spans
SESSION 2 – Composite Structures Thursday 3 June, 08.50–09.45 Chairman: William C. Brown, UK
Co-chairman: Henrik Christensen, Sweden
Plenary Session Svensson, H.S. The Development of Composite Cable-Stayed Bridges Byers D.D., Hague S.T., McCabe S.L. & Rogowski D.M. Comparison of Slab Participation: Assumed for Design vs. FEA Veje E., Møller Nielsen P., Pedersen F. & Fuglsang K. Yamuna Cable Stayed Bridge at Allahabad/Naini, India de Boer A. & Waarts P.H. Probabilistic FE analysis of a cable stayed composite bridge Poster Presentations Xia G. A & Kindmann R. A Method for the Creep Analysis of Composite Cable-Stayed Bridges Christensen H., Madsen K. & Petersen C.R. Composite Structures in the Øresund Bridge
SESSION ÖRESUND Thursday 3 June, 10.15–12.30 Chairman: Niels J. Gimsing, Denmark
Co-chairman: Karl-Otto Sicking, Sweden
Plenary Session Lundhus P. Build a Link – Goals, Principles, Strategies and Results Falbe-Hansen K. & Larsson Ö. The Øresund Bridge: Project Development From Competition to Construction Nissen J. & Rotne G. Getting the Balance Right. The Øresund Bridge - Design Concept Gimsing J. The Øresund Bridge: The Tender Project Svensson E. From Eurocodes, Special Investigations and Risk Analysis To Design Requirements for the Øresund Coast to Coast Structures Hauge L. & Petersen A. Detailed Design of the Cable Stayed Bridge for the Öresund Link Olofsson I. Design Coordination of a Design-build Project Sørensen, L.Th. & Thorsen N.E. The Öresund Bridge, Erection of the Cable-Stayed Main Span
KEYNOTE LECTURES Friday 4 June, 08.30–09.15 Jörg Schlaich, Germany, Cable-Stayed Bridges with Special Features Manabu Ito, Japan, Stay Cable Technology Overview
SESSION 3 – Cable-Stayed Bridges for Railways Friday 4 June, 09.15–10.15 Chairman: Manabu Ito, Japan
Co-chairman: Ole Damgaard-Larsen, Denmark
Plenary Session Bitsch N. & Hauge L. Design of Girder and Cables for Train Load Sham R. An Innovative Technique for Fitting Trackwork Alignments Through the Railway Envelope of a Cable-Stayed Bridge Gimsing J. & Thomsen A. Comfort Criteria for High Speed Trains on The Øresund Bridge Poster Presentations Karoumi R. Nonlinear Dynamic Analysis of Cable-Stayed Bridges Excited by Moving Vehicles Bruno D. Grimaldi A. & Leonardi A. Deformability of Long-Span Cable-Stayed Bridges for Railways
SESSION 4 – Stay Cable Technology Friday 4 June, 10.45–12.15 Chairman: Manabu Ito, Japan
Co-chairman: Ole Damgaard Larsen, Denmark
Plenary Session Dumoulin, C. Active Tendon Actuators for Cable-Stayed Bridge Marchetti M. & Lecinq B. Stay Adjustment: From Design Perspective to On Site Practice Suzuki Y., Hiyama Y., Kondo T., Kawakami T, Suzuki M., Moriuchi A., Damping Device in Stay Cables of Meiko Central Bridge El Kady H.M., Arockiasamy M., Samaan S., Bahie-Eldeen Y., Bakhoum M.M. & El Gammal, M.A. Damping Characteristics of Carbon Fiber Composite Cables for Application in Cable-Stayed Bridges Bournand Y. Development of New Stay Cable Dampers González J.L. & Sobrino J. A. Fatigue Reliability Evaluation of Cables in Cable-Stayed Bridges. Case Study: The Sama de Langreo Bridge McGuire G.J. PTI Cable Stay Recommendations Poster Presentations Mizoe M., Muroi S., Horii T., Isobe T., Kiyota R. & Imada Y., The Super High Damping Rubber Damper on the Stay-cables of Meiko East Bridge. Hemmert-Halswick A. & Sczyslo S. Corrosion Protection of Locked Coil Ropes at Road Bridges Magonette G., Renda V., Bournand Y., Hansvold C., Jenner, A.G. & Fösterling H. Experimental Analysis of a Large-Scale Cable-Stayed Mock-up Stubler J., Domage J.B. & Ladret P. Vibration Control of Stay Cables Preumont A., Bossens F., Helduser S. Bonnefeld R. & Försterling H. Active Tendon Control of Cable-Stayed Bridges: Control Strategy and Actuator Design Roos, F., Noisternig J.F. CFRP-Tendons -Development and Testing Bojan J. Bevc L. & Sonda D. Laboratory Tests of the Anchorage Plates for the Cables Seo-Kyung C. & Seung Wook J. Erection of Composite Deck for Seohae Bridge
SESSION 5 – Observation, Maintenance and Repair, followed by Closing Session Friday 4 June, 13.45–16.30 Chairman: Jørn Lauridsen, Denmark
Co-chairman: Hans Ingvarsson, Sweden
Plenary Session Popa V. & Stanciu M. Bridge Consolidation by Using Cable-Stayed Method Yamagiwa I, Utsuno H., Endo K. & Sugii K. Application of the Identification of Tension and Flexural Rigidity at Once to the Bridge Cables Gentile C. & Martinez F. Dynamic Characteristics of Two Newly Constructed Curved Cable-Stayed Bridges Suzuki Y., Mizuguchi K., Sakuma S., Maekawa T., Ueda T. & Kobayashi Y. Field Observation on Aerodynamic Response of Meiko West Bridge Reinholdt P., Veje E. & Kalvslund J. Rehabilitation of the Luangwa Bridge Laigaard J. & Pedersen L. Design of Structural Monitoring Systems Bloomstine M.L. & Stoltzner E. The Faroe Cable-Stayed Bridge -Maintenance Experience with Major Components Andersen H. & Hommel D.L. & Veje E.M. Emergency Rehabilitation of the Zárate-Brazo Largo Bridges, Argentina Yamaguchi K. Manabe Y., Sasaki N. & Morishita K. Field Observation and Vibration Test of the Tatara Bridge Poster Presentations Gomez R., Muria-Vila D. Sanchez-Ramirez R. & Escobar J. A. Second Monitoring and Surveillance of the Response of a Cable-Stayed Bridge Cunha Á., Caetano E., Calçada R. & Delgado R. Dynamic Tests on Vasco da Gama Cable-Stayed Bridge Fuzier J.P., Stubler J. & Grattepanche D. The Øresund Stay Cables: Design for Fatigue Resistance and Easy Maintenance
History of cable-stayed bridges Niels J GIMSING Professor BKM, DTU DK-2800 Lyngby, Denmark
Niels J Gimsing, born 1935, is professor at the Technical University of Denmark since 1976. He has at several occasions acted as specialist consultant during the design of major bridges.
Introduction The principle of supporting a bridge deck by inclined tension members leading to towers on either side of the span has been known for centuries but it did not become an interesting option until the beginning of the 19th century when wrought iron bars, and later steel wires, with a reliable tensile strength were developed. A limited number of bridges based on the stayed girder system were built – and more proposed – but the system was never generally accepted at that time. In 1823 the famous French engineer and scientist C.L. Navier published the results of a study on bridges with the deck stiffened by wrought iron chains and with a geometry as shown on the original drawing in Fig.1. It is interesting to note that Navier considered both a fan shaped and a harp shaped system in configurations that today would be denoted multi-cable systems. So the cable systems were actually up-to-date, but in contrast to the present practice the backstays were assumed to be earth anchored, as seen in the lower half of Fig.1. Navier’s final conclusion was that the suspension system should be used instead of the stayed system [1]. This conclusion was to a large extent based on observations of stayed bridges that had failed.
Fig.1 Bridge systems investigated by Navier in the 1820s.
In the early stayed bridges it proved very difficult to arrive at an even distribution of the load between all stays. Thus imperfections during fabrication and erection could easily lead to a structure where some stays were slack and others overstressed. The stays were generally attached to the girder and pylon by pinned connections that did not allow a controlled tensioning.
The problems encountered and the recommendation by Navier resulted in a very limited number of stayed girder bridges being built up to the 1950s, whereas systems where the suspension system was combined with the stayed system was used in many major bridges built in the second half of the 19th century. As an example, Fig.2 shows the Albert Bridge across the Thames in London. In this bridge from 1873 both the parabolic top ‘cable’ and the stays were made of eye bar chains. The Albert Bridge still exists so the system has certainly proved its durability.
Fig.2 The Albert Bridge across the Thames in London. The combination of the suspension and the stayed system was also applied in a number of bridges built in France in the 1880s, but the most notable bridges of this type were designed by John A. Roebling and built in the United States – among these the longest cable supported bridge of the 19th century: the Brooklyn Bridge [2]. Introduction of the self anchored cable-stayed bridge system Around the turn of the century the French engineer A.V. Gisclard developed an earth anchored, stayed system in which not only the inclined stays but also the tension members at the deck level were made of cables. In the 1920s the system by Gisclard was developed further by substituting the horizontal cables by the deck girders and changing the earth anchored system to a self anchored system with compression rather than tension along the deck – for example used in the Lezardrieux Bridge from 1925. So in reality the system of the modern, self anchored cable-stayed bridges was developed at that time. The combined suspension and stayed system used extensively at the end of the 19th century was abandoned from the beginning of the 20th century and substituted by pure suspension systems. However, in 1938 Dischinger proposed a system Fig.3 Dischinger’s proposal for a bridge in which the central part of the span was carried between Köln and Mühlheim. by a suspension system whereas the outer parts were carried by stays radiating from the pylon top. This system was proposed for a cable supported bridge with a 750 m main span to be built across the Elbe River in Hamburg.
In connection with the reconstruction of German bridges after the war, the Dischinger system was proposed at several occasions (Fig.3) but it was never used for actual construction. One of the reasons is undoubtedly the pronounced discontinuity of the system both with respect to the structural behavior and to the appearance. The discontinuity reflects Dischinger’s discontent at the original Roebling system with its much more continuous configuration achieved by overlapping the multi-cable stayed system and the suspension system. In the publication of his own system, Dischinger categorically stated that the stays of Roebling's bridges had proved to be completely inefficient! Although never adopted for actual construction, the proposals by Dischinger undoubtedly had a considerable influence on the subsequent introduction of the pure cable-stayed bridge. Thus, the Strömsund Bridge, which is generally regarded as the first modern cable-stayed bridge was designed by Dischinger. The bridge was of the three-span type, a system commonly used for suspension bridges, and it had a main span of 182.6 m flanked by two side spans of 74.7 m (Fig.4). The stays were arranged according to the pure fan system with two pairs of stays radiating from each pylon top. The steel pylons were of the portal type supporting the two vertical cable systems arranged on either side of the bridge deck. The deck girder contained two plate girders positioned outside the cable planes to allow an "invisible" anchoring of the stays inside the plate girders.
Fig.4 The Strömsund Bridge.
The start of a new era for cablestayed bridges was to a large extent due to the improved technique of structural analysis allowing calculation of cable forces throughout the erection period and thereby assuring the efficiency of all cables in the final structure as well as a favorable distribution of dead load moments in the deck. Probably, such calculations were for the first time made for the erection of the Strömsund Bridge.
Regarded as a plane system, the Strömsund Bridge is statically indeterminate to the eighth degree, but by dividing the load into a symmetrical and an antisymmetrical part, the number of redundants could be reduced to four. This was well within acceptable limits for the numerical work that could be performed with the slide rule and the mechanical calculators available at the beginning of the 1950s. The German era After the Strömsund Bridge the next true cable-stayed bridge to be erected was the Theodor Heuss Bridge across the Rhine at Düsseldorf - opened to traffic in 1957 (Fig. 5). With a main span of 260 m and side spans of 108 m it was considerably larger than the Strömsund Bridge. Also, the Theodor Heuss Bridge was more innovative by introducing the harp shaped cable system with parallel stays and a pylon composed of two free-standing posts fixed to the bridge deck structure. The harp
configuration was chosen primarily for aesthetic reasons giving a more pleasant appearance of the two cable systems when viewed from a skew angle.
Fig.5 The Theodor Heuss Bridge. The Theodor Heuss Bridge gave a very clear indication of the cable-stayed bridges' potentials initiating an impressive development of cable-stayed bridges first in Germany and later throughout the world in the decades to follow. The second cable-stayed bridge to be erected in Germany was the Severins Bridge in Köln (Fig.6). This bridge featured the first application of an A-shaped pylon combined with transversally inclined cable planes, and it was the first to be constructed as an asymmetrical two span bridge with a single pylon positioned at only one of the river banks. The cable system of the Severins Bridge was of the efficient fan shaped type, which is in good harmony with the A-shaped pylon. The cross section of the deck girder was essentially the same as used in the Theodor Heuss Bridge with two box girders connected by the orthotropic steel deck. Because of the substantial compression in the girder due to the one-sided arrangement of the pylon, the application of a steel deck was particularly advantageous in the Severins Bridge, as axial compression could be distributed over a large crosssectional area. At both ends of the cable-stayed portion, the deck girder was made continuous into the adjacent box girder spans.
Fig.6 The Severins Bridge in Köln.
Although one of the very first cable-stayed bridges, the Severins Bridge still stands as a most successful bridge. The design of the pylon with its pronounced dimensions and the way the deck girder "floats" through the pylon constitute fine solutions to the design problems faced. The third German cable-stayed bridge, the Norderelbe Bridge at Hamburg, introduced the central cable plane with pylons and stay cables positioned in the central reserve of the motorway - a system that in the following years became the preferred system for the majority of cable-stayed bridges to be constructed in Germany - as well as in several other countries. In some of its other design features the Norderelbe Bridge was more unusual, e.g. with pylons twice as high as required for structural reasons and with a cable system looking as if the main task was to support the pylon and not the deck girder (Fig.7). In the mid 1980s the Norderelbe Bridge had to go through a major rehabilitation program and as part of this the cable system was Fig.7 The original Norderelbe Bridge. modified to a more sensible configuration. So today the Norderelbe Bridge is less peculiar in its appearance. After the Norderelbe Bridge came the Leverkusen Bridge (opened in 1964) across the Rhine. This bridge had the same centrally arranged cable plane, but here the cable system was of the harp configuration with two sets of stays connected to each pylon. Each stay comprised two individual cables composed of seven locked-coil strands. The multi-cable system In the early cable-stayed bridges built at the end of the 1950s and the beginning of the 1960s each stay cables was generally composed of several prefabricated strands to achieve the large cross sections required in these bridges with their limited number of cables. However, the multi-strand arrangement of the individual stay gave a number of drawbacks such as complicated anchorage details in the girder and difficulties in replacement of strands. These drawbacks could be eliminated if the number of stays was increased so that each stay cable could be made of a single strand and this led to the introduction of the multi-cable system. The first two multi-cable bridges to be built were the Friedrich Ebert Fig.8 The Rees Bridge.
Bridge and the Rees Bridge both designed by H. Homberg and built across the Rhine. The Friedrich Ebert Bridge contains a central cable plane with two pylons, each supporting 2×20 stays with diameters ranging from 91 to 123 mm, depending on the position of the actual stay. In the Rees Bridge two cable planes each containing a harp-shaped multi-cable system with 2×10 stays were used (Fig.8). Multi-cable systems lead to a more continuous support of the deck girder, and at the same time the cable forces to be transmitted at each anchor point are reduced, so that a local strengthening of the girder at the anchorages can be avoided. During erection advantages are to be found due to the much shorter deck cantilevers required to reach from one anchor point to the next, and in the final structure the smaller stay units will ease a replacement. These advantages would subsequently result in a general acceptance of the multi-cable system in almost all cable-stayed bridges. However, in that process it should later be realized that the multi-cable system also presented some disadvantages such as a higher vulnerability to excitations and increased total wind load on the cable system.
Fig.9 The Knie Bridge in Düsseldorf.
In 1969 a notable cable-stayed bridge, the Knie Bridge, was opened to traffic in Düsseldorf (Fig.9). In this bridge the cable system was of the harp configuration with relatively few parallel stays, but in contrast to earlier bridges with the harp system, intermediate supports were added under every cable anchor point in the side span. This increased the efficiency of the harp system to such an extent that it was possible to use a very slender deck girder with an open cross section, i.e. with insignificant torsional stiffness.
In the Knie Bridge an asymmetrical layout similar to that of the Severins Bridge was used with the pylon placed on one of the river banks only. Despite the considerable height of the pylon (114 m) it was possible to compose it of two free-standing posts without any struts or bracing to stabilize laterally.
First parallel-wire strands In 1972 the completion of the Mannheim-Ludwigshafen Bridge across the Rhine marked the first application of a parallel-wire strand in a major cable-stayed bridge. Each strand (with 295 ungalvanized wires of 7 mm diameter) was anchored by a new type of socket called a HiAm socket with increased fatigue resistance due to the application of a cold filling material containing epoxy compound. Furthermore, the Mannheim-Ludwigshafen Bridge introduced an interesting combination of materials, with the deck girder made entirely of steel in the main span and entirely
of concrete in the side span (Fig.10). This combination was very well justified, as the side span (through the application of an intermediate pier) had a maximum free span of 65 m, whereas the main span had a free length of 287 m. Actually, the higher dead load of the side span proved directly advantageous as it reduced the requirement for a vertical anchoring of the girder. The combination of concrete girders with intermediate supports in the side span and steel girders in the main span was subsequently used in several notable cablestayed bridges constructed in the 1980s and 1990s. The cable-stayed Köhlbrand Bridge in the port of Hamburg exhibits the first application of the multi-cable system in a bridge with double cable planes supported by A-shaped pylons (Fig.11). The modified fan system was one of high efficiency which gave advantages not only in the design of the final structures but also during erection as no temporary supports or temporary stays were required. Fig.10 The Mannheim-Ludwigshafen Bridge under construction.
From the same period is another remarkable German cable-stayed bridge: the Düsseldorf-Flehe Bridge across the Rhine. Despite a main span length of 367 m it was chosen to build a two-span cablestayed structure with only one pylon on one of the river banks. This necessitated a pylon with a height of 150 m above ground. In Fig.11 The Köhlbrand Bridge. contrast to the general German practice the pylon was made of concrete, and its lambda (λ) configuration was chosen to give support to the central cable plane with a harp shaped cable system in the side span and a modified harp in the main span. In appearance the pylon of the Flehe Bridge is not very harmonic, especially when compared to other, more recent λshaped pylons. For a period of almost twenty years the evolution of cable-stayed bridges was to a very large extent taking place in Germany but in the following years the activities shifted to other locations on the globe. The evolution outside Germany During the late 1950s and the 1960s a relatively modest number of cable-stayed bridges were built outside Germany and most of these bridges were based entirely on the German design philosophy.
In the UK the Wye Bridge on the Welsh approach to the Severn Suspension Bridge had been completed in 1965 and this bridge was quite unique by having only one set of stays leading from the pylons to the deck. Based on a similar design concept the Erskine Bridge in Scotland (Fig.12) followed in 1971. Despite its main span of considerable length it also had only one stay leading from each of the two pylons to the deck girder in the 305 m long main span so the girder had to span more than 100 m without support from the cable system. Despite this fact, the deck girder was designed with a depth of only 3.05 m, which is of the same magnitude as found in cable-stayed bridges with several stays supporting the girder at much smaller intervals. As the stay had to be made with a very large cross-sectional area it was composed of 24 helical strands each 76 mm in diameter. During erection of the system with only one permanent stay from each pylon it was necessary to use two temporary stays to reduce the moment in the deck girder when cantilevering from the pylon to the adjacent cable anchor point in the main span. In France the completion in 1975 of the Saint Nazaire Bridge across the Loire River marked a step further for the cable-stayed bridges as it was the first bridge of this type to span more than 400 m. The pylons consist of an upper A-shaped part of steel and a lower pier shaft of concrete. The cable system is of the multi-cable fan type with each stay made of a single locked-coil strand. Fig.12 The Erskine Bridge.
The first major cable-stayed bridge with an earth anchored cable system, the Indiano Bridge across the Arno near Firenze (Fig.13), had a 206 m long main span supported by two fans radiating from the tops of 45 m high pylons leaning slightly backwards. From the pylons, earth anchored back stays
Fig.13 The Indiano Bridge across the Arno at Firenze. continue to anchor blocks transmitting both the vertical and the horizontal component of the cable force to the soil.
The special problems related to the construction of cable-stayed bridges with earth anchored cable systems were overcome in the Arno Bridge by erecting the deck girder on temporary piers before adding the pylons and the cable system. Cable-stayed concrete bridges In the first two decades after the completion of the Strömsund Bridge the evolution of cable-stayed bridges was to a very large extent dominated by steel bridges with orthotropic decks together with plate or box girders and cellular pylons. However, as a remarkable exception from this a cable-stayed bridge of unusual proportions (and based on a very different design philosophy) had been completed already in 1962: The Maracaibo Bridge in Venezuela, designed by Riccardo Morandi (Fig.14). Here both the pylons and the deck girder were made of concrete, thereby introducing a structural material that had not earlier been used in the main elements of cable supported bridge superstructures. Furthermore, it was the first multi-span cable-stayed bridge.
Fig.14 The Maracaibo Bridge. To allow one-way traffic of ships in and out of Lake Maracaibo, it was chosen to build a bridge with five 235 m long main spans. Each of these spans comprises a double cantilever supported by only one pair of stays radiating from a triangular pylon structure designed to stabilize the system for asymmetrical loads. Between the ends of the cantilevers small suspended spans are arranged, so that the system regarded as a plane system is externally determinate. The application of only one set of stays necessitated a heavy box girder to span from the pylon to the cable supported point, and during construction a large truss was required to support the formwork. The Maracaibo Bridge was later followed by two other major cable-stayed bridges designed by Morandi, the Polcevara Viaduct in Genova and the Wadi Kuf Bridge in Libya. However, all of the designs of Morandi were of such a personal style that they did not to any large extent serve as models for the cable-stayed bridges of concrete to come. A pioneer among the type of concrete cable-stayed bridge to become more fashionable was the Donaukanal Bridge in Vienna (Fig.15) with a main span of 119 m. The deck contains a concrete box girder and the stays are composed of parallel mono strands. The Donaukanal Bridge has a very pleasing appearance and harmonic proportions, and the construction procedure was quite unique as
the bridge was cast in two halves on either side of the canal and subsequently turned into position after installation and tensioning of the stay cables. The application of a multi-cable system in a cable-stayed concrete bridge was first seen in the Brotonne Bridge across the Seine. Here a central cable plane was combined with a box-shaped deck girder, made partially of prefabricated elements. The stays were made of parallel seven-wire strands of a type used for tendons in post-tensioned concrete. Corrosion protection was achieved Fig.15 The Donaukanal Bridge in Vienna. by inserting the parallel strands in stainless steel tubes, subsequently filled with cement grout. The anchoring of the seven-wire strands was initially made by ordinary wedge anchors, but to increase the fatigue strength, especially for pulsating loads, a supplementary anchoring was established by adding epoxy mortar inside a steel tube extending from the wedge anchorages. Another example on the use of the multi-cable system in a cablestayed concrete bridge can be found in the Pasco-Kennewick (Fig.16). Here, the double cable systems in the fan configuration assure an efficient support of the deck both vertically and torsionally. The stays, each made of a single parallel-wire strand, are inside a grouted polyethylene tube and with HiAm anchors. The deck girder was erected by the segmental method using heavy prefabricated elements having the full width of the roadway. Fig.16 The Pasco-Kennewick Bridge.
The twin bridges across the Parana River in Argentina (Fig.17) from1978, were in many ways based on the same design philosophy as used for the PascoKennewick design. However, the deck girders of the Parana Bridges were made of steel. They were the first cable-stayed bridges to transfer heavy railway loading. This gave special design problems which to a certain extent were accentuated by a one-sided position of the single track subjecting the two vertical cable systems to traffic loads of different intensity. For this reason it was necessary to use different dimensions for the stays in the two sides, the heavier cables being required for the railway side.
After less than 20 years of service one of the stay cables in the Parana Bridges broke without warning and as a result a major repair work had to be initiated at the end of the 1990s. The superiority of cable supported bridges in crossing navigable waters was clearly demonstrated in the early 1980s when a new cablestayed Tjörn Bridge was built to replace the original arch bridge after it had been hit by a misnavigated ship. The new bridge was built with a span of 366 m, 86 m more than the span of the arch bridge, and this allowed both pylons to be located on land 25 m from the coastline.
Fig.17 The Parana Bridge.
The Tjörn Bridge belongs to the group of cable-stayed bridges with different structural materials in the side spans and the main span (Fig.18). The side spans are designed as continuous concrete girders with intermediate column supports at each cable anchor point whereas the main span is made as a steel box with orthotropic steel deck overhangs.
During the 1980s the activity within the field of cable-stayed bridges was considerably reduced Fig.18 The Tjörn Bridge. in Europe compared to the previous decades, and most of the bridges built did not deviate much in size or design features from those already constructed. There were, however, a few exceptions from this rule. In 1984 the completion of the Barrios de Luna Bridge in Spain gave a further indication of the competitiveness of concrete as structural material not only for the pylons but also in the girder of cable-stayed bridges (Fig.19). With a main span of 440 m the Barrios de Luna Bridge surpassed the span of the Saint Nazaire Bridge by a margin of almost 10% and became for a couple of years the record-holder amongst cable-stayed bridges. The Farø Bridge in Denmark was opened in 1985 and it comprised a 290 m long main span supported by a central cable plane. The girder had originally been designed by the owner as a concrete box but an alternative bid based on a steel box proved to be competitive and was chosen for construction. The concrete pylons form a further development of the diamond-shaped pylons originally introduced in the Köhlbrand Bridge. Thus, in the Farø Bridge the lower triangle is extended all the way down to the water surface (Fig.20) rather than being supported on high pier
shafts. Furthermore, the Farø Bridge showed the first application of corrosion protection of the box girder interior by dehumidification of the air.
Fig.19 The Barrios de Luna Bridge.
Fig.20 The Farø Bridge.
Within cable-stayed bridges both the type with a central cable plane above the median reserve and the type with two cable planes outside the roadway area had been extensively applied in the first three decades of the modern evolution. To some extent the choice between the two options seemed to depend on the designer's preference rather than on a rational, unbiased comparison between advantages and drawbacks. H. Homberg had clearly preferred the central cable plane concept wherever it was applicable, i.e. where the road to be carried had a median reserve. It is therefore not surprising that Homberg's largest cable-stayed bridge, the Rama IX Bridge in Bangkok was designed with a central cable plane, despite the span of 450 m. The cable system is of the multi-cable, modified fan configuration and all stays are made of single locked-coil strands, among these the largest diameter locked-coil strand fabricated so far with a diameter of 174 mm. The deck girder in the main span is a quasi trapezoidal, five cell box with the full width of the bridge deck (32.5 m) and with a depth of only 4 m. The American experience A pioneer among cable-stayed bridges in North America was completed in Montreal already in 1969: the Papineau Bridge (Fig.21) with a main span of 241 m. In several of its design features this
bridge could resemble the Leverkusen Bridge and other German bridges with a central cable plane and a deep, but relatively narrow, box girder under the wide orthotropic bridge deck. The cable system was of the fan type with only two sets of stays radiating from each pylon top. Each stay cable was composed of several helical bridge strands of galvanized wires, and as a novelty each strand was covered by a hot extruded polyethylene coating with a minimum cover of 5 mm - a protective system that should later be used extensively.
Fig.21 The Papineau Bridge in Montreal.
Apart from the Papineau Bridge and a limited number of other bridges the activity within construction of cable-stayed bridges had been very low in North America during the 1960s and the early 1970s, but from then on the situation changed dramatically.
In Florida a ship collision accident had given a clear indication of the inadequacy of the navigation opening in the 250 m long main span of the Sunshine Skyway. It was, therefore, decided to replace the existing two parallel bridges by a single bridge having a 360 m long cable-stayed main span. Two designs were prepared for the bridge, one based on a composite deck and two cable planes along the edges of the bridge deck, and the other as a pure concrete box and a single central cable plane. Both designs were put out for tender and the result showed a very close race between the two options. The final choice was to construct the concrete bridge according to a design based on the principles initially introduced during design and construction of the Brotonne Bridge in France. With its main span of 366 m the Sunshine Skyway was at its completion in 1986 the longest cable-stayed bridge in the USA (Fig 22). The composite girder alternative for the Sunshine Skyway was based on a system with two longitudinal plate girders directly under the cable planes and a large number of transverse girders to give support to the deck slab of reinforced concrete. In its main features this concept was subsequently applied in another North American bridge, the Alex Fraser Bridge (Annacis Island Bridge) at Vancouver in Canada. With its main span of 465 m the Alex Fraser Bridge (Fig.23) became the record-holder among cable-stayed bridges for a period of five years. Fig.22 The Sunshine Skyway Bridge.
The potentials of the composite girder concept was clearly demonstrated during the construction of the Alex Fraser Bridge. Thus, the cantilevering from one cable anchor point to the next was easily accomplished by the relatively light steel girders, allowing the stay cables to be added before the heavy concrete deck was erected using precast slabs. At the same time the concrete slab could be efficiently utilized to transfer the axial compression induced into the girder by the horizontal components of the stay cable forces. The advantages of applying composite girders in cablestayed bridges should in the years to follow the construction of the Alex Fraser Bridge lead to a situation where this system was gradually being preferred for the majority of cable-stayed bridges in North America. In the USA the general trend throughout the 1980s was to simplify the design of especially the girders in cablestayed bridges. Within concrete bridges a good example on this trend is the Dames Point Bridge at Jacksonville in Florida. With a main span of 396 m the bridge surpassed the Sunshine Skyway as the longest concrete cable-stayed bridge in North America.
Fig.23 The Alex Fraser Bridge.
The cable system of the Dames Point bridge is a multicable harp system supported by concrete pylons with a considerable flexural stiffness in the longitudinal direction. This gave the cable system very good deformational characteristics so that the girder could be made with a depth of only 1.5 m corresponding to 1/260 of the main span length.
In principle the structural system of the girder in the Dames Point Bridge corresponds to that of the Alex Fraser Bridge, i.e. with two longitudinal girders beneath the cable planes and numerous transverse girders. However, in the Dames Point Bridge the longitudinal girders are made as solid concrete ribs with a depth of 1.5 m and a width of 2.5 m allowing a most efficient anchoring of the stay cables. Seen in comparison with the Pasco-Kennewick Bridge - the first major concrete cable-stayed bridge in North America - the Dames Point Bridge clearly shows the simplifications in girder design. The Japanese development In Japan the cable-stayed bridges were introduced already in the late 1950s but the first bridges of
Fig.24 The Rokko Bridge in Kobe.
this type were not characterized by special design features so they had little influence on the further developments. However, in 1977 the Rokko Bridge, the very first double deck cable-stayed bridge, was completed in Japan (Fig.24). The deck is made as a truss with a depth of approx.8 m to give ample headroom, daylight, and fresh air on the lower deck. The cable system is of the multi-cable type with each stay composed of two parallel-wire, mono-strand cables. In a much larger scale the double deck concept was later used for the twin cable-stayed bridges, the Hitsuishijima and the Iwagurojima Bridges (Fig.25), that form a part of the Seto Ohashi between Honshu and Shikoku. Each of the two neighbor bridges has spans of 185 m - 420 m - 185 m. The traffic is running on a two level truss with a four-lane expressway on the upper deck and a double
Fig.25 The Hitsuishijima and Iwagurojima Bridges of the Seto Ohashi. track railway (with provisions for a later addition of two more tracks) on the lower deck. The cable systems are of the modified fan configuration with two vertical cable planes positioned directly above the deck trusses. Thus, a high efficiency of the cable supporting for both vertical and torsional loading is achieved.
Fig.26 The Meiko Nishi Bridge in Nagoya.
An elegant cable-stayed bridge was completed in Japan in 1985 across the port of Nagoya, the Meiko Nishi Bridge (fig.26). Here the roadway is carried by a semi-streamlined box girder supported by two inclined cable planes radiating from the top of A-shaped pylons. With the chosen pylon shape and the fan shaped cable systems, the Meiko Nishi Bridge constitutes a fine example of a highly efficient cable-stayed bridge. In Tokyo a tricky design problem was overcome in the late 1980.s by constructing the world’s first Scurved cable-stayed bridge (the Katsuhika Harp Bridge) comprising a central ‘twisted’ cable plane and two pylons of different height (Fig.27).
Fig.27 The S-shaped Katsuhika Harp Bridge in Tokyo.
The double deck configuration was again applied in the Yokohama Bay Bridge opened to traffic in 1989. With its main span of 460 m the bridge was only 5 m shorter than the Alex Fraser Bridge in Canada - at that time the recordholder amongst cable-stayed bridges. The truss of the Yokohama Bay Bridge has its top chord made as a 39 m wide and 3 m deep, streamlined box girder, whereas the bottom chord and the diagonals are of more conventional bluff box sections. The total depth of the truss is 12 m corresponding to 1/38 of the main span length. From the point of view of appearance the Yokohama Bay Bridge is quite successful as the truss is well-proportioned and the pylons have a clear and simple geometry (Fig.28). Eventually, the bridge will carry 12 lanes of vehicular traffic on two decks but initially only the upper deck has been opened to traffic.
Fig.28 The Yokohama Bay Bridge
In Japan the parallel-wire strands have been used extensively and new types have been developed to improve the corrosion protection.
Conclusion With the description of some cable-stayed bridges completed at the end of the 1980s the historical review shall be concluded, but to show that the evolution of cable-stayed bridges has continued into the 1990s Table 1 shows the ten longest cable-stayed spans to be found at the turn of the millenium. It is seen that all of these bridges have been completed during the 1990s. Longest cable-stayed bridges in the year 2000 No.
Name
Span
Traffic
Country
Year
1
Tatara Bridge
890 m
Road
Japan
1999
2
Normandie Bridge
856 m
Road
France
1995
3
Qingzhou Minjiang Br.
605 m
Road
China
1998
4
Yangpu Bridge
602 m
Road
China
1993
5 6
Meiko Chuo Bridge Xupu Bridge
590 m 590 m
Road Road
Japan China
1997 1996
7
Skarnsund Bridge
530 m
Road
Norway
1991
8
Tsurumi Fairway Bridge
510 m
Road
Japan
1994
9 10
Øresund Bridge Iguchi Bridge
490 m 490 m
Road+rail Road
Denmark/Sweden Japan
2000 1991
Table 1. The ten longest cable-stayed bridges at the turn of the millennium It is interesting to note that seven of the ten longest cable-stayed bridges are located in the Far East (China and Japan), and that the remaining three bridges on the list are from Europe. In the four and a half decade passed since the Strömsund Bridge was opened the cable-stayed bridges have developed to become dominating in the span range from 200 m to 500 m. Under specific conditions the cable-stayed bridges might even be competitive against suspension bridges up to spans of more than 1000 m. However, it remains to be seen if in the near future the cablestayed bridges will actually pass the present maximum span length of 890 m in the Tatara Bridge. References [1]
Troitsky, M.S., Cable-Stayed Bridges, BSP Professional Books, London 1988
[2]
Gimsing, Niels J., Cable Supported Bridges – Concept and Design, Wiley, Chichester 1997
Retrospect and Prospect of Cable-stayed Bridges in China
Haifan XIANG Professor Tongji University Shanghai, China
Haifan Xiang, born 1935, finished his postgraduate study in civil engineering at Tongji University in 1958
Summary A brief review of cable-stayed bridge construction activities in the last two decades of 20th century in China is given, and in particular, some large cable-stayed bridges to be probably built in the first two decades of the 21st century in the country are also introduced. Most of these large cable-stayed bridges will be built to cross some sea straits in the state highway network along the pacific coastal line of China. Recent developments of cable-stayed bridges in China including hybrid system, single pylon system, stay cable system and wind-resistant studies for very longspan cable-stayed bridges are also mentioned.
1.Introduction and Historical Review The modern cable-stayed bridge was born in 1950’s, while Dischinger from Germany designed the Stroemsund Bridge in Sweden. The construction of modern cable-stayed bridges in China initiated in 1972, relatively later compared with other developed countries. The first modern cable-stayed bridge in China was built in 1975, and its technology was developed through three stages in the past 30 years. In the first period from 1972-1982, some concrete cable-stayed bridges were built. The completion of Jinan Bridge over Yellow River in 1982 with a main span of 220m may be regarded as a successful conclusion of this learning period. In the second period from 1982-1990, 19 cable-stayed bridges were constructed in 12 provinces, The main span-length was raised to 260m for Yonghe bridge, and 288m for Dongying Bridge, which was the only cable-stayed bridge with a steel deck at that time. In the 3rd period in 90’s, many cable-stayed bridges with main spans beyond 400m have been built following the experiences obtained. The successful construction of Nanpu Bridge in Shanghai with a main span of 423m was a millstone, which encouraged the provincial bridge engineers to design and construct long-span cable-stayed bridge in their own provinces. The major cable-stayed bridges in China with span length beyond 400m are listed in Table 1, in which those bridges under construction or under designing are also listed. 4 single pylon cablestayed bridge with a main span over 200m are also listed in Table 2. Up to now, more than 100 cable-stayed bridges have been built in China, so China might be the
country of building more cable-stayed bridges than any other countries in the world. Bridge Name Location Main Span Year of Deck Type Completion 1 Nanpu Bridge Shanghai 423 m 1991 composite 2 Yangpu Bridge Shanghai 602 m 1994 composite 3 Yunxian Bridge over Han River Hubei 414 m 1994 P. C. nd 4 2 Wuhan Bridge over Yangtse River Hubei 400 m 1995 P. C. 5 Tongling Bridge over Yangtse River Anhui 436 m 1995 P. C. nd 6 2 Chongqing Bridge over Yangtse Chongqing 444 m 1995 P. C. River 7 Xupu Bridge Shanghai 590 m 1996 composite 8 Kap Shui Mun Bridge Hong Kong 430 m 1997 steel 9 Ting Kau Bridge Hong Kong 475 m 1998 composite Guangdong 518 m 10 2nd Santou Bay Bridge u.c(1999) mixed 11
2nd Nanjing Bridge over Yangtse Jiangsu River rd 3 Wuhan Bridge over Yangtse River Hubei Jingsha Bridge over Yangtse River Hubei Qingzhoulu Bridge Fujian Zhanjiang Bay Bridge Guangdong Junshan Bridge over Yangtze River Hubei Prov.
628 m
u.c.(2001)
steel
618 m 500 m 605 m 480 m
u.c.(2001) u. c.(2002) u.c u.c.
mixed P.C. composite P. C.
17 Dafoushi Bridge over Yangtze River Chongqing
460 m 450
u.c u.c
steel P. C.
18 Zhenyang Bridge over Yangtze River Jiangsu Lingdingyang West Channel Guangdong 19
400 m 950 m
u.d u.p
steel steel
20
1200 m
u.p
steel
12 13 14 15 16
Chongming Bridge over Yangtze River
Shanghai
Table 1. Major Cable-stayed Bridges in China(L>400m)
Bridge Name 1 2 3 4
Shimen Bridge Sanxianzhou Bridge Zhaobaoshan Bridge Haihe Bridge
Location Main Span Chongqing Fujian Zhejiang Tianjin
230 238 m 258 310
Year of Completion 1988 u.c u.c u.c
Deck Type P.C. P.C. P.C. steel
Table 2. Single Pylon Cable-stayed Bridges in China ( L>200m)
2 Long-span Cable-stayed Bridges for 21st Century in China 2.1 Large Crossing Projects on State Highway Along Pacific Coastal Line To meet the requirements of the rapid development of economy in China, the central government
has planned a new state highway network for 21st century. This new network (Fig.1)will mainly consist of 5 lines from North China to South China(so called 5 longitudinal lines) and 7 lines from West China to East China(so called 7 transverse lines) as a skeleton. The 5 lines from the North to the South are: 1. Tongjiang to Sanya, 2. Beijing to Fuzhou, 3. Beijing to Zhuhai, 4. Erlianhaote to Hekou and 5. Chongqing to Zhanjiang. The 7 lines from the West to the East are: 1. Suifenghe to Manzhouli, 2. Dandong to Lhasa, 3. Qingdao to Yingchuan, 4. Lianyungan to Huoerguoshi, 5. Shanghai to Chengdu, 6. Shanghai to Ruili and 7. Hengyan to Kunming. In these 12 lines, 2 longitudinal lines (1 and 3) and 2 transverse lines (4 and 5) as shown in Figure.1 by thick lines are required to be built in this century, and others have been planned to be completed in the first two decades of 21st century. Among these lines it is worthy to emphasize the state highway starting from Tongjiang of Helongjiang Province, Northeast China, and ending at Sanya of Hainan Province, South China, because this line goes through all big cites along the pacific coast, the economically developed area of China. On this line there are five large strait crossing projects, which are more challenging to the engineers. From north to south, these large projects can be distinguished as Bohai Sea Strait, Yangtse River Estuary near Shanghai, Hangzhou Bay, Lingdingyang at Pearl River Estuary and finally Qiongzhou Sea Strait.
Figure 1. State Highway Skeleton Network in China Yangtse River is the largest and longest river in China, starting from the Qinghai-Xizang Plateau, and ending into the East Sea at Shanghai. The state highway along the coastal line is planned to cross over Yangtse river near Shanghai. Because of the high requirement of the navigation at the river estuary district, a long-span bridge with a main span more than 1200 m and a side span of 500m for the movable channel is needed. The archipelago of Zhoushan, at the outer fringe of Hangzhou Bay is near Shanghai and very rich in harbour resources. From Shanghai to Zhoushan of Zhejiang Province, it is needed to build a
highway, and on the way bridges have to be built over Hangzhou Bay and connecting the isles of the archipelago at Zhoushan. To connect Zhoushan Isles, based on the pre-feasibility study carried out by the Tongji Bridge Engineering Consultant, several long-span cable-supported bridges are suggested. Due to the requirement of 300,000t of the navigation ability, one cablestayed bridge with a main span of 900m and a suspension bridge with a main span of 1630m are proposed. As the increase of the economy of the Pearl River region and the blossoming trade between the mainland and Hong Kong, SAR, more border crossings are required. To find the best solution for the whole route structures, a conceptual design competition has been opened to several bridge design institutes in China. Up to now, the competition has finished to the first step, the results show that the bridge over the East Lingding Channel close to Hong Kong might be a hybrid cable-supported bridge with a main span over 1400 m proposed by the Bridge Design Institute at Tongji University[Xiang, Chen, 1998]. Figure 2 shows the structural schematic of the bridge alternative, it is a hybrid system, which is based on the idea of how to increase the torsional stiffness of the bridge. Another alternative design might be a conventional suspension bridge, but it seems that it is very difficulty to meet the aerodynamic instability criterion except that a slotted deck is used, and also the two huge anchorage blocks to be built in the deep water might be very costly. Again for the West Lingding Channel, a detail cost analysis between a conventional suspension bridge and a cable-stayed bridge with a main span of 950 m was carried out. The better alternative might be the later as shown in Figure 3, which has a mixed deck like the Normandy Bridge.
Figure 2 Structural schematic of the East Lingding Channel Bridge Proposed by Tongji University
Figure 3 Structural Schematic of a Cable-stayed Bridge Proposed by Tongji University for West Lingding Channel Qiongzhou Sea Strait, located at south of China, might be the most difficult sea strait to be bridged among all sea straits in China. It separates the mainland and the Hainan Province, an island which is a special economic zone, with more than 7 million people. This strait, about 20 km wide, with an average water depth of 60 m and maximum water depth of 80-102m, has very bad natural conditions. The site not only is often hit by typhoons and high tidal current, but also has possibilities of very strong earthquakes. Up to now there are not any detailed designs for the strait, what have been done are only some conceptual proposals. Generally speaking, those proposals include a series of large multi-span suspension bridges with span lengths of 2000m and 3000m, and multi-span cable-stayed bridges with span lengths of 1000m. there are also some other suggestions combined with bridges and tunnels. 2.2 Major Cable-stayed Bridges over Yangtze River Since the 1st Wuhan Bridge was finished at the end of 50’s, 17 bridge over Yangtze River have been constructed during the past 4 deades, in which 3 bridges are cable-stayed bridge. To meet the requirement of the developing of regional economy, the local governments along the Yangtse River Valley have decided to build more bridges over Yangtse River to form the local highway network. Several long-span cable-stayed bridge with main spans of more than 400m are now under construction or planning(see Table 1). 2.3 River Crossing Projects for Ring Roads of Big Cities In China, many provincial capitals or municipalities are located at big riverside, such as Shanghai at Huangpu River, Hangzhou of Zhejiang Province at Qiangtang River, Nanchang of Jiangxi Province at Gan River, Changsha of Hunan Province at Xiang River, Nanjing of Jiangsu Province and Wuhan of Hubei Province as well as Chongqing, a new municipality, at Yangtse River. All these big cities need multi-ring roads to lighten the increasing pressure of heavy traffic problems, therefore, some bridges including several cable-stayed bridges have to be built for connecting both riversides
3 Recent Developments of Cable-stayed Bridges in China The most important advantage of cable-stayed bridges is its variety of configuration, ease of construction and competitive cost . So the cable-stayed bridge has been becoming the main type of long-span bridges within a large range of span-length from 200-800m. According to the recent level of technology, the cable-stayed bridge with concrete deck has made
a break through 500m. The single-pylon type can be used in the case with a main span from 200300 m, even over 300m. The Haihe Bridge with a main span of 310 m in Tianjing is an example. It is more appropriate to adopt the composite deck type in the range of main span from 500-700m in order to decrease the deck weight, the dimension of cable and pylon as well. For the cablestayed bridge with a main span beyond 700m, the steel deck should be considered. If the side spans are on land or shallows, a mixed deck type with short spans of PC deck in the side span might be a optimal design by increasing the stiffness and improving the wind-resistant safety of cantilevering construction. The A or inverse Y type pylon with two inclined cable plane can make a main contribution in torsional stiffness of cable-stayed bridges, it provides a good condition in using simple-fabricated and economic open deck cross section, which can usually meet the requirement of windresistance, instead of closed box deck or separated twin side boxes. However, for some case of very narrow deck with only 2 lanes. The closed box deck is still necessary , even together with some additional measures, in order to have enough wind resistant capacity.
4 Competition and Compromise between Cable-stayed Bridges and Suspension Bridges Cable-stayed bridge and suspension bridge are currently the only two available types for very long-span bridges beyond the span-length of 600m. Except in the case of having good geological condition, general speaking, the cable-stayed bridge alternative should be more favorite for span-length less than 700m because of the expensive cost of anchorage for suspension bridges. The span length between 700 to 1000m is a competitive zone between these two bridge types. In the recent design competition for west Lingdingyang Channel, a cable-stayed bridge alternative with a main span of 950m behaves more economic and stable in strong wind compared with traditional suspension bridge alternatives with a same spanlength. The only disadvantage of very long-span cable-stayed bridge is that, the pylon suffered large wind loading during the cantilevering erection stage, to which more attention should be paid. We believe that the penetration of 1000m for the span-length of cable-stayed bridge will surely be accomplished in the near future. There were many discussions concerning the limit span of cable-stayed bridge in 70’s. Prof. Leonhardt suggested a cable-stayed bridge alternative with 1800m span-length for the Messina strait crossing and verified the feasibility for such a extra long-span cable-stayed bridge. Some researchers reported that, there exists stability problem due to the axial force in the deck, while the span-length of cable-stayed bridge reaches 1200m and more. In this case the bi-stayed system could be a solution, which will postpone the limit span of cable-stayed bridge and may also be regarded as a concession from the fully self-anchored system. A real compromise between cable-stayed and suspension system is the so-called Dischinger-type or cable-stayed and suspension hybrid system, in which the main span consists of two cablestayed side sections and a central section suspended on the main cables. The cable-stayed sections can also be designed as concrete deck, which forms a mixed deck together with central steel deck section in order to improve the wind-resistant behavior. The main cable may sustain the deformation of cantilever of cable-stayed sections during erection, which will also reduce the buffeting response of the pylon under strong wind. Although the fatigue problem in the hangers near the connection points of two different sections should be solved, the compromise between
two types in their competition zone might be an optimal solution. Finally, we should say, when good geological condition for anchorage is provided with, the traditional suspension bridge alternative is still a most natural, reasonable and esthetical type for very long-span bridges, and 1200m should be a satisfactory limit span for the original selfanchored cable-stayed bridge.
5.Comparison Between Two Stay Cable Systems The stay cable for cable-stayed bridge was developed continuously in solving its anchor, fatigue, corrosion protection and wind-induced vibration problems since this bridge type was born in fifties. Only two cable systems used in China nowadays. 5.1 Parallel Wire Cable System with HDPE Coat This cable system was initiated in Japan on the basis of electric cable technology. The Shanghai Municipality decided to establish a new stay cable factory in 1988 for providing the parallel wire cable system, while Shanghai Nanpu Bridge was under construction. Since then, the loading capability of cable has been increasing to over 10,000KN with colored skin, and the products was used in the majority of cable-stayed bridges in China. At the present time, a non-circular, nonsmooth surfaced cable is being developed for solving the rain/wind-induced vibration problem for the construction of 2nd Nanjing Bridge over Yangtze River with a main span of 628m, which will be the longest cable-stayed bridge in China. This type of cable has been adopted in the Tatara Bridge in Japan with a record span of 890m, and the biggest cable system composed of 421 Φ7 galvanized wires with a loading capacity over 10,000KN was used is Yokohama Bay Bridge in Japan and Third Qiantang River Bridge in China as well. 5.2 Parallel Strand Bundle Cable System Coated Individually by HDPE This system was initiated in France with a main advantages in the case of creation for individual strand and in doing final adjustment by jack with smaller distance of travel. This type of cable system has been used in many cable-stayed bridges in Europe, especially in Normandy Bridge with a main span of 856m, and has been spreading in some cable-stayed bridges in China, such as 2nd Santou Bay Bridge with a main span of 518m. The domestic product is developed by OVM Corp. in cooperation with Tongji University. Generally speaking, two types of cable system have their respective advantage. The parallel wire system is easier and speedy, when the loading capacity is smaller; and the parallel strand system should be considered for the cable with bigger loading capacity.
6. Wind-resistant Studies for Very Long-span Cable-stayed Bridges 6.1 Nonlinear Theories for Torsional Divergence Figure 4 shows the structural schematic of the 2nd Shantou Bay Cable-stayed Bridge, locating at Shantou, Guangdong Province, a strong typhoon-prone area in China, which has a main span of 518 m and a concrete- steel mixed deck. A full aeroelastic wind tunnel model was carried out in the wind tunnel laboratory at Tongji University. The torsional divergence phenomena was observed, which happened before fluttering. The critical wind speed of torsional divergence is 120 m/s, which is lower than the flutter wind speed of 134 m/s, and is much lower than that
estimated from the linear estimation[Scanlan], say 209 m/s. South
North
Figure 4 Structural schematic of the Second Shantou Bay Bridge It was found that nonlinear effects have to be considered in the analysis, including the nonlinearity of wind loading, which increases not only with the increasing of wind speed , but also with the deflection of the structure, and the total torsional structural resistance decreases also with the increasing of wind speed. Figure 5 shows the divergence mode shape of the bridge obtained from analysis, similar with the divergence mode observed in the wind tunnel. It should be emphasized that the non-linear torsional divergence should be checked also for cable-stayed bridges with steel closed box girders.
Figure 5 Divergence mode shape of the Second Shantou Bay Bridge 6.2 Numerical Simulation of Flutter Analysis We started to try to use CFD technique in bridge aerodynamics in 1997, followed the pioneer work by Walter and Larsen of Denmark. Figure 6 shows the cross section shape and finite element grid of 2nd Nanjing Cable-stayed Bridge over Yangtze River, and Figure 7 shows the comparison of flutter derivatives of the bridge between calculation based on CFD technique and wind tunnel testing.
Figure 6 Cross section shape and finite element grid of No.2 Nanjing Cable-stayed Bridge over Yangtze River(Main span 628 m)
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Figure 7 Comparison of flutter derivatives of No.2 Nanjing Bridge over Yangtze River between calculation and testing A flutter analysis based on both the flutter derivatives obtained from wind tunnel testing and the CFD technique was carried out. A satisfied result was obtained. We think that in the near future, the CFD technique might be widely used in bridge aerodynamics, such as for flutter analysis, buffeting estimation and wind loading. 6.3 Aerodynamic Selection for Bridge Cross Sections The design procedure of Qingzhoulu Bridge over Ming River at Fuzhou of Fujian Province is very interesting. This bridge, now under construction, has a main span of 605 m and a deck of 29m wide, and its wind speed for flutter instability checking criterion is 70 m/s. So, a steel box girder with a streamlined shape is the first choice. A wind tunnel testing carried out at Tongji University proved that the critical flutter wind speed is much higher than 70 m/s, but the client is not satisfied with the design, they think the steel box alternative is too expensive and they want the bridge has a composite deck with a open cross section as shown in Figure 8. However, a wind tunnel testing shows that the critical flutter wind speed at +3 degree wind attack angle is only 55 m/s, much lower than 70 m/s. Different countermeasures are considered to increase the flutter stability, including fairings, stabilizers, deflectors and skirt plates. Finally, an optimized skirt plate(Figure 8) is found out, which increases the critical flutter wind speed up to 72 m/s. This example shows that the aerodynamic measures are efficient to increase the aerodynamic stability.
Figure 8 Cross section of Qingzhoulu Bridge over Ming River
7. Concluding Remarks z
The construction of modern cable-stayed bridges in China initiated in 1972, relatively later compared with other developed countries. Up to now, more than 100 cable-stayed bridges have been built in China. It is still a high tide to build more cable-stayed bridges in the country, as in this period, a lot of bridges with a main span range of 300-900 m are needed. So, China will be one of the hot places to build cable-stayed bridges in the next 2 decades.
z
Based on the experience of cable-stayed bridges in China and other countries, we can expect that the main span of traditional cable-stayed bridges will go up to 1,200 m, reaching to its limitation. The hybrid system could be an optimal solution for bridges with a span length beyond 1,200 m.
z
Cable-stayed bridges with composite decks and a span length less than 700 m is much cheaper than those with steel box decks. The aerodynamic stability can be greatly improved with additional aerodynamic countermeasures.
z
Also serious wind/rain-induced cable vibration has occurred at several cable-stayed bridges in China, bridge engineers should pay more attention to this problem, especially for very long-span cable-stayed bridges.
Reference [1] Ewert, S., 1997. Neue Grossbrueken in China. Bautechnik 74, Heft 2: 123-127 [2] Lin, Y. P.; Zhang, Z. H. & Ma, B., 1996. Xupu Cable-stayed bridge, Shanghai, SEI, 166-167 [3] Ostenfeld, K. 1992. Aerodynamics of large bridges. SEI, 186-189 [4] Qu, Q. L.; Lin, J. Y., 1996. Chongqing second Yangtse River bridge. SEI, 150-151 [5] Simiu, E. & Scanlan, R. H. 1996. Wind Effects on Structures, Fundamental and Applications to Design, John Wiley & Sons, Inc. New York [6] Xiang, H. F. 1991. Cable-stayed bridge in China. Cable-Stayed Bridges, Recent Developments and their Future, Editor: Ito, M. et al, Elsevier. [7] Xiang, H. F. 1993. Bridges in China. Tongji University Press, A&U Publication(HK)Ltd. [8] Xiang, H. F. 1995. Buffeting response analysis and control of long-span bridges. A State of the Art in Wind Engineering, Ninth International Conference on Wind Engineering, New Delhi. [9] Xiang, H. F.; Chen, A. R.& Lin, Z. X. 1998. An introduction to the Chinese wind-resistant design guideline of highway bridge. Journal of Wind Engineering and Industrial Aerodynamics 74-76 [10] Xiang, H. F. & Chen, A. R. 1998. 21st century bridges in China, Bridge Aerodynamics, Proceeding of the international symposium on advances in bridge aerodynamics, Copenhagen, Denmark, 10-13
Developments in Concrete Cable-Stayed Bridges in the United States Marcos P. LOIZIAS Director of BridgeEng Sverdrup Civil, Inc. New York, NY, USA
Summary This paper reviews the developments in cast-in-place and precast concrete cable-stayed bridges in the United States. It describes characteristic structural details, aerodynamic considerations and presents the methods of construction of these bridges. Some significant bridges are discussed in detail along with their cost competitiveness with steel alternatives.
1.
Introduction
The competitive bidding process between steel and concrete alternatives, previously required by the Federal Highway Administration for bridges costing over $10 million, stimulated creative developments in the design and construction of concrete cable-stayed bridges in the United States. While many characteristics of the concrete cable-stayed bridges in the United States are similar to those in other parts of the world, several developments originated and were further refined in the United States. For cast-in-place construction, they include the use of flexible girder and open cross-section constructed by a cable-supported formtraveller. For precast construction, they include the use of delta frames to support separate box girders and provide for a single plane of suspension.
2.
Cast-in-Place Concrete Cable-Stayed Bridges
The open deck cross-section has dominated cast-in-place concrete construction in the United States, proven easy to form and structurally efficient. It consists of longitudinal rectangular edge girders that support transverse floorbeams and a top slab. As the section is torsionally weak, it requires suspension from two planes of stay-cables. The open section has a low drag coefficient and is efficient aerodynamically particularly as the width of the bridge increases and the section approximates a flat plate.
The Dame Point Bridge The 792.48m long three-span symmetrical Dame Point Bridge in Jacksonville Florida is the first cast-in-place concrete cable-stayed bridge built in the United States. With a 396.24m long center span and flanking spans of 198.12m each, is still the longest concrete cable-stayed bridge in the Western Hemisphere. The bridge is a high level crossing over the St. Johns River and provides for a vertical navigation clearance of 53.34m. It is the only bridge in the United State where the superstructure is fixed to the towers. The concrete deck is 32.23m wide and carries six traffic lanes with provisions for a seventh lane by removing the median barrier. The edge girders are 2.44m wide and vary in depth from 1.52m to 1.85m at the towers where the compression from the cable thrust forces becomes the greatest. Post-tensioned transverse floorbeams are spaced at 5.33m on centers and support the reinforced concrete deck slab that varies in thickness from 229mm to 559mm at the areas of maximum compression. The stay-cables are spaced at 5.33m along the girder and arranged in a harp configuration. They are anchored at H-shaped towers with vertical legs extending 91.4m above the deck.
Figure 1. The Dame Point Bridge, Florida In another unique for the United States application, the stay-cables utilized parallel 32mm diameter Dywidag thread bars. The grade 1040 thread bars were pressure grouted inside thick steel pipes that were designed to resist any post-grouting loads on the bridge, i.e.
overlay and live loads, in a composite action between bars and pipe. The steel pipes were welded on the deck to their required length using full penetration welds and x-rayed to assure their fatigue capacity under live load. The bars were coupled with mechanical couplers in 18.28m lengths to their final length and stressed individually in a balanced procedure to assure the same force in all bars. The superstructure was built by the balanced cantilever method using a specially designed light-weight formtraveller that rolled over both edges of previously constructed segments. The formtraveller was designed to support casting of the entire monolithic pour of edge girders, floorbeam and deck slab in a typical 32.23m wide by 5.33m long segment. During casting of a segment, the formtraveller was supported at the front by an extension of the erected cable and strut and hanger connections to the previously cast segments. The Dame Point Bridge was initially let in 1979 with the lowest bid for the concrete cable-stayed bridge at $64.8 million compared to $84.8 million for a steel cable-stayed alternative. Due to the unfavorable bond interests rate market at the time, the owner of the bridge had decided to put the project on hold. The bridge was re-let in November1984 during which time the contractors were allowed to bid on the original designs or submit their own alternate designs in steel or concrete. The lowest bid was for the original concrete cable-stayed bridge design at $47 million with no bids received for the steel alternative. The bridge opened to traffic in March 1989. The Talmadge Memorial Bridge The Talmadge Memorial Bridge over the Savannah River, Georgia features a three-span cable-stayed main structure with a 335.28m center span and flanking spans of 143.15m each. It provides a vertical navigation clearance of 56.4m. The bridge deck is 24.54m wide and carries four traffic lanes. The edge girders are 1.37m deep by 1.37m wide. A 282mm thick slab is supported by transverse floorbeams spaced at 8.91m and 8.61m at the center span and flanking spans respectively to match the cable spacing. The stay-cables are arranged in a semi-fan configuration and anchored at Hshaped towers. The superstructure passes through the towers supported by the stay-cables and vertical bearings at the roadway strut. The stay-cables consist of parallel 15mm diameter seven-wire low relaxation prestressing strands, pressure grouted within a black polyethylene (HDPE) plastic pipe and wrapped in a light-colored PVF tape. This is the most common type of cable system used in cablestayed bridges in the United States. The bridge was built by the balanced cantilever method using formtravellers to support the entire segment consisting of edge girders, floorbeam and deck slab. The movement of the formtraveller to the casting position required a boggie beam and intermediate cable adjustments to control the positive bending moment demand in the girders during rolling of the traveller. At the casting position, the contractor utilized water ballast tanks on the
formtraveller to minimize the need for additional cable adjustments and control negative moment demand in the girders. The weight of the water was approximately 70% of the concrete weight and the water was released as the pour of concrete for the segment progressed. Vertical and diagonal tie-downs were required during construction to stabilize the deck against wind vibrations. The bridge was let in June 1987 with the lowest bid for the concrete cable-stayed bridge at $25.7 million compared to $26.9 million for a steel composite cable-stayed alternative. The Maysville Bridge The Maysville Bridge over the Ohio River, Kentucky features a three-span cable-stayed main structure with a center span of 320.04m and flanking spans of 135.03m each. It provides for a vertical navigation clearance of 23.5m. The bridge carries one of the most slender cable-stayed spans in the western hemisphere with a center span to width ratio of 18. The 17.78m wide deck is designed for four traffic lanes. The edge girders are 1.37m wide by 1.37m deep. The 254mm thick slab is supported by transverse floorbeams spaced at 7.69m in the center span and 7.39m in the flanking spans to match the spacing of stay-cables. A 38mm thick latex concrete overlay is added over the deck for protection. The stay-cables are arranged in vertical planes in a semi-fan configuration and anchored at H-shaped towers that extend 68.6m above the deck. The towers utilize a hollow boxsection above the roadway and solid rectangular section below. The size of the towerhead at 6.09m long by 2.59m wide was dictated by strength demand as well as the layout of the stay-cable anchorages to allow stressing and future adjustments of the cables from the tower. The wind studies for the bridge included a topographical model of the complex terrain surrounding the bridge site to assess the directionality of the wind and full aeroelastic and sectional model tests to confirm the bridge’s aeroelastic stability against flutter and vortex excitation. For the consideration of vortex excitation, peak acceleration limits were set to 0.05g for a wind velocity up to 13.4m/s and 0.10g for greater velocities, as suggested by the ASCE Committee on Loads and Forces on Bridges. The corresponding allowable peak deflection criteria, based on the calculated lowest vertical and torsional frequencies of 0.306 Hz and 0.506 Hz, were respectively 134mm and 0.38 degrees. For the basic benchmark wind tunnel test conditions, zero degrees angle of wind attack and smooth flow, vertical vortex-induced oscillations occurred at 9.36 m/s with a peak amplitude of 122mm. The addition of low turbulence was found to significantly decrease peak vertical excitations. The torsional vortex-induced motions in smooth flow were found well below the 0.05g criterion. The wind speed for the onset of flutter in smooth flow was in excess
of 53.4m/s compared to the flutter criterion of 37.4m/s based on a 100,000 year return period 10 minute average wind at deck level. The bridge was let in December 1996.The concrete cable-stayed bridge bid at $38.3 million was not the low bid. The state went on to construct a steel composite cable-stayed bridge alternative which was bid at $36.4 million. The Cape Girardeau Bridge The Cape Girardeau Bridge over the Mississippi River, Missouri features a three-span cable-stayed main structure with a center span of 350.52m and side spans of 142.65m each. It provides for a vertical navigation clearance of 18.9m. The bridge site is closed to the New Madrid region which has been the most seismically active region in the central and eastern North America. The bridge is designed for a ground acceleration coefficient of 0.36g with a 90% probability of not being exceeded in 250 years which essentially corresponds to a repeat of the largest earthquake that shook New Madrid in 1811 at a surface wave magnitude (Ms) of 8.5. The 28.6m wide deck carries six traffic lanes. The edge girders are 1.52m wide by 1.52m deep. The 254mm thick slab is supported by transverse floorbeams spaced at 7.62m in the center span and 7.24m in the flanking spans to match the spacing of stay-cables. A 76mm thick silica fume overlay is added over the deck for protection. The stay-cables are arranged in vertical planes in a semi-fan configuration and anchored at the H-shaped towers that extend 75m above the deck. The superstructure passes through the towers supported by the stay-cables and vertical bearings at the roadway strut. Longitudinal fixity at the two towers is accommodated through shock transmission devices (STU) capable of transmitting a longitudinal force of 15,000 KN at each tower leg. The STU devices provide for translation fixity for all fast moving (transient) loads and could accommodate a total movement of 178mm under the combined effects of temperature fall and creep and shrinkage of concrete. Tie-downs at the anchor piers provide free longitudinal translation. The geo-seismic studies for the bridge included evaluations of near-fault rupture potential, soil liquefaction, site response and spatial incoherence of ground motion. The seismic analysis was based on a time history response analysis and considered multiple support excitations and substantial forces (22,000 KN) from sloughing of liquified soil. In addition to the longitudinal and transverse horizontal motions, the design included a vertical motion equivalent to 70% of the longitudinal motion. To preserve the integrity of the bridge without significant damage, the substructure and connections were designed for the elastic earthquake loads.
From the wind tunnel tests, the wind speed for the onset of flutter in smooth flow was found in excess of 62.4m/s compared to the flutter criterion of 41m/s based on a 100,000 year return period 10 minute average wind at deck level. At zero degrees angle of wind attack and smooth flow, vertical vortex-induced oscillations occurred at 18.3 m/s with a peak amplitude of 91mm, but were completely suppressed with the addition of low turbulence. The bridge was let in June 1996.The concrete cable-stayed bridge bid at $51.5 million was not the low bid. The state went on to construct a steel composite cable-stayed bridge alternative which was bid at $50.85 million. The Owensboro Bridge The Owensboro Bridge over the Ohio River, Kentucky features a three-span cable-stayed main structure with a center span of 365.76m and flanking spans of 147.83m each. It provides for a vertical navigation clearance of 17.49m. The 23.06m wide deck carries for four traffic lanes. The edge girders are 1.37m wide by 1.45m deep. The 279mm thick slab is supported by transverse floorbeams spaced at 8.08m in the center span and 7.85m in the flanking spans to match the spacing of staycables. A 38mm thick LMC overlay is added over the deck for protection. The stay-cables are arranged in vertical planes in a semi-fan configuration and anchored at the H-shaped towers that extend 75.36m above the deck. The superstructure passes through the towers supported by the stay-cables only. Longitudinal fixity at the towers is provided through shock transmission devices. The bridge was let in July1997.The concrete cable-stayed bridge bid at $58.98 million was not the low bid. The state went on to construct a steel composite cable-stayed bridge alternative which was bid at $55.45 million. The Chelyan Bridge The Chelyan Bridge over the Kanawha River, West Virginia features a three-span cablestayed main structure with a center span of 181.05m and flanking spans of 75.4m each. It provides for a vertical navigation clearance of 22.98m above the normal pool elevation. The 22.68m wide deck carries four traffic lanes and a 1.52m wide sidewalk. The edge girders are 1.37m wide by 1.52m deep. The 279mm thick slab is supported by transverse floorbeams spaced at 7.69m in the center span and 7.39m in the flanking spans to match the spacing of stay-cables. A 32mm thick LMC overlay is added over the deck for protection. The stay-cables are arranged in a semi-fan configuration and anchored at H-shaped towers with vertical legs extending 42.98m above the deck. The tower legs are stiffened at deck
level with a stiff strut. There is no strut above the roadway, providing thus a clean and simplistic appearance to the structure. The superstructure passes through the towers supported by the stay-cables and vertical bearings at the roadway strut. From the wind tunnel tests, the wind speed for the onset of flutter in smooth flow was found in excess of 45.9 m/s compared to the flutter criterion of 41m/s based on a 100,000 year return period 10 minute average wind at deck level. At zero degrees angle of wind attack and smooth flow, vertical vortex-induced oscillations occurred at 20.9 m/s with a peak amplitude of 152mm, but were reduced to negligible levels with the addition of low turbulence. The bridge was let in May 1995.The concrete cable-stayed bridge bid at $26.89 million was not the low bid. The state went on to construct a steel truss alternative which was bid at $25.9 million. Other Cast-in-Place Concrete Projects Another cast-in-place concrete cable-stayed bridge built in the United States is the Cochrane Bridge over the Mobile River in Alabama. It features a 238m long center span and flanking spans of 110m each. The deck section consists of twin trapezoidal box girders connected with transverse diaphragms. The bridge was opened to traffic in August 1991 at a construction cost of $70 million. The Sidney Lanier Bridge over the Brunswick River in Georgia is currently under construction. It provides for a three-span symmetrical cable-stayed main span structure with a center span of 381m long and flanking spans 190.5m each. The bridge was let in October 1996 with the lowest bid for the concrete alternate at $65.5 million compared to $70.1 million for a steel composite cable-stayed alternate.
3.
Precast Segmental Concrete Cable-Stayed
The most distinctive cross-section for precast construction is the torsionally stiff box girder supported by a single plane of stay-cables along the centerline of the bridge. Variations in the cross-section include a single cell box and twin boxes connected with delta frames for wider bridges. The box girder has large lateral strength and is fairly efficient aerodynamically with low drag coefficient. The Sunshine Skyway Bridge The Sunshine Skyway Bridge in Tampa Florida is the largest precast concrete cablestayed bridge in the United States. It features a three-span cable-stayed main span structure with a center span of 365.76m and flanking spans of 164.59m each. It is a high level crossing providing for a vertical navigation clearance of 53.35m.
The bridge is conceptually very similar to the Brotonne Bridge in France with the exception that the entire segment is precast in a monolithic unit. A typical segment is 29.9m wide by 3.66m long. It consists of a single cell box with inclined webs and internal struts provided to transfer the stay-cable forces from the anchorage area at the top slab to the bottom of the girder and over the full depth of the section. The depth of the box girder is 4.26m. The bridge is supported by a single plane of cables along the centerline of the bridge. The cables are arranged in a fan configuration and are continuous through the pylon with the angle of stays with respect to the deck varying from 22 to 47 degrees. The cables are anchored at the box girder at 7.31m centers. The stay-cables consist of 60 to 80 15mm diameter seven-wire low relaxation prestressing strands pressure grouted in steel pipes. The cables were overstressed before grouting and then released after the grout had set in order to introduce permanent compression in the grout. Damping devices are provided at deck level to control cable vibrations. The towers consist of a single shaft pylon above the deck and twin elliptical box pier shafts below. The pylon, the box girder superstructure and the twin pier shafts are all rigidly connected together. Longitudinal movement is accommodated by the flexibility of the twin pier shafts.
Figure 2. The Sunshine Skyway Bridge, Florida The bridge was constructed by the balanced cantilever method. The precast segments were lifted to position from barges by a pair of winches attached to the end of the cantilevers. The segments were basically prestressed in the precasting yard in the
transverse and vertical direction, while a limited amount of longitudinal prestress in the top slab permitted the cantilever construction before placing the permanent cables. External longitudinal tendons, laid above the bottom slab and draped inside the box section to be anchored at the stay-cable anchor block at the top slab, were prestressed to resist the combined effects of live load bending moments, temperature gradients and creep and shrinkage of concrete. The bridge was let in 1982 with the lowest bid for the concrete cable-stayed bridge at $106.6 million compared to $109.3 million for a steel composite cable-stayed alternative. The bid price included the cost for the high level approach spans. The bridge was opened to traffic in April 1987. The Neches River Bridge The Neches River Bridge in Texas features a five-span continuous cable-stayed bridge with a center span of 195.07m, side spans of 85.34m and end spans of 42.67m. It is a high level bridge with a vertical navigation clearance of 43.6m. The 17.1m wide deck consists of a precast segmental trapezoidal box girder with inclined outside webs connecting directly to the edges of the top slab without cantilevers. Internal struts provided intermediate support to the top slab. The 2.44m deep box is supported by two vertical planes of stay-cables anchored directly at the connection of webs and the top slab. The cables are arranged in harp configuration and are continuous over saddles at the pylons. The typical segment length is 3.05m, with cable spacing along the girder at 6.1m. The piers and pylons are made of precast segments assembled by vertical post-tensioning. The side spans, considered as a natural continuation of the approach spans were constructed up to the pylons by the span-by-span method of construction with temporary piers and assembly trusses. The center span was then constructed from the pylon in onedirectional cantilever. The center span segments were raised from barges by winches attached to the cantilever. The construction cost for the project was $22.8 million. The Chesapeake and Delaware Bridge The 1,417m long Chesapeake and Delaware Bridge in Delaware features a 502.92m long precast concrete cable-stayed bridge with a center span of 228.6m. It is a high level bridge with a vertical navigation span of 42.1m. The 38.4m wide superstructure features twin parallel trapezoidal box girder segments. Each box girder is 17.92m wide and 3.65m deep. One of the most significant features of the bridge is that the box girders are independent of each other in the approach spans while in the cable-stayed main span they are tied together with precast delta frames that
transfer the loads from the girders to a single plane of stay-cables. The stay-cables arranged in harp configuration, are continuous over a curved saddle in the pylon and anchored to the precast delta frames, allowing stressing of the cables at the deck level. The stay-cables carried up to 85 15mm diameter seven-wire strands pressure grouted in steel pipes. The typical segment length is 3.05m, with the cable spacing along the girder at 6.1m. The transition piers are made of 3.05m long precast segments assembled by vertical posttensioning. The pylon is cast-in-place in 3.05m increments to match the precast posttensioned piers. The pylons extend 56.2m above the deck. The construction of the 228.6m long center span began from each pylon in a onedirectional cantilever method of erection. With the entire erection done from above, box girder segments were transported with segment haulers over the previously completed portion of the bridge and set in-place simultaneously at the tip of the cantilever using crawler cranes. The cable-stayed side spans leading to the pylon were constructed as a continuation of the approach spans, built in typical span lengths of 45.7m by the span-byspan method of erection using an overhead gantry. The bridge was let in December 1991 with the lowest bid for the concrete cable-stayed bridge at $57.9 million compared to $64.7 million for a steel composite cable-stayed alternative. The bid price included the cost for the high level approach spans. The bridge was opened to traffic in 1995. The James River Bridge The James River Bridge in Virginia is very similar to the C & D Canal Bridge, featuring twin parallel trapezoidal box girder segments connected with delta frames and supported by a single plane of stay-cables along the centerline of the bridge. The 466.3m long cable-stayed bridge has a center span of 192.0m and provides for a vertical navigation clearance of 44.2m above the James River. The superstructure is 38.4m wide. Each box girder is 17.92m wide by 3.65m deep and carries three traffic lanes. The cables are spaced at 6.1m along the deck and are anchored every other segment at the delta frames. The stay-cables consist of parallel seven-wire prestressing strands pressure grouted in PE pipes. The cast-in-place pylons extend 40.8m above the deck. The bridge was opened to traffic in July 1990 at a construction cost of $34 million. The Cooper River Bridge The 5,029m long Cooper River Bridge in South Carolina also features twin parallel trapezoidal box girder segments connected with delta frames and supported by a single plane of stay-cables along the centerline of the bridge.
The 518.16m long cable-stayed bridge has a center span of 243.84mm and provides for a vertical navigation clearance of 47.24m above the Cooper River. The superstructure is 33.03m wide. Each box girder is 14.35m wide by 3.05m deep and carries three traffic lanes. The cast-in-place pylons extend 50.4m above the deck. The bridge was let in November 1986.The concrete cable-stayed bridge bid at $106.61 million was not the low bid. The state went on to construct a steel truss alternative which was bid at $89.42 million. The bid price included the cost of the high level approach spans. Other Precast Projects Two other precast concrete cable-stayed bridges were built in the United States. They are the Pasco-Kennewick Bridge in Washington with a 229m long center span and triangular-shaped box girder superstructure supported by two planes of stay-cables, and the East Huntington Bridge in West Virginia with a center span of 274.4m and featuring an open cross-section with transverse steel floorbeams. Several other precast segmental concrete cable-stayed bridges were carried through final design but not built. The projects included the 6th Street Bridge in West Virginia bid at $28.6 million compared to $24.5 million for a steel truss alternative, the Roosevelt Lake Bridge in Arizona where a steel arch at $18.7 million came over $5 million lower than the cable-stayed bridge alternative, and the Baytown Bridge in Texas where a steel composite cable-stayed bridge was built at a construction cost of $91.25 million while no bids were received for the concrete alternative.
4.
Conclusion
Concrete cable-stayed bridges have been proven very competitive with steel alternatives for spans in the range of 180m to 400m. With dramatic increases in concrete strengths and quality, good aerodynamic performance, superior durability, ease of inspection and maintenance and contractor’s familiarity with this type of construction, concrete cablestayed bridges are expected to be competitive in upcoming bridge projects that require main navigation spans in the range of 500m.
The Innovative William Natcher Cable-Stayed Bridge
Vijay CHANDRA P.E,. Sr Vice President Parsons Brinckerhoff New York, NY, USA Received an M.S. degree (Advanced Structures) from the University of London and a B.E. degree from the University of Mysore, India
Ruchu HSU P.E., Supv. Structural Engineer Parsons Brinckerhoff New York, NY, USA Received an M.S. degree (Civil Eng.) from Polytechnic University of New York and a B.S. degree from National Cheng-Kung University, Taiwan
Introduction For the Kentucky Transportation Cabinet (KTC), Parsons Brinckerhoff (PB) designed a steel state-of-the-art cable-stayed bridge (See Figure 1) that successfully competed against a concrete alternate cable-stayed bridge. The bridge spans the Ohio River connecting Owensboro, Kentucky and Rockport, Indiana. The contract was bid in September 1997 and construction began in November of the same year. There were three bidders for the project. Two of the lowest bids were for the steel alternate. The selected bid price was $55.45 million, excluding the main tower foundations, which were bid at $14.55 million and built earlier due to funding issues.
Figure 1. Elevation View of the Natcher Bridge Being one of the longest cable-stayed spans over the US inland waterway system, we had to carefully evaluate the design to develop an efficient, safe and durable bridge. Also, one of our original objectives was to make the bridge “user-friendly” for the contractor, inspectors and maintenance personnel. To accomplish this, we went beyond normal US stay cable technology.
Some of the bridge’s noteworthy features include: • Simple and flexible details of the girder-to-stay cable anchoring system • Efficient prefabricated composite steel stay cable anchoring system in the towers • Simple and efficient superstructure fixity connection at the Kentucky side tower • Continuity of the superstructure at the anchor piers with the approach girders • Flexible stay cable specification to accommodate all present anchoring systems
Bridge Configuration
Total Width of Structure Number of Traffic Lanes Superstructure Approaches A. Land: Prestressed Concrete Beam Spans Depth Spacing B. Water: Steel I-Beam Spans Depth Spacing Superstructure Cable-Stayed Steel Edge I-Girder with Floor Beams Spans Girder Depth Floor Beam Spacing Deck Slab Thickness Latex Modified Concrete Overlay Thickness Substructure
Foundations
Kentucky Approach 21.28 m 4
Main Span 23.68 m 4
Indiana Approach 21.28 m 4
Four equal spans of 33.5 m 1.68 m Six at 3.11 m
Five equal spans of 41.8 m 1.83 m Seven at 2.67 m
84-152-84 m 3.7 m 3.74 m
84 m 3.7 m 3.74 m
203 mm None
152-366-152 m 1.52 m 4.57 m 229 mm 38 mm
203 mm None
Pile bents over land
Hammerhead piers at anchor piers
Pile bents over land
Hammerhead piers in water
Diamond shaped piers at tower piers
Hammerhead piers in water
Drilled shafts 1.22 to 2.44 m diameter up to 40 m deep
Drilled shafts 1.83 m diameter up to 25 m deep
Drilled shafts 1.22 to 1.83 m diameter up to 34 m deep
Aesthetics Function was the overriding factor in defining various bridge elements. For instance, the shape of the tower piers was based on economy, functionality, constructibility, inspectability, maintainability, torsional deck stability, cable connectivity, etc. However, aesthetics also played a role once the shape was selected. Our in-house architects sculptured the exposed face at the top by giving it definition in the form of reliefs and striations. Our experience shows that architects play a useful role in shaping a bridge, as long as form is not put ahead of function.
Design Criteria The following design criteria were used on the project: • American Association of State Highway and Transportation Officials (AASHTO) HS-25 truck load • Barge impact forces over the length of the total bridge, specifically: − Land approach: single 180-ton empty jumbo barge moving with the current at 100-yearflood condition − Water approach and main crossing: 15 (3 x 5) fully loaded jumbo barges with tow moving under power with the normal current or single 1,700-ton jumbo barge moving with the current at 100-year-flood condition (Maximum force = 13,300 to 17,800 kN) • Seismic Force–per AASHTO Seismic Performance Category B • Restricted channel closing to barge traffic • 100-year return wind speed = 130 kph • Scour plus barge impact = 50% scour depth for normal flow and 100% scour depth for 100year-flood flow • Gravity, thermal and transient loads • Stay cable replacement with only the two far lanes fully live loaded • Accidental loss of a cable with all lanes fully loaded
Hydraulic Analysis When obstructions are placed in a river or floodplain, the flow characteristics of the river are affected. Flow is of particular concern to bridge designers because it affects scour, which is the scooping out of soil around bridge foundations. The faster the current, the worse scour can be. Therefore, care must be taken to avoid creating fast-flow conditions when choosing the span arrangement for a bridge. Hydraulic analysis determines the flow velocities associated with various span arrangements in order to determine the optimum span placement. The flow velocities are then used to calculate the severity of anticipated scour and the depth needed for the bridge foundations. We performed a state-of-the-art hydraulic analysis and scour evaluation of the 6.4-kilometerwide floodplain of the Ohio River in the area of the Natcher Bridge. This evaluation included the main river crossing and the relief structures in the overbank areas on the Kentucky floodplain side. We performed a 2-D finite element hydraulic analysis of 89 square kilometers of the Kentucky floodplain in the vicinity of the crossing, using the Finite Element Surface Water Modeling System (FESWMS). The computer model was validated and calibrated using known flood information for the Ohio River in the vicinity of the bridge. The program provided flow and discharge vectors at every nodal point. Although more than 14 alternatives, including 8 to 10 options each, were studied, only two adequately met the specified criteria: • Flow rate not to exceed 1.22 meters/second immediately downstream of the bridge • Backwater elevation not to exceed 76 millimeters/second
After a detailed comparative evaluation was performed, examining cost, hydraulics, operations and maintenance, KTC selected the alternative with five flood relief structures in the overbank area on the Kentucky side. Utilizing information provided by the FESWMS model and the Federal Highway Manual on scour (HEC18), scour at each main bridge pier and at the flood relief bridges were computed for both contraction as well as general scour. The information provided by the velocity vectors and the scour analysis also assisted in determining ship impact forces.
Tower Piers The importance of tower piers and their shape cannot be overemphasized because they are the most dominant element of a cable-stayed bridge. After a careful evaluation of tower shapes during preliminary design, PB selected a diamondshaped (also known as an A-shaped) tower (See Figure 2). The shape of the tower improved the torsional stiffness of the superstructure and ensured the stability of the bridge during construction and to seismic and wind loads when completed. The Natcher Bridge will have two identical concrete A-shaped towers supporting three superstructure spans through stay cables. The towers will be 100.6 meters high, rising 79.3 meters above the bridge deck. Each tower has two inclined legs above the deck and a trapezoid-shaped head to contain all the cable anchors. Below the deck, the two tower legs bend inward and are held in position with a tie strut.
Figure 2. Tower Piers
The superstructure passes through each tower between the legs and sits on top of the tie strut with bearings under each edge girder. Bearings at the Kentucky tower are fixed, while those at the Indiana tower are expansion type. At the base of the tower head, a 1.5 x 1.5 meter opening is provided for easy equipment access from the roadway level. Meanwhile, lightening arresters and air beacons are housed at the top of the tower.
The tower legs are 4.88 x 2.44 meters above the roadway and 4.88 x 3.66 meters below the tension strut, which is prestressed to a jacking force of 70,300 kN to resist dead load plus live load tension. Polyethylene sheathing is used for prestressing tendons in the struts.
Superstructure Continuity The superstructure consists of steel edge girders with steel floor beams (See Figure 3). The edge girder web is inclined at 8° for the inclined stay cables anchored at the towers. The floor beams are spaced at 4.57 meters. To control torsion in the floor beams during precast slab erection, a central beam is added. The deck slab consists of precast concrete units with cast-in-place (CIP) infills. The slab is connected to the edge girders and floor beams by shear studs. A 38-millimeter overlay of latex modified concrete will be placed on the deck slab. A unique feature of the Natcher Bridge involves the transition from the cable-stayed back spans to the adjacent approach spans at the anchor piers (See Figure 4). In cable-stayed bridges, challenging design issues arise in the vicinity of anchor piers where a transition occurs from the
cable-supported structure to a conventionally supported structure. Therefore, many important elements are located in this area, including: • Counterweights and tie-downs to secure the anchor cables • Windlocks to prevent relative transverse movement between the deck and anchor pier • Bearings for both the cable-stayed spans and the approach spans
Figure 3. Superstructure Detail
Figure 4. Transition at Anchor Pier
We rigidly connected the approach girders to the cable-stayed edge girders and floor beams because they were designed to be continuous over the anchor piers. There is no relative rotation between the two adjacent spans. The bearings at the anchor piers allow the structure to slide longitudinally over the anchor pier. In the transition area, six longitudinal approach girders are framed into the two cable-stayed edge girders through a series of three floor beams. Moments are transferred by upward and downward forces on these floor beams. The approach girders, edge girders and floor beams are all 3.7 meters deep at this location, beyond which the two cable-stayed edge girders gradually decrease to a typical depth of 1.52 meters.
The beauty of the connection to the approach girders is that the approach dead load reaction resists part of the uplift. The remainder of the uplift is resisted by concrete counterweights. The counterweights are integrated into the superstructure and placed so that their center of gravity coincides with the centerline of bearing at the anchor pier. The counterweights are provided at each anchor pier to completely balance the uplift, even for the worst loading case with a full live load exclusively on the main span. This system offers several advantages at the anchor piers, including: • Absence of deck joints • Approach spans assist in resisting uplift • Live load stress range reduced in anchor cables • Deck slope continuity maintained AASHTO also requires provisions to resist an additional uplift force equal to the maximum live load upward reaction. This was addressed by adding a simple cable tie-down device, which is installed slack to allow for thermal movement of the deck. Longitudinal Fixity The longitudinal forces at the Kentucky tower are resisted by two brackets that drop down from the edge girder and hug a heavily reinforced concrete pedestal. Steel reinforced elastomeric bearing pads that rest between the steel brackets and the pedestal transfer the longitudinal force. The pad has a Teflon surface that bears against the bracket so that rotation of the girder is not hampered.
Windlocks at Anchor Piers One windlock is provided at each anchor pier, located at the centerline of the bridge, under the floor beam. As the name implies, windlocks provide transverse restraint against wind; however, they also restrain transverse movement caused by impacts and seismic events. The controlling load case was barge impact, and the windlocks were designed to transfer a 4,400-kN impact force to the superstructure at ultimate capacity. We also anticipated that some elements of the windlock might be damaged in the event of a full barge impact. Therefore, these parts were designed to be easily replaced. Service load design was used for normal wind load. The wind locks were designed to accommodate necessary longitudinal and vertical movement, as well as free rotation of the superstructure about the anchor pier. Each is comprised of two assemblies: • A lower assembly, attached to the pier cap with anchor bolts • An upper assembly, bolted to the underside of the floor beam bottom flange
Stay Cables and their Connection Early in the design process, we specified greased and sheathed strands (or flo-fil epoxy-coated strands) with grout in a PE pipe. Since coextruded PE pipe had recently become available in the US, both black PE pipe with Tedlar tape wrapping and coextruded pipe with a white exterior were specified (subsequently, the contractor opted to use the coextruded pipe). Also, while spiral beads on the outside of the pipe were accepted as a means to reduce rain/wind vibration, cross ties were provided to reduce the effects of galloping. During design, total flexibility was provided for the stay cable anchorage, wedge, wedge socket and Hi-Am types. In addition, both individual and multi-strand jacking were included in the specifications to provide flexibility. Cable-to-Girder Connection (Non-Stressing End) PB designed a simple bolted splice connection between the connection plate and girder web (See Figure 5). This completely eliminates torsion of the girder, allowing the connection to be located between floor beams. To provide for shear flow in the edge girder where the top flange has been slotted, we designed an angle to be bolted to the connection plate and to the top flange, along the slot. The connection plate is a flat steel plate that passes through a slot in the top flange of the edge girder as an extension of the edge girder web. A bolted splice connection is used to avoid Figure 5. Cable-to-Girder Connection stress concentration and reduce the risk of cracking in the weldment. The other end of the plate is cut into a tuning fork shape with two prongs, between which a thick-walled pipe is welded. The cable is installed by inserting its anchor head into the steel pipe. A ring nut or a shim plate then supports the anchor head to bear against the end of the pipe. Two additional plates welded to the connection plate and to the pipe stiffen the pipe against squashing and reduce the required thickness of the connection plate. These plates give the cross section of the connection a cruciform shape. They are tapered and stop above the top of the castin-place portion of the concrete deck, which is poured around the connection plate. The cruciform shape is an open section that allows easy access for inspection. Below the edge girder top flange, the splice connection can also be easily inspected.
The cable anchorage is located above the deck. Construction workers, inspectors and maintenance personnel can access the cable anchors directly without using expensive special equipment. The cables are also protected against accidents and vandalism because the steel pipes enclose the cable to a distance of 2.4 meters above the deck. Once again, maximum flexibility is provided with this cable anchorage system. Depending on the contractor’s preference, the anchorage can be shipped with the steel edge girder floor beam assembly, shipped and erected separately, or attached to the cable prior to installation. Cable-to-Tower Connection (Stressing End) For the Natcher Bridge, PB designed steel frames attached to the interior walls of the cable anchorage chamber by shear studs. These frames carry the horizontal component of the cable force, and transfer the vertical component to the concrete (See Figure 6). They can also transfer unbalanced cable forces during cable replacement or loss. Each tower head contains 12 steel frames, each supporting two side span cables and two main span cables. A frame consists of two built-up channels with flanges inclined to match the slope of the inner tower walls. A cap plate with a steel pipe is welded to each end of the channels, and the inclined flange and cap plates are attached to the tower walls with shear studs. The cable bears against inclined support plates that are sandwiched between the channel flanges. Maximum flexibility was provided in the fabrication, assembly, Figure 6. Cable-to-Tower Connection transporting and erecting of these steel frames. They can be preassembled in the shop to whatever height the fabricator and contractor are comfortable with or they can be assembled in the field. The closed chamber at the top of the tower piers provide a protected environment for the cable anchorage and is a convenient location for cable stressing operations. Platforms located at each cable level will facilitate the inspection and maintenance of the frames and anchorages.
Wind Tunnel Testing To ensure aerodynamic stability, a wind study was performed for the bridge that included wind data collection and analysis and wind tunnel tests. Rowen Williams Davies and Irwin, Inc. (RWDI) was retained to perform the wind study. Wind tunnel tests were performed on both a sectional model and a full aeroelastic model. The aeroelastic model was used for testing the bridge during four construction stages, as well as when completed. The various criteria used for testing the Natcher Bridge encompassed: • Design wind speed of 132 kph to compute static wind loads • Design flutter speed of 154 kph to study the dynamic wind effect • Structural peak acceleration limits of 5% of gravity up to 48 kph and 10% of gravity above 48 kph for studying vortex excitation All models were tested for smooth and turbulent air flows. The vortex excitation was within the criteria and occurred around 72 kph. Flutter speed was around 192 kph, well above the 154 kph predicted every 100,000 years at the site.
Though baffle plates in the mid-third of the main span were found to be necessary during the sectional model tests, they were later removed during aeroelastic model studies due to the 3-D action of the stay cables.
Construction Sequence Designing for anticipated construction stages is as important as designing the structure itself, particularly on complex structures such as cable-stayed bridges. Without careful planning, many delays can ensue during construction, leading to increased costs. To limit such impacts, we closely evaluated construction conditions. Because access to the Ohio River’s shipping channel must be maintained during construction, the bridge’s cable-stayed spans were designed to be constructed using the balanced cantilever segmental method (ensuring that shipping lanes will remain free of temporary construction supports). The construction sequence for the balanced cantilever method involves the following steps: 1. The tower is constructed. 2. A centrally positioned superstructure segment is erected at the tower and supported by temporary bracing in the area of the towers. 3. The remaining superstructure segments are erected sequentially on alternate sides of the tower until connections are made at the approach pier and, finally, at mid span. Additionally, each superstructure segment is erected in the stages listed below: 1. A steel frame is lifted into position by a barge-mounted crane and field spliced to the edge girder of the previously installed segment. It is allowed to cantilever freely. 2. Two stay cables connecting the steel frame to the tower are installed and tensioned to an initial length. 3. The six precast deck panels are installed and cast-in-place concrete closure strips are placed between them and along the edge girders of the previously installed segment. 4. The two cables are tensioned to their final length, and the procedure is repeated on the opposite side of the tower. Two-level tensioning of the cables is planned to control both erection and “locked-in” stresses in the deck and edge girders. Also, to reduce bending moments in the tower caused by wind loads and Figure 7. Typical Construction Stage construction sequence imbalances, a temporary tie-down is connected to the superstructure of the back span (See Figure 7). In addition, weights are strategically positioned and repositioned on the deck to control stresses in the superstructure.
Construction Status Presently, Traylor Brothers, the low bid contractor, has completed the Kentucky side approach pier foundations, some of the approach piers and the inclined legs of the two main tower piers (See Figure 8). The tension strut of the Indiana tower pier is under construction, while the main tower pier foundations were completed under a previous contract. The overbank approach embankment and flood relief structures are also complete.
Conclusion The design of the William Natcher Bridge was a challenge in which PB faced tough competition from the concrete alternative. Because early completion of the main tower foundations under a separate contract eliminated one of the major advantages of a steel cable-stayed bridge, namely a less expensive foundation due to lighter loads, we needed to be bold and innovative in other areas without sacrificing safety, strength and durability. We also wanted the bridge to be easy to inspect and maintain. Hands-on inspection and future maintenance are critical for bridge Figure 8. Kentucky Approach Pier Foundations longevity. When taken together with the fact that the cable anchors of cable-stayed and Inclined Legs of Two Main Tower Piers bridges are traditionally very difficult to access, PB made the accessibility and maintainability of these areas two of the most important factors to be addressed during design. We developed innovative ideas for cable-to-tower and cable-to-deck connections as well as for the elimination of uplift and deck joints. Our design allows inspectors and maintenance crews to perform hands-on work by walking directly to the cable anchors without using any special equipment. These innovations will result in the first user-friendly cable-stayed bridge in the United States.
Acknowledgements The authors express our sincere thanks to the Kentucky Transportation Cabinet, Mr. Steve Goodpastor and Mr. Henry Phillips, for allowing us the opportunity to design the bridge and for their cooperation and assistance during the design phase. We also appreciate the assistance of Mr. Jim Lyle of KTC during construction and Mr. Charles Raymer for his assistance during the hydraulic study. In addition, we wish to express our sincere appreciation to the American Institute of Steel Construction; the National Steel Bridge Alliance; the contractors, fabricators and erectors; Dr. Schlaich and Partners; and many in-house experts for their contributions and important suggestions during the design phase.
Identification of minimum width-to-span ratio of long-span cable-stayed bridges based on lateral torsional buckling and flutter analyses
Masatsugu NAGAI
Xu XIE
Professor Nagaoka University of Technology Nagaoka, Japan
Kaihatsu Consultant Co., Ltd. Tokyo, Japan
Hiroki YAMAGUCHI
Yozo FUJINO
Professor Saitama University Urawa, Japan
Professor University of Tokyo Tokyo, Japan
Summary This paper describes static and dynamic instability analyses of long-span cable-stayed bridges such as finite displacement analysis under displacement-dependent wind load and flutter analysis based on modal coordinate. Using a 1400-meter cable-stayed bridge model, in which four cross sections of the girder having different widths with a fixed depth of 3.5 meters are selected, static and dynamic instability analyses are carried out. Instability behaviors of them are made clear and, finally, the design material for identifying a minimum width-to-span ratio of the girder is presented, which ensures safety against the instabilities.
1. Introduction In the design of long-span cable-stayed bridges, ensuring safety against static and dynamic instabilities under wind load is an important issue, because the shape and dimension of the girder are controlled mainly by above instabilities. However, static and dynamic instability phenomena of long-span cable-stayed bridges have not been made clear so far. In this paper, using a 1400meter cable-stayed bridge model, static and dynamic instability analyses such as a nonlinear static analysis under displacement-dependent wind load and a flutter analysis based on multimode coordinate are carried out. Four types of the cross section of the box girder having different widths of 25,28,32 and 35 meters with a fixed depth of 3.5 meters are chosen. A spanto-width ratio is from 56 to 40, and a span-to-depth ratio is 400. It is recommended, for ensuring safety against out-of-plane instability under wind load, that the span-to-width ratio should be less than 401). However, in this study, the larger values are employed. If the value of 40 is inevitable for ensuring safety against instability under wind load, the width of the girder become large regardless of the number of traffic lanes. This means that long-span cable-stayed bridges become less competitive compared with other alternatives such as suspension bridges. Hence, an identification of the minimum width of the girder becomes an important issue. The employed box girders are preliminary designed, in which the yield point of steel is only selected to be an instability criterion. By carrying out above instability analyses, the critical wind velocities of lateral torsional buckling and flutter are investigated. Finally, the design material for obtaining minimum cross-sectional shape and dimension of the girder is presented.
2. Analytical Procedure Static nonlinear analysis under displacement-dependent wind load and flutter analysis based on modal coordinate had been explained in our previous papers2)3)4). Hence, we explain the procedure briefly. 2.1 Finite Displacement Analysis Under Displacement-dependent Wind Load When the girder is subjected to the wind load, it displaces in the horizontal direction and starts rotating. Due to the rotation of the girder, three components of aerodynamic forces such as the drag force, lift force and aerodynamic moment vary, because they are dependent on the angle of wind attack. This displacement-dependent characteristics of wind loads are taken into account in the analyses. Furthermore, the wind load acting on the cable and the change of the tension in cables are also considered. Fig.1 shows aerodynamic coefficients experimentally measured for a cable-stayed bridge5). In the figure, CD,CL and CM are aerodynamic coefficients with respect to the drag force, lift force and aerodynamic moment, respectively, and α is the angle of wind attack. In this analysis, these coefficients are used for the calculations. CD ,CL ,CM 5 4 3 2 1 0 -1 -2 -3
CD CL CM
-15
-10
-5
0
5
angle of attack (degree)
10
15
Fig.1: Aerodynamic coefficients 2.2 Flutter Analysis Based on Modal Coordinate A fundamental equation of flutter analysis is derived based on modal coordinate. The unsteady drag force of the girder is derived based on quasi-steady theory, and the unsteady lift force and aerodynamic moment are derived based on flat plate theory. The unsteady drag and lift forces of the cables are derived based on quasi-steady theory. The fundamental equation of flutter analysis is given by q q [φ ]T [(M BC − FR ) − iFI ][φ ] + [φ ]T [K BC ][φ ] = {0} qC q C
(1)
Where, {q} is the generalized displacement, which corresponds to the global vibration, {qC } is the generalized displacement of the cables, which corresponds to the cable local vibration, [M BC ] and [K BC ] are mass and stiffness matrices, respectively, and [FR ] and [FI ] are matrices consisting of real and imaginary parts of the unsteady aerodynamic forces, respectively, [φ ] is the modal matrix which is obtained by carrying out eigenvalue analysis of the whole structure, in
which cable local vibration is neglected. Assuming the reduced frequency, complex eigenvalue analysis is carried out, then we obtain complex eigenvalue of λ = λ R ± iλ I . When the sign of the damping ( ξ = λ R changes from plus to minus, flutter occurs.
2
2
λR + λI )
3. Bridge Model Fig.2 (a) shows a side-view of a cable-stayed bridge model. Center and side spans are 1400 and 680 meters, respectively. In the side span, three intermediate piers are installed at a distance of 100 meters in order to increase in-plane flexural rigidity. Fig.2 (d) is a front view of the tower, and the tower height from the deck level is one fifth of the center span length. Fig.2 (b) shows the cross-sectional shape of the girder. A depth of the girder is 3.5 meters. A span-to-depth ratio of the model is 400, which is larger than that used in the design of conventional steel cablestayed bridges. The selected widths of the girder are 25, 28, 32 and 35 meters, respectively, and the span-to-width ratios of them are from 56 to 40. These four models are preliminary designed. The cross-sectional properties of the girder are determined by applying the following design conditions. 1) The thickness of 12mm is used for both deck plate and lower flange. Taking into account of longitudinal ribs, which are expected to bear the axial force, their effective thickness is assumed to be 20mm. The thickness of the web plate is 15mm. 2) The dead load per unit length ( WD ) is calculated by Eq. (2). (2) WD = 1.4 AS γ S + 70 (KN / m ) Where, AS is the cross-sectional area of the girder, a coefficient of 1.4 is to take account for the load from diaphragms, cross beams and so on, γ S is the weight density of steel and a constant values of 70 KN / m is the superimposed dead load such as the pavement, handrail, curb, attachment and so on. 3) The live load per unit length is 38 KN / m . 4) The design wind velocities of the girder and cables are assumed to be 60 and 70m/s, respectively. Those of them at the stage of erection are 70% of above values. 5) The drag coefficients ( C D ) of the girder, cable and tower are assumed to be 0.8, 0.7 and 1.4, respectively. Dimension of the girder is determined by using the following criteria: (γ 1 = 1.7) σ D + σ L < σ y γ 1 − 19.6 ( MPa)
σ D + σ w < σ y γ 2 − 19.6 ( MPa)
(γ 2 = 1.15)
! "
Where, σ D , σ L and σ W are stresses from dead, live and wind loads, respectively, σ y (=451Mpa) is the yield point of the employed steel and γ is the factor of safety. A value of 19.6MPa is the margin, because the bending moment under dead load, shear lag effect, shear stress and so on are not taken into account at this preliminary design stage. To satisfy Eq.(4), the thickness of the plate is increased as shown in Fig.2(c). This is in order to increase out-of-plane flexural rigidity of the girder efficiently. In the bridge axis direction, the section of Xu as shown in Fig.2 (a) is reinforced. Table 1 shows the cross-sectional properties of the girder preliminary designed. In the table, the figures in the parenthesis are ones for the reinforced girder.
(m)
10 C L 132
A
3@100 =300 680
Xu 380 20
C
B
Xu 20
20
660
20
1400
148
(a) Side-view Bu x
2%
7 40
Hw
y
46
(b) Cross section 0.02
5 Tup 0.015
12 0.04
B 30
10
0.008
(d) Tower
(c) Increase of plate thickness for region 'Xu'
Gider
Fig.2: Bridge model Bu (m)
Hw (m)
25
3.5
28
3.5
32
3.5
35 3.5 tower (per one column)
A (m2) 1.314 (2.243) 1.433 (2.147) 1.642 (2.070) 1.761 (2.046) 1.760
Ix (m4) 2.560 (4.050) 2.849 (3.985) 3.269 (3.943) 3.939 (4.432) 30.67
Iy (m4) 75.65 (177.3) 102.6 (204.6) 151.5 (234.6) 193.2 (261.1) 40.32
J* Iw W Xu (m4) (m6) (KN/m) (m) 5.767 90.431 210.3 200 (9.395) (314.4) (281.8) 6.542 131.3 223.1 180 (9.365) (358.8) (278.1) 7.583 212.7 245.6 120 (9.561) (383.2) (278.6) 8.330 282.0 258.4 80 (9.739) (421.5) (280.4) 39.27 189.6 * longitudial ribs are neglected
Table.1: Cross-sectional properties of the girder and tower
Cross-sectional area of the cable is designed under the condition that a live load-to-dead load ratio is 0.25 and the allowable stress is 588MPa. The allowable stress assumed is around 7% lower than that of 628MPa, which has been used in Japan. In-plane load-carrying capacity of one of the models, which has a width of 25 meters, is examined by employing 3D elasto-plastic finite displacement analysis6)7). Under uniformly distributed load applied throughout the bridge length, the load parameter of 2.9 is obtained, which is a ratio of the applied load to dead load. Fig.3 shows interaction curves between axial force and bending moment for different three points, A, B, C in the girder shown in Fig.2 (a). In the figure, N and M are the produced axial force and bending moment, respectively. Ny and MP are the yield axial force and full plastic bending moment. The stress produced in the girder at the tower point, C, reaches yield point, followed the redistribution of the stress resultants and, finally, the bridge collapses when the axial force at points A and B reaches the yield axial force (N/Ny = 0.98). Fig.4 shows an incremental displacement at ultimate state. It is seen, at points A and B, that the vertical displacement increases rapidly. The obtained value of 2.9 is considerably
large. Hence, it is concluded that the safety of the employed models against in-plane instability is ensured. From this result, it is also interesting to know that the ultimate strength of the girder will be controlled by local buckling instability of stiffened plates and that the larger span-to-depth ratio exceeding 400 is expected to be used. N/Ny
N/Ny
1.0
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.0
0.0
N/Ny
N 0.85M + = 1.0 Ny Mp
0.2 0.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
1.0
0.0
0.2
0.4
0.6
M/MP
M/MP
(a) at Pt.A
0.8
(b) at Pt.B
0.8
1.0 M/MP
(c) at Pt.C
Fig.3: Interaction curves
Fig.4: Incremental displacement at ultimate state
4. Results and Discussions 4.1 Lateral Torsional Buckling Instability Under Wind Load Fig.5 shows lateral displacements, vertical (upward) displacements and rotational angles at the middle of the center span of the bridge. Fig.6 shows those at the tip of the cantilevered girder of the cable-stayed bridge under construction. In case of the completed bridge in Fig.5, at the wind velocity of around 60m/s, nonlinear behavior of the vertical displacement and rotational angle becomes prominent and, in the range of the wind velocity from 75 to 80m/s, they diverge. This is lateral torsional buckling. In case of the bridge under construction, since the system is flexible, the larger lateral displacement is obtained. At the wind velocity of around 50m/s, nonlinear behavior of the vertical displacement becomes prominent and, in the range of the wind velocity from 65 to 70m/s, the bridge becomes unstable. In all models, the critical wind velocities calculated are high enough compared with the design wind velocity. Figs.7 and 8 show the tensions in cables. In case of the completed bridges, at the wind velocity from 75 to 80m/s, they start decreasing rapidly. In case of the bridge under construction, in the range of the wind velocity from 65 to 70m/s, they also start decreasing. These rapid decreases of the tensions in the cables are due to rapid increase of the upward displacement of the girder.
30 25 20 15 10 5 0
(m)
10 8 6 4 2 0 -2
Bu=25m Bu=28m Bu=32m Bu=35m
(m)
10 Bu=25m Bu=28m Bu=32m Bu=35m
(degree) Bu=25m Bu=28m Bu=32m Bu=35m
8 6 4 2 0
0 10 20 30 40 50 60 70 80 90
0 10 20 30 40 50 60 70 80 90
0 10 20 30 40 50 60 70 80 90
(a) lateral displacement
(b) vertical displacement
(c) rotational angle
wind velocity (m/s)
wind velocity (m/s)
wind velocity (m/s)
Fig.5: Displacement at the middle of center span (after completation) 60 50 40 30 20 10 0
(m)
30 25 20 15 10 5 0
Bu=25m Bu=28m Bu=32m Bu=35m
(m)
14 12 10 8 6 4 2 0
Bu=25m Bu=28m Bu=32m Bu=35m
0 10 20 30 40 50 60 70 80 90
0 10 20 30 40 50 60 70 80 90
wind velocity (m/s)
wind velocity (m/s)
(a) lateral displacement
(degree) Bu=25m Bu=28m Bu=32m Bu=35m
0 10 20 30 40 50 60 70 80 90
(b) vertical displacement
wind velocity (m/s)
(c) rotational angle
Fig.6: Displacements at the tip of the cantilevered girder (under construction) 12 10 8 6 4 2 0
(MN)
Bu=25m Bu=28m Bu=32m Bu=35m
12 10 8 6 4 2 0
(MN)
Bu=25m Bu=28m Bu=32m Bu=35m
0 10 20 30 40 50 60 70 80 90
0 10 20 30 40 50 60 70 80 90
wind velocity (m/s)
wind velocity (m/s)
(a) windward
(b) leeward
Fig.7: Tensions in uppermost cable in the center span (after completation) (MN)
10
10
8
8
6
6
4 2 0
Bu=25m Bu=28m Bu=32m Bu=35m
0 10 20 30 40 50 60 70 80 90
wind velocity (m/s)
(a) windward
4 2
(MN)
Bu=25m Bu=28m Bu=32m Bu=35m
0 0 10 20 30 40 50 60 70 80 90
wind velocity (m/s)
(b) leeward
Fig.8: Tensions in uppermost cable in the center span (under construction)
Fig.9 shows the maximum normal stress in the girder at the tower point. In case of the completed bridge, when the wind velocity of all models reaches around 70m/s, the normal stress exceeds yield point. Since the plastic region spreads in a limited range of the girder, it will not lead to immediate collapse of the bridge. However, strictly speaking, elasto-plastic finite displacement analysis is recommended for identifying exact buckling instability. In case of the bridge under construction, the maximum normal stress exceeds yield point when the wind velocity is around 60m/s. In this case, elasto-plastic finite displacement analysis is also recommended. 700 600
(MPa)
700 600 500
right hand side of eq.(4)
σy
500
(MPa) right hand side of eq.(4)
σy
400
400 300
300 Bu=25m Bu=28m Bu=32m Bu=35m
200 100 0
Bu=25m Bu=28m Bu=32m Bu=35m
200 100 0
0 10 20 30 40 50 60 70 80 90
0 10 20 30 40 50 60 70 80 90
wind velocity (m/s)
wind velocity (m/s)
(a) completed bridges
(b) bridges under construction
Fig.9: Maximum normal stress in the girder at the tower point 4.2 Effect of Aerodynamic Coefficients on Instability Behavior In the analysis carried out in 4.1, the aerodynamic forces presented in the paper5) are used. However, it is natural to consider that the aerodynamic coefficients vary depending on the cross sectional shape and it is interesting to identify how the behavior changes depending on the aerodynamic coefficients. Unfortunately, since the aerodynamic coefficients for the employed cross section are not obtained, we try to carry out instability analysis using differently assumed values. It is seen, from Fig.5, when the rotational angle exceeds 3 degrees, that nonlinear behavior of it becomes prominent. Hence, when the angle of attack is larger than 4 degrees, the values of CD and CL are multiplied by 1.5 and between 3 and 4 degrees, linear interpolation is used. Fig.10 shows thus assumed aerodynamic coefficients and solid notations are new ones. Since the coefficient of aerodynamic moment (CM) is small, it is kept to be the same. CD,CL ,CM 5 4 3 2 1 0 -1 -2 -3
CD CL
1.5CD 1.5CM
CM
-15
-10
-5
0
5
angle of attack (degree)
Fig.10: Assumed aerodynamic coefficients (solid circles)
10
15
Figs.11 (a) and (b) are upward deflections and rotational angles at the middle of the center span of the completed bridge and Fig.12 is upward defections at the tip of the cantilevered girder. In case of the bridge after completion in Fig.11, the deflections diverge in the range of the wind velocity from 65 to 70m/s. This wind velocity is around 10m/s lower than those obtained in 4.1. In case of the bridge under construction, the deflections diverges in the range of the wind velocity from 55 to 60m/s. This is also around 10m/s lower than those obtained in 4.1. From these results, though the obtained wind velocity is still higher than the design wind velocity, it is known that instability behavior strongly depend on the aerodynamic coefficients. 10 8 6 4 2 0 -2
(m)
10 Bu=25m Bu=28m Bu=32m Bu=35m
8 6
Bu=25m Bu=28m Bu=32m Bu=35m
4 2 0 0 10 20 30 40 50 60 70 80 90
wind velocity (m/s) (a) vertical displacement
0 10 20 30 40 50 60 70 80 90
wind velocity (m/s) (b) rotational angle
Fig.11: Displacement at the middle of the center span (after completion) 30 25 20 15 10 5 0
(m) Bu=25m Bu=28m Bu=32m Bu=35m
0 10 20 30 40 50 60 70 80 90
wind velocity (m/s)
Fig.12: Vertical displacements at the tip of the cantilevered girder (under construction) 4.3 Flutter Onset Wind Velocity Table 2 shows the flutter onset wind velocity of the completed bridge and the bridge under construction, respectively. In the table, the figures of 30 and 20 are the number of modes employed which are needed to obtain the converged wind velocities. The figures in the parenthesis are the results when the effect of the cable local vibration is taken into account. From the results, it is found that flutter onset wind velocity is higher than the critical wind velocity under static wind load. It is also found that the effect of the cable local vibration is prominent. Finally, it is concluded that the dimension of the girder is controlled by instability under static wind load. Model Bu=25m Bu=28m Bu=32m Bu=35m
Completed 30-mode Selberg 120 130 (141) 120 130 125 132 127 133
Under construction 20-mode Selberg 99 40 (151) 109 95 105 98 107 100
Table.2: Flutter onset wind velocity
5. Concluding Remarks The followings are main results obtained from this study. 1) In all models, the flutter onset wind velocity, even in case of the bridges under construction, exceeds around 100 m/s and is higher than the critical wind velocity of lateral torsional buckling under static wind load. Hence, the static instability under displacement-dependent wind load controls the dimension of long-span cable-stayed girders. 2) On condition that the bridge is designed based on the procedure explained in Sec.3, the girder with a width-to-span ratio of around 1/55 can be used. However, for saving the steel weight, if we employ the steel with higher strength, the ratio of 1/55 has to be reconsidered. Because it results in the reduction of flexural and torsional rigidities of the girder. Hence, in such case, instability analyses have to be employed. 3) Aerodynamic coefficients affect critical wind velocity. Hence, for attaining higher critical wind velocity, controlling the aerodynamic characteristics of the girder becomes an important issue.
References [1]. [2]. [3]. [4]. [5]. [6]. [7].
F.Leonhardt and W.Zellner : Past, present and future of cable-stayed bridges, CABLESTAYED BRIDGES (ed. by M.Ito et al.), Elsevier, pp.1-33, 1991 X.Xie, H.Yamaguchi and M.Ito : Static behaviors of long-span cable-stayed bridges, Proc. of JSCE, No.537/I - 35, pp.205-215, 1996 (in Japanese) X.Xie, H.Yamaguchi and M.Nagai : Static behaviors of self-anchored and partially earthanchored long-span cable-stayed bridges, Int. Jour. of Structural Engineering and Mechanics, Vol.5, No.6, pp.767-774, 1997 M.Nagai, X.Xie, H.Yamaguchi and Y.Fujino : Static and dynamic instability analyses of 1400-meter long-span cable-stayed bridges, IABSE Symposium Kobe 1998, IABSE Reports, Vol.79, Kobe, Japan, pp.281-286, 1998 V.Boonyapinyo, H.Yamada and T.Miyata : Nonlinear buckling insatiability analysis of long-span cable-stayed bridges under displacement-dependent wind load, Jour. of Structural Engineering, JSCE, Vol.39A, pp.923-936, 1993 X.Xie, M.Nagai and H.Yamaguchi : Ultimate strength analysis and behavior of long span cable-stayed bridges, Jour. of JSCE, No.598/I - 44, pp.171-181, 1998 (in Japanese) M.Nagai, X.Xie, H.Yamaguchi, K.Nogami and Y.Niida : Elasto-plastic behavior and strength of 1400-meter long-span cable-stayed bridges, Proc. of Nordic Steel Construction Conf. 98, Vol.2, Bergen, Norway, pp.573-578, 1998
Computer Based Optimising of the Tensioning of Cable-Stayed Bridges Arne BRUER Civil Engineer Teknisk Data AS Oslo, Norway
Heinz PIRCHER Senior Partner TDV GesmbH Graz, Austria
Heinz BOKAN Partner TDV GesmbH Graz, Austria
Summary A numerical approach to reduce the calculation effort when attempting to minimise the number of stressing operations during the erection of cable-stayed bridges is shown. The proposed method is illustrated with sample calculations from a small example and from the Uddevalla bridge which is currently under construction.
The Problem The solution for the optimum tensioning strategy for long span cable-stayed bridges can be an extremely tedious and time-consuming process for the following reasons: Practical reasons • • •
Tensioning one cable affects the forces in all the other cables Cables can not, in reality, withstand compressive forces but stressing an adjacent cable may apparently cause this condition. Stressing of the stay cables is an expensive procedure due to the difficulty in the cable stressing procedure.
Analytical reasons • • • • •
A minimal cable tensioning strategy whilst saving a considerable amount of time and money during the construction phase greatly complicates the analytical phase of the design process. Definition of the tensioning strategy is interrelated with the chosen erection method and the simulation of the erection procedure using the structural model can be very complicated. The deck girder and pylon system must behave reasonably during all phases of construction. i.e. the deflections should be neither excessive nor incompatible with type of construction. Creep and Shrinkage (applicable where some or all the bridge elements are concrete or partially concrete members) greatly complicates the analytical process. “Uplift conditions” could exist at the temporary supports which further complicates the analysis. Whilst special “Non-tension” members could be used, this greatly increases the degree of indeterminacy and hence the speed of analysis.
All of the above practical and analytical reasons obviate the need for a consistent, standard, non trial and error type approach to the solution for these complex structures. It is possible to use a unit load system of analysis tied to the bridge construction method, relate this to an estimate of the max/min final live load moment envelope and through this, where possible, minimise the cable stressing operations.
The proposed method will always achieve a solution, which must then be checked for structural consistency by the user. The results can be structurally unacceptable as the solution is directly achieved from a set of simultaneous equations. The structural unacceptability may arise from such things as “compression in the cables” or “unacceptably high stresses” etc. • •
Structurally acceptable results clearly demonstrate that the parameters chosen to define the structure and its construction are correct and also define the required tensioning and construction strategy Structurally unacceptable results will point the way for modification of the parameters to be used in the next analysis. (The modification would typically be to the “Ideal Bending Moment Diagram” – Refer below)
Choosing the System and manipulating the Moment Diagram. The basic bridging system must be chosen and optimised before the stressing strategy design can be found. The system is chosen through a series of considerations such as required bridge functionality, availability and cost of materials, Clients requirements etc. The bridging system is considered, from this analytical viewpoint, as basic given information. Integral with the bridging system choice is the concept that almost any moment diagram can be achieved in the deck and in the pylon by adjusting the following Degrees of Freedom: • The tensioning forces in the stay cables and their stressing procedure • The support movements (translation – longitudinal and vertical) • Prefabrication shape of the deck girder and the pylon • The erection procedure of the deck and the pylon
Finding the “Ideal Moment Diagram” for dead load. Once the basic information has been defined in principle, the effects of the traffic / pedestrian loads and any additional loading – balustrade / guard-railing / surfacing / etc. on this “fundamentally defined” structure can be estimated. The load capacities of the deck sections and the pylon sections can then be compared with the live plus additional dead load envelopes and the “ideal” dead load force diagrams may then be defined. The sign of the “ideal” dead load force diagrams may well be of opposite sign to the diagrams resulting from normal load directions. This demonstrates the distinct advantage of cable supported structures where the initial dead load moment diagram can be easily manipulated to suit the design needs.
Establishing the “Unit Force Equations” Principles General When the “ideal” dead load force diagrams have been defined then the system of unit forces can be mathematically equated to these “ideal” dead load force diagrams. The process for defining the tensioning sequence and amount, the deck and pylon construction sequence as well as any required deck/pylon prefabrication effects then begins. Process Principle:
• • •
The unit loading system is first defined for the final stage structure in order to establish reasonable member sizes. This process usually involves certain re-definitions of the member sizes and program re-runs to prove structural integrity. Once reasonable values have been achieved the “unit force method” can be extended to the construction stage analysis. Each construction stage can be checked and proven for design compliance.
Degrees of Freedom The most commonly selected unit forces or Degrees of Freedom (N.B these “DOF´s” are not the same as the structural system DOF´s) in the structural system include: • A unit shortening of the cable (causing an axial cable tension) – or a unit tensioning causing an axial cable shortening. • A unit translation of a rigid support (transverse or longitudinal movement at a pier or abutment support). – A longitudinal force applied at the end of the deck changes the moments by changing the cable forces which act on the deck.
Setting up the “Unit Force Equations” •
Define the unit loading cases and the “ideal moment diagram”. The same number of unit loading cases must be defined as the number of “Fixed Moment” points chosen on the structural model to represent the “ideal moment diagram” (or vice-versa!). Principles in Example below: • The “ideal dead load bending moment diagram” is defined for the deck girder by bending moments at 9 points along the girder (positions A, B, C ...... I). • Nine unit loading cases are selected for setting up the simultaneous equations. • The 8 unknown “required” stay cable forces – chosen in this case to be 1000 kN. • One unit translation at the end support – chosen in this case to be 50 cm settlement. The solution to the equations (the unknowns) will be the factor by which the unit loads should be factored to achieve the “ideal dead load bending moment diagram”. Note: There is no fixed prescription for the selection of the unit loading cases. The designer is free to choose whatever he wishes. This flexibility is demonstrated in the example by the nonselection of the two stay cables adjacent to the pylon (positions E and F). The 1000 kN unit cable force was selected to be of the same order of magnitude as the final cable force because of 2nd Order considerations. (Refer below for further description of 2nd Order effects.) The “ideal moment diagram” for dead load is given below and is very different from the dead load bending moment diagram (MP) which would result if the loading was applied to the structure with un-stressed cables. N.B. Care must be taken in the selection of sensible and unrelated “ideal moments” as if one is related to another (i.e. dependent on it) then a singularity in the equations will result and there will be no solution. Provided there is no singularity, a solution will be reached.
Figure 1. The following system of linear equations is set up: MA = MP + MT1=1 . X1. + MT 2 =1 . X 2+ ........ MT 8=1 . X 8+ MT J . X 9 . . . . MI = MP + MT1=1 . X1. + MT 2 =1 . X 2+ ........ MT 8=1 . X 8+ MT J . X 9 MA....... MI MP MT1=1... MT 8 =1 MJ
Final stage moment at the current position (including tensioning + jacking). Permanent load moment at the current position (without tensioning or jacking). Bending Moment due to each unit tensioning at the current position. Bending Moment due to unit jacking of the end support at the current position.
The X 1 ...... X 9 factors set up in the unit loading cases are the unknowns in the set of linear equations which are found by the solution of these equations. Note that the system of equations is not symmetrical and the diagonal coefficient may be zero. This is to be considered when solving the equations. This basic solution defines the cable forces and the jacking force for the final stage and, at the moment, does not include the effects of: the sequence of construction stages, the creep, 2nd Order Theory or the non linearity of the cables due to the sagging effects. The basic principles must therefore be extended to accommodate these effects. Construction Stage analysis. A similar system of unit loading cases can be defined for the construction stage analysis. The unit loading cases are, in this case, applied to the different structural systems which exist at the individual construction stages. The sketches below, which show a few of the construction stages, demonstrate the principle of the method of analysis. The loading cases for each construction stage are combined to form the set of simultaneous equations which must be solved to find the required multiplication factors for the unit loadings.
Figure 2
Creep – a rational linear approach There is a general belief that creep design is a non-linear problem and therefore it is often approached in an empirical manner using some “rules of thumb” or “past experience” to assess its affects. This approach is particularly prevalent where the structural concrete is subjected to the many and varying loads which occur during the multiple construction stages of large cablestayed bridges. Taking account of creep effects using the CEB-FIP model code is even more complex than was the case using more traditional methods. Inspite of the above statements it can be shown through a series of mathematical equations that the effects of creep can be treated in a linear manner. The derivation for the effects of creep is founded on the known fact: {εe} . φ = {εc} (Elastic Strain * Creep Factor = Creep Strain) Decomposing the structure down to element level, the above equation is applied to each individual element by applying the generalised displacement method rules for calculating initial strain type loads: Define {εe} over the element. Define {εc} = {εe} . φ over the element. The member end displacements {δc} are found by weighted integration of the strain vector over the element length in the usual way. The member end forces are calculated and the system of equations are assembled and solved for nodal displacement {δ} in the usual way. ({δ} - {δc}) . [k] = {FI} gives the internal forces due to creep. The system of analysis is completely linear up to this point. In the specific case of creep, cognisance must be taken of the age differences in the concrete as well as the various ages of different parts of the structure at the time of each increment of load application (εe is no longer constant but varies with time). A finite difference approach in time is applied here and using a linear variation over a time interval, we can say: {εt} = {ε0} . t 1 – t +{ε1} . t– t 0 ∆t ∆t This equation can then be put into the basic displacement equation: at time t0 , {εe} is known and then by solving the equations for {δ} at time t = t1 a recursive formula can be derived which results in a linear relationship at time t1 such that the equation including the effects of creep is the same as the original equation with the exception that the modulus E is replaced by E A detailed description of the whole procedure is given in Ref. 2 and the 1+φ*0.5 theoretical background for the finite difference approach to solve “initial value problems” is described in Ref. 3. The essence of the above statement is, that all the creep influences on the final distribution of internal forces and displacements are related in a linear manner to the elastic strain which itself initially caused the creep. The principles of linear superposition may, in consequence, be applied and the total creep occurring during a single time step may be decomposed into single contributions: Considering one of the prescribed ideal moment positions: M creep = M p + M c t =1 . X 1 + M c t =2 . X 2 + M c t =3 . X 3 .............etc. M creep therefore consists of one part which is related to the permanent load and the other parts are related to the unit loads described above which are linearly coupled to the same unknown factors X 1 ...... X 9. As before the basic concept can now be applied; the effects of creep for permanent loads and for unit loads are decomposed into separate contributions from each time interval and then summed. The system of equations for defining X 1 ...... X 9. therefore remains linear. The only
approximation made is the assumption that the behaviour within any single time step is linear which is consistent with the usual application of the “finite differences in time” approach.
Second Order Theory and cable non-linearity (due to cable sag) Since the element stiffness depends on the axial force (in the case of 2nd Order Theory as well as for cable sag), the basic displacement method equations become non-linear. The equations defining the solutions for X 1 ...... X 9, which were proved to be linear for the creep case above, also become non-linear. An iterative approach must therefore be applied: The Simple Approach • •
Estimate X 1 ...... X 9, and use this estimate of the unknowns to find the variable stiffness which on substitution into the equations hopefully gives a solution which is close to the final behaviour. Correct the estimate of X 1 ...... X 9 and calculate again.
A Better Approach Use the tangent stiffness for calculating the influence of the application of a small increment to each unit loading case. The equations can then be transformed to define the iterative correction for X 1 ...... X 9 and a procedure such as the Newton Raphson method can be set up. The tangent matrix for the 2nd Order Theory or even large deflections (with respect to suspension bridges) can be similar to that usually applied in the “Large Deflection Theory”. E.g the corrective term N/L is added into the appropriate position in the element stiffness matrix. The cable sagging effects can be accommodated by deriving dS/d ∆x from the well known “Peterson Formulae” (Ref. 4). Where S means the Cable force and ∆x is the cable extension. Convergency is accelerated and guaranteed, when using the tangent matrix with the Newton Raphson approach as long as a real solution exists.
The Results from the sample analysis. This particular example was chosen not only to demonstrate the principles of analysis but also to demonstrate the effects of 2nd Order Theory and of creep on the structure. The results from a few selected points have been chosen for demonstrating these principles: Final Stage cable forces (kN) resulting from the different analyses Cables Posn E Posn F Table 1.
1st order theory & creep 1073.9 1000.8
2nd order theory – no creep 1079.8 1003.5
2nd order theory & creep 718.6 663.9
Initial Stage cable forces (kN) resulting from the different analyses Cables Posn B Posn I Table 2
1st Order Theory & creep 1775.52 1788.02
2nd Order Theory – no creep 1484.44 1468.22
2nd Order Theory & creep 1833.65 1840.82
Pylon Moments (kNm) resulting from the different stage analyses (design system) Construction stage 1 2 3 4 5 Final Table 3
1st Order Theory & creep -500.00 -471.0 -466.2 -463.1 -2151.6 -2019.0
2nd Order Theory – no creep -41 -32 -33 1493 -617 -617
2nd Order Theory & creep -503.0 -472.0 -464.0 -538.0 -2413.0 -1977.0
Pylon Moments (kNm) resulting from the different stage analyses (1st system) Construction stage 1 2 3 4 5 Final Table 4
1st Order Theory & creep 0 0 0 10492.4 10651.0 244.1
2nd Order Theory – no creep -
2nd Order Theory & creep 0 0 0 15657.0 15567.9 1126.0
Minimum Deck Girder Moment Envelope (kNm) (design system) Construction stage 1 2 3 4 5 Table 5
1st Order Theory & creep -4338 -4129 -4194 -3951 -3792
2nd Order Theory – no creep -4851 -4877 -4835 -5018 -5089
2nd Order Theory & creep -4347 -4223 -4228 -3982 -3819
Maximum Deck Girder Moment Envelope (kNm) (design system) Construction stage 1 2 3 4 5 Table 6
1st Order Theory & creep 1876 3232 2906 3675 3906
2nd Order Theory – no creep 1238 2420 2756 2860 3146
2nd Order Theory & creep 1935 3401 3098 3775 4018
These above results highlight: • The importance of accurate creep action assessment and shows that creep effects are critical to the structural integrity and must be accurately calculated and can not simply be assessed from some “arbitrary rules”. It can be seen that the creep in the deck affects the cable forces which in turn affect the deck and pylon moments significantly. The pylon moments are modified to such a degree that they are even reversed in construction stage 4. • The importance of consistent construction stage checks as the moments in the pylon, whilst being quite acceptable in the final stage are excessive in the construction stage under the 1st system of analysis. • The significant changes to the pylon moments caused by 2nd Order effects. (The pylon is highly compressed and therefore sensitive to additional moments from the deflected shape). • The easy parameter design check: • Whilst a solution to the 1st system of analysis was found, the pylon failure in construction stage 4 & 5 was easily identified. • Inspection of the 1st system showed that the translational fixity at the pylon was the cause of the excessive moments. Removal of this fixity proved to be an adequate modification to the design system.
Construction Stage Analysis – forwards or backwards? The traditional method of carrying out the construction stage analysis is to start at the “Final stage structure” and gradually reduce the structure (going backwards) stage by stage until the first construction stage is reached. It is argued that this method is the most likely to achieve the fastest result as it starts from a structurally correct solution - the final stage – which may possibly have been defined using the unit load method described above. Whilst this argument does have much merit, it falls down when problems are subsequently found at a particular construction stage. The check then reduces to a trial and error method. Using the proposed unit load method, the forwards or backwards solution are equally possible and equally simple as even the creep principles described above can be adapted for the backwards solution by solving “the equations” for ε0 instead ε1.
The Uddevalla Cable-Stayed Bridge A bridge which was designed using the principles described above is the Uddevalla CableStayed Bridge. This cable-stayed bridge is the central part of a continuous 1712m crossing over the Sunningesund waterway between Uddevallamotet north and Uddevallamotet south in Sweden. The approach viaducts, comprising twin steel box girders with a concrete slab, are rigidly connected to the main bridge on either side and provide overall longitudinal structural stability. The cable-stayed bridge portion comprises a 414 metre main span, symmetrical side spans of 179 metres and two 85 metre high (above the deck girder) diamond shaped concrete pylons which anchor the fan shaped stay cable arrangement. The stay cables, which support the bridge deck on either side, are anchored at 13.32 metre centres in the longitudinal direction. The bridge deck structure carries 6 lanes of traffic and comprises a composite, open steel grid structure with a 240 mm thick concrete top slab which spans longitudinally over the diaphragms. The deck edge beams (I type beams) also have a thin walled shell structure connected to the side which in addition to acting as a wind spoiler provides some torsional stiffness to the edge beams.
More comprehensive descriptions and details of the Uddevalla Cable-Stayed Bridge can be found in Ref. 4. Given below is a summary of the principles used in the analysis of the Uddevalla Cable-Stayed Bridge using the unit load method: The “Degrees of Freedom” (or unknowns) chosen for the unit load analysis were: • All the stay cables – a unit tensioning • Translation at one cable-stayed bridge pylon support ( “X” and “Y” directions) The Uddevalla Cable-stayed Bridge construction requires a 3 stage stressing procedure: Stage I stressing provides support for the new steel portion of the deck during assembly. The cables are initially stressed to provide support and to counteract excessive deflection before making the welded connection to the existing deck. Stage II stressing provides support for the whole structural self weight comprising the steel plus pre-cast concrete top slab elements. The procedure is simple as the stressing jacks from the previous stressing operation are still connected. The first Unit load analysis to find the cable forces is carried out at this stage. Stage III stressing is required for counteracting the superimposed dead load and creep effects on the pylon deflection. The procedure is required because the stringent minimal pylon moment criteria precludes a sufficient pylon pre-camber. The second Unit load analysis to find the retensioning cable forces is carried out at this stage. The “Ideal Moment diagram” chosen for the initial dead load is shown below together with a general bridge arrangement. Note the unusual shape in this “Ideal Moment diagram” in the deck girder was dictated by a strict limitation prescribed for the pylon moments which takes cognisance of the “very severe” environmental conditions for reinforced concrete weathering/corrosion. In order to comply with this stipulation, the “Ideal Moment diagram” had to include a minimal moment condition in the pylon.
Figure 3
Ideal Moment Diagram
Figure 4 The diagrams below show the time dependency of a few characteristic results from the analysis. The time axis is not to scale but shows a sequence of the different actions. Stages 1-16 are the cable tensioning and deck cantilevering stages. The deck construction is complete at the end of stage 16, the additional dead load is applied in stage 17 and stage 18 is for creep and shrinkage up to “time infinity”. Cable force variation in side span cables 5, 6, 7 and 8 (numbering from the pylon)
Figure 5 Main span moment variation at cable 2 north and cable 2 south (numbering from the pylon)
Figure 6
Moment variation in pylon at the top of the footing
Figure 7
References: [1] C. Hansvold, Sunnungesund Cable-Stayed Bridge, IABSE Symposium Kobe 1998 [2] Heinz Pircher, Finite Differences to simulate creep and shrinkage in pre-stressed concrete and composite structures, Proceedings of the Int. Conf. on computation Modelling of Concrete Structures, edited by H. Mang, N. Bicanic, R. De Borst, Pineridge Press 1994 [3] O. C. Zienkiewicz, R.L. Taylor, The finite Element Method, Fourth Edition Volume 2 [4] C. Peterson, Abgespannte Maste und Schornsteine Statik und Dynamik, Berlin: Ernst + Sohn 1970
Evolution of design trends in cable-stayed bridges
Miguel A. ASTIZ L. Fernández TROYANO Javier MANTEROLA Prof. Dr. Civil Engineer Dr. Civil Engineer Prof. Dr. Civil Engineer Carlos Fernández Casado S.L. Carlos Fernández Casado S.L. Carlos Fernández Casado S.L. Madrid, Spain Madrid, Spain Madrid, Spain Miguel A. Astiz, born in 1950, received his civil engineering degree from the Polytecnical University of Madrid in 1973.
Leonardo Fernández Troyano, born in 1938, received his civil engineering degree from the Polytechnical University of Madrid in 1963.
Javier Manterola, born in 1936, received his civil engineering degree from the Polytechnical University of Madrid in 1961.
Summary This paper presents an overall perspective of how cable-stayed bridge design has evolved during the last twenty five years. This perspective is supported mainly on the authors’ personal experience as well as on well known cases. Aesthetics, technogical advances both in structural analysis and materials, reliability improvements and increased public interest are considered as the factors which have developped an impressive activity in this field. At this point specific codes seem to be necessary to maintain the level of quality which has been reached until now.
1.
Introduction
Athough 40 years old, modern cable-stayed bridges have undergone a radical evolution along the last 25 years. Technological advances applied to analysis, materials fabrication and construction have driven the designers to face very different problems along these years. In fact, the design of a cable-stayed bridge is a rather standard activity nowadays while it could be considered exceptional a few decades ago. What are the reasons for such a change? Practice and experience are good reasons. Knowledge on cable-stayed bridges has progressed steadily; conferences and symposia on cable-stayed bridges are being organized and they get a great success. As a consequence of all this universal engineering effort, the world record for the span length has increased by a factor of about three in thirty years and, what is more important, the cable-stayed bridge has become a very common alternative to be considered when designing a new bridge. Our personal experience reflects this general trend. We entered into the cable-stayed bridge field in 1974 with the Glorias Catalanas footbridge in Barcelona and we had the opportunity to design, three bridges and nine years later, the Barrios de Luna bridge, a world record span length at the time. After this very rapid growth, the cable stayed bridge has become a common alternative in many of our projects. We will present in this paper a general perspective of how aesthetics, general structural design, codes, structural analysis, cable technology and construction methods may influence the design of a cable-stayed bridge and how the influence of these topics has changed along the last decades. The question to be finally asked refers to the relative importance of engineering and architectural concepts in the design of cable-stayed bridges.
2.
Bridge design
For a bridge designer, the bridge has to be seen mainly as a means for fulfilling a number of functional and safety requirements. Then the static aspects have to be present during the creative phase of conceptual design. This may not always be true and examples can be found where statics was not even considered during the conceptual design; the resulting bridge may badly engineered but it may also be a great architectural achievement. What is the reason for choosing a cable-stayed alternative? In some cases this is the obvious solution: there are no alternatives in a certain range of span lengths: roughly from 300 to 900 meters. But most of the cable-stayed bridges which are being built have a span length which is lower than 300 meters. At this stage the cable-stayed bridge has to be compared to other classical alternatives such as the girder or the arch bridge. Apart from economical considerations which are supposed to be the decisive arguments when we decide on the best alternative to solve an engineering problem, the cable-stayed bridge adds a bonus which is very difficult to evaluate: cable-staying opens a very broad field for crativity in the design of the towers and the cable system and, to a lesser extent, in the design of the deck. From a purely static point of view, the cable system is responsible for one of the most important changes which may be appreciated in the evolution of cable-stayed bridges: the multiple stay concept. At the beginning, the cable-stayed bridge was understood as a continuous girder which was supported at a limited number of supports by the cables; many years ago, engineers found out that it was much more effective to design many stays, located at small distances; as a consequence, the deck behaves like a beam on an elastic foundation and bending moments are reduced and better controlled during construction. An important side effect of this evolution is the increased aesthetical importance of the cable system. The fact that there are many cables allow the designer to shape new plastic effects while preserving the original static role of the cables. A very illustrative example can be found in the Ebro and the Lérez bridges [1] which were designed at a 20 year interval with the same concept for the pylon and for the static cable system but with different cable distributions. The Ebro bridge has two planar backstay systems while in the Lérez bridge the backstay system shape hyperbolic paraboloid surfaces. There are some reasons to explain the differences between these two cable systems: the Ebro bridge is a motorway bridge with important constraints with respect to the horizontal alignment of the carriageway while the Lérez bridge is located in an urban environment and there is a roundabout just behind the pylon where larger counterweights may be fitted. All these functional requirements still leave some room for to achieve an important visual impact in the Lérez bridge(fig. 1).
Fig.1. The Lérez bridge, Pontevedra, Spain (1996) A single tower seems to be a good departure point to produce new staying systems. In the Malecón footbridge [2] we combined a complex deck structural work (torsion combined with an arch effect in the horizontal plane) to hang it from one edge. In this way the stays define a surface which may be observed by the pedestrians who are crossing the bridge. The backstays oppose a radically different concept (fig. 2). Some of these ideas were also present in the
Glorias Catalanas footbridge. This is obviously not the most economical alternative to cross the river but it shows how it is possible to depart from classical solutions for a small budget increase (at least in footbridges and for small span lengths).
Fig.2. The Malecón bridge, Murcia, Spain (1996) The tower is the other important aesthetical feature of a cable stayed bridge. It complements the cable system and both are mutually dependent. As a matter of fact it is very difficult to consider both elements as separate entities either from the structural or from the aesthetical point of view. As pylons in cable stayed bridges are tall and many tension forces are applied on them at different points, the structural problem is by no means simple but the possibilities for asthetical expressivity are still high. The structural and the functional problems have made engineers to design different alternative arrangements: H-shaped towers for bridges with two planes of cables (fig. 3a), A (fig. 3b), inverted Y and diamond shaped towers both for single and double plane of cables and vertical pylons for any kind of bridges (fig. 3c). From a purely structural point of view, the inverted Y shape seems to be the most effective since it has been used in most of the major cable-stayed bridges recently built.
Fig. 3.
Tower design: a) Barrios de Luna bridge (1983); b) Sama de Langreo bridge (1986); c) Papaloapan bridge (1995); d) Bocairente.
As a matter of fact, the single vertical or slightly inclined pylon is a cable-stayed mast and this is one of the most stable structures which can be designed; the tent is a representative example. Spatial staying allows a perfect absorption of all the horizontal forces and it allows a large variety of cable arrangements (fig. 1). Only one aspect has to be kept in mind: the horizontal components of cable forces have to be balanced either at deck level or below to avoid expensive foundations. Nevertheless this is not a very restrictive constraint since there are many ways to comply with it. As the spans become longer, it is not possible to think in terms of truly spatial cable arrangements; it is still possible to maintain a certain degree of three-dimensionality by anchoring the cables on both deck edges and on the vertical pole of an inverted Y pylon as it is being done on the longest cable-stayed bridges. But at this point we may also discover the beauty of the single pole in such bridges like the Brotonne bridge. The pylon is usually subjected to moderate transverse forces and it can be designed as a free standing tower in the transverse direction. This idea has brought some great german bridges such as the well known Bonn Nord and Oberkassel. This solution may be extended to a double plane of cables alternative as in the Nordbrücke, in the Kniebrücke or in the more recent Queen Elizabeth II and Oresund bridges. Our Papaloapan bridge (fig. 3c, 4) is also an example of a cable-stayed bridge with unconnected vertical pylons; it is important to notice that this alternative was shown to be valid even in the presence of very significative wind and seismic forces.
Fig. 4. Papaloapan bridge, Mexico, 1995 An aspect which we consider very important in the design of the towers is the way to fit cable anchorages. If we want to enhance the design of the tower and its aesthetical relation with the cables, an effort should be produced to hide the anchorages as much as possible and to avoid any perturbation in the aesthetics of the tower. Many good ideas have been proposed along the history of cable-stayed bridges; a good example is the internal gallery of the Faro and Normandie bridges among many others.
In some of our bridges we have hidden the cable anchorages in vertical slots (fig. 5a, 5b). In another case we designed a steel saddle which was embedded in the tower concrete (fig. 5b) to serve as cable anchorage both for front and back stays. Another alternative for medium span bridges consists in making the cable continuous through the pylon and establishing the conection by means of an external tube (fig. 5c). In large bridges this is a minor problem since the dimensions of anchorages become negligible as compared to the tower dimensions. Nevertheless the structural and geometrical problems which arise when both cable fans cross each other inside the pylon still exist and the previously mentioned alternatives are good solutions to solve them. From a purely aesthetic point of view, the design of the deck is not as important as the design of the tower or the cable system. This is mainly an engineering problem. In this sense we only consider today two deck types: the closed box and the slab, either alone or on top of longitudinal edge girders, with or without transverse beams. The closed box is a somewhat universal solution since it is used both for edge stayed and for center stayed decks; although the shape depends on the staying system. It is probably a mandatory solution for long span bridges where torsional deck stiffness is necessary (Normandie, Tatara, Skarnsundet). For smaller spans, the slab is a very attractive solution since it allows a higher slenderness, as in the Evripos bridge (1/477), a simpler construction (either cast-in-place or prefabricated) and a good wind performance. The slab on edge girders combines the bending stiffness of the closed box and the possibility to concentrate longitudinal compression stresses in the line of action of deck anchorages. Although many of our first designs were closed boxes as in the Barrios de Luna bridge, most of our recent projects are slabs (fig. 6); the closed box is still necessary in those cases where the staying system requires a torsional contribution from the deck; these cross sections show a general trend towards higher slenderness (the Ozama bridge deck is heavier because it carries highway and railway traffic).
Fig. 5. Cable and tower interaction: a) Cross section of the Lérez bridge tower; b) Steel saddle of the Papaloapan bridge; c) Cable connection to the tower in the Ozama bridge.
Fig. 6. Deck cross section of a) Barrios de Luna bridge, b) Sama de Langreo bridge, c) Papaloapan bridge, d) Ozama bridge, e) Bocairente bridge Prefabricated decks can find very interesting applications in cable-stayed bridges. Prefabrication has already been used in many bridges but at a small scale. We begin to think in terms of large deck units which can be operated and assembled for short spans and for a reduced number of cable stays. Our Bocairente bridge (fig. 6e, 7) is an example of a radical use of prefabrication since the deck, the pylons and the struts are prefabricated. This also an example of how cable system and pylon design are related to define a unique concept both in terms of structural design and formal expression. Another important development which can be observed in the last decades is the growing applications of composite structures. The composite deck is specially well suited to the cablestayed bridge since it combines a good capacity for axial compression forces, lightness and many possibilities for prefabrication and for quick erection. Annacis, Houghly and Ting-Kau are good examples of such application. Another iteresting and completely different type of composite construction for the deck is the one which was used in the Normandie bridge where concrete was used in the side spans and in part of the main span. Applications of composite construction to pylons are also increasing mainly in relation with the interface between cables anchorages and tower concrete. Another possiblity which has been proposed as a way to limit the compression forces to be transmitted by the deck consists in designing the cable system in such a way that the deck would be tensioned in the middle of the span. This is a very attractive possibility for long spans but the erection process would be more difficult and cable forces would increase.
Fig. 7. Bocairente bridge, Spain, 1999.
The span length distribution is the origin of most differences between cable-stayed bridges. The ration of side span length to main span length has important consequences in terms of structural behaviour and aesthetics. Shorter side spans are usually necessary to increase global stiffness and for long spans; they also give to the bridge a more powerful character. Longer side spans create somewhat more equilibrated schemes; stiffness may be increased by means of intermediate supports and deck ballasting in the side spans. Span distribution is generally determined by topographical constraints and it gives to the bridge most of its identity.In this respect, the single pylon symmetric bridge is a possibility which has also been considered with very positive results (Isère, Alzette among others).
3.
Codes
There are no specific codes for cable-stayed bridges. We may qualify this situation as not surprising since it also happens with other bridge types. Twenty years ago the ASCE Recommendations [3] were a useful (although too simple) reference since the cable-stayed technology was relatively new for most engineers. The first topic which began to be worrying for engineers and administrations was long term cable behaviour with respect to fatigue and corrosion. The PTI Recommendations [4] were an effort to give an answer to this concern. These recommendations reflected the state of the art cable technology which was reached in the late seventies and they still are a good reference, specially with respect to fatigue problems [5]. The cable-stayed bridge field is still open to innovation and we find new ideas almost in any new bridge which is presented to the engineering community. It is very difficult to write standards for such structures and these standards would probably constrain new developments. Bridge engineers and administrations tend to consider the cable-stayed bridge as any other type of bridge; then loads and material specific design rules are the same as, for instance, in a girder bridge. This decision is reasonable since the present methods of analysis allow a very precise knowledge of stresses in any element of the bridge. In level by designing the concrete elements in agreement with, say EC2, and by limiting the cable stress to 45% of tensile strength, which is an old but generally admitted rule? What is the safety level against windinduced vibrations? Many questions are still unanswered. our usual mathematical models, cables are modelled by means of truss elements and deck and pylons are modelled by means of beam elements but all of them are treated in a similar way. The cable-stayed bridge is a complex structure and our models give us information on stresses in any part of it. Methods of structural analysis have also changed very significantly in the last two decades. The finite element method has become available for every engineer and not only for linear analysis but also for geometrical and material non-linear analysis. Partial factor methods based on reliability studies have become widespread and we now may use codes which are based on this approximation: CEB-FIP Model Code, Eurocodes, AASHTO LRFD Specifications. But for the cable-stayed bridge several questions arise. Are all these standards really applicable for a highly redundant structure? Do we get the same safety A good approximation to the safety problems may come from the use of the possiblities of structural analysis. Ultimate states can be modelled today and it has been done in real projects [6,7]. This is a rigourous method to define the safety level of any structure although it usually gives less conservative results that the application of standard design rules, specially for steel and composite structures. This approximation is being used with any kind of bridge to solve local and global problems. In the case of the specific problems of cable-stayed bridges, global ultimate state can be investigated in this way. As an example of such applications, the transverse stability of single pole pylons and decks may be studied on the basis of a fully nonlinear model (geometrical and material) with a higher accuracy and reliability than by trying to
define the bifurcation point through a linear model based on the geometric stiffness matrix [8]. Although the cable-stayed bridge is highly redundant, non-linear analyses as well as scale model testing [9] show that with the present design methods the cables would yield first in the ultimate state. The slender deck would reach its ultimate state soon afterwards. Nevertheless all these analyses show that the global safety factor is greater than 2, which is coherent with the design rules which are being used for the cables. This figure may seem too high but it somehow takes into account the uncertainty about the long term behaviour of the cables. Another point of raising concern is the possibility of a local buckling problem in the deck which could trigger a global instability of the whole bridge (obviously in steel or composite decks). Such possiblity should be considered by a modification of the corresponding partial factors. The cable-stayed bridge has also some specific properties which should be considered in the codes. One of them is the dead load control. The construction method which is mostly used includes a very precise control of cable stresses and dead loads; a small error in the deck dead load will be detected immediately through the cantilever vertical displacements and the top of pylon horizontal displacements. In such circumstances, the partial factor to be applied to dead load should be close to unity, as it has been done for the Oresund project. In relation also with the balanced cantilever method of construction, some standards consider an unbalanced live load to be applied during construction; sometimes this unbalanced load is a small fraction, say 5% or even 2%, of total dead load. This unbalanced load may be caused by temporary construction loads but this possibility can be avoided through a tight control on site and any unbalance would be detected through vertical displacements of the deck. Anyway some stiffness has to be provided against this effect to take into account wind forces; for such effect, a buffeting analysis or a reduced vertical load could solve the problem. The AASHTO/ASBI Specifications for Segmental Bridges are a good reference although not specifically written for cable-stayed bridges [10]. Reliability analyses are necessary at this point to define well founded values for these unbalanced loads. Cable-stayed bridge design and analysis is quite well known by now and, in spite of this fact, it is still an open field with almost no standards. It is necessary to build an international effort to reflect this accumulated knowledge in a code which might serve as a worldwide reference.
4.
Cable technology
The reliability increase of the cables is one of the factors which may be responsible for the present day development of cable-stayed bridges. All the cable fabricators proposed in the seventies anchoring systems to avoid transmitting live loads through jaws. They obtained a good success by filling the anchorage with some propietary compound which allows direct transmission of variable loads to the structure of the anchorage. The possible corrosion problems were dealed with two alternative solutions: either by using locked-coil galvanized cables or by protecting the cables with a polyethilene duct filled with mortar. The second solution has been giving good results as we had the opportunity to test the cables of the Las Glorias footbridge when it was dismantled 20 years after construction to move it to another location [11]. We are also presently involved in the process of changing one locked-coil cable of the Ebro bridge to analyze it and to define its present condition. Today other alternatives exist: stainless steel tubes, individually coated strands, two and three level protection systems. Individual protection of the strands has a major advantage since it avoids local damage when handling the cables and increases fatigue resistance of steel. We can say today that long term behaviour of the cables is no more a source of concern provided
we use the right alternatives. All the problems suffered by the cables have not only brought an important technological lap from the fabricators; today bridge designers have to leave open the possibility of changing the cables. When long term behaviour of the cables will be known more precisely, changing the cables will be either avoided or considered as a normal maintenance operation to be done at very long time intervals. A problem which is still not completely solved comes from cable vibrations. The use of dampers (Brotonne, Sunshine Skyway) is opposed to the design of a net of transverse wires (Normandie) although the design rules for such transverse system are still not clear; cable fabricators are beginning to develop new connection systems which make these complex cable systems easier to build and more reliable. In any case none of these is probably the optimum solution; research on aerodynamic devices (protuberances) seems more promising since it tries to fight the cause of the problem and not its effects.
5.
New applications
As in any active field, new applications arise every day. Many of them are architectural. Others are new engineering solutions. Both of them are interesting. As engineers, we should understand that the public interest on cable-stayed bridges is partly due to the input of architects. In any case we will focus here on the engineering solutions. The cable-staying concept may be undestood as a kind of external prestressing. We have recently built at Osormort (Spain) a continuous concrete girder bridge with eleven, 40m long, spans; each span is stayed by creating a sort of vertical pylon in the center of the span, underneath the deck (fig. 8). The stays are anchored at the deck, close to the piers. This solution allows a very slender deck design (1/25) and it is very effective to support the dead load, which is an important part of total applied load. As cable stress is almost constant, standard prestressing steel cables are used instead of stay cables. A new field for application of cable-stayed bridges may be perceived from this example. Extradosed prestressing generates a kind of bridges which are formally similar to cable-stayed bridges but with some important structural differences. The most important comes from the fact that cables are not very effective in supporting live loads and, consequently, stress variations are small; this fact allows higher working stress levels [13]. This type of application seems to be very promising for medium range continuous girders (120 to 150 m span) where the cable system may be understood mainly as a way to create a variable depth cross-section; these cables would only help in supporting the dead load but they would allow a significant reduction in the girder depth and weight. The Bocairente bridge which was shown before (fig. 7) may be an example of such application. There is still an open field for innovation between the girder bridges and the cable-stayed bridges. We are presently building a bridge with a 180m long main span(fig. 9) where the towers are lower than usual (h/l=1/6.6). This is not an extradosed bridge; the reason for such a design is mainly a search for formal compatibility with an older suspension bridge which is located nearby.
Fig. 8. Osormort bridge, Spain, 1995
Fig. 9. Ozama bridge, Dominican Republique, 1999 Among some of the projects we are working on, we find interesting a proposal for a multispan cable-stayed curved bridge. Transverse cable forces are balanced by means of a stay connecting the pylon top to the outside edge of the deck. But, to enhance the curved character of the bridge, we have leaned the tower outwards (fig. 10). This tower inclination slightly helps in balancing cable forces but we find that it offers a new perspective of the cable system and its relation with traffic on the deck. Finally every designer has many proposals which were formulated at some time and were not accepted or did not win the design competition. It happened because they were not costeffective or because they were judged too risky or, simply, because they were not the best. Nevertheless many of them are interesting and their only defect is not being born. We could find real treasures of imagination in many of these unknown projects and they will probably arise as new cable-stayed bridges will be built.
Fig. 10. Proposal for a curved multi-span cable-stayed bridge.
6.
Conclusions
Cable-stayed bridge design has already arrived to what we could call a classic period. General design parameters and techniques are well established. There is still room for innovation and this fact is very challenging for engineers. This type of bridges has attracted general public interest and as new bridge design and construction is partly becoming a social or political event, we may be entering into a baroque period, specially for the short span range. Contributions from architects may seem disturbing for many engineers but they should be looked with interest since they bring a new insight into a problem which we, as engineers, tend to see mainly as a statics and optimization problem. Very often the client, a public administration (and, by this way, the society) is not asking for the optimum solution in engineering terms, but just for good design. We should try to fulfill these demands. At this point it is very important to define some rules for design to keep cable-stayed bridges as safe as they have been till now.
References [1]. Fernández Troyano L, Manterola J. & M.A.Astiz, ", “The Inclined Towers of the Ebro and Lérez Bridges”, Structural Engineering International, 4/98, 258-260, 1998 [2]. Fernández Troyano L. & Manterola J., “Spatial Cable-Stayed Bridges”, Spatial Structures:Heritage, Present and Future, de. G.C.Giuliani, SGE, Milan, pp. 1019-1026 (1995) [3] ASCE, “Tentative Recommendations for Cable-Stayed Bridge Structures”, Proc. ASCE, Journal of the Structural Division, 103, ST5, 929-959, 1977 [4] PTI, “Recommendations for Stay Cable Design, Testing and Installation”, Post-Tensioning Institute, 1990 [5] Elices M, Llorca J. & Astiz M.A., “Fatigue of steels for concrete reinforcement and cables”, in “Handbook of Fatigue Crack Propagation in Metallic Structures”, ed. A. Carpinteri, Elsevier, 1994. [6] Kovacs I., Svensson H.S. & Jordet E., "Analytical Aerodynamic Investigation of CableStayed Helgeland Bridge", Journal of Structural Engineering ASCE, 118, 147-168, 1992. [7] Biwer R., Crémer J.M., Hubert F. & de Ville de Goyet V., “Cable-Stayed Bridge upon Alzette”, . ", Proc. Conf. Cable-Stayed and Suspension Bridges, Deauville, 413-420, 1994 [8] Ren W.X., "Ultimate Behavior of Long-Span Cable-Stayed Bridges", Journal of Bridge Engineering, ASCE, 4,No.1, 30-37, 1999 [9] Walter R., Houriet B., Isler W. & Moïa P., "Cable-Stayed Bridges", Thomas Telford, 1988 [10] AASHTO/ASBI, "Guide Specifications for Design and Canstruction of Segmental Bridges, American Segmental Bridge Institute, 1998 [11] Fernández Troyano L, Manterola J. & Astiz M.A., "Footbridge of the Glorias Catalanas, Barcelona", FIP Notes, 1996/2, 13-14, 1996 [12] Matsumoto M, Hikami Y. & Kitazawa M., "Cable Vibration and its Aerodynamic/Mechanical Control", Proc. Conf. Cable-Stayed and Suspension Bridges, Deauville, 439-452, 1994 [13] Ogawa A., Matsuda T. & Kasuga A., “The Tsukuhara Extradosed Bridge near Kobe”, Structural Engineering International, 3/98, 172-173, 1998
Aerodynamic and Structural Dynamic Control System of Cable-stayed Bridge for Wind Induced Vibration Masao MIYAZAKI Gen. Mgr, Steel Struct.Group Sumitomo Heavy Industries Co., Ltd. Japan
Masao Miyazaki, born 1948 received his Dr. Eng. from the University of Tokyo in 1991. Since 1976 he has been acting as a researcher in the aerodynamic design field of bridges and steel structures. He is head of Bridge Eng. Division of. Member of JSCE, JSSC and JSWE.
Summary This paper reports on the wind endurance and vibration control measures for the tower and cables of a 325 meter-long continuous three-span steel cable-stayed bridge with a central span of 175 meters. Deflectors were installed on the tower where horizontal members were omitted due to design requirements, and aerodynamic vibration control measures by the use of U-stripes were taken for the cables that were likely to be subject to rain vibration. It was so arranged that both measures should be maintenance-free.
1. Introduction This is a continuous three-span steel cable-stayed bridge with a central span of 175 m and a side span of 75 m. Since the location is a scenic spot in Seto National Park, attentive consideration was given from the viewpoint of landscape. And finally a cable-stayed bridge based on the image of a bow was adopted. The towers and side spans were constructed in large blocks by the use of a floating crane while the center span was installed by the cantilever method.
Figure 1 General Drawing of the Bridge
2. Vibration Control Measures for the Tower The stability of the tower against winds both during construction and after completion was examined through wind tunnel testing. It is often considered that the tower is relatively free of problems in terms of wind endurance after completion due to this bridge size. However, it has only recently been learned that intentional omission of horizontal members in this type of bridge will considerably reduce wind endurance.
Figure 2 Shapes of Tower and Deflector Based on the results (Figure 3) of the wind tunnel testing, it was predicted that the tower of the completed bridge would be subject to galloping due to wind in the direction of the bridge axis, i.e., at right angles to the tower, when the wind velocity exceeded about 18 m/s. This is a socalled destructive vibration, which diverges quickly. When structural damping was increased, the responses moved into vortex-induced vibration in the low wind speed range and galloping in the higher one. When the structural damping increased to 4% in logarithmic terms, both types of vibration were almost completely suppressed at wind velocities below the design wind speed. As vibration control measures against galloping, changes in the shape of the tower or in the crosssectional shape of tower poles or installation of dampers are proposed. It was decided to install deflectors at four corners of the tower out of consideration for landscape design, influence on the substructure, and ease of future maintenance. The shape of the tower legs and optimum intervals between them were determined by means of wind tunnel testing. In the experiments, the weights of the girders and cables were taken into account as factors affecting vibration, in addition to the weight of the main tower. The results (Figure 4) of the experiments showed that deflectors installed at a distance of approximately 40% the tower height from the top will ensure the necessary wind endurance for the completed bridge.
Figure 3 Vibration of Completed Bridge (without vibration control measures)
Figure 4 Vibration of Completed Bridge (with vibration control measures) The cantilever method was employed for the construction of the main girder in the center span of this bridge. When this construction method is used, the typhoon season is generally avoided if wind endurance comes into question. It is unavoidable, however, that the tower should stand in isolation for a certain period of time. In this state, it is expected that galloping, i.e., in-plane vibration of the tower at right angles to the bridge axis, will be generated under the influence of the wind in the direction of the bridge axis. This situation is avoided in advance by the installation of deflectors, which are usually installed on completed bridges. On the other hand, it was predicted that the wind at right angles to the bridge axis would generate vortex-induced vibration due to bending motion in the direction of the bridge axis at around the wind velocity of 10.5 m/sec to 12.6 m/sec, creating stresses in excess of the resisting moment at the foot of the tower. However, this vibration is suppressed when two lower side cables are installed, increasing the mass that works against the aerodynamic force to damp the vibration associated with aerodynamic instability. Therefore, two small passive tuned mass dampers (TMD) were installed at each tower top to control the vibration while the tower stands in isolation during construction. In designing the TMD, the allowable amplitude of the tower, defined in terms of acceleration tolerance,
was assumed to be 50 gal during work, and 300 gal in a non-working condition according to the standards adopted by Honshu-Shikoku Bridge Authority. The variables
such as damping forces necessary for the design of the dampers were determined by wind tunnel testing. The damping effect was verified through experiments during construction.
Figure 5 Results of Wind Tunnel Test (Sc-A Diagram)
Figure 6 TMD for Tower during Construction
Figure 7 Deflector for the Tower of the Bridge completed
3. Vibration Control Measures for Cables 3.1 Aerodynamic Vibration of Cables It is well known that vibration of cables on cable-stayed bridges poses problems. Vibrations generated on cables are classified as follows according to the mechanisms of their generation.(1)Vortex-induced vibration, (2)Wake galloping, (3)Rain vibration Vortex-induced vibration, which is induced by trailing vortices of cables, and wake galloping, which is generated when downstream cables are placed in the wake flow of upstream cables arranged in parallel, have been known for a relatively long time. Of these, wake galloping was studied only in relation to power transmission lines where distances between cables were as large as 10 to 20 times the cable diameters [2] [3]. The wake galloping that occurs on cable-stayed bridges is characterized by relatively small cable-to-cable distances of less than 6 times the cable diameter. On the other hand, rain vibration, which is associated with aerodynamic instability, was first recognized during the construction of major cable-stayed bridges in Japan such as Meikonishi Bridge and Iwaguro-Jima Bridge and later observed on cables of many cable-stayed bridges [4] [5]. Such aerodynamic vibrations are generally caused by strong winds that involve rain. Although vibration of a large amplitude was also observed on Higashi-Kobe bridge in high winds without rain [6], it is distinguished from rain vibration. Regarding the vibration of cable-stayed bridges associated with aerodynamic instability, it is possible to devise control measures by clarifying the mechanism of their generation. Thus, vortex-induced vibrations may basically be controlled by suppressing the generation of trailing vortices or by disturbing the simultaneity of flow separation. However, the mechanisms of wake galloping and rain vibration (including similar vibration generated by winds without rain) still remain to be clarified. 3.2 Rain Vibration Rain vibration is a type of aerodynamically induced vibration, whose occurrence has recently been confirmed on cable-stayed bridge cables coated with polyethylene tubes. Typically, it is generated in high winds with rain. Its characteristics appear to differ from those of vortexinduced vibration and wake galloping. The actual bridge where rain vibration was first observed in Japan was Meikonishi Bridge, a 758 m long cable-stayed bridge with a central span of 405 m [7]. The cables on this bridge weighed 5.1 kg/m after grouting and their logarithmic decrement • of vibration was approximately 1%. The cables were 125 to 165 mm in diameter with typical cable diameter being 140 mm. Formerly, it was thought that several conditions must be satisfied for vibration to occur and that rain vibration would occur only under extremely limited circumstances. The conditions of vibration occurrence that were known then include: (1) Vibration is generated on cables that have a downhill grade in the wind direction, its amplitude reaching a maximum when the wind blows at an angle of 45 degrees to the surfaces of the cables. (2) For occurrence of vibration, it is indispensable that rivulets (small stream) of rain should be formed flowing down the top and bottom surfaces of the cables.
(3) The vibration is an in-plane vibration (oscillations in the inner direction of the cables) in a relatively lower mode and has a larger amplitude than vortex-induced vibration. (4) The rivulets vibrate together with the cables. (5) The formation of rivulets is affected greatly by the conditions of cable surfaces, wind velocity, wind direction, and rainfall. Since the formation of rivulets, especially on the top surfaces of cables, was indispensable for generation of vibration, it was thought that vibration similar to galloping was generated due to asymmetry of the burble point and relative motion of the elevation angle when the flow separates from the rivulets on the top and bottom surfaces. Later, along with the progress of studies on the characteristics of rain vibration and on the mechanism of vibration generation, vibration control measures changed form structural dynamic measures (which suppress vibration forcefully by dampers and the like) to aerodynamic measures (which try to eliminate the source of vibration). The first such measure was the parallel protrusion method employed for Higashi-Kobe Bridge. However, it was replaced by hydraulic dampers and viscous shear dampers because of its high cost of fabrication and difficulty of construction. Rubber with high damping capacity came into use to avoid installation of awkwardlooking dampers on cable-stayed bridges, which attach importance to landscape. Even in this case, the fact that physical properties of rubber depend on temperature presented a problem. However, this problem has largely been solved. 3.3 Vibration Control Measures for Cables the Bridge Aerodynamic vibration control measures were used for the top-layer cables, which are most liable to rain vibration because of their length and diameter. Regarding other cables, rubber dampers with high damping capacity were installed at the tips of anchor tubes of the cables in the middle three layers where there remains possibility of rain vibration. In a vibration experiment, •= 0.02 to 0.03 was achieved by the rubber with high damping capacity.
Figure 8 Aerodynamic Vibration Control Measure for Cables One of the distinguishing features of rain vibration is the formation of rivulets on the top and bottom surfaces of cables. The existence of rivulets appear to be closely related to the generation of vibration and their effects can be examined through reproduction of rain vibration in a wind
tunnel by the use of the equipment shown in Figure 9. Figure 10 shows the results of an experiment and formation of rivulets when water was applied to the top and bottom surfaces of cables. The cables used were 3 m long and 150 mm in diameter. To make it easier to check the effect of Scruton numbers, cables lighter than actual ones were used. It can be seen from the Figure 10 that rain vibration started to occur at wind velocity of around 9 m/s. The vibration increased its amplitude sharply with increase in the wind velocity. However, observation was made only up to a wind velocity of 20 m/s. And no properties were observed from that point on. This resulted in a serious lack of information, which fact was learned later. For clarification of phenomena encountered for the first time, sufficient consideration is necessary. As shown in the figure, rivulets form only on the bottom surfaces of cables in low winds and they form both surfaces of cables only when the wind velocity is sufficiently high. This indicates that rivulets form in such a way as to counterbalance the wind pressure.
Figure 9 Cable Model Installed in the Wind Tunnel
Figure 10 Relationship between Wind Speed and Formation of Rivulets While one might be tempted to conclude that formation of rivulets on top and bottom surfaces of cables is the necessary and sufficient condition for the generation of rain vibration, actually the phenomena of aerodynamic instability are often very complicated. So is rain vibration. An example of aerodynamic force generated is shown in Figure 11. Under the circumstances where rain vibration is generated, the aerodynamic force is 2% at the most in terms of the logarithmic
decrement although it has a small amplitude. This is important when considering the vibration control measures for cables as described later.
Figure 11 Aerodynamic Force in Rain Vibration
Figure 12 Drag Coefficient and Reynolds Number
3.4 Mechanism of Vibration Damping [8] [9] In this method, the polyethylene tubes that coat cables are provided with V-groove stripes (Ustripes). The damping effect of U-stripes on the vibration associated with aerodynamic instability is understood as follows. (1) Damping of vortex-induced vibration: U-stripes act as surface roughness to raise an apparent Reynolds number up to the supercritical Reynolds-number region. As a result, the Karman vortices that existed in the wake flow area in the subcritical Reynolds-number region disappear, and thus generation of vortex-induced vibration is restrained. (2) Damping of rain vibration: The effect of surface roughness raises an apparent Reynolds number up to the supercritical Reynolds-number region, shifting the burble point further downwind than the subcritical Reynolds-number region. Consequently, pressure distribution on the surface changes due to reattachment, preventing the formation of rivulets. Apart from this, the U-stripe grooves forcefully guide the water flowing down the cable surfaces, preventing rivulets from forming in particular places.
4. Conclusion This paper reported on the stability of the cable-stayed bridge against winds. The vibration control measures designed for the bridge based on the results of wind tunnel testing are summarized as follows. (1) For the tower, deflectors were installed to protect the completed bridge against galloping and tuned mass dampers (TMD) were used to restrain vortex-induced vibration during construction. (2) For the cables, U-stripes were provided in the surfaces of the polyethylene tubes on the toplayer cables as countermeasures against rain vibration while rubber with high damping capacity
was installed on the middle-layer cables. No vibration was observed on the bridge under construction or the completed bridge.
References [1] "Design, fabrication, and construction of Yuge Ohashi Bridge." Sumitomo Heavy Industries Technical Report, 1995. 11 [2] Simpson, A "Stability of subconductors of smooth circular cross section." Proc. The Institution of Electrical Engineers, Vol. 117, pp. 741 - 750, 1970 [3] Simpson, A. and T. V. Lawson "Oscillations of twin power transmission lines." Proc. Wing Effects on Buildings and Structures, Vol. 2, 1968 [4] National Land Development Technology Center "Research report on wind endurance of cable-stayed bridges." 1989. 2 [5] Civil Engineering Research Center "Reports on vibration control measures for long-span cable-stayed bridges." 1993. 3 [6] Matumoto, M., Y. Hikami and M. Kitazawa "Cable vibration and its aerodynamic/mechanical control." in Cable-stayed and suspension bridge (Deauville), 1994. 10 [7] Higami, S. "Rain vibration of cable-stayed bridge cables." Journal of Wind Engineering , No. 27, 1986 [8] Miyazaki, M. "A study on distribution of wind pressure acting on bridge structure and wind endurance." dissertation at Tokyo University, 1990. 12 [9] Miyazaki, M. "Aerodynamic control method for vibration of bridge cables." 1st Inter. Con. Struct. Control, 1995.7
Seismic Design for The Cape Girardeau Cable-Stayed Bridge Steven T. HAGUE Prof. Eng. HNTB Corporation Kansas City, MO, USA
Steve Hague was born in 1959, earned his Bachelor and Masters degrees at Texas A&M University and is a licensed Professional Engineer
Summary In 1927, the Missouri Highway Department, now the Missouri Department of Transportation, constructed a 1450-meter crossing of the Mississippi River near Cape Girardeau, Missouri. Now this two lane bridge is scheduled for replacement with a new four lane cable-stayed structure. The proposed structure has an overall length of 1206 meters, and was designed in both concrete and steel alternatives for competitive bidding purposes. The main span unit is comprised of a three-span, 636-meter cable-stayed unit with a 350-meter navigation span. The approaches are of typical steel plate girder construction.
Figure 1 This new bridge is located within the New Madrid Seismic Zone, the location of three of the largest seismic events to occur within the interior of a tectonic plate and the site of the most violent series of earthquakes ever recorded, and is a candidate to experience a significant earthquake within its design life. Although not actually recorded, studies of the available data indicate that the events of the winter of 1811-1812 had surface wave magnitudes (Ms) of about 8.6, 8.4, and 8.7 and it is suggested that the recurrence interval of magnitude 8 earthquakes in this region is approximately 550 to 1200 years. In addition to the probability of a significant earthquake, the geology of the site may be characterized as having deep, liquifiable soils which are subject to frequent flooding and the
potential for extensive scour. These site conditions, combined with the significance of the design earthquake event, generated some unique design challenges. The design issues presented will demonstrate the methodology used to consider the significance of the design earthquake, the site specific ground motion, and the effect of liquefaction and lateral spreading forces on this structure.
Introduction Although often overshadowed by the seismicity of the American west coast, the New Madrid, Missouri region is a very real and significant seismic threat to the midwestern region of the United States. The general public, even if aware that earthquakes often occur in the central United States, does not readily admit the potential destruction that would follow a major event. Fortunately, state departments of transportation, the U.S. Federal Highway Administration (FHWA), and many local building code officials are acutely aware of the risk and the damage - in terms of loss of life as well as economic losses - which would follow even a moderate event in the New Madrid region. New structures are now designed in accordance with current seismic guidelines developed from observation of structural behavior during earthquakes and millions of dollars worth of research. However, both the research funding and empirical evaluations focus on conventional structures. In this paper, we will look at a bridge structure which is somewhat outside the norm for earthquake design and the methods used to ensure that the structure is as capable of resisting seismic loading as our current state of knowledge will permit while maintaining the reliability that the travelling public has come to expect from its infrastructure.
The Project The relocation of Missouri Route 74 - Illinois Route 146 will cross the river approximately 200 meters downstream of the existing bridge at an angle of approximately 15 degrees to the direction of flow. The proposed structure has an overall length of 1206 meters and is comprised of a three-span, 636-meter steel/concrete composite cable-stayed unit and 570 meters of conventional steel plate girder approach structure. The main span unit will be a 4lane, symmetrical cable-stayed unit supported by two planes of cables 28 meters apart. The cables are attached to the steel edge girders at a uniform spacing of approximately 10 700 millimeters. The Illinois approach structure has 11, 52-meter steel plate girder spans supported on concrete piers and founded on deep, large diameter drilled shafts. The city of Cape Girardeau, Missouri is located within the New Madrid Seismic Zone, the location of the most violent series of seismic events ever recorded and is a candidate to experience a significant earthquake within the not so distant future. Studies of the available data indicate that the three most significant events of the winter of 1811-1812 had surface wave magnitudes (Ms) of about 8.6, 8.4, and 8.7. It has been suggested that the recurrence interval of magnitude 8 quakes in this region is between 550 and 1200 years.
P ro je c t L o c a tio n
Figure 2 In addition to the probability of a significant earthquake, the geology of the site may be characterized as having deep, liquifiable soils which are subject to frequent flooding and the potential for extensive scour. These site conditions, combined with the significance of the design earthquake event, generated some unique design challenges for both the structural and geotechnical engineers.
The Site The Mississippi River is one of the world's great rivers. Flowing with commerce; it provides a major transportation corridor for inland barge traffic and generally contributes to the economy of the entire midwest. The Mississippi River flows for some 3600 kilometers, draining approximately 40 percent of the continental United States. At St. Louis, Missouri, the Mississippi is joined by the Missouri River, the longest river in the U.S., which adds approximately 1800 m3/s to the average discharge of the river. Near Cape Girardeau, Missouri, the Mississippi River drains more than 1 850 000 square kilometers spread over twelve states and three Canadian provinces. At the site, the channel is 600 meters in width with a 1100-meter wide floodplain. The floodplain is bounded by high bluffs on the west and controlled by a levee on the east. The river is also a significant route for inland shipping with some 75 million tonnes of cargo shipped through the region annually.[1] This cargo is transported in barge tows up to 370 meters in length; typically comprised of up to a dozen barges, tied three across, and powered by a single tug. Therefore, the navigation requirements for this location are critical as demonstrated by the U.S. Coast Guard requirement for a channel width of 250 meters normal to the flow of the river. By establishing the navigation span at 350 meters it was possible to achieve considerable savings in the foundations by not having to construct a major foundation in the deepest section of the Mississippi River channel. In addition, a privately owned drydock facility is located immediately adjacent to the project right-of-way, downstream of the bridge and an added benefit of the longer span was to continue to allow access to the drydock.
Scour At Cape Girardeau, the 5-year flood discharge is over 17 000 m3/s at a mean velocity of about 2 m/s. However, at times the discharge may be as much as 32 300 m3/s with an average channel velocity approaching 3 m/s. Several hydraulic models were developed using the U.S. Army Corps of Engineers HEC-2 computer program. The models utilized the velocity distribution and normal bridge routines to generate the water surface elevations, flow depth, and stream velocity. The FHWA publication "Evaluating Scour at Bridges," HEC-18, was used to predict scour for both the 100-year and 500-year flood frequencies. The scour analysis indicated that the total scour depth, defined for this project as the sum of the effects of long-term scour (aggradation/degradation) and local scour, may be as much as 15 meters near the main channel and up to 8 meters near the Illinois levee. Since the new bridge will span from the east levee, near the existing bridge abutment, to well beyond the west bank, it was determined that the contribution of contraction scour to the total scour value would be negligible.
Site Geology Geologically, the project is located on the eastern edge of the Ozark uplift and the southwestern boundary of the Illinois basin. The bedrock formations at the site are mostly limestone, with minor amounts of shale, upon which the new bridge is to be founded. The limestone is overlain by a granular, liquifiable material to a depth of approximately 25 to 30 meters. Although the area is heavily faulted, the faults are considered to be inactive. The bridge is located within approximately 80 kilometers of New Madrid where there is a significant probability for a devastating earthquake within the next few years. During the series of events of 1811 and 1812, there were more than 200 moderate to large earthquakes and some 2000 total events with well documented evidence of liquefaction and having effects being felt as far away as Washington, D.C. [2]
Design Criteria The Bill Emerson Memorial Bridge represents a significant investment of public funds, and as such, required that the Missouri Department of Transportation (MoDOT) develop a design criteria to protect the travelling public, both roadway and navigation traffic, and their investment against those external events which could reasonably be expected to occur. Additionally, the criteria recognizes the importance of the structure to the economic wellbeing of the region as well as the difficulty of certain types of post-seismic repair. Therefore the general criteria for the bridge were established as follows: provide for six lanes of AASHTO HS20-44 (modified) live load provide minimum navigation clearances of 250 meters normal to the flow of the river and 18 meters above the 2 percent flowline protect against barge impact based upon a 365-meter tow, travelling at 5 meters per second at the 2 percent flowline elevation
design for the 100-year scour condition, with only one-half of the anticipated scour during earthquake design design for earthquake forces in accordance with the "Geotechnical Seismic Evaluation" report provide for operation of the structure following the design event resist seismic forces in the tower piers within the elastic range
Design Earthquake The New Madrid region has been the most seismically active region of central and eastern North America. The events of the winter of 1811-1812 are well documented and have been the subject of a significant volume of research over the years. Nuttli's study [3] of the damage and felt effects of these events indicates that the surface wave magnitudes were on the order of 8.5. Other studies have reached similar conclusions regarding the magnitude of that series of events. Between 1813 and 1990 over 23 earthquakes having magnitudes of 4.5 or greater were documented in the New Madrid area. [4] By using a map of acceleration contours having a 90 percent probability of not being exceeded in 250 years, it can be shown that the peak rock acceleration at the site is approximately 0.36g. Based on input from the project design team, MoDOT selected this as the design event and, considering that Ms 8 or larger events are anticipated every 550 to 1200 years, [5] the design earthquake is essentially a repeat of the 1811 and 1812 events. Woodward-Clyde Consultants, the project seismic subconsultant, then developed response spectra for the site based on published data for the central and eastern U.S. with the peak rock acceleration of 0.36g. Exploratory borings were made and shear wave and compression wave velocity tests conducted. The results of these investigations were used to develop three separate spectrum compatible site specific acceleration time histories for the seismic analysis of the bridge. These time histories were derived from the 1985 Michoacán, Mexico (Mexico City) earthquake and the Val Pariso and Pichulema records of the 1985 earthquake in Chile. These records were selected for their epicentral distances and the magnitude of the recorded event; however, these events do not necessarily represent a large earthquake on a continental intraplate source. The time history files provided were in the form of accelerations, given as a fraction of gravity, over a period of about sixty seconds. These time histories were established for two orthogonal directions with consideration given to the directional uncertainty of the design event. These files also included the effect of spatial incoherency and the phased effect of the ground motion due to the piers being located over such a long expanse. Although the vertical component of the design earthquake was not directly considered it was included in the model by applying a percentage of one of the horizontal accelerations in a vertical direction simultaneously with the separate horizontal components. In addition to the rock accelerations, Woodward-Clyde generated surface spectra which included the soil amplification effects of the soils along the Illinois bank of the Mississippi River.
Liquefaction and Lateral Spreading As previously noted, the Illinois side of the site consists of some 30 meters of alluvium; primarily loose to medium-dense sands. Both the comprehensive geotechnical investigation and the investigation conducted to evaluate specific geological conditions related to the seismic evaluation for the bridge revealed Standard Penetration Test (SPT) blow counts as low as 4 with only thin seams of material having blow counts above 16 in the upper 25 to 30 meters of alluvium. With these poor soil conditions and the high level of shaking which is expected to occur during the design earthquake, widespread liquefaction is anticipated to a depth of up to 25 meters below grade. In addition to the liquefaction, lateral spreading is also anticipated. The gently sloping banks, especially between the main channel and the levee on the Illinois shore, could flow as much as 3 meters toward the channel while in a liquefied state. Clearly this will produce large horizontal forces on the bridge foundations at a time when there is little lateral support.
Preliminary Design As with all projects, the design process for a bridge of this magnitude is an iterative one, requiring multiple revisions and redesign of many components along the way. Because of the location of the bridge, and the potential for a significant earthquake, the design team attempted to minimize backtracking by working with the seismic subconsultant at the earliest stages. After the development of the basic structural concept, input from the seismic engineers was necessary to confirm the preliminary design and to prepare the models for final design analyses. It was noted that liquefaction presents little problem for the cable-stayed unit since the three supporting piers are founded on huge footings keyed into rock; however, the approach spans are considerably different. As noted earlier, these foundations are located in an area with very deep, highly liquefiable soils. When combined, the liquefaction and the depth of anticipated scour eliminated spread footing type foundations from consideration. After extensive studies of various soil improvement techniques, it was determined that any soil improvement would be ineffective due to repeated degradation and aggradation of the channel. Thus, the early input from the geotechnical engineers permitted the elimination of both spread footings and driven steel piles as viable foundation alternatives and led to the selection of large diameter drilled shafts socketed into rock.
Design Methods It was obvious at the earliest stages of design that the governing load case would be a combination which included earthquake forces. Other combinations, those including scour and barge impact, were also considered significant but not viewed as potentially governing the design of the bridge. Due to the large number of seismic related load combinations, those combinations with and without scour and those with and without liquefaction, it was
determined that the design would be for one event only, with a final force check with the two secondary events. The computer program used for the analysis of the structure, T187, was developed by HNTB specifically for the design and analysis of segmental and cable-stayed bridges. Within its “dynamics” module, the program performs a linear time history analysis based upon support accelerations. Using the Wilson-theta method, the program computes and stores velocities and displacements for each degree of freedom at each time step, thereby allowing the user to stop and restart the dynamic analysis and to modify the structure at any predetermined point within a dynamics run. The program also allows the user to accelerate each supported degree of freedom with a different transient load and to begin the acceleration at different times. Based upon user input of estimated damping percentages, the program calculates the appropriate Rayleigh damping coefficients, assuming damping to be proportional to mass and stiffness, and applies these coefficients to the mass and stiffness matrices during the run. The program will then compute displacements, forces and reactions for each time step and provide the user with his choice of maximum or minimum values for a given list of members. Since the joint displacements are saved by time step, the user may elect to open the dynamic displacement file at a later date in order to compute additional results. For design, it was determined that this bridge is an essential structure, thereby requiring that the bridge remain serviceable following a moderate earthquake, and sustain only minor damage as a result of the maximum credible event. By minor damage, we intend that the structure would remain operational although expansion joints, bearings and other easily repaired components could sustain some damage. And since there is very little data regarding the confinement of large, hollow concrete sections, or the performance of such sections beyond the elastic range, the tower piers were designed to remain elastic thorughout the design earthquake. Additionally, the approach span piers are sufficiently large that they remain elastic under all load conditions. Cable-Stayed Spans The initial steps in the analysis were to confirm that the acceleration time history files provided by Woodward-Clyde Consultants were being read correctly by the analysis program. This included a preliminary run which computed maximum relative joint displacements between the accelerated supported joints and generated a plot of the relative displacements throughout the event. These were compared to, and corresponded well with, the 10 centimeter maximum relative displacement and the continuous record of relative displacements predicted by the seismic subconsultant. Computed absolute displacements at the supports were also compared to the predicted values, and again the values correlated well. These investigations provided the confidence that the 10 000 points in each of the acceleration records provided were being correctly read by the analysis program. Initial earthquake design runs for the cable-stayed unit indicated that without any longitudinal restraint at the tower piers, the design preference, the bridge would experience movements up to 1200 millimeters in each direction at the ends of the unit. Further study indicated other undesirable effects with full fixity and full longitudinal restraint at the tower piers. These conditions caused live load rotations and temperature rise and fall to place higher, often undesirable, demands upon other bridge elements. The erection analyses concluded that
construction of the bridge with full fixity would generate forces much higher than those observed with no restraint. However, the fixity studies also revealed that there were some advantages to fixity as well. The wind induced motion of the bridge could be reduced while the flutter velocity threshold increased and longitudinal displacements under the various live load combinations could be minimized. Reduced movements would then require smaller expansion joint devices and relieve the required movement capacity of the side span tie down devices. These studies led to the conclusion that the cable-stayed spans should be restrained longitudinally, either with some type of bearing or key. Development of preliminary alternative details for this type of restraint indicated that the most effective solution would be one which allowed limited translation, that caused by slowly applied loads such as a uniform temperature change, and free rotation under all loading conditions. Several types of seismic isolation and damping systems were considered; however, it was determined that force transfer would provide the most efficient solution. Both isolation and additional damping were studied to evaluate the potential impact on the design and cost of the structure. The overall stiffness contribution of the stay cables and the length of the main span reduced the effectiveness of both alternative solutions. It was determined that force transfer was the most practical solution, and for this bridge it is achieved through the use of an earthquake shock transfer device. This device, comprised of a cylinder filled with silicon putty and a piston, is capable of transferring forces in both tension and compression. Therefore, the "double action" of the unit simplified the design of the connections to the structure and permitted transfer of earthquake forces at an elevation much lower than the stay cable connections. The tower piers, which support the bulk of the load, are supported by a spread footing and a dredged caisson on rock at Piers 2 and 3, respectively. Other foundation types were studied, however, it was determined that another foundation type was not justifiable given the magnitude of the earthquake forces and the depth of water and alluvial soils. Approach Spans Liquefaction presents little problem for the cable-stayed unit since the supporting piers are founded on huge footings keyed into rock; however, the approach spans are considerably different. As noted earlier, these foundations are located in an area with very deep, highly liquefiable soils. When combined, the depth of liquefaction and anticipated scour eliminated spread footing type foundations from consideration. Even soil improvement techniques were considered ineffective due to degradation and aggredation of the channel. After studying several possible alternative solutions including pile and drilled shaft foundations and various soil improvement methods, it was determined that piers supported on drilled shafts to rock would be the most economical solution. These shafts, which are drilled through water-bearing sand to a depth of up to 30 meters will require casing for installation. Therefore, the decision was made to require that the casing for the shafts be left in place and used as additional confinement steel during extreme condition seismic events. These conditions are generally after loss of lateral support of the shafts due to either scour or liquefaction. The analysis of the structure for the extreme event condition was
conducted within the T187 "dynamics" routine. Since the solution method is based upon the values of displacement, velocity and acceleration of the joints at the previous time step, it was possible to simulate liquefaction and loss of lateral support in the foundation by varying the foundation stiffness during the run. In this way, we were able to analyze the structure with various foundation support conditions, fixity at the piers, and multiple restrainer combinations. Ultimately it was determined that the drilled shaft option, placed in permanent casing was the best overall foundation for the site. We found that no one foundation support condition governed all aspects of the design. Primarily the half-scour and liquefied states governed the design of the piers and foundations while the forces in the structure with full support controlled the design of the bearings and superstructure connections.
Conclusions Although the New Madrid fault zone lies within approximately 80 kilometers of the bridge site, the design seismic event is for a magnitude 8.5 earthquake, and the bridge must withstand the seismic forces within the elastic range, the design of the Cape Girardeau replacement bridge was a success. Each point of the design criteria was met without creating unnecessarily complex details and without significant added cost to the structure. The electronic transfer of files related to the design earthquake and the cooperation of all parties, including MoDOT, HNTB Corporation, and both the wind and seismic consultants all helped to identify and solve problems before they became too difficult or costly to handle. In this, the seismic analysis, wind studies and final design and detailing of the bridge remained on schedule and within the client's budget.
Acknowledgments The author extends his thanks to the Missouri Department of Transportation for permission to share their experiences and knowledge of the seismic evaluation and design of the bridge and Woodward-Clyde Consultants for much of the data, testing and graphics used in the compilation of this paper and its presentation. [1]. [2]. [3].
[4]. [5].
Based on U.S. Army Corps of Engineers data for locks at River Mile 274, at St. Louis, Missouri in 1989 and 1990. Nuttli, Otto W., The Effects of Earthquakes in the Central United States, 2nd ed., May 1990, Center for Earthquake Studies, Southeast Missouri State University Nuttli, Otto W., “The Mississippi Valley Earthquakes of 1811 and 1812: Intensities, Ground Motion and Magnitudes,” Bulletin of the Seismological Society of America, Vol. 63, No.1, 1973 Nuttli, 1990 Johnson, A.C. & Nava, S.J., “Recurrence Rates and Probability Estimates for the New Madrid Seismic Zone,” Journal of Geophysical Research, Vol. 90, No. B8, July 10, 1985
Cable-Stayed Bridges for Urban Spaces
António REIS
Armando PEREIRA
Techn.Dir GRID-Cons. Eng. Lisbon-Portugal
Civil Engineer GRID-Consulting Engineers Lisbon-Portugal
José PEDRO
Daniel SOUSA
Civil Engineer GRID-Consulting Engineers Lisbon-Portugal
Civil Engineer GRID-Consulting Engineers Lisbon-Portugal
Summary Design concepts and case studies for cable stayed bridges, in which aesthetics and environmental conditions required particular consideration related to its integration in urban spaces are reported. The solutions adopted for decks, towers and cable-stayed arrangements are compared. Structural, aerodynamic behaviours and execution methods are discussed for concrete cable stayed bridges.
1.
Introduction
The design of a cable-stayed bridge in an urban space requires particular consideration of aesthetics and environmental integration. Complex geometrical constraints, due to in-plan curved alignments, traffic maintenance requirements during erection stages and aspects related to the structural behaviour and the competitiveness of cable-stayed solutions, are a challenge for designers. Very often, classical cable-stayed solutions namely, symmetrical solutions with two pylons, are not the most efficient ones to overcome difficult urban site conditions. Besides, for short to medium spans, Owners and Designers tend to avoid cable-stayed solutions for urban sites due to economical and environmental integration reasons so, beam and slab type of bridges are usually selected for urban viaducts. However, as referred by Christian Menn [1], “the general public was never captivated by modern bridge construction. Beam bridges were largely perceived as boring”. These aspects shall be taken into consideration by civil engineers at the conceptual design stage. The architecture of bridge design is a civil engineering problem.
2.
Aesthetics and Environmental Demands
In the last few years, a tendency to adopt cable stayed bridges for spans ranging from 150 to 500 meters has been observed. For urban spaces, cable stayed bridges have been adopted most frequently over rivers and not very often in urban viaducts where long spans are unnecessary. However, even for small to medium spans, some advantages of cable stayed solutions should be considered: the transparency of the solution, reducing the number of piers. the slenderness of the deck. the reduction of traffic disturbances during execution. Open spaces with very few constraints, are ideal locations for cable-stayed solutions with a 3 span scheme and two masts. However these conditions are infrequent in places where urban bridges and viaducts have to be built. The lack of symmetry at some of these locations, namely due to existing constructions, the skew alignment of the upper and lower roadways, the existing of the interchanges or roundabouts, may require asymmetric solutions for reducing the visual impact. Besides, urban bridges should not spoil the sites but to improve the quality of the environment for the benefit of the citizens. The classical rule-“form follows function”, should not be adopted as a limiting principle at the conceptual design stage, but as a guideline. Bridges are very often landmarks for the cities; innovation and creative ideas are necessary [2].
3.
Stay Cables: Arrangement and Visual Impact
A single plan of stays-axial type cable arrangement is likely to be the best choice for integration into an urban space where multiple visual obstructions exist. Besides, avoiding the visual impact of the crossing of stays for skew views of the bridge, is a well-known advantage. However, to adopt an axial staying scheme an increased torsional stiffness of the deck is required for transverse load distribution and aerodynamic stability. All the bridges herein discussed were designed according to this concept. In Fig. 1, a cable stayed solution for a 92m main span urban viaduct was shown to be the best solution for environmental integration.
Figure 1 -A symmetrical solution for a cable-stayed viaduct for a highway in the city of Funchal, Madeira Island.
Figure 2 – Symmetrical stay-cable arrangement for the Viaduct of Fig.1. The stays (31 to 43 strands - ∅15mm), with an axial arrangement, are 5 m distance apart only, at the deck level (Fig.2). This bridge is currently under construction in the city of Funchal. However, in-plan curvature of the deck, makes the adoption of axial cable-stayed solutions more difficult. For the case shown in Fig. 3 and 4, The Stº Tirso Bridge, in the North of Portugal, a 3D arrangement of stays was adopted to solve a 61m end span. A set of backstays, in a single plan, was introduced for longitudinal stability of the pylon. Concentrating the anchorage of the stays, at approximately 3 points, creates order and a 3D image of the bridge consistent with the helicoidal access ramp. The architectural integration of the bridge structure with the railway station (Fig.3), was achieved. Six (2x3) cable stays were adopted at the end span, 37 strands (15mm) each. The 3 backstays have 70 strands each. All the strands were stressed at the top of the mast. The anchorages at the deck level (Fig.5) are located in such a way to reduce permanent bending actions in the pylon. The resultant transverse and longitudinal horizontal forces induced by the stays at the top of the mast, were minimised by adjusting the cable forces at the end of the construction. This bridge was opened to traffic in the summer of 1998.
Figure 3 - The Stº Tirso Bridge over the river Ave - a 3D stay cables arrangement.
Figure 4 - Longitudinal section of the Stº Tirso Bridge. Another design case of an urban viaduct, where a cable-stayed solution was selected in a design competion, is shown in Fig. 6 and 7. A main span of 120m allows the crossing of a highway and several railway lines. For this particular case, we designed a completely asymmetric solution. It was important to understand the urban planning issues, since the viaduct will be built along an avenue with a green park.
Figure 5 - Anchorages at the deck level of the Stº Tirso Bridge. A classical symmetric solution, for the stay-cable arrangement, with a single mast, considered as well as an alternative solution at the preliminary design, would never attain the aesthetical objectives of the urban planning. The Owner decided to select the asymmetric solution, even taking into consideration its cost being about 15% higher than the symmetric solution. The staying scheme, consists in a single layer of 37 to 43 strands of 15mm diameter, spaced at 8,0m along the main span; the back stays (2x3) arranged in two planes, have 67 strands of 15mm each. These backstays are anchored at the deck level by prestressed concrete crossbeams and have a 3D arrangement of the anchorage at the top of the tower. Figure 6 -An asymmetric stay-cable solution for the “Praça das Flores” Viaduct in Oporto.
Figure 7 – “Praça das Flores” Viaduct: longitudinal section with the arrangement of the cablestays.
4.
Decks: Aesthetics and Structural Performance
For cable-stayed bridges in urban spaces, if an axial arrangement of stays is preferred, a sufficient torsional stiffness for the deck for aerodynamic stability is required. Besides, transverse cross section deformations under asymmetric live loading shall be taken into consideration if an axial stayed scheme is adopted. Single cell box girders with prestressed steel diagonals, as we adopted several years ago in the Socorridos Bridge [3], are usually the simplest solution. This type of solution was adopted for the “Praça das Flores” Viaduct (Fig.8).
Figure 8 - The “Praça das Flores” Viaduct: A trapezoidal box girder deck. For viaducts located in urban areas, if a very slender deck is required, the standard trapezoidal single cell box girder may be replaced by a triangular type box girder (Fig.9) as we adopted for the Viaduct in Funchal. The main advantage is aesthetical, because keeping the same depth (2,0 to 2,20m minimum for cast in situ prestressed concrete decks) the triangular superstructure is apparently much more slender. However, the torsional stiffness is reduced for the triangular shape and so the torsional vibration frequency. In Table 1, a comparison is made for the 3 types of decks adopted for the bridges previously referred to, in what concerns the main parameters controlling the aerodynamic stability. For short spans, say up to 70 meters, a slender concrete voided slab is a very simple and feasible solution. However, the dead weight may be 30 to 40% more than a box girder resulting in additional cost for the stays.
Figure 9 - Cross-section for the Viaduct in Funchal - A triangular shape box girder deck. For the Stº Tirso Bridge, a voided slab was adopted for all the spans including the end span (61m) that is elastically supported at the mid span section by two planes of 3 stay cables (Fig.5 and 10). The natural torsional frequency (Table 1) is higher for the trapezoidal box girder deck due to the increased J compared to the other sections.
Figure 10 - Cross-section for the Stº Tirso Bridge - A voided slab cable stayed deck. Besides, the torsional frequency of the Stº Tirso Bridge is significantly affected by the transverse flexibility of the pylon. With a rigid pylon, fb increases from 1.29Hz to 1.98Hz. This type of solution - an axial cable-stayed slab is feasible. Introducing an axial central rib as adopted by Cremer et al [4] at the “Kortrijk” Bridge may increase the torsional stiffness. frequencies. DL(kN/m)
DL/m2
J (m4)
fb(Hz)
ft (Hz)
Pr.Flores Viaduct
18.0
253.0
14.1
13.61
0.84
2.66
Viaduct in Funchal
21.5
326.5
15.2
4.80
0.80
1.58
Stº Tirso Bridge
13.0
245.0
18.8
4.20
0.76
1.29
b (m)
Table 1 - Deal Load (DL), torsional stiffness factor (J) and natural bending (fb) and torsional (ft) The structural behaviour under asymmetric loading and the aerodynamic stability of the triangular box girder was studied. However, this deck presents good relationships span/width =4.3 and torsional / flexural vibration frequencies ft /fb = 2 for aerodynamic stability.
This was confirmed [5] at the wind tunnel where a sectional model (1.45m long; 1/50 scale) was tested for aerodynamic stability and to determine the aerodynamic coefficients. The wind angles of attach were varied between - 5º and 6º and the wind speeds correspond in the prototype to 133km/h to 266km/h. The drag coefficient varies between 1.1 and 1.3, being the maximum observed for 232km/h. No aerodynamic instabilities were detected or any kind of vortex shedding; the analysis of drag and lift coefficients shows a stable behaviour also with respect to gallop instabilities.
5.
Towers : Aesthetics and Functional Requirements
The geometry of the towers shall result from aesthetics, structural and functional requirements. Functional requirements shall be here understood as including constructional demands, namely clearances for anchorages at the top of the pylons, horizontal and vertical clearances at the deck level and safety with regard to structural instability. The height of the pylon, herein referred as the part of the tower above the deck, is related to the acceptable minimum angle of the cables with the deck. For classic cable stayed solutions, this angle may be of the order of 20º, resulting in a pylon height of about 20% of the span for solutions with two towers (Fig. 2) and 35 to 40% of the span for single pylon solutions. If the stay cables do not extend throughout the span (Fig. 6 and 7), what may be convenient for aesthetics in urban viaducts, the height of the pylon may be reduced.
Figure 11 - Anchorages at the top of the pylon of the Viaduct in Funchal.
Figure 12 - Anchorages at the top of the pylon of the Stº Tirso Bridge.
Figure 13 - The tower of the “Praça das Flores” Viaduct.
The anchorages at the top of the pylon and the horizontal clearances at the deck level may require a variable width for the pylon. That may be required “to cross” the cables if a 3 plane arrangement is adopted as in Fig. 12 and 13 or to have enough space at the inside of an anchorage steel tower head for stressing operations as in Fig. 11. For these cases the width of the pylon increases toward the top. A different approach, due to functional requirements, was adopted for the “Praça das Flores” Viaduct. We decided to insert a central walkway. Besides, an innovative shape for the tower (Fig. 13) was adopted as a result of aesthetical and structural requirements - the tower should be an emblematic element for the urban park; the tower should have a sufficient longitudinal bending stiffness to reduce the forces at the backstays, and the bending moments in the vertical shaft of the pylon. The balance of horizontal components at the top of the mast for the permanent actions was achieved by adjusting the stay forces. In Fig. 14 one compares the bending actions under live load in the vertical shaft of the tower with and without the inclined leg. To accommodate the walkway a “door” was open in the tower. A detailed finite element analysis of this part of the tower was done to find out the flow of internal forces and the local bending actions. The tower shaping results from two triangles connected by their bases, resulting in an appearance consistent with the triangular arrangement of the stay cables. The “door” has a triangular (“gothic”) appearance as well.
H[m]
-2066 - 10000
H[m]
70
70
60
60
50
50
40
40
30
30
20
20
- 5000
0
5000
10000
- 10000
- 5000
6402 0
10
10
0
0
5000
10000
Figure 14 - Comparision of the bending actions in the vertical shaft of the tower of Fig 13, with and without the inclined leg.
6.
Construction: Site Constraints and Execution Methods
The construction of bridges located in urban spaces is very much influenced by site constraints, namely disturbance in existing traffic conditions, environmental noise impact and safety during erection stages. For the bridge cases previously reported, two different methods were adopted - span by span, cast in situ deck on a formwork supported from the ground for the Stº Tirso Bridge and balanced cantilever, with cast in-situ segments, for the other two viaducts. To stress the stay cables of the Stº Tirso Bridge, it was necessary to control the interaction of the deck with the formwork in order to control the decompression limit state at the end span. The maximum allowable vertical deflection at the anchorage section was evaluated as being 30mm. After reaching this value, the formwork girders were lowered at the supports and a 2nd stressing operation was carried out. The process was continued until the specified stresses in the stay cables have been reached. For the viaduct in Funchal, the 5,0m segments are casted in two stages - 1st the lower flange and webs and 2nd the top flange, due to the shape of the cross section. Each stay is stressed only after moving the equipment to the next segment. The construction scheme for the viaduct in Oporto requires the casting of the 8,0m segment in two stages - 4.0+4.0m, stressing the adjacent cable stay before casting the 2nd stage.
7.
Conclusions and Final Remarks
Aesthetics, environmental integration, structural performance and execution methods were discussed for the design of cable-stayed bridges of short to medium spans located in urban areas. Three case studies of recent bridge designs were reported. The advantages of using axial cablestayed solutions and asymmetric configurations were shown; these concepts have been adopted by the authors in another bridge currently being designed (Fig. 15). The deck, 30m width, is a composite box girder deck where the webs are replaced by a 3D steel truss. The lower flage has a pedestrian function, since the bridge will be located between two green parks. The solution select in a design competition is expected to be a landmark for the city.
Figure 15 - A model for the “Europa” Bridge in Coimbra, Portugal.
8.
References
[1]
C. Menn - Functional Shaping of Piers and Pylons. Structural Engineering International, Vol.8, nº 4, 1998. A.J.Reis - Designing Post-tensioned Concrete Bridges for Innovation, in Post-Tensional Concrete Structures, FIP Symposium, Vol. 1, pag. 963, 1996. A.J.Reis, A.Pereira - Socorridos Bridge: A Cable-Panel Stayed Concept. International Conference A.I.P.C. - F.I.P. Deauville 1994, Proceedings - Vol. 1, pag. 343/350. J.M.Cremer, V.Ville de Goyet, A.Lothaire, L.Ney, V.Radu - Some Innovative CableStayed Bridges. International Conference A.I.P.C.-F.I.P. Deauville 1994, Proceedings - Vol. 1, pag. 235/260. F.Branco, P.Mendes, J.Ferreira – “Ensaios em Túnel de Vento do Tabuleiro do Viaduto sobre o Caminho do Comboio”. Relatório IC-IST, EP nº 10/97.
[2] [3] [4]
[5]
A new method to assign initial cable forces for prestressed concrete cable-stayed bridges Dr. Dewei Chen, born 1956, received his degrees from Tongji University of Shanghai.. He is now an Associate Professor of the department.
Dewei CHEN Associate Professor Tongji University Shanghai, China
Summary The determination of initial cable forces in a prestressed concrete cable-stayed bridge for a given vertical profile of deck under its dead load is an important but difficult task that affects the overall design of the bridge. A new method utilizing the idea of force equilibrium is presented in this paper for their determination. The method can easily account for the effect of prestressing and the additional bending moments due to the vertical profile of the bridge deck. It is much more rational and simpler than the traditional “zero displacement” method, and it is able to achieve bending moments in the bridge deck approaching those in a continuous beam over rigid simple supports.
Introduction The cable-stayed bridge is a modern form of bridge which is both economical and aesthetic. It has been extensively employed in the construction of long-span bridges in the past few decades. However this kind of structures are highly statically indeterminate, and therefore many schemes of initial cable forces are possible. In the particular case of prestressed concrete cable-stayed bridges, it is especially important to choose an appropriate scheme of initial cable forces while the bridge is under dead load only. Owing to shrinkage and creep, the deflections will change with the passage of time and the internal forces may also redistribute. Should an inappropriate scheme of initial cable forces be chosen, an unfavourable pattern of internal forces may be locked in subsequently, for which there may be no simple solution. Theoretically it is possible to search for a “stable” scheme of initial cable forces under which there is the minimum redistribution of internal forces and time-dependent displacements. However it is usually very difficult in view of the many factors affecting the subsequent timedependent deformations. For example, many cable-stayed bridges are constructed using cast insitu segmental cantilever construction, which gives rise to complex effects of shrinkage and creep because of the different ages of concrete. The presence of longitudinal prestressing also complicates the problem further. Inevitably some simplifying assumptions have to be made.
1
Review of Existing Methods The scheme of initial cable forces giving rise to bending moments in the bridge deck approaching those of an equivalent continuous beam with all the supports from cables and towers considered as rigid simple supports is generally acknowledged to be both rational and practical, as the long term behaviour of the bridge is reasonably “stable”. The problem hinges upon how to achieve this scheme of initial cable forces. There are two main categories of methods in achieving an appropriate scheme of initial cable forces in prestressed concrete cable-stayed bridges [1-6], namely the optimization method [2-5] and the “zero displacement” method [6]. In the optimization method [2-5], the initial cable forces are chosen based on the optimization of certain objective functions which may either be related to structural efficiency or economy. In this method, the total strain energy is often one of the objective functions to be minimized. It is necessary to impose the constraints for optimization very carefully, or else the resulting schemes may sometimes become impractical. On the other hand, the traditional “zero displacement” method [6] is more straight forward in theory, and it enables the designer to fine-tune the initial cable forces as well as the structural configuration. If a straight and horizontal bridge deck is supported on a number of stay cables, the horizontal components of the cable forces have little effect on the bending moments of the deck, and hence the bending moments are primarily governed by the vertical components of the cable forces and the dead load. In the “zero displacement” method, an appropriate scheme of initial cable forces is obtained by making the deflections at the cable anchorages vanish. When the deck gradient is negligible, the resulting bending moments in the deck are essentially those of an equivalent continuous beam with all supports from cables and towers considered as rigid simple supports. However, when the vertical profile of the bridge deck is significant by reason of traffic requirements or otherwise, the basis of this method is itself questionable. As the horizontal components of the cable forces will induce additional bending moments in the deck, the resulting bending moments are likely to cause substantial redistribution in the long run. In this case, what really matter are the bending moments because they will affect the long term behaviour of the bridge. Whether the corresponding displacements are zero or not is immaterial, as they can be adequately controlled by appropriate precamber or preset of the deck during construction. In this paper, a new method utilizing the idea of force equilibrium is presented for the determination of a “stable” scheme of initial cable forces. The method can easily account for the effect of prestressing and the vertical profile of the bridge deck, and therefore it is much more rational as well as simpler than the traditional “zero displacement” method. Two numerical examples using real cases of prestressed concrete cable-stayed bridges are presented to demonstrate the versatility of the proposed method.
The Force Equilibrium Method In the force equilibrium method, the cable-stayed bridge is modelled as a planar structure. The method works on an evolving substructure eventually comprising the bridge deck and towers, and searches for a set of cable forces which will give rise to desirable bending moments at selected locations of the substructure. As the method works only on the equilibrium of forces rather than deformation, there is no need to deal with non-linearity caused by cable sag and other effects. The method is therefore computationally efficient.
2
First of all, certain sections of the bridge deck and tower are chosen as control sections where the bending moments are adjusted by varying the cable forces. Consider a typical single tower cable-stayed bridge, as shown in Figure 1, in which the connection between the bridge
Figure 1. A typical single tower cable-stayed bridge.
Figure 2. Stage 1 model for cable-stayed bridge shown in Fig. 1. deck and tower is monolithic. To established the target bending moments, only the bridge deck is considered. All supports from the cables and tower are replaced by rigid simple supports, as shown in Figure 2. This is regarded as the Stage 1 model for the sake of subsequent discussions. The prestressing to be applied during construction is also taken into account. The bending moments caused by dead load in the bridge deck under such modified support conditions are then taken to be the target bending moments. It is noted that the prestressing to be introduced after the completion of the bridge deck is not taken into account here. These target bending moments are adopted because the effects of creep and shrinkage of concrete tend to change the bending moments towards these target values in the long term anyway [1]. If the initial bending moments in the towers can be controlled at the same time, the scheme of initial cable forces is reasonably stable. It is further assumed here that factors such as the differences in age among deck segments are insignificant in the long term and therefore they are neglected. Fig. 3 shows the same bridge as in Fig. 1, except that all cables are taken away and replaced
Figure 3. Model for stage 2 and stage 3 for cable-stayed bridge. by the internal forces. This simplified model applies to both Stages 2 and 3. The only difference between these two stages lies in the degree of sophistication. The cable forces are taken as independent variables for adjustment of bending moments at the control sections. Normally the bending moment at each deck section where a cable is anchored is treated as a control parameter. It should be pointed out that wherever a model consists of a back-stay anchored at the deck above an end pier, where the deck carries no bending moment, the corresponding cable force can be treated as an additional variable to improve the structural efficiency further. For example, the bending moment at the deck-tower junction or that at the tower base may be taken to be an additional control parameter as they are critical sections affecting the long term behaviour. The target bending moments at the deck sections are those obtained from the Stage 1 model whereas the target bending moment at the chosen tower section is normally set as zero.
3
The above arguments can also be extended to other configurations of cable-stayed bridges. In a symmetric single tower cable-stayed bridge without back-stays anchored above end piers, the bending moments in the tower should normally be zero under dead load, and therefore there is no need to treat any of these as a control parameter. In a two-tower cable-stayed bridge of symmetric arrangement, it is only necessary to consider one half of the bridge with appropriate boundary conditions at the middle section to account for symmetry, and the above reasoning can similarly be applied. The main purpose for setting up the Stage 2 model is to evaluate the approximate influence coefficients, which are the bending moments at the control sections caused by a unit load in a certain cable. In order not to introduce the non-linearity of cable stiffnesses, some simplifying assumptions are made. The self-weight of each cable is neglected, and hence the forces at the ends are roughly equal. The bending moments in the deck are primarily determined by the cable forces acting on the deck, and to a lesser degree by the cable forces acting on the tower. Therefore the cable forces acting on the tower are neglected in the calculation of bending moments in the deck. Similarly in the calculation of bending moment at the control section at the tower, only the cable forces acting on the tower are taken into account. The errors introduced by these simplifying assumptions will be almost eliminated by iterations in the next stage. Considering the equilibrium of the Stage 2 model, the following equation can be written
{ M } = [m] {T} + { M } 0
d
(1)
where { M 0 } is an N-dimensional vector containing the target bending moments M i0 derived from the Stage 1 model, [m] is an N×N matrix containing approximate influence coefficients mij for the Stage 2 model in which mij is the bending moment at the ith control section caused by a unit force in the jth cable, {T } is an N-dimensional vector containing the cable forces
Tj , { M d } is an N-dimensional vector containing the bending moments M id caused by only
dead load and prestress in the Stage 2 model, N is the number of cables considered in the model, i is the subscript corresponding to the ith control section and j is the subscript corresponding to the jth cable. If { M 0 } contains the bending moments of the equivalent continuous beam on rigid simple supports as obtained from the Stage 1 model, and the control sections are well chosen so that the matrix [m] is non-singular, an initial estimate of the cable forces {T 0 } can be calculated from the Stage 2 model as (2) {T 0 } = [m]−1 { M 0 } − { M d }
(
)
However the cable forces {T 0 } obtained above are only rough estimates as the Stage 2 model does not take into account the interaction among tower, cables and deck. It is therefore necessary to build the Stage 3 model. In the Stage 3 model, the interaction among tower, cables and deck is taken into account by iterations. The cable forces at the deck anchorages are taken as independent variables in the optimization process, and the self-weight of each cable can also be introduced. Using the initial estimate of the cable forces {T 0 } , as well as the bending moments { M d } caused by
dead load and prestress in the Stage 2 model, the updated deck bending moments { M 1} can be calculated from the Stage 3 model. Such bending moments are normally different from the
4
target bending moments
{M } , 0
and hence it is necessary to introduce some adjustments
{∆T } of the cable forces given by 1
{∆T } = [m] ( { M } − { M }) −1
1
1
Using the updated cable forces
0
(3)
{T } given by 1
{T } = {T } + {∆T } 1
0
1
the updated deck bending moments
(4)
{M } 2
can then be calculated again from the Stage 3
model. Notice that the approximate influence matrix [m] for the Stage 2 model has been used in the Stage 3 model, and hence further iterations are necessary. Further adjustments
{∆T } may be obtained by 2
{∆T } = [m] ( { M } − { M }) −1
2
2
0
resulting in more accurate cable forces
(5)
{T } given by 2
{T } = {T } + {∆T } + {∆T } 2
0
1
2
(6)
This process can be repeated until the updated deck bending moments
{M } . 0
{M } n
converge to
This is summarized in the flow chart shown in Figure 4.
Numerical Examples Two numerical examples are presented to demonstrate that the present method is both rational and reliable. Both are taken from existing prestressed concrete cable-stayed bridges in China, but some minor simplifying modifications are made. Example 1. A single tower prestressed concrete cable-stayed bridge with harp arrangement The first example is a single tower prestressed concrete cable-stayed bridge, situated in Ningbo City, China, with spans of 90m and 105m. The moment of inertia (ID), the cross sectional area (AD) and the Young’s modulus (ED) of the deck are 4.706m4, 12.145m2 and 3.5×107kN/m2 respectively. The stay cables are of the harp arrangement. Three types of stay cables are used, and their respective cross sectional areas (AS) are 0.013m2, 0.0166m2 and 0.0208m2. The Young’s modulus of the stay cables (ES) is 2.1×108kN/m2. The tower is stepped with the biggest section below the bridge deck and the smallest section over the length where the cables are anchored. The moments of inertia (IT) of the tower are 11.212m4, 19.939m4 and 79.688m4. The corresponding cross sectional areas (AT) are 14.46m2, 19.0m2 and 45m2 respectively, while the Young’s modulus (ET) is 3×107kN/m2. The information on the prestressing is omitted for brevity. Three different vertical profiles of the bridge deck have been considered. The bridge deck is straight and horizontal in Case 1. In Cases 2 and 3, both the vertical profiles consist of a symmetric parabolic summit curve of 180m horizontal length and a straight tangent of 15m.
5
The highest point is precisely at the tower location. The gradients of the straight tangents for Cases 2 and 3 are 3% and 9% respectively. Figure 5 shows an elevation of the bridge for Case 3.
Figure 5. A single tower P.C. cable-stayed bridge with harp arrangement. The present method was applied to optimize the bending moments in the bridge deck for the three cases, and the tolerance value used to terminate iterations was 5kNm. The results for Case 3 are shown graphically in Figures 6-8. Notice that the deck bending moments after optimization agree well with the target values obtained from an equivalent beam on rigid simple supports, except at the tower section which was not chosen as a control section. The abrupt jumps in bending moment are caused by prestressing. The bending moment at the tower base is also very close to zero after optimization. The three cases were also analyzed by the “zero displacement” method using 0.001m as the
Figure 6. Internal forces in bridge deck of example 1 (Case 3). a) Target bending moment in deck in kNm; (b) Bending moment in kNm; (c) Shear force in kN; (d) Axial force in kN.
Figure 7. Cable forces of Example 1 (Case 3) in kN.
Figure 8. Internal forces in tower of Example 1 (Case 3). a) Bending moment in kNm; (b) Shear force in kN; (c) Axial force in kN.
6
tolerance value to terminate iterations. The initial cable forces for the three cases obtained by the present method are tabulated in Table 1 and compared to those obtained by the “zero displacement” method. It is observed that when the bridge deck has no slope, i.e. Case 1, results from the above two methods are effectively the same. There are, however, marked differences in the other two cases, especially in the cables close to the tower. Case 1
Case 2
Case 3
Cable
Present
Zero Disp.
Present
Zero Disp.
Present
Zero Disp.
No.
Method
Method
Method
Method
Method
Method
1
14045
14045
14483
14398
15458
15351
2
3931
3931
3969
3975
4044
4065
3
8832
8832
8919
8915
9130
9116
4
6757
6757
6798
6800
6836
6841
5
7242
7242
7200
7200
7126
7125
6
6900
6900
6825
6818
6637
6630
7
7727
7727
7561
7590
7283
7311
8
6676
6676
6605
6497
6224
6117
9
6707
6707
6016
6416
5428
5826
10
2889
2889
4251
2754
3971
2484
11
14618
14618
11288
14323
11143
13758
12
14619
14619
11298
14339
11118
13769
13
2887
2888
4245
2747
3961
2474
14
6706
6706
6013
6414
5422
5820
15
6680
6680
6607
6499
6222
6115
16
7714
7714
7552
7582
7270
7299
17
6948
6948
6867
6860
6678
6671
18
7064
7064
7024
7025
6931
6934
19
7304
7304
7340
7339
7427
7421
20
6998
6998
7027
7032
7028
7044
21
10768
10768
10922
10912
11560
11524
22
8924
8924
9306
9311
9908
9924
Table 1
Initial cable forces for Example 1 (kN)
Example 2. A single tower prestressed concrete cable-stayed bridge with semi-fan arrangement shown in Fig. 9 The second example is also a single tower prestressed concrete cable-stayed bridge, situated in Jilin Province, China, with spans of 95m and 132m. The moment of inertia (ID), the cross sectional area (AD) and the Young’s modulus (ED) of the deck are 5.1m4, 10.579m2 and 3.5×107kN/m2 respectively. The stay cables are of the semi-fan arrangement. Three types of stay cables are used, and their respective cross sectional areas (AS) are 0.020m2, 0.019m2 and 0.013m2. The Young’s modulus of the stay cables (ES) is 2.1×108kN/m2. The tower is stepped in a manner similar to Example 1, and the moments of inertia (IT) are 17.92m4, 24.01m4 and 47.73m4. The corresponding cross sectional areas (AT) are 17.92m2, 13.44m2
7
and 37.20m2 respectively, while the Young’s modulus (ET) is 3×107kN/m2. The effects of prestressing is not considered in this example for simplicity. The vertical profile consists of a symmetric parabolic summit curve of 190m horizontal length and a straight tangent of 37m. The highest point is again precisely at the tower location. The gradient of the straight tangent is 6%. The results obtained using the present method are shown in Figure 6, indicating very good agreement between the deck bending moments and the target values, shown in Figure 912.
Figure 9. A single tower P.C. cable-stayed bridge with semi-fan arrangement (Example 2).
Figure 10. Internal forces in bridge deck of Example 2. a) Target bending moment in kNm; (b) Bending moment in kNm; (c) Shear force in kN; (d) Axial force in kN..
Figure 11. Cable forces of Example 2 in kN.
Figure 12. Internal forces in tower of Example 2. (a) Bending moment in kN; (b) Shear force in kN;
(c) Axial force in kN.
8
Conclusions A new method utilizing the idea of force equilibrium is presented for the determination of an optimum scheme of initial cable forces in a prestressed concrete cable-stayed bridge for a given vertical profile of deck under its dead load as well as prestress. In the proposed method, the stiffnesses of the cables do not enter into the calculations, and it therefore obviates the need for introducing non-linearity into the algorithm. The bending moments, rather than the displacements, of the deck are taken as parameters to be controlled. The additional bending moments caused by the vertical profile of the deck can also be taken into account. Two real prestressed concrete cable-stayed bridges have been investigated using the proposed method, which demonstrate that it is both rational and practical. It is also observed that, as far as the initial bending moments of the tower are concerned, the harp arrangement is less favourable than the fan or semi-fan arrangement, as the cables are anchored over a larger length in the former case. The proposed method is also a handy tool for optimizing the bending moments in the tower.
Acknowledgements The financial support of the block grant from “the Scale B”, The Scientific Committee of P.R. of China is acknowledged.
References [1]. [2]. [3]. [4]. [5]. [6].
Analysis of Secondary Stresses in Prestressed Concrete Cable-stayed Bridges due to Creep (in Chinese), Shanghai Institute of Design and Research in Municipal Engineering, P. R. China, 1983. Furukawa, K., Sugimoto, H., Egusa, T., Inoue, K. and Yamada, Y., Studies on optimization of cable prestressing for cable-stayed bridges. Proceedings of International Conference on Cable-stayed Bridges, Bangkok, 1987, 723-734. Lu Q. and Xu Y.G., Optimum tensioning of cable-stays (in Chinese). Chinese Journal of Highway and Transport, P. R. China, 1990, 3(1), 38-48. Simoes, L.M.C. and Negrao, J.H.O., Optimization of cable-stayed bridges with boxgirder decks. Proceedings of the 1997 5th International Conference on Computer Aided Optimum Design of Structures, Rome, Italy, 1997, 21-32. Negrao, J.H.O. and Simoes, L.M.C., Optimization of cable-stayed bridges with threedimensional modelling. Computers and Structures, 1997, 64 (1-4), 741-758. Wang, P.H., Tseng, T.C. and Yang, C.G., Initial shape of cable-stayed bridges. Computers and Structures, 1993, 46(6), 1095-1106.
9
Begin Input properties of cable-stayed bridge (Figure 1) Set up the Stage 1 model (Figure 2) Calculate the target bending moments {M 0} from the Stage 1 model (Figure 2) Set up the Stage 2 model (Figure 3) Calculate the approximate influence matrix [m] from the Stage 2 model Calculate the bending moments {M d} caused by dead load and prestress from the Stage 2 model Calculate an initial estimate of the cable forces {T 0} from {T 0} = [m]-1 ({M 0}-{M d}) Set up the Stage 3 model (Figure 3) Calculate the updated bending moments {M } caused by {M d} and {T 0} from the Stage 3 model 1
Set i = 1 Calculate the adjustment {∆T i} to the cable forces from {∆T i} = [m]-1 ({M i}-{M 0}) Calculate the updated cable forces {T i} from {T i} = {T 0} + Σ{ ∆T j} Set i = i + 1 Calculate the updated bending moments {M i} caused by {M d} and {T i-1} from the Stage 3 model No
Check convergence ||{M i}-{M 0}|| < δ ? Yes End
Figure 4. Flow chart describing the present method. 10
Bridges with Spatial Cable Systems - Theoretical and Experimental Studies Tina VEJRUM Dr. Eng. COWI AS Lyngby, Denmark Tina Vejrum, born 1968 obtained her degree in 1993, Ph.D. in 1997. Joined COWI in 1996. Project Engineer, Major Bridges, Aerodynamics
Anton PETERSEN Civil Eng. COWI AS Lyngby, Denmark Anton Petersen, born 1950 obtained his degree in 1974 and joined COWI in 1975. Chief Engineer, Technical Manager, Bridges.
Summary In cable-stayed bridges with small width-to-span ratios the girder becomes inefficient in transferring lateral loads in bending. Furthermore, the critical load for lateral buckling decreases. A solution could be to apply a so-called spatial cable system that provides both vertical and lateral support for the girder.
1.
Introduction
The present trend within design of cable supported bridges moves towards decreasing width-tospan ratios, see Figure 1.1. This lateral slenderness is either the result of a very long span with a standard deck width or it may be due to an extremely narrow girder used in connection with a moderate span. The first situation becomes relevant because an increased span does not necessarily call for a wider deck since the deck width is more a question of requirements for road and rail traffic. The latter situation could occur in areas with small traffic intensity and thus limited demands concerning deck width. Taking into account the developments in construction techniques and cost, it may become feasible from an economical point of view to build these bridges despite the low traffic volume. In an earth-anchored system, the lateral wind load is transferred partly by the girder in transverse bending and partly by the cable system due to the deflection of the cable planes. In a traditional self-anchored system with vertical cable planes, the wind load has to be transferred entirely by the girder in transverse bending as there will be no pendulum effect. Furthermore, in a selfanchored cable system the girder is subjected to a considerable compressive normal force induced by vertical loads. As the girder becomes more narrow the transfer of lateral loads in bending looses in efficiency. Adding to the lateral load on the girder itself is also approximately half of the wind load on the
cable system, as each stay cable will transfer half of its wind load to the pylon and half to the girder. As a consequence, the static and dynamic behaviour of the structure both during construction and in the completed stage might turn out to be unacceptable, Gimsing (1997) and Gimsing (1994). Width-to-Span Ratio 0.25 Completed Bridge
Buchenauer
Erection stage 0.2
0.15 Nord-Elbe Friedrich Ebert Theodor Heuss Severin
0.1
Stromsund
0.05
0 1955
Erskine Duisburg-Neuenkamp
Maracaibo Severin (erec.)
1960
1965
Pasco-Kennewick Sunshine Skyway 2nd Severn Faro Rama IX Luling Baytown Annacis Brotonne Oresund Rande Barrios de Luna Kohlbrand Tampico Ikuchi Wadi Kuf Tjorn Quincy Karnali River St. Nazaire Knie (erec.) Helgelands Tatara Normandie Skarnsundet Karnali River (erec.)
Rees Bridge Knie
1970
1975
1980
1985
1990
1995
2000
Year of Completion
Figure 1.1 Development in lateral slenderness for cable-stayed bridges. Adapted from Larsen (1997). A possible solution to problems associated with lateral wind load on cable supported bridges with small width-to-span ratios is to apply a so-called spatial cable system that provides both vertical and lateral support for the girder.
Figure 1.2 Architectural model of a cable-stayed bridge having a spatial cable system.
A full three-dimensional support of the girder will require at least three mutually inclined cable planes forming a spatial network of cables. However, to achieve symmetry four cable planes will generally be preferable, see Figure 1.2.
Until present pseudo-spatial cable systems have been applied for pedestrian and pipeline suspension bridges some of these spanning more than 300 m. This paper presents the results of studies on a prototype cable-stayed bridge with a spatial cable system having an 800 m main span and a girder width of 8 m. This gives a width-to-span ratio of 1:100 which is close to a factor of 2.5 compared to the width-to-span ratios found in cable-stayed bridges built until present, see Figure 1.1. Side spans of the prototype bridge are 250 m long. The investigations are divided into three parts: Analytical analyses and related parametric studies, FE-calculations and finally a model test. The research was carried out at the Technical University of Denmark as part of a Ph.D. project, Vejrum (1997).
2.
Analytical Investigations and Parametric Studies
In order to determine the range of inclination of cable planes that is realistic to consider for spatial cable systems, analytical analyses and parametric studies on the prototype bridge are carried out. These show that optimum height of a pylon supporting a spatial cable system does not differ from what is found for a pylon supporting a traditional cable system with vertical cable planes. Thus for the prototype bridge a pylon height above bridge deck of 120 m is chosen, see Figure 2.1.
120 m 30 m
An evaluation of material cost and of deflections due to wind load indicates that the pylon width, b, should range from half the pylon height to the full pylon height. This results in a lateral inclination of cable planes between 1:4 and 1:2, see Figure 2.2.
b
Figure 2.1 Basic geometry of spatial cable system.
The total cost includes contributions from stay and anchor cables and from pylons. The cost of the girder is assumed to be independent of the cable system geometry and is not included in the parametric study on material cost. Deflections are due to elongation of stay cables and to rotation of the pylon caused by elongation of anchor cables. Both contributions and the total deflections are shown in Figure 2.2. 2,0
1,6 1,4
Stay and anchor cables
9
Pylon
8
Lateral deflections at midspan [m]
1,8
Normalized cost
10
Total cost
1,2 1,0 0,8 0,6 0,4 0,2
Total deflections Stay cables Anchor cables
7 6 5 4 3 2 1
Price ratio: r
0
0,0 0
40
80 120 160 Pylon width, b [m]
200
240
0
40
80
120
160
200
Pylon width, b [m]
Figure 2.2 Parametric study on prototype bridge. Pylon height fixed to 120 m. Left: Total cost of structure. Price ratio: Unit price of cable steel / unit price of structural steel. Right: Lateral deflections due to wind load. Design wind speed at girder level: u = 45 m/s.
240
3.
FE-analyses
General presentation of spatial cable systems 3.1 Four different layouts of the spatial cable system are studied and compared by means of numerical analyses, see Figure 3.1. Focus is on the behaviour for wind load, in particular with respect to deflections. The dead load of the girder including railings, surfacing and bridge equipment is 42.7 kN/m. All cables are designed to have a dead load stress of 450 MPa.
a)
b)
c)
d)
Figure 3.1 Four different layouts of the spatial cable system. The basic static behaviour for wind load on the four layouts is explained in Figure 3.2. System a) is considered a "fully spatial (three-dimensional) cable system". We define the term "fully spatial" as cable systems where lateral loads are transferred by the same cables as are used for carrying vertical loads. This way, the dead load of the girder and the cables themselves is used to prestress the cables and thus make transfer of lateral forces possible by increasing or decreasing the prestress. With system a) the lateral force can be transferred by the cable system without any aid from the girder. In system b) the girder needs to have a certain torsional stiffness, because the two cables per section of cable anchorage do not intersect at the centre of gravity of the girder and thus torsion arises.
Consequently the girder has to transfer torsion from one section of cable anchorage to the next, where the torsional moment is reversed. With cable system c) the transfer of lateral forces by the cable system results in local vertical bending of the girder. This is not expected to cause difficulties, since the girder will have a certain vertical bending stiffness to allow transfer of vertical loads from the loading point to the sections of cable anchorage. Finally, in cable system d) the girder needs to have a considerable torsional stiffness, if lateral forces are to be transferred by the cable system. In this cable system the torsional moment is not reversed at the next section of cable anchorage as it was the case for cable system b), so with cable system d) the transfer of lateral forces by the cable system gives rise to global torsional moments to be transferred by the girder.
Figure 3.2 Basic static behaviour of four layouts of spatial cable system subjected to lateral load, U. As described above, cable system a) is the only system of the four that can be considered as truly fully spatial. However, it has some disadvantages compared to the other three. Most importantly, the number of cables is twice the number required for the other systems. This leads to a higher wind load on the cable system. Furthermore, the process of adjusting cables when mounted is more time-consuming and complicated when the number of cables is doubled.
Cable system a) and b) have crossing cables which might lead to a relatively complicated structural detail. Furthermore, the requirements for clearance have to be met. Advantages and disadvantages of the four spatial cable systems are listed in Table 3.1. Cable system
Advantages
Disadvantages
a)
Fully spatial (lateral forces can be transferred without any aid from the girder)
Larger wind load on the cable system Adjusting of cables more complicated Crossing cables
b)
Only half the number of cables compared to a)
Only partially spatial (local torsion) Crossing cables
c)
Only half the number of cables compared to a) No crossing cables
Only partially spatial (local bending) Unsymmetrical with respect to bridge axis
d)
Only half the number of cables compared to a) No crossing cables
Only pseudo-spatial (global torsion)
Table 3.1 Comparison of advantages and disadvantages related to the four spatial cable systems.
Deflections due to wind load 3.2 The following structural features of the girder are used in the study: A = 0.35 m2
Ilat = 2.6 m4
Ivert = 0.31 m4
Itor = 0.92 m4
Girder deflections due to wind load are shown in Figure 3.3. Deflections of cable system b) and c) are identical. The larger deflections of system a) are related to the higher wind load on the cable system because the number of cables is the double. Wind on the cable system causes 66% of the midspan deflection in the case of system a). Wind on the girder accounts for 31% while 3% of the deflection is due to wind on the pylon. The relatively large deflections of the pseudospatial cable system d) are due to global torsion that has to be transferred by the girder. A parametric study reveals that torsional stiffness of the girder has to be increased by a factor of 10 to reduce deflections to the same level as found for the other three spatial systems. Studies on the aerodynamic behaviour of bridges with spatial cable systems are presented in Larsen (1999) and Larsen (1997).
Lateral deflection of girder [m]
Cable system a) Cable system c)
Cable system b) Cable system d)
14 12 10 8 6 4 2 0 -700
-600
Abutment
-500
-400
-300
Pylon
-200
-100
0
100
200
Distance from midspan [m]
300
400
500
Pylon
600
700
Abutment
Figure 3.3 Lateral deflections for wind load on structure. Comparison of four layouts of the spatial cable system. Note: The girder has no lateral support at the pylons. Buckling stability 3.3 In Table 3.2 the buckling stability of the girder is compared for the four layouts. The FEcalculation is an eigenvalue buckling analysis where compression is induced by a uniformly distributed vertical load. The critical loads are normalized by the lowest critical load for vertical buckling which is identical for all four layouts due to the design criterion for the cable cross sections. Cable system
Lateral asymmetric
Lateral symmetric
Vertical symmetric
a)
0.91
0.93
1.0
b)
0.93
0.96
1.0
c)
0.93
0.97
1.0
d)
0.81
0.76
1.0
Table 3.2 Critical loads according to an eigenvalue buckling analysis. Loads are normalized with respect to the lowest critical load for vertical buckling (a symmetric mode). The analyses show that the modelled bridge type having an extremely narrow girder supported by a spatial cable system is not likely to exhibit any stability problems in its completed stage, since the critical loads for buckling instability equal approximately 12 times the characteristic traffic load. However, as a distinctive feature related to a bridge having a narrow girder, the critical loads for lateral and vertical buckling are practically identical. This is in contrast to existing cable-stayed bridges where the critical load for lateral buckling is significantly higher than for vertical buckling.
4.
Model Test
Introduction 4.1 A comparative experimental study on both lateral and vertical girder instability phenomena is carried out on a model of the bridge in the erection stage. The geometrical length scale is 1:80. The parameter to be varied is the lateral inclination of cable planes, see Figure 4.1. Seven tests with different geometries of the cable system were carried out. Figure 4.1 Test setup used in comparative experimental study The aim of studying both lateral on bridges with plane and spatial cable systems. The model and vertical instability with girder is 5 m long. basically - the same model influenced fundamentally on the design of the model itself as well as on the test setup and procedures. The experimental study focuses on spatial cable systems but with two geometries of plane cable systems as reference tests (laterally free or restrained). Thus in order to facilitate the change from plane to spatial cable systems the pseudo-spatial system d) was chosen. Design of the model 4.2 Only vertical load was used to induce compression in the girder. To ensure the possibility of both vertical and lateral instability phenomena to develop, no restraint - lateral nor vertical - arising from loading arrangement or measuring equipment are allowed. Load was applied in the form of plummets placed on scales at each cable set. In the prototype bridge, the distance between the cable sets is 20 m at the girder. In the physical model in scale 1:80 this would cause some difficulties regarding spacing and joints. Consequently, the number of cable sets in the model is reduced to 5. The expected critical loads for the prototype bridge exceed the yield strength of the stay cables by a factor of two to three. In order to be able to study instability phenomena experimentally the load carrying capacity needed to be increased without changing the axial stiffness of the cables. It was decided to use solid rods and model the axial stiffness of the cables with tension springs. The needed load carrying capacity was out of range for standard spiral springs available. Instead, tension springs were constructed from a pile of steel discs working in compression. The discs are placed inside a steel cylinder and are activated by pulling an axle through their central holes, see Figure 4.2. Cable forces and in situ stiffness of the cylindrical springs are measured by means of transducers placed in series with the springs.
Figure 4.2 Principle of cylindrical tension springs. The aim of the model test requires a quite accurate 3D-measuring method for the girder position. Furthermore, no lateral nor vertical restraints arising from the measuring equipment are allowed. These requirements make surveying methods a logical choice. The girder is modelled by a solid rectangular aluminium profile. Dimensions are chosen in accordance with the ratio between critical load for lateral and vertical buckling of the prototype bridge girder. Sectional forces in the model girder are determined from strain gage measurements. Test program and results 4.3 At first two reference tests on a plane cable system were carried out in order to provide the range of the critical loads. Pure lateral instability was observed for the girder without any lateral support, whereas pure vertical instability was obtained by restraining the girder laterally with steel wires fixed to the columns of the test setup in order to prevent instability in this direction. Results for all geometries of the spatial cable system will lie within this range of critical loads. Then the pylon width or lateral inclination of cable planes was gradually increased with the intention of increasing the critical load for lateral instability which would finally exceed the critical load for vertical instability, see Figure 4.3 left. We believe this is the first time an experimental parametric study on the buckling stability of a narrow cable supported girder has been carried out. In Figure 4.3 expected and actual test results are shown.
Critical load
Critical load per scale 300 290 Vertical instability
II
280
Lateral instability (expected results) VI
270 260 Lateral instability
III
Plane cable systems
VII
IV
240 Spatial cable systems
V
250
230 I
220 210
Laterally free plane system Laterally restrained plane system
Pylon width, b
200 0
10
20
30
40
50
60
70
80
90
100
Pylon width, b [cm]
Figure 4.3 Left: Critical load and type of instability as function of pylon width (i.e. inclination of cable planes as the pylon height is kept constant). Right: Test results. Laterally free plane system, Test I. Laterally restrained plane system, Test II and VI. Spatial systems, Test III, IV, V and VII. Test I is the laterally free plane system, while Test II and VI are the laterally restrained plane system. The model girder had to be changed after Test V and therefore one of the reference tests was repeated with the new girder. The result of Test III is in very good agreement with the critical load predicted by FE-calculations. However, from this point no increase in critical load was observed when cable planes were further inclined. Measurements of in situ stiffness of the cylindrical springs led to a possible explanation. During calibration of the springs it was observed that the response was not as stable as intended. Through the test series the relative stiffness of the two springs forming a set increased with the stiffer springs located in the same side of the girder in four out of five cable sets. This difference in axial stiffness induced lateral forces on the girder making lateral instability more critical than vertical instability. Furthermore, the lateral forces arising from a certain difference in axial stiffness of the cable elements increase when cable planes are further inclined. This probably explains why an increase in critical load was not observed for the more spatial systems, Test IV, V and VII. FE-calculations confirm the destabilising effect due to difference in axial stiffness. Based on the test results and FE-calculations it seems that the spatial cable system can provide the necessary elastic support for a girder with a small width-to-span ratio to prevent lateral buckling of being more critical than vertical buckling when lateral inclination of cable planes is around 1:4. Thus the requisite inclination of cable planes to reduce the lateral deflections to an acceptable level also stabilises the narrow girder with respect to lateral buckling that would otherwise have a lower critical load than for vertical buckling.
5.
Conclusions
Based on the investigations carried out in the present work it is concluded, that arranging a spatial cable system is a promising way of solving problems related to applying a girder with a small width-to-span ratio.
6.
Acknowledgement
The Ph.D.-project was carried out with financial support from The Danish Research Councils (STVF). The advisors Professor Niels J. Gimsing and Associate Professor, Ph.D. Henrik Stang are gratefully acknowledged for their supervision.
7.
References
[1].
Gimsing, N.J. (1997): "Cable Supported Bridges - Concept and Design", 2nd ed., John Wiley & Sons Ltd., Chichester, England.
[2].
Gimsing, N.J. (1994): "Suspended Bridges with Very Long Spans", International Conference on Cable-Stayed and Suspension Bridges, Deauville, France, Proceedings vol. 1, pp. 489-504.
[3].
Larsen, S.V. (1999): "Aerodynamic Performance of Cable-Supported Bridges with Small Width-to-Span Ratios", Proceedings of the IABSE Conference on "Cable Stayed Bridges, past, present, future", Malmö, Sweden.
[4].
Larsen, S.V. (1997): "Long and Narrow Cable Supported Bridges Subjected to Wind Load", Ph.D. thesis, Danish Maritime Institute and Department of Structural Engineering, Technical University of Denmark.
[5].
Vejrum, T. (1997): "Bridges with Spatial Cable Systems. Theoretical and experimental studies with special emphasis on lateral buckling stability of the girder", Ph.D. thesis, Series R, No. 19, Department of Structural Engineering and Materials, Technical University of Denmark.
Design and Construction of a CFRP Cable Stayed Footbridge
Fig. 1
Jens CHRISTOFFERSEN Civil Engineer, Ph.D., HD COWI Lyngby, Denmark
Lars HAUGE Civil Engineer COWI Lyngby, Denmark
Henrik ELGAARD JENSEN Civil Engineer, Ph.D COWI Lyngby, Denmark
John BJERRUM Civil Engineer Danish Road Directorate Copenhagen, Denmark
Artist's impression of Herning footbridge, courtesy Møller & Grønborg Architects & Planners
Summary The paper describes a research and development project carried out in order to gain practical knowledge of the use of non-corrosive reinforcement. As a key element of the project, a footbridge with total length of 80 metres has been constructed
1.
Introduction
The first bridge in Denmark, and one of the first in the world to be built with extensive use of Carbon Fibre Reinforced Polymer (CFRP) materials is in the final stage of construction in the Danish town of Herning. The cable-stayed bridge has one central pylon, dual cable planes and a total length of 80 m. The bridge will facilitate pedestrians and emergency vehicles crossing a railway switchyard. The bridge will be the longest so far constructed by the exclusive use of CFRP stay cables. The bridge deck is post-tensioned with 6 CFRP tendons, and a 40 meter section of the bridge deck reinforced with CFRP bars and stirrups. The opposite 40 meter section will be reinforced with a combination of conventional steel and stainless steel reinforcement.
The bridge is a key element of a R&D project, initiated by the Danish Road Directorate in 1997. A consulting team, headed by COWI, has been awarded a contract for investigating the possible use of FRP materials in bridges, and subsequently to design a footbridge with extensive use of FRP materials. The construction contract for the trial bridge was awarded to Skanska A/S. The aim of the R&D project is to evaluate the use of non-corrosive materials in bridge construction. The Danish Road Directorate has an intensive interest in non-corrosive materials, being responsible for the operation and maintenance of the Danish main road network which includes more than two thousand bridges. The heavy use of de-icing salts in the winter periods, combined with frequent freeze-thaw cycles, have rendered traditional reinforced concrete bridges prone to damage, initiated by reinforcement corrosion. The most frequent damage to reinforced concrete bridges in Denmark can be linked to corrosion in bridges parts that are exposed to the chlorides in the de-icing salts. Edge beams and lower sections of bridge columns are especially prone to damage. The deck reinforcement corrodes only severely infrequent, due to strict use of bituminous water proofing membranes on the bridge decks. The water proofing membranes are usually replaced at 25-30 years intervals, and the associated operations constitute a considerable part of the total maintenance costs and cause severe traffic restrictions. The substitution of steel reinforcement with advanced composite materials or high grade stainless steel reinforcement may render the use of bituminous membranes superfluous and possibly result in lower maintenance costs and less traffic disturbance during maintenance operations. Whether the total net present value of bridge construction and life time operation cost will be reduced by use of non-corrosive materials is influenced by the cost of the alternative materials as well as the increase/decrease in construction costs due to different aspects within the construction process. Furthermore, the objective of the R&D project is to obtain experience in using composite posttensioning and stay cables. During the last 30 years a vast number of post-tensioned bridges as well as cable supported bridges have been damaged due to tendon or cable corrosion world wide. The possibility to use non corrosive cable materials might be feasible despite the high initial costs of CFRP materials due to the reduced risk of very expensive cable or tendon replacements during the service life of bridges.
2.
Bridge Articulation
The bridge primarily consists of a deck, supported by 16 cable stays anchored to a central pylon as shown in the figure below. The walkway is 3.5 metres wide and the total width of the deck approximately 5 metres. The dual cable planes support the bridge deck at 9 meter intervals. Due to aesthetic reasons, the bridge is designed without the traditional back span piers. The asymmetric live load is balanced by anchoring the outer stay cables to the foundation structure below the abutment and thereby fixing the top of the pylon. The connection between the CFRP stay cables and the foundation is achieved by using stainless steel bar tendons, suited for the exposed position below the bridge deck.
Fig. 2
Elevation and Section of Herning Footbridge. Required clearance for rail tracks shown below the deck.
3.
Initial R&D project
After being awarded the contract, COWI carried out a thorough survey of literature on FRP materials and the use of the materials in civil engineering, [97.1]. While carrying out this survey the team at COWI had very good access to the latest information through the associated team of experts, acknowledged below. The investigation focused on Glass Fibre Reinforced Polymer (GFRP), Aramide Fibre Reinforced Polymer (AFRP) and Carbon Fibre Reinforced Polymer (CFRP). Each of the mentioned FRP materials can be produced by several types of resins of which epoxy, vinyl-ester and poly-ester are the most common. Epoxy based resin was chosen as the most promising matrix material due to its very good mechanical and chemical resistance properties.
Tensile Strength
Young's Modulus
Density
CFRP
1700-3000 MPa
140-300 GPA
1600 kg/m3
AFRP
1200-2100 MPa
50-120 GPA
1300 kg/m3
GFRP
1500 MPa
50 GPA
2400 kg/m3
Table 1. Typical properties of the most common FRP materials The possible fibre materials were evaluated on a number of factors of which the most important are shown in the table below.
GFRP
AFRP
CFRP
Environmental resistance
-
+
+
Tensile strength
+
+
++
Fatigue strength
0
-
++
Young's modulus
-
-
++
Creep/relaxation
-
0
++
Stress fatigue
-
-
++
Density
+
++
++
Material price
++
-
-
Table 2. Comparison of FRP properties: - not good, 0 neutral, + good, ++ very good. Considering the material parameters, CFRP was chosen to be the FRP material with the highest potential for future use in bridges, although the material price of CFRP is astounding at present. The primary reason for rejecting GFRP was doubt regarding the long term environmental resistance when cast in concrete, and its proneness to low level stress fatigue. AFRP was determined to have a low Young's modulus that might may be a limiting factor in bridge design. It was also noted that most manufacturers are focusing on CFRP and GFRP.
4.
Design of the Footbridge
Prior to the design, a project specific design basis was compiled, as the Danish codes of practice do not cover structures of advanced composite materials. A design level of reliability corresponding to "High Safety Class" in the Danish codes was chosen, and the corresponding partial safety factors determined by probabilistic analyses. Material parameters were obtained from potential manufacturers. 4.1 Stay Cables Special attention was devoted to the ultimate limit state, governed by cable stay failure, by anchorage slipping or by damage due to vandalism. Anchoring of CFRP cables to facilitate the full use of the extremely high tensile and fatigue strength is one of the most challenging problems within CFRP cable development. Several manufacturers have solved the problems caused by the low transverse and inter laminar shear strength of CFRP with unidirectional fibres. High gradients of shear at the anchors have notoriously lead to reduction in the static tensile strength as well as in the fatigue strength, but various manufacturers have solved the problem by developing special anchors, typically of the socket type, Erki & Rizkalla [1993].
The possibility of damage to the cables by fire/heat or by mechanical damage due to impact or cutting by hand held tools was identified as a serious risk early in the project. To reduce the risk of stay failure due to vandalism, the stay cables are protected as shown in the figure below. A HDPE sleeve is extruded on the free stay cable between the anchors. A 2 mm stainless steel tube in two parts is clamped onto the HDPE sheath. Finally, the lower part of the stay cables is protected by a 5mm stainless steel tube that serves the dual purpose of protecting the cables and reducing the stay movement in the anchor zone. The protective measures are not eliminating the possibility of damage, but are intended to discourage vandals before major damage occurs. Regardless of the protective measures indicated above, the bridge has been designed to prevent collapse in case of abrupt failure of one stay cable or static failure of two adjacent cables.
Fig 3.
CFRP cable stay with protective enclosures. The load cell will be used to monitor stay forces.
4.2
Bridge Girder
The deck is basically a slab, supported at both edge beams by the stay cables at nine metres intervals. The weight of the deck is reduced by using seven cut-out ducts. The ducts are discontinued between the stay anchors to form internal cross beams in the deck at these points. The design of the CFRP reinforced part of the bridge girder has been considerably influenced by the intrinsic linear elastic nature of the CFRP reinforcement which would result in a bridge deck with a brittle flexural failure mode, if a usual reinforced concrete design was carried out. Prior to the design two philosophies were evaluated. The first was to cope with the brittle failure mode by raising the total level of safety of the deck. This does not eliminate the possibility of brittle
failure, but reduces the probability of undesired events. The second evaluated method, and eventually adopted, was originally proposed by Mitsuyoshi et. al. [1993]. It aims at asserting ductile flexural failure, despite the linear CFRP reinforcement. By confining the compression zone in the concrete with stirrups, the ultimate strain of the concrete can be raised substantially. Combining this effect with the amount of tensile reinforcement that ensures an over-reinforced failure, a ductile failure governed by concrete crushing can be developed, as shown in the figure below of the original Japanese tests.
Fig 4. Test results of unconfined (No. 6) and over-reinforced and confined beams( No. 3 & 5), Mitsuyoshi et. al. 1993
Fig. 5 7-wire CFRP reinforcement as used in Herning Footbridge, courtesy Tokyo Rope Mfg. Co.
The confined and over-reinforced cross sections were adopted in the longitudinal direction as well as in the internal cross beams between the stay cables. This design is in accordance with the traditional Danish design philosophy, based on ductile failure modes. However, in comparison with the design method described first, the increase in cost is considerable due to the elevated CFRP quantities. The CFRP reinforcement, longitudinal bars and stirrups, are all 7 wire strands of varying dimensions, supplied by Tokyo Rope Mfg. Co. The stirrups are shaped at the factory prior to setting of the matrix resin and cannot be modified on site. In the future, the use of thermo-plastic resins may result in CFRP reinforcement products that can be modified on site; a most desirable possibility.
Fig 6.
Typical cross section of the bridge deck showing CFRP reinforcement of type CFCC from Tokyo Rope Mfg. Co.
While designing the bridge deck using CFRP stirrups, focus was on the reduced strength of the stirrups due to transverse action at the corners. Test results found in the literature suggested a strength reduction of up to 60% of the axial capacity of the stirrups due to the transverse action. To get specific knowledge of the strength reduction of the used stirrup type, an experimental program was carried out at the Technical University of Denmark. The results indicated that a reduction factor of 0.4 would be sufficiently conservative, and this factor was applied in the design in excess to the partial safety factor on the tensile strength of the reinforcement. Further tests at the Technical University of Denmark were carried out in order to verify the bond and anchor capacity of the CFRP reinforcement. The 7-wire strands were found to bond excellently to the concrete due to mechanical interlock.
Fig 7. Deviator for unbonded CFRP tendon in internal cross beam. The bridge deck is post tensioned by six 7-wire tendons. The tendons are placed un-bonded in the cut-out ducts with saddle points at the internal cross beams between the stay anchor points. The post tensioning reduced the amount of plain reinforcement in the longitudinal direction that was necessary to ensure over-reinforced cross sections. The use of longitudinal un-bonded posttensioning facilitates the structural monitoring as the individual tendons can be replaced in the future and the original tendons inspected. Use of un-bonded tendons has the added benefit in comparison with traditional bonded tendons of smeared tendon strain in the ultimate limit state. Thereby the risk of brittle tendon failure at the point of maximum flexure of the deck prior to concrete compression failure is reduced. 4.3
Pylon
The pylon is constructed of weathering steel that fits in well at the switchyard area. Due to the limited free space between the rail tracks, the pylon had to be very slender. This was accomplished by anchoring the top to the foundations below the abutments by connecting the outer stay cables with "back stays" below the bridge deck. The pylon is an airtight structure, assembled in a shop and transported to the bridge site and erected in one piece.
5.
Construction
The bridge is being constructed by Skanska A/S as main contractor. Strict restrictions have been imposed on the contractor with respect to operations on the rail areas. With the exception of short shutdown periods, while the contractor performs specific operations, service of all tracks is maintained during the construction period. The abutments and pylon foundation were built using conventional reinforced concrete. All foundations are piled due to soft top layers of ground. The contractor opted to build the 40 ton steel pylon in a shop and transport it to the bridge site at night in one piece after securing the necessary permits from relevant authorities. The pylon was erected by a mobile crane, levelled and bolted to the foundation. All CFRP materials were delivered by ship from Japan. Stay cables, post tensioning tendons and longitudinal CFRP bars were shipped on coils, whereas the stirrups were shaped by the manufacturer and shipped duly secured in wooden boxes. After arrival the CFRP products were stored in a protective environment to prevent damage from mechanical impact that could occur if stored as conventional steel reinforcement on the construction site. The contractor placed the CFRP reinforcement and tendons in the form work and secured the reinforcement by using plastic strips instead of the usual binding twine. A curious, but not trifling measure, was to secure the very low density CFRP reinforcement against uplift while casting the concrete. The operations regarding reinforcement placement and concrete casting and vibration had been adjusted after a trial casting of a 2 meter section of the bridge deck. The CFRP reinforcement was protected from damage by encasing the vibrators in approximately 1015 mm of synthetic material. The contractor's staff was prevented from stepping directly on the CFRP reinforcement prior to setting of the concrete. The post-tensioning tendons are tensioned by using a hydraulic jack. The elongation of the 80 meter CFRP tendons during tensioning is considerable due to the relatively low modulus of elasticity. Consequently an adoption bar between the socket type anchor and the jack was used. In the future, development of permanent wedge type anchors for CFRP tendons would be an improvement both with respect to the jacking operations and by being more flexible than the fixed length tendons with socket anchors fitted by the manufacturer. At present the socket type anchor has superior fatigue strength and was consequently chosen. The cable stays are placed and tensioned stage wise. The tensioning was carried out based on geometrical requirements to ensure symmetric loading of the pylon and optimal longitudinal profile of the deck under dead load.
6.
Structural Monitoring
A program for structural monitoring of the bridge in the coming years has been set up. It has the dual purpose of ensuring detection, if a severe structural deficiency should occur in the structure, and to facilitate information about the function and durability of the CFRP components.
The first purpose will be achieved by regular measurements of the stay cable forces, tensile stress in chosen CFRP reinforcement bars, and precision measurement of the bridge's geometry. Information about the performance of the CFRP components will be gathered by the following proposed initiatives: • Replacement of an original stay cable at 5 year intervals followed by close inspection of the cable and the anchors. • Replacement of an original post tensioning tendon at 5 year intervals followed by close inspection of the cable and the anchors. • Pull-out tests on protruding CFRP bars to determine long term bond strength. • Measurements on built-in corrosion cells to determine the time at which conventional steel reinforcement would corrode. • Periodic general inspections of the bridge.
7.
Scope for Future use of Non-Corrosive Reinforcement in Bridges
During the last decade much attention has been devoted to transferring FRP technology from the aero-space and defence industries to the construction industry. The focus has primarily been on material characteristics and mechanical behaviour of single structural members. Initially, the extreme strength to density and stiffness to density ratios were identified and theoretic efforts initiated to determine the envelope of possibilities by using advanced composites, Meier [1987], Meier [1992]. Secondly, the very good durability of certain FRP products was identified and use as substitutes for steel in exposed structural parts proposed. Finally, the use of composites for post-strengthening of concrete structures was proposed, and experimental programs carried out to determine feasible operation and design methods. So forth the most successful area of FRP use in the construction industry has been post strengthening of concrete structures by bonded laminates for flexural strengthening of beams or by improving the ductility and capacity of concrete columns by column winding methods, Sieble [1995]. In these areas, FRP solutions have proven to be able to compete with traditional solutions within technical and economic terms. The successful FRP use for post strengthening structures can be tributed to devoted research, large scale trial projects and development of commercially available products with associated design and operation guidelines. Finally, the post strengthening methods, bonded laminates as well as column winding, take advantage of situations at which alternatives are costly. Consequently, the high material cost does not prohibit the use. A similar path may be feasible for other FRP applications. The present Danish trial project is an opportunity to gain information on all aspects of FRP-use in bridges from design to construction. Based on knowledge from this and other trial projects, advanced composites could find their place in bridge engineering. The interesting challenge at present is to develop a FRP application that not only substitutes steel but takes advantage of the composites' intrinsic parameters in structural solutions that conventionally are either expensive or technically deficient.
8.
Acknowledgements
The financial support from the Danish Agency for Development of Trade and Industry (Erhvervsfremme Styrelsen) is kindly acknowledged. Furthermore the valuable technical and scientific support from professor Atsuhiko Machida (University of Saitama), professor Urs Meier (EMPA), professor Frieder Seible (UCSA), professor Henrik Stang (Technical University of Denmark), Risø National Laboratories and Fiberline Composites A/S are acknowledged.
9.
References
[1].
[97.1] 'FRP materials for cable stays, prestressed- and plain reinforcement in Danish Road Directorate, 1997.
bridges',
[2].
Meier [1987] 'Proposal for a Carbon Fibre reinforced Composite Bridge Across the strait of Gibraltar at the Narrowest Site', Proceedings Institute of Mechanical Engineers, Vol. 01 No. B2, 1987.
[3].
Meier [1992] 'Carbon Fiber-Reinforced Polymers: Modern Materials in Bridge Engineering', Structural Engineering International, No. 1, 1992.
[4].
Erki et. al.[1993] 'Anchorages For FRP', Concrete International, June 1993.
[5].
Seible et. al.[1995]'Earthquake Retrofit of Bridge Columns with Continuous Carbon Fiber Jackets - Vol. 2, Design Guidelines', Advanced Composites Technology Transfer Consortium, Report No. ACTT 95/08, UCSD, 1995.
Erection of the Uddevalla Bridge Petter FALLER Production Mgr Steel Constr. Alfr. Andersen A/S, Oslo, Norway
Carl HANSVOLD Eng. Mgr Johs Holt A/S Oslo, Norway
Helge NILSSON Design co-ordination Mgr Skanska Teknik AB Göteborg, Sweden
Per-Ola SVAHN Design Mgr Skanska Civil Engineering AB Göteborg, Sweden
Summary The Uddevalla bridge, located on the Swedish west coast close to the town Uddevalla, is part of the motorway E6 between Oslo and Gothenburg. Construction of the bridge started in mid 1997 and scheduled completion is summer 2000. This paper gives a description of the bridge and the erection methods. Emphasis has been put on erection of the bridge superstructure.
1
Introduction
The E6 highway between Oslo in Norway and Malmö in the southern part of Sweden has during the last ten years been continuously upgraded to a motorway standard. The highway acts as an important link for the communication from Scandinavia to Europe. One critical stretch is the by-pass of Uddevalla, which is located in the end of a deep fjord. The existing road passes east and through the central part of Uddevalla. After extensive investigations during the last thirty years it was decided that the new road will pass west of Uddevalla. The new route is approximately 9 km and will save 12,8 km in total length for the road E6. The route passes through very sensitive locations. The southern side of the fjord has both archaeological and geological values that are classified as of national interests. At the northern side of the fjord there is a location of established dwelling houses, which partly interfere with the suggested route. The Swedish Road Administration performed a conceptual design and the tender work started in May 1996. The tender was an alternative design proposed by the Swedish contractor SKANSKA. The design-build contract was signed in January 1997. The detailed design of the bridge is carried out by SKANSKA Teknik AB, a subsidiary of SKANSKA AB, in co-operation with the Norwegian consulting firm Johs. Holt A.S.
2 2.1
Description of the Bridge Overall configuration
The bridge is a high-level bridge of total length 1712 m carrying 4 traffic lanes, figure 1. The central cable-stayed section provides a navigation clearance 190 m wide and 52 m high over the Sunninge Sund. The approach bridges to either side of the cable-stayed section at the centre, have a total length of 506 m at the south side and 434 m at the north side. The spans increase from 50 m at the north abutment to typical 88 m towards the centre. The cross-section of the superstructure is constructed using two separate steel box girders with concrete deck cast in situ. The central cable-stayed bridge is made up of a 414 m main span and two 179 m spans either side. The cables are arranged in slightly inclined cable planes nearly parallel to the tower legs. They are anchored at equidistant intervals along the bridge deck of 13,32 m except for the outer 3 back stays which are concentrated at the anchor piers N5 and S5.
Figure 1. Elevation of the bridge The entire structure is continuous with expansion joints only at the abutments. Continuity between the approach bridges and the cable-stayed bridge is provided by a heavy concrete transition structure. The six piers at axes N5-N7 and S5-S7 are hinged to the bridge superstructure and contributes to the stability of the bridge in the longitudinal direction. All other piers are equipped with sliding bearings. 2.2
Bridge superstructure
The bridge cross-section in the stayed spans, figure 2, is a composite structure of an open steel grid and prefabricated concrete slab elements. The wind nose, connected to the outer longitudinal I-beam, is a load bearing thin walled shell structure. The stay cables are directly connected to the web of the 1,7 m high longitudinal girders. The slab elements are spanning longitudinally and are connected by loop reinforcement in the cast in place joints. The thickness of the concrete elements is 240 mm and longitudinal reinforcement of 20 mm bars at spacing 160 mm is generally provided to achieve satisfactory strength and limitation of crack widths to 0,20 mm.
Figure 2. Bridge cross-section. 2.3
Towers
The towers are made of concrete grade K55 according to the Swedish Standard BBK 94. They are diamond shaped and rise to elevation 140, figure 3. At the tower top the stay cables are anchored inside steel boxes fixed to the concrete by shear studs. The tie-beam between the tower legs is fully post-tensioned for the outward thrust from the tower legs. 2.4
Stay cables
The stay cables consists of 22 to 77 strands (15,7 mm), individually galvanised, waxed and sheathed. The bundle of strands is covered by an external HDPE pipe. The void between the strands and the external pipe is maintained empty. The stay cables and anchorage system is delivered and installed by VSL. Cable vibrations have been a problem on several cablestayed bridges. To our knowledge, no well documented theory exists for evaluating the risk for such vibrations. Thus the following precautions have been taken:
Figure 3. Tower S1
– – –
The external HDPE pipes have ribs to prevent so called rain-wind vibrations . The cables will be equipped with a friction damper attached to the lower cable anchorage. The cable system shall allow for future installation of transverse stiffening ropes if deemed necessary.
3
Overall erection scheme of the bridge
The erection of the bridge comprises the following main operations: 1. Foundation work and construction of abutments, piers and towers using climbing formwork.
2. Launching of the approach bridges and casting of the concrete slab. 3. Construction of the transition structure at pier N5 and S5. 4. Erection of the cable-stayed bride. Connection to the transition structure. 5. Connection of the approach bridges to the transition structure. The entire bridge is now continious. 6. Completion works such as installation of concrete barriers and pavement of asphalt layer. The situation at the bridge site in autumn 1998 is shown in figure 4.
Figure 4 The bridge site in autumn 1998 The actual design of the main bridge superstructure needs several of different professions. Steel, concrete and cables need skilled workers and normally different contractors have to co-operate closely during the erection. Furthermore close co-operation with the designer is necessary during all phases of erection. For the Uddevalla bridge the erection is organised as follows: The main contractor SKANSKA is responsible for the overall co-ordination of the erection. They deliver the concrete panels for the bridge deck and perform the casting of the joints on site. The steel contractor Alfred Andersen delivers the steel grid. On site they are responsible for the lifting works with the derrick cranes and welding of the steel sections together. The cable contractor JV Internordisk Spännarmering/VSL delivers anchors, staypipes and strands. On site they are responsible for the erection of the cables.
4
Erection of the approach bridges
The superstructure of the two approach bridges comprises a steel box girder with a composite deck of concrete. The steel box girders are fabricated in 16 21,5 m long pieces with weights up
to 82 tons. They are welded together on the site behind respectively abutment and launched to the final position. The deck is casted in-situ with a movable formwork. The spans of the approach bridge vary from 50 m to the most typical 88 m span.The bridge is performed in a horizontal radius of 1750 m, which have a significant influence on the launching work. The steel box girder is equipped with a launching nose, shaped with a slope versus the steel girder to take care of the deflection of the cantilever during the launching. The length of the nose is determined by the strength of the steel box. The actual length of the nose is 30,5 m, which gives a maximum deformation of the nose tip of approximately 2,1 m during the launching. The launching is performed on temporary sliding bearings, which are placed on the permanent neotopf bearings. The sliding bearing has a length of 1,2 m and consists of a steel plate with sliding plates of PE-material on top. The painted steel girder slides direct on these plates. A critical point for the steel girder is the risk for buckling in the web due to the patch load from the bearing. The web has been temporarily reinforced near the lower flange over a length of approximately 24 m, where the maximum reaction forces will appear. When the steel girder is launched to its final position the temporary sliding bearings are removed. The deck is casted in-situ with a movable formwork in steps of 22 m. The height between the ground and the bridge deck together with the need of an efficient production lead to a design with a continuos casting from respectively abutment. To avoid high tensile stresses in the concrete above the piers, where the girders are continuos, the steel girder was pre-loaded with a weight of 300 tons. The load was placed to give a negative bending moment in the steel girder during casting and hardening of the deck above these piers. This method has been performed with a good result. Launching of steel box girder is shown in figure 5.
Figure 5 Launching of steel box girder
5
Erection of the cable-stayed spans.
The superstructure of the cable supported spans is constructed by the balanced cantilever method. Two starter segments on either side of the tower are first constructed on fixed scaffolding. After tensioning of the cables the scaffolding is removed and the lifting derricks assembled. The standard erection cycle, consisting of 5 main stages, then follows: A. A steel grid of length typical 13,32 m, width 26,06 m and weight about 70 tonnes consists of two longitudinal edge-beams, three cross-beams and two cable anchorages. It is lifted by the derrick and temporarily fixed to the previous steel section. After control of local geometry in elevation and plan welding of the main beams can begin. The steel grid is a rather flexible structure, and auxiliary bracings are used to ensure correct geometry during lifting and installation. The bracings also provide the necessary lateral support of the slender cross-beams when loaded with the concrete elements. B. The cables are installed and stressed to a first stressing stage. C. The derrick lifts the concrete elements in place. Geometry and cable forces are checked, and possible adjustments performed. D. The joints between the concrete elements and the edge beams are cast. E. When the concrete has reached a compressive strength of 25 MPa the cables are stressed to their final length. The derrick is then moved in position for lifting of the next segment. The cables are stressed at the tower head in two steps, at stage B and E, using monostrand jacks. In addition, a final tuning of the back-stays will be performed in parallel with completion works, e.g. installation of concrete barriers and pavement of asphalt layer. At stage C the rather flexible steel grid is loaded by the dead load of the concrete elements and the cable forces applied at stage B. The cable forces have to be carefully determined such that no harmful deflections or stresses are built into the deck section when composite action is established at stage D. Stage C is thus an important control stage as regards geometry and cable forces. The first stressing operation will be based on measurement of force. For the second stressing and other cable adjustments, both cable forces and elongations (jack stroke) will be specified with the latter as the prime control parameter. For the stages described above local geometry and cable forces will be surveyed. For every third segment a complete survey of the entire cantilever will be carried out. A detailed analysis of all structural systems during erection and for the completed bridge has been performed. The analysis takes into account the various loads at each erection stage, the cable forces and the effects of temperature, creep and shrinkage. Procedures for survey containing all necessary data for construction as well as data for easy corrections have been established. Exchange of data between the bridge site and the design office in Oslo will be based on electronic mail transmission. The bridge deck is temporarily fixed to the tower during free cantilevering. Extensive analyses of wind buffeting show that additional supports of the cantilevers are necessary. Temporary
struts to the ground are installed at a distance of 40,5 m to either side of the tower in order to reduce the wind-induced bending of the tower in the vertical plane. At cantilever length 124,86 m these struts are replaced by a new support at distance 107,1 m from the tower on the landside. This support takes vertical and horizontal forces thus reducing both vertical and transverse oscillations of the cantilever. It also allows for vertical jacking of the bridge deck in order to ease the connection of the bridge to the transition structure at pier N5 (S5). Stiff steel supports were selected instead of more simple tie-down solutions. One reason for this is the rather strict project specifications allowing only limited tensile stresses but no cracking of the towers during the entire construction period. After connection of the main bridge to the transition structure at pier N5 (S5) erection of the remaining segments in the main span follows. Before closing at midspan the cantilevers are jacked approx. 75 mm in outwards in order to compensate for creep and shrinkage effects.
6
Concluding remarks
The construction work is now well under way. The situation on site in beginning of February is that launching of the steel box girders of the approaches is nearly completed, and about 50% of the concrete slab has been cast. The north tower N1 was completed in Dec. 1998 while the south tower S1 will be completed in March 1999. Erection of the main span is in progress. Scheduled opening of the bridge for traffic is May 2000.
Acknowledgements Owner: Contractor: Steel contractor: Stay cables: Structural design:
Swedish Road and Bridge Administration, Region West. Skanska Civil Engineering AB, Bridge Department. Alfred Andersen mek. verksted & stöberi A/S. Internordisk Spännarmering AB / VSL International Ltd. Skanska Teknik AB in co-operation with Johs. Holt A.S.
Cable-Stayed GFRP Footbridge across Railway Line Mikael W BRAESTRUP Dr. Eng. RAMBØLL Copenhagen,.Denmark
Mikael W Braestrup, born 1945, is a Senior Consultant at the RAMBØLL Bridge Department. Current assignments include the 16 km Øresund Link between Denmark and Sweden, in particular the design basis, involving application of the Eurocode system.
Introduction The use of fibre reinforced plastic (FRP) in bridge building is fairly novel. The first European example is the 113 m long Aberfeldy Footbridge, a cable-stayed bridge spanning 63 m over a stream on a Scottish golf course, installed in the early nineties. In June 1997 a new FRP bridge for pedestrians and cyclists was opened at Strandhuse near the Danish town Kolding. As the first advanced composite bridge in Scandinavia it has the further distinction of being the first FRP bridge crossing a busy railway trunkline. The cable-stayed bridge is constructed entirely of glass fibre reinforced plastic (GFRP), and it is the result of a collaboration between a local producer of pultruded GFRP profiles, a major consulting engineering company, and a public owner who was willing to consider an innovative replacement of a footbridge removed due to the increased clearance profile resulting from electrification of the railway. The erection of the bridge was carried out in just 18 hours. The total capital costs are 5 -10 % higher than alternative designs in steel or concrete, but this is offset by the resistance of the GFRP material to water, frost, and de-icing salts, implying that cosmetic maintenance only is envisaged for the next 50 years. The bridge, known as the Fiberline Bridge after the producer, is shown in Fig 1.
Description The width of the bridge is 3.2 m, and the length is 40.3 m, with spans of 27 m and 13 m. The stays are 100 x 100 mm2 GFRP cables. The 1.5 m deep girder and the 18.5 m high, asymmetrically placed pylon are constructed from standard GFRP profiles bolted together. The 12 different profiles used are shown in Fig 2, and Fig 3 shows the bridge seen from below. The only steel components are the bolts and the inserts in the concrete foundations. The total weight is 12.5 t, less than half of a corresponding steel structure.
1
Fig. 1. Fiberline Bridge at Kolding, Denmark
Fig 2. Standard Profiles
Fig 3. Underside of bridge
2
Design The bridge is designed for a live load of 5 kN/m2 plus a 50 kN moving point load, representing a snowplough or the occasional ambulance. In accordance with Danish code tradition limit state design based upon the partial coefficient method is used. Thus the load factors are 1.0 on dead loads and 1.3 on live loads. The material partial coefficients on strength and elastic modulus are 1.8 and 1.9, respectively. The two pairs of stays on either side of the pylon minimize the deflections Fig 4. Design Manual which would otherwise result from the low stiffness of the GFRP material. A general Design Manual, see Fig 4, for structures in pultruded FRP profiles has been developed, including shaping and connection, and resistance to chemical attack and fire exposure. Manufacture
Fig 5. Pultrusion of GFRP Profile
Fig 6. Connection by Bolting
The GRFP stays, as well as the profiles used for bridge girder and pylon, are produced by pultrusion. Pultrusion is a continuous process whereby the fibreglass reinforcement is pulled trough a permanent form, into which the polyester resin matrix is injected, see Fig 5. The matrix is cured by means of catalyst addition and heating. The profiles are cut to length and shaped by ordinary hand tools. The profiles may be coloured as desired, but an aesthetically more pleasing finish is obtained by surface coating, and light grey and blue tones were chosen for the bridge. Assembly was carried out by stainless steel bolts, see Fig 6. Bolting is clearly not the most suitable joining method for the highly anisotropic pultruded profiles, and glued connections are under development. The strength, stiffness and bolt pull-out strength of the profiles are subject to regular testing. Fig 7 illustrates the testing of a beam for flexural properties.
3
Fig 7. Test Rig for Flexural Testing
Installation Due to the continuous operation of the railway, construction activities on site were only allowed during 8 hours of the night between Saturday and Sunday. The bridge was manufactured in three pieces, comprising the pylon and the two girder spans. Fig 8 shows a bridge section being loaded onto a trailer for transport to the bridge site. The erection took place during three night sessions, see Fig 9.
Fig 8. Bridge Section
Fig 9. Erection of Bridge
Cost Fiberline has compared the actual costs of the bridge with corresponding designs in steel and concrete, see Table 1 below. The conversion to Euro is done at the rate of DKK 7.50 to one Euro. For the FRP option the development costs are included under design.
4
Costs in 1000 Euro Design Foundations Materials Shaping and Joining Erection Surface Treatment Miscellaneous Total
FRP 55 55 105 55 25 10 25 330
Steel 25 70 15 80 55 25 35 305
Concrete 20 80 80 80 15 35 310
Table 1. Cost Comparison Monitoring
Fig 10. Mounting of Strain Gauges
Fig 11. Monitoring from Control Station
The fact that the bridge crosses a busy railway line causes sharp focus on safety and reliability, and a system is established to monitor structural stresses and deformations due to changing loads. Key bridge components, including the stays, are fitted with strain gauges, see Fig 10, wired to a permanent control station, shown in Fig 11. Universities are invited to use the bridge as a test site. To monitor temperatures, wind speeds and directions a weather station is installed at the top of the pylon, see Fig 12.
5
Fig 12. Weather Station on Top of Pylon Conclusion Although data on long-term performance is still outstanding, the Kolding experience indicates that FRP is a viable material for minor bridges with a premium on swift erection and minimal maintenance. To make full use of the potential of this novel structural material it is pertinent to develop technology for gluing of profiles, as well as new architectural forms.
6
Ting Kau Cable Stayed Bridge: Challenges in the Construction Process Don BERGMAN Buckland & Taylor Ltd. Hong Kong
Introduction The Ting Kau Cable-Stayed Bridge in Hong Kong provides a vital new link between the Western New Territories and the expressway linking Kowloon with the new Chek Lap Kok Airport on Lantau Island. The US$225 million design construct contract for the bridge was awarded by the Hong Kong Highway Department in August 1994 with completion scheduled for July 1997. The bridge opened to traffic in May 1998.
Fig. 1: General Arrangement The bridge is a light and innovative structure spanning the 900 m wide Rambler Channel. At 1177 m in length, the bridge is one of the longest cable stayed structures in the world and is one of only a few multi-span cable-stayed bridges in existence (Fig. 1). The design has several unique features which are responsive to the difficult site and schedule constraints for the project. These design features however created specific challenges for the construction team: • • • •
Monolithic steel tower heads which house the upper cable stressing anchors permit shop fabrication of these complex elements under controlled conditions. (require 190 tonne heavy lift into place at the top of the 200 m towers). Stabilizing stays with deck level struts provide the necessary transverse stiffness and strength for mono-leg towers which could be easily slip formed. (require heavy lift of 50 tonne struts and load transfer to stabilizing stays) The mono-leg tower places a minimal footprint in the Rambler Channel where foundation and ship impact criteria are onerous. (requires temporary stabilization of slender mono-leg tower during construction) Twin decks with intermittent transverse cross connecting members and four stay planes (Fig. 2) minimize the weight of the transverse deck members and provide excellent aerodynamic performance in the severe wind climate. (geometry and detail difficulty with four girders, simultaneous installation of four stays)
1
•
•
Longitudinal stabilizing cables (LSC’s) diagonally connecting the top of the main tower to the deck at the side towers, provide longitudinal stiffness and capacity to the balanced central main span cantilever. (the LSC’s are the longest cable stays erected to date, the Main cantilever is longest balance cantilever erected to date) Deck grids could be shop prefabricated and preassembled under controlled conditions to deal with the complex 3D deck and cable anchorage geometry which includes a superelevated, curved, variable width deck at the Ting Kau side span (requires quality prefabrication and preassembly)
Fig. 2: Deck Arrangement The ability to prefabricate and preassemble had the greatest potential to impact construction. Ideally it would permit fast efficient erection with relatively unskilled crews. In order to achieve this however it was necessary to obtain high quality steel fabrication from the start. The components had to be fabricated and preassembled in the correct sequence, with assurance that quality welding and geometry control was being achieved.
Steel Fabrication Success relied on the choice of a steel fabricator with the necessary qualifications and facilities. That choice in this case was based primarily on economics. The fabricator had relatively little relevant bridge experience and the outcome of the project was largely determined by this fundamental decision. The first and most critical elements to be fabricated were steel tower heads which are large complex pieces with many heavy restrained welds requiring carefully planned weld procedures and sequences (Fig. 3). As fabrication progressed testing revealed weld cracking. A time consuming program of NDT, repair and reinforcement substantially delayed the delivery of the tower heads. The slip formed Ting Kau tower, which was completed first, waited six months to receive the first tower head. Under the original schedule, erection of the tower heads for the three cantilevers was to be staggered. This spread the resource demands at the three cantilevers and permitted the re-use of crews and equipment. To recover the lost delivery time for the tower heads, it became necessary to reduce the scheduled stagger making additional heavy lift equipment necessary. Contractual payment clauses for fabrication encouraged early completion of the simplest, highest tonnage deck components, the cross girders, even though most were not immediately required for pre-assembly and erection. Delay in the preassembly of the first deck grids resulted. These grids 2
were subsequently shipped with many of the secondary fixtures having not been preassembled. The result was costly and cumbersome assembly of these elements in place. The fabricator’s organization made use of multiple levels of subcontractors. Control of the work was difficult. The lower level subcontractors tended to feel no direct responsibility to the main sub contractor if more than one level separated them. Pre-assembly of the steel deck grid presented unique challenges. Due to variations in deck width, cross girder spacing, cross girder length, and deck slab thickness, the camber of the cross girders varied significantly. It was necessary to preassemble the deck unstressed, i.e. with no deck concrete in place. If one imagines a complete deck with the concrete slab in place, with correct as-built girder and cross girder geometry, and then imagines removing all of the concrete deck slab to “unstress” it, the result would be the theoretically correct “unstressed” geometry. The difficulty is that the cross girders which have different cambers want to deflect and end rotate by differing amounts. The result was an “unstressed” deck grid where the girders are trying to restrain the differing cross girder rotations. The “unstressed” grid would therefore have built-in moments in the cross girders and built-in torques in the main girders. This “unstressed” geometry is in fact stressed and cannot be achieved in preassembly without unreasonable effort. Ultimately a truly unstressed preassembly geometry was Fig. 3: Tower head derived. The resulting preassembly geometry was a compromise which attempted to minimize the warping of the main girders, the amount of error in final cross girder camber, and the error in target girder profile. Welding quality control was thrown into question late in the fabrication after defects were found in previously accepted welds. Many of the critical welds such as those for the connection of the cable anchorages to the main girders were found to be defective and a large and costly program of weld repairs was required some of it on steel which was already erected.
Tower Head Erection The first steel erected was the tower heads which provide the stressing anchorage at the top end of the stay cables. The steel tower heads are boxes up to 31 m in height, 4 m in width and 1.5 m in depth. After lifting and positioning, the tower heads are concreted in and stressed to the tower top. The tower heads weighed 150 tonnes each for the Ting Kau and Tsing Yi towers and 190 tonnes for the Main central tower. The tower heads were lifted into place using a pair of 200 tonne heavy lifting strand jacks on beams mounted on the tower top (Fig. 4). The beams carried the jacks on a sliding cross frame at each end. The cross frames allowed the tower head to be slid into position for concreting and stressing onto the tower top.
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The tower heads were transported to the site by water, lifted onto self propelled heavy load platform trailers which were used to position and hold the unit while rotating to the vertical (Fig. 3).
Fig. 4: Tower head heavy lift
Lifts began only after confirmation of a three day site specific wind forecast for winds less than 14 m/s. A secondary cable wind restraint system was used to stabilize the tower head during the lift. Prior to lifting, tower head weights and centers of gravity were confirmed. The as-built tower head weights tended to be greater than the design weights in part as a result of the repairs and reinforcement noted above. The lifting frames were designed for the theoretical tower head weight and erected by the time the as-built weights were known. As a result it was necessary to re-design the wind restraint system for the heaviest lift at the Main tower to minimize any additional vertical wind loads applied to the lifting frame.
Prior to lifting the Main tower head, inspection revealed cracking in several of the welds for the lifting beams. A detailed program of NDT and weld repairs was implemented prior to lifting. Delays in the delivery of the tower heads allowed a significant layer of corrosion to build up on the lift strands. While there was no damage or significant section loss, the corrosive layer had to be power washed off the strands prior to lifting so that the anchor wedges would not fill and slip during the repeated gripping and regripping required during the lift.
Starter Panel Erection Following preassembly, the starter panel grids were transported to the site and positioned at the tower base. Using the tower top heavy lifting gear again the grids were rotated to vertical, lifted to final deck level, lowered into deck level hinges on falsework, and rotated to horizontal (Fig. 5). The grids were lifted with the transverse bearings attached to the inside of the interior girders. To orient the interior girders for splicing the cross connecting girders and grouting the bearings to the tower, the outside girders were temporarily supported below final elevation. Precast panels were then installed, the starter panel stays installed and the heavy lift strands released. Large vertical downwards displacements of the starter panel Fig. 5: Starter panel erection were expected when the lifting equipment was erected on the starter panel and the adjacent deck grids were
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lifted. The starter panel stays were therefore temporarily installed short of final length to lift the starter panel and provide vertical clearance between the panel underside and the tower transition. Care was taken in positioning and squaring the starter panel grids to match the preassembly geometry prior to erecting the precast panels. Errors in the starter panel plan geometry would be passed on to all subsequently erected panels either side.
Tower Strut Erection Once the starter panels were erected heavy lifting beams and strand jacks were mounted on the starter panel to lift the horizontal struts for the transverse stabilizing cables (Fig. 6). A pair of precast panels were left out of the starter panel deck in order to pass jacking strands through the deck to the strut. As with the tower heads, the jacks were positioned on sliding cross beams allowing the strut to be correctly positioned for grouting and stressing onto the tower leg. The struts were released from the heavy lift gear as soon as a minimum number of strands for the transverse stabilizing stays were installed. This permitted removal of the heavy lift gear and start of erection of the derrick supports (sleds) and the derricks themselves. A sequence of strand installation for the transverse stabilizing stays was chosen which minimized the movement of the tip of the strut and permitted installation directly to force. Specific final forces are required in the stabilizing stays such that under typhoon, the leeward stays will just come slack. It was necessary to calculate installation forces which after all elastic, creep, and shrinkage shortening of the tower had taken place, would result in the specified final force. Fig. 6: Strut heavy lift During construction the transverse stabilizing stays initially exhibited significant rain/wind vibrations. The vibrations were temporarily restrained using nylon ropes connected some distance up each stay. A system of permanent dampers was subsequently designed, fabricated, and installed just after the opening of the bridge. It is interesting to note that these were the only stays on the bridge which did not have HDPE sheaths with raised spirals to inhibit rain wind vibrations.
Derrick Cranes Deck mounted stiff leg derrick cranes were chosen for lifting steel grids and deck panels. Derricks do not rely on counterweights for stability but rather tie down to and use the deck structure itself to resolve the lifting reactions. The arrangement is therefore light and minimizes the bending effects imparted to the deck by the construction loads. Derricks are typically
5
mounted on a sled structure which distributes the reactions to the deck framework and also facilitates movement of the derrick after completion of each new deck grid (Fig. 7). The twin deck arrangement of the bridge made it necessary to use a pair of derricks at each cantilever tip. Twelve stiffleg derricks were therefore required for the three towers. Erection of the sleds and derricks, load testing, and commissioning of the derricks was directly on the critical path for the project. This process took 7 weeks for the first pair of derrick cranes. The last pair was completed in 4 weeks. Because the process of erecting and commissioning the derricks was so time consuming, the decision was taken to eliminate the last pair intended for the Ting Yi land span. Instead a crawler crane with 66 m of main boom and 54 m of luffing jib was positioned on the approach road in the Tsing Yi land span and used to erect the land span superstructure. This decision reduced the time to erect the Tsing Yi cantilever by approximately 4 weeks. After each segment was completed the derricks were released from the deck, lowered onto Hillman rollers positioned over each cross girder, and pulled ahead to the next position using hydraulic tirfors. Release, lowering and preparation to roll would take approximately 4 to 6 hours. Rolling, and tiedown for the next segment would take approximately 8 to 10 hours. The required strength of the newly cast infill joints was 20 MPa for rolling and 30 MPa for lifting. In total, erection of each starter panel, including the derrick cranes which were needed to begin the typical deck erection sequence, took 18 weeks for Ting Kau, 19 weeks for Main and 11 weeks for Tsing Yi which used only two derricks. Note that in order to make room for the second set of derricks at Main and Ting Kau, a second deck grid needed to be erected and the first derricks rolled onto it. Complete erection of the three cantilevers including the starter panel durations above, took 37 weeks for Ting Kau (22 grids), 34 Fig. 7: Derricks at starter panel weeks for Main (39 grids) and 25 weeks for Tsing Yi (24 grids). Approximately one half the time to erect each cantilever was therefore consumed by the start up process. This is an aspect of this type of project which does not always receive due attention, but where full optimization can yield substantial schedule benefits. Extensive efforts were put into insuring safe operation of the derricks. These included load testing, operator training, instrumentation for load and reach limits, detailed checks and signoffs for derrick translation, tiedown, and operation, and certification by the Hong Kong authorities. Despite these efforts, a serious accident occurred during erection of the last sea side grid for the Tsing Yi cantilever. A failure occurred in the derrick sled which resulted in the grid being dropped to the barge below. The grid was destroyed and the barge severely damaged. Fortunately no workers were injured. The failure was traced to a missing weld detail, which was hidden inside a box beam anchoring the rear derrick tiedown. The accident occurred on 3 January 1998. A replacement grid was fabricated in Spain, flown piece small to Hong Kong, and erected by 27 February 1998. The last closure between the Main and Tsing Yi cantilevers was delayed slightly as a result, but by carrying out some of the finishing work such as placement of
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the waterproof membrane and asphalt surfacing prior to closure, no time was lost on the overall schedule.
Typical Deck Erection Cycle The critical path for erection of the superstructure ultimately passed through the Main cantilever, which is the longest of the three. The challenge was therefore to minimize the erection cycle times there. Because full welded grids were erected on both ends of the cantilever and lifting off the water at both ends made delivery relatively simple, it was possible to consistently produce four day erection cycles (Fig. 8). This was one of the great successes for the project. Operations were carried out over a twenty four hour period where necessary.
Fig. 8: Typical four day deck cycle
Cycle times for the piece small grids in the Ting Kau and Tsing Yi land spans were typically longer ranging between 5 and 8 days. The longest cycle times were required for the Ting Kau land span where material delivery to the derricks was complicated by the terrain, the wide deck and the large members.
Stay Cable/Precast Panel Installation After each steel grid was erected and bolted to the previous grid, the next step was to install stays and precast panels. One precast panel and a stay installation platform was first installed over each of the four girders. This provided the work area for the stay crew. The platforms carried a cutting table, a deviator wheel for guiding the strands into the stay sheath and a winch for returning the pulling cable back to the deck after each strand. The HDPE sheath containing the master strand was first erected and the master strand tensioned to force. The installed length was then checked against the reference length. All master strands were carefully measured and marked when cut by the supplier. If the length confirmed the tension the remaining strands were pulled into place and stressed to the master strand tension by matching the monostrand jack pressure that of a load cell remaining on the master strand. The stay installation procedure for a composite deck must insure that the correct non-composite girder bending moments and geometry are locked in when the joints are cast. The procedure which requires simultaneous installation of precast deck panels and cable strands must also insure that no overstresses occur in the girders at any intermediate stage. If too may panels are installed without strands to carry the load, the girder will be overstressed in hogging. If too many strands are installed without panels to load the strands, the strand force will drop to a level where proper anchorage cannot be assured. For Ting Kau the lower bound strand force was set at 20 kN by the cable supplier. Computer modeling the sequence of strand/panel installation for each of the grids showed that an upper bound strand force could be established which would insure no overstress. The upper and lower bound strand forces were then used to control strand/panel 7
erection. When the strand force approached the upper bound force, panel installation would stop while strand installation continued until the strand force dropped. When the strand force began approaching the lower bound force, strand installation would stop while panel installation continued and the strand force increased. This method of control proved to be simple and effective. The result was a stay installed to the correct force, insuring correct non-composite bending moments in the girder. After installation of the stays and panels, and casting of the infill joints, the stay was then stressed to the final calculated length, not force. Final stressing to length has proved to be the most effective method of achieving correct final geometry. Demands placed on the cable installation crews were severe, particularly at the Main cantlever which operated on a four day cycle and required some of the largest stays. In December of 1997, approximately 1200 tonnes of cable stays (more than many complete bridges) were erected in a single month.
Precast Panel Support The precast panel support detail makes use of shims welded to the cross girder top flange over the web. Four stiffened rebar loops in the corner of each panel rest on these shims to support the precast at the correct level. This detail relies on close tolerances in as-built cross girder camber to achieve acceptable deck geometry. The actual as-built camber of the cross girders was in general less than theoretical and in some instances even negative. This resulted in high shim stacks, stud extensions and extra rebar in the haunches created over the cross girders. Formwork was now also required between the soffit of the precast and the top flange of the girder rather than the simple sealing strips originally intended.
Temporary Wind Restraints The stiffness and stability of a typical cable stayed bridge in its complete form is derived from two elements - a heavy main span - typically longer than the side span - combined with anchor stays connecting the tower top to a fixed anchor point in the side span. Neither of these two elements are present during erection by balanced cantilever. Stability during erection is therefore
Fig. 9: Temporary wind restraints 8
often more critical than for the completed bridge. This was particularly important for Ting Kau where the main cantilever is the longest balanced cantilever ever erected and the wind climate is so severe. Stability under typhoon was required for wind speeds up to 95 m/s. This could only be insured through the use of a system of temporary cable restraints. Arrangements were proposed and wind tunnel tested at the design stage. The final system (Fig. 9) has several significant aspects: • • •
•
Prior to installation of the cable restraints, the deck was stabilized by fixed longitudinal connections of the interior girders to the tower. Once the cable restraints were installed, the longitudinal connections at the tower were disconnected so as not to attract a disproportionate share of the restraining forces. In order for the Main cantilever to progress beyond 170 m, the permanent longitudinal stabilizing cables (LSC’s) had to be installed to restrain the rocking response of the cantilever (longitudinal tower bending). This in turn required that to resist the horizontal anchor forces generated by the LSC’s, the TY deck be temporarily connected longitudinally to the abutment and the TK cantilever have its full cable restraint system in place. Note that the LSC’s are self anchoring with the deck in the final condition. In order for the Main cantilever to progress beyond 170 m, the Main deck also had to be connected to the Ting Kau deck by means of cross connecting cable ties to restrain the weathervaining response of the cantilever (plan deck rotation). The Ting Kau deck also had to be connected laterally to the anchor pier in order that the Ting Kau cantilever top could provide restraint.
The typhoon season in Hong Kong is between June and November. Peak gust wind speeds by month as measured at Waglan Island together with the erected length of the Main cantilever are shown (Fig. 10). The critical 170 m length was not to be reached until the end of November. The peak wind speeds for December through Fig. 10: Monthly wind speed versus erected Main cantilever length March drop to as little as one half of the peak typhoon wind speed. The temporary wind restraint system, which was designed for full typhoon could therefore be reduced as follows: •
The cross connecting cables were eliminated. This was a substantial saving. These cables would have been installed slack at all times, to be tensioned only in a wind event. The cables would have interfered with deck erection and would have required cumbersome moveable temporary anchorages.
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•
The LSC’s needed only to be started at a cantilever length of 200 m and complete by a cantilever length of 260 m. This meant that erection of the main cantilever need not stop while the LSC’s were being installed.
The temporary cable restraints were installed to force. Master strand tensions were calculated for the installation stage and remaining strands were balanced to the master strand force. With the exception of concrete placement, deck erection was permitted to proceed simultaneously with temporary cable installation once the master strand was in place.
Closures The Ting Kau and Tsing Yi side spans are permanently tied down with link plates and rocker bearings connecting the girders to the TK anchor pier and TY abutment. The rocker bearings were first installed and stressed to the anchor pier/abutment, the anchor grids were erected on adjustable falsework over the bearings and the rocker bearings field welded to the girders. Sidespan closure was made by jacking the anchor grid towards the cantilevered deck and splicing. The Main/TY closure was made by releasing the post-tensioning bars tying the TY deck to the abutment. The Main/TK closure was made by releasing the TK longitudinal restraint cables in the side span.
Geometry and Stay Forces The bridge geometry was checked closely for each stage of construction, as follows: •
• •
After erecting a new grid the plan alignment was checked. Adjustments were made before the precast panels were erected and the alignment locked in. Alignment was controlled by adjustment of temporary cross bracing installed in each grid during preassembly. Alignment adjustments of up to 20 mm over a grid were common. Demand on the cross braces was the greatest in the TK land span where the wide curved deck reached 60m in width and 6% in crossfall. Coordinates of the tower anchorage and the deck anchorage for the new stay were checked for use where the master stand force did not agree with the reference length. After installation of stays and panels, the deck and tower geometry, and final stay installation force were confirmed against theoretical before placement of infill concrete was permitted. After placement of the infill concrete the global deck and tower geometry were confirmed against theoretical.
Detailed global surveys of the deck profile were done before placement of the asphalt wear surface. The asphalt was placed in two lifts a nominal 55 mm base course and a constant 30 mm friction course. Using the deck survey, base course thicknesses were determined along the deck to produce the best ride possible while staying within the +/- 15 mm thickness tolerance. After the final deck closures a global survey of the bridge was carried out and stay forces checked by monostrand liftoff. A set of final stay adjustments were calculated to “tune” the deck geometry and stay forces. After closure 145 of the 428 deck stays were adjusted. Of these stays 129 were shortened by monostrand jacking and 16 were lengthened using a full size annular jack. Stay adjustments took approximately two weeks to complete and were done independently of the
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other finishing work on the bridge. Final adjusted deck geometry was typically within 50 mm of theoretical.
Conclusions The complete success of an innovative design such as the Ting Kau Cable stayed bridge must come from careful consideration of both the final product and the construction process. In this case the design innovations produced an efficient final design and also presented opportunities and challenges to the construction team to optimize the construction process. While many of the challenges were met, opportunities to fully realize the potential construction benefits of the design were in some cases missed.
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Seismic response of partially earth-anchored cable-stayed bridge Toshiyuki SUGIYAMA Associate Professor Yamanashi University Takeda, Kofu JAPAN
Toshiyuki Sugiyama, born 1954 received his Dr. Eng degree from Univ. Tokyo 1984
Summary The dynamic characteristics of partially earth-anchored cable-stayed bridge subjected to strong earthquake motion are discussed based on the results of time-history response analysis. The bridge type is three spans continuous girder type with multiple cables and its main span length is 1000 meters. Finite Element Method is applied to the dynamic analysis. Hyogo-ken Nanbu Earthquake (Kobe Earthquake) record including both horizontal and vertical components is adopted as input earthquake motion. Only the direction of motion parallel to the bridge axis is considered. Soil-structure interaction and phase-lag of input earthquake motion that arises among two piers and two anchored points of side-span cables are neglected here. It has been revealed that the maximum vertical displacement at the center of main span of partially earth-anchored cable-stayed bridge is enough smaller than the deformation limit although the maximum deformation of partially earth-anchored cable-stayed type is larger than that of self-anchored one. The results also show that the stress resultants of partially earthanchored cable-stayed bridge are considerably smaller than those of self-anchored one. These results indicate that no problem may occur from seismic viewpoint in case of the application of partially earth-anchored cable-stayed bridge to long span bridge with main span length of about 1000 meters. And it is also cleared that the consideration of only horizontal earthquake motion is sufficient in case of the execution of dynamic response analysis of cable-stayed bridge with 1000m mainspan length.
1. Introduction When cable-stayed bridge is applied to long span bridge with about 1000m center span length, large axial force that acts on the main girder probably becomes a serious problem as it may cause the buckling of main girder. To reduce this axial force, partially earth-anchored cable-stayed bridge has been proposed by Gimsing[1]. And a few studies have been carried out to discuss the static characteristics of this type of bridge by Kaneko et al. [2]. However, the seismic characteristics of partially earth-anchored cable-stayed bridges have not been estimated in detail. The purpose of this study is to discuss the dynamic response of partially earth-anchored cablestayed bridge subjected to strong earthquake motion based on the results of time-history response analysis. Partially earth-anchored cable-stayed bridge with 1000-meter main span length is selected as the subject of study and its seismic characteristics are compared with those of selfanchored one. The bridge type is three spans continuous girder type with multiple cables. Finite Element Method and Newmark's method are applied to the dynamic analysis. Hyogo-ken Nanbu Earthquake (Kobe Earthquake) record including both horizontal and vertical components is adopted as input earthquake motion.
2. Analytical model Fig. 1 shows the partially earth-anchored cable-stayed bridge with main span length of 1000m. The upper six cables in each side span are anchored to the earth. Self-anchored cable-stayed bridge with 1000m main span length is illustrated in Fig. 2. The cross sectional area and second moment of area of each structural element are shown in Table 1. These two types of cable-stayed bridges are selected as the subject of investigation here and their dimension and cross sectional properties are the same as the bridges taken into account in reference [2]. Especially, partially earth-anchored type as shown in Fig. 1 was one of the bridges that were
Fig. 1 Partially Earth-anchored Cable-stayed Bridge
Fig. 2 Self-anchored Cable-stayed Bridge
Main grinder Cable upper part Pylon lower part
Cross Sectional Area 0.8626 ~ 0.9996 m2 0.0097 ~ 0.0141 m2 1.1760 m2
Second Moment of Area 1.1166 ~ 1.3226 m4
1.4700 m2
12.411 m4
9.9810 m4
Table 1 Cross Sectional Properties of Cable-stayed Bridge proposed for Tatara Bridge planning by Dr. Kaneko's bridge design group, although this type was not adopted in practice. The following two supporting conditions are considered in this study; 1) one end of main girder is fixed by hinge bearing and other points are supported by movable hinge bearings;
Fig. 3 Hyogo-ken Nanbu Earthquake Record 2) one pylon and main girder are rigidly connected. As any significant difference between self-anchored type and partially earth-anchored one has not been recognized regarding to the dynamic response in the transverse direction of bridge axis [2], only the direction of motion parallel to the bridge axis is considered here. Hyogo-ken Nanbu earthquake record is adopted as input earthquake motion. Both horizontal and vertical earthquake motions are taken into account. Figs. 3(a) and (b) show the horizontal and vertical component records of Hyogo-ken Nanbu earthquake, respectively. Fig. 4(a) and (b) are the power spectrum density diagrams corresponding to Fig. 3(a) and (b), respectively. Soil-structure interaction is neglected. And phase-lag of input earthquake motion that arises among two piers and two anchored points of side-span cables is also neglected here. In the analysis based on Finite Element Method, main girder and pylon are assumed to be one beam and one column whose cross sectional properties are shown in Table 1.
Fig. 4 Power Spectra of Hyogo-ken Nanbu Earthquake Records Each cable is assumed to be a member that resists only tensile force. The length of each finite element is 10[m] according to the result of investigation regarding to the convergence of lower order eigenvalues. The initial values of stress resultants of main girder, pylons and cables are obtained from the static analysis in which only dead load acts on each type of cable-stayed bridge. In order to estimate the effect of vertical earthquake motion on the dynamic response, the following two cases are taken into account in time history analysis; that is, a) dynamic response under only horizontal earthquake motion (designated ‘CASE-1’ hereafter) and b) dynamic response under both horizontal and vertical earthquake motions (designated ‘CASE-2’).
3. Results of dynamic response analysis 3.1 Vertical Displacement of Main Girder Fig. 5 shows the maximum vertical displacement of main girder along bridge axis under Hyogoken Nanbu earthquake motion. In this figure, left-hand part shows the vertical displacement in case of supporting condition 1), and the right-hand part presents the one in case of supporting condition 2). And in Fig. 5, each line corresponds to the following cases; solid line : partially earth-anchored type in CASE-2 broken line : partially earth-anchored type in CASE-1 dotted line : self-anchored type in CASE-2 one dot chain line : self-anchored type in CASE-1 (These four kinds of lines in Figs. 6 9 correspond to the cases described above, too.) From Fig. 5, it can be recognized that maximum vertical displacement at the center of centerspan in case of supporting condition 2) is smaller than those in case of supporting condition 1). This fact means that the supporting condition 2) is more preferable than supporting condition 1) from the point of view of smaller deformation. Accordingly, only the results in case of supporting condition 2) are discussed hereafter. From Fig. 5, the following facts are also found; 1) the maximum vertical displacement of partially earth-anchored type is about twice as large as that of self-anchored one in case that only the horizontal earthquake motion is input; 2) in case that both horizontal and vertical motions are considered, any significant difference between self-anchored type and partially earth-anchored one is not recognized. 3) the maximum displacement of main girder of partially earth-anchored type in CASE- 2 is approximately the same as that in CASE-1, although the former is a bit larger than the latter; 4) the maximum vertical displacement at the center of center-span of partially earth- anchored type is enough smaller than the deformation limit although the value of 3[m] for deformation limit in Japanese specification is not expressed in Fig. 5.
Fig.5 Maximum Vertical Displacement of Main Girder 3.2 Horizontal Displacement of Pylon Fig. 6 presents the maximum horizontal displacement of pylon along its height. From this, it can be recognized that the horizontal displacement of pylon of partially earth-anchored type becomes larger than that of self-anchored one. However, it is also known that the maximum displacement at the position where the lowest cable of main span is anchored to the pylon takes approximately the same value.
Fig. 6 Horizontal Displacement of Pylon 3.3 Axial Force of Main Girder The maximum values of axial force that acts on the main girder are shown in Fig. 7. From this, it can be recognized that the maximum axial force in case of partially earth-anchored type is at most about 50% of the one in case of self-anchored type. It is also found that any significant difference between CASE-1 and CASE-2 is not recognized. This means that the consideration of only horizontal earthquake motion is enough when the dynamic response analysis of cablestayed bridge with 1000m main span length is executed.
Fig. 7 Axial Force of Main Girder 3.4 Bending Moment of Main Girder Fig. 8 illustrates the maximum values of bending moment of main girder. Regarding to the bending moment, the values in CASE-2 are considerably smaller than those in CASE-1. Its reason may be as follows; in case that the vertical and horizontal earthquake components are input simultaneously, the dynamic behavior of main girder becomes complex and the effects of both horizontal and vertical motions are offset.
Fig. 8 Bending Moment of Main Girder 3.5 Stress Resultants of Pylon Fig. 9 shows the axial force, shear force and bending moment which act on the pylon. Except the shear force, the tendency is the same as the bending moment of main girder. In case of shear force, the differences among four cases are very small.
Fig. 9 Stress Resultants of Pylon
4. Concluding remarks The dynamic response of partially earth-anchored cable-stayed bridge subjected to strong earthquake motion is investigated based on the results of time-history response analysis. It has been revealed that the maximum vertical displacement at the center of center span of partially earth-anchored type is enough smaller than the deformation limit although the maximum deformation of partially earth-anchored cable-stayed type is larger than that of self anchored one. The results also show that the stress resultants, i.e., axial force of main girder and axial force and bending moment of pylon of partially earth-anchored cable-stayed bridge are considerably smaller than those of self-anchored one. These results indicate that no problem may occur from earthquake resistant viewpoint in case of the application of partially earth-anchored cable-stayed bridge to long span bridge with center span length of about 1000 meters. And it is also cleared that the consideration of only horizontal earthquake motion is sufficient in case of the execution of dynamic response analysis of cable-stayed bridge with 1000m main span length.
References [1] Gimsing, N.J.: Cable Supported Bridge -Concept and Design-, John Wiley & Sons, 1983. [2] Kaneko, S., Nakayama, T., Mukoyama, T., Iwaki, T. and Takekawa, S.: Applicability of Partially Earth-anchored Cable-stayed Bridge to Long-span Bridge, Journal of Construction Management and Engineering, No. 510/VI-26, pp.113-124, March 1995 (in Japanese).
Charles River Crossing:A Gateway To Boston Vijay CHANDRA Chief Bridge Engineer Bechtel/Parsons Brinckerhoff Boston, MA, USA
Anthony RICCI Manager of Structures Massachusetts Highway Department Boston, MA, USA
Christian MENN Consultant to the Central Artery/Tunnel Project Zurich, Switzerland
Raymond McCABE Senior Vice President HNTB, Inc Fairfield, NJ, USA
1.
Introduction
Boston’s Central Artery/Tunnel (CA/T) project involves many innovative underground structures. However, the project’s keystone is the Charles River Crossing, featuring a hybrid cable-stayed bridge that will be the first of its type in the US. The river crossing will provide virtually the only access to Boston from the north, straddling the Charles River in an historic area where Paul Revere began his famous ride and the Battle of Bunker Hill took place. Accordingly, there is great interest in ensuring that the bridge features a distinctive design while also providing a dramatic gateway to the city’s downtown. The immense CA/T project consists of many kilometers of tunnels, six major interchanges, a long-span parallel crossing of the Charles River connecting Storrow Drive to the north and the cable-stayed bridge. Major project funding is being provided by the Federal Highway Administration (FHWA). Parsons Brinckerhoff Inc., in joint venture with Bechtel (B/PB), is serving as project management consultant for the Massachusetts Turnpike Authority (MTA), the owner. B/PB prepared the bridge type studies, performed preliminary designs of selected structure types, managed and oversaw preparation of the final design by HNTB, Inc./Figg Engineers, and is managing construction. MTA is providing oversight of the project’s design and construction phases.
2.
Design Constraints
Major physical constraints for the bridge in the Charles River crossing area include: • Orange Line subway ventilation building adjacent to the south main pier • Orange Line tunnel alignment traversing the bridge alignment at an angle, requiring the north main pier foundation to straddle it • A 0.92-meter-diameter waterline located below the south main pier • Steep 5% grade entering a tunnel at the south end and tying into a three-level interchange at the north end • Potential interference with a CA/T highway tunnel exit ramp to be constructed at the south end of bridge • Existing double-deck bridge and its ramps, which must remain in service during construction of the new bridge
•
3.
Existing Charles River lock and dam system abutting the bridge on the east side
Bridge Type Selection
The Charles River Crossing must meet the objectives of numerous state and federal regulatory agencies, including the FHWA. The bridge design must present sound engineering solutions to numerous site constraints while also meeting community expectations that the structure create a distinctive “signature” on Boston’s skyline. To fulfill these goals, the project team conducted a bridge type study and assembled a multidisciplinary team of experts in structural engineering, highway design and engineering, urban planning, construction, environmental engineering, architecture, and cost and scheduling control. Initially, the project team identified 16 bridge types, each with a main span measuring 227 meters. The sixteen designs included three arch bridges, four truss bridges, a segmental box girder bridge, a fin-back concrete bridge, a suspension bridge and six cable-stayed bridges. The engineering team then analyzed each option for a wide variety of impacts, including alignment, design, environmental, urban design, constructibility, ease of inspection, maintenance and cost, before narrowing the field to seven bridge types for further study. They included a two-hinged arch, a simple span truss and five cable-stayed bridges. The cable-stayed bridges, both symmetrical and asymmetrical designs, varied between 10 and 12 traffic lanes and featured single- and double-tower configurations. It was also decided that the cable-stayed bridges could be built using steel, concrete or a hybrid of both, and that tower pier shape was flexible. An evaluation matrix was prepared based on priority factors as well as a quality rating for the impacts previously mentioned. From the field of seven candidate bridges, two cable-stayed designs emerged that best met the demanding site conditions: an asymmetrical 10-lane bridge with twin, inverted Y-shaped towers and two cantilevered lanes, and a symmetrical 10-lane bridge with a single A-shaped tower. From these two finalists, the Massachusetts Highway Department selected the twin tower asymmetrical design, citing its smaller inverted Y towers as a Figure 1. The First Hybrid Cable-Stayed Bridge in the US benefit in reducing the visual scale of the bridge to be more appropriate with its surroundings (See Figure 1). The initial concept for this asymmetrical bridge was proposed by the renowned Swiss engineer, Dr. Christian Menn, who was retained as a consultant during preliminary design to help ensure that the bridge met community expectations.
Preliminary designs were then prepared for steel, concrete and hybrid alternatives for the asymmetrical cable-stayed structure. Although each alternative posed unique challenges, a committee composed of international experts convinced the project team that only the hybrid design should be continued due to its relatively short back spans compared with the main span. The back spans will feature “heavy” cast-in-place post-tensioned concrete construction to counterbalance the “light” main span constructed of steel floor beams and edge girders with a precast concrete composite deck. By using this configuration, the bridge will become the first hybrid cable-stayed structure built in the US.
4.
Site-Specific Seismic Study
The Charles River Crossing will be a lifeline to Boston. Like all major interstate highway structures, it is considered “important” for seismic considerations. This means that the bridge should be serviceable after the design earthquake, sustaining only minor damage. Therefore, due to the structure’s critical role and its unusual design features, a site-specific seismic study was undertaken. Evaluating seismic sources in the New England area was based on the latest developments in seismic source zone characterization and attenuation relationships for the eastern US. Both 2% and 5% damping for the 500-year operating design earthquake and 2,000-year maximum design earthquake return periods were developed for the Charles River Crossing.
5.
Aesthetics
The shape of the tower piers and the cable arrangement (main span cables splayed out from the tower with back span cables centered in the median) evolved from technical requirements. For example, the proximity of the Orange Line vent building to the south tower and the need for the foundation of the north tower to straddle the subway alignment below, necessitated truncating the columns below the roadway. The tower shape was itself dictated by the torsional rigidity required in the transverse direction due to the cantilevered ramp on the east side. In addition, the cable arrangement resulted from the proximity of Leverett Circle ramps (approximately 0.61 meters) on the south side, which must remain in service while the new structure is built. Splaying the cables in the back span was further impacted by existing Leverett Circle ramp supports. Technical issues aside, aesthetics played an important role in shaping the structure, making it a true gateway to Boston. This concern even extended beneath the structure, where openings were provided in the wide main span deck to prevent a permanent shadow from being cast on the water.
6.
Bridge Configuration
The Charles River cable-stayed bridge features a 56.4-meter-wide, five-span hybrid superstructure with a main span of 227 meters; two south back spans of 34.2 and 39.6 meters; and two north back spans of 51.8 and 76.2 meters (See Figure 2). The tower piers are an inverted
Y shape (See Figure 3) and the back spans consist of multi-cell concrete box girders, 3 meters deep and 38.4 meters wide. Main structural elements include a 3-meter-wide central spline beam and four secondary webs with internal diaphragms spaced at 4.6-meter intervals (See Figure 4). The spline beam, in turn, is supported by a single plane of cables spaced at 4.6 meters.
Figure 2. Bridge Elevation
Figure 3. Tower Elevation
The main span consists of precast concrete deck panels acting compositely with longitudinal steel box edge girders and transverse steel floor beams (spaced at 6.1 meters on center) by means of cast-in-place closure strips (See Figure 5). The box edge girders are supported by cables anchored on the outside at 6.1-meter intervals. On the main span side, the two-lane ramp (SA-CN) is carried on floor beam extensions cantilevered to one side of the main line deck. Lightweight precast concrete deck panels are used for the ramp to minimize eccentric dead loads. On the back spans, the ramp is a single-cell concrete box girder, independent from the cable-stayed structure, with roadway joints at the tower interfaces. Open-grid fiberglass closure panels partially cover the underside of the main span superstructure to create a more aesthetic underbelly.
The many design challenges of the Charles River cable-stayed bridge are discussed in the following pages.
Figure 4. Concrete Back Span Typical Section
Figure 5. Main Span Typical Section 6.1
Foundation and Drilled Shaft Design
The tower foundations consist of footings on 2.44-meter drilled shafts designed to carry a working load of 2,270 tonnes each. At the north tower, the footing and the supporting drilled shafts straddle the Orange Line tunnel. Measures were taken to ensure that the tunnel is not adversely impacted by foundation construction activities. The drilled shafts closest to the Orange Line tunnel are placed outside a 1.52-meter buffer zone and the project team investigated the effect of lateral forces transmitted from the drilled shafts through the surrounding soil to the Orange Line tunnel. As a result, the two shafts closest to the tunnel are to be installed within 2.74-meter-diameter isolation casings. Meanwhile, the south tower foundation is very close to the existing subway ventilation building on the west side, while also bridging a 0.9-meterdiameter waterline. As a result, the three drilled shafts closest to the ventilation building will also be isolated within a 2.74-meter-diameter isolation casing. 6.2
Strut at Tower Piers
The change in direction of the tower legs at the deck level produces large tension forces in the tower strut, which also serves as the transition from the main span composite steel superstructure to the post-tensioned concrete box girder back spans. These forces, which are carried in the spline beam of the back spans, need to be transferred to the edge box girders of the main span or vice versa. The edge girders, in turn, are then attached to the main-span cables. As a result, special attention was focused on strut design, while shear lag effects and tension stresses in the concrete were also carefully evaluated.
In addition, the imbalance of bending, shear and axial load forces in the main span and back spans under different loading combinations produce torsion, bi-axial bending and bi-axial shear stresses in the tower strut. Due to the critical structural nature of the strut, which will be posttensioned in stages to a total initial jacking force of 25,000 tonnes, limiting principal tensile stresses to pre-determined values under the working loads was an important design consideration. 6.3
Concrete Back Spans
Two major challenges in the design and detailing of the south back span were due to the physical overlap of the plan area of the proposed bridge, a tunnel ramp at the south interface, and the presence of numerous Figure 6. Spline Beam existing, temporary and future ramps under the north back span. At the south interface, the design solution features an early termination of the main line bridge deck (by approximately 15.24 meters), while extending the central spline beam the full length as a cantilever to receive and anchor the first three cables (See Figure 6). Heavyweight ballast concrete with a density of 4,000 kg/m3 will be placed in the box girder cells within the last three floor beam bays to counteract the local reduction in superstructure weight due to the early termination of the roadway. The cantilever extension of the spline beam is housed in a vault built into the slab on grade roadway of the adjoining project contract. To reduce the impact of north back span construction to ramp traffic by limiting ramp closures and detours, final design and detailing of the north back span was conducted based on the incremental launching construction method. However, after a detailed evaluation, the contractor proposed and the project team accepted a value engineering proposal to cast-in-place the north back span using falsework. 6.4
Steel Edge Girders and Floor Beams
The edge girders are asymmetrical steel box sections with an inclined bottom flange and an inclined fascia web. Typical edge girder field sections are 18.3 meters long, supported by three stay cables. To achieve a full moment connection between the tower and the edge girders, a base plate connection with 35-millimeter-diameter, 1,034 Mpa post-tensioning bars is used. Floor beams, spaced at 6.1 meters longitudinally, will span 42.7 meters between box edge girders and cantilever approximately 13.7 meters to carry two lanes of traffic outside the east plane of the stay cables. Additionally, an edge beam provided at the fascia of the cantilevered section will distribute truck loads to multiple floor beams. 6.5
Stay Cables
Project design documents required stay cables strands to be either greased and sheathed or completely filled with epoxy. Also, flexibility was provided concerning the type of anchorage, wedge or socket or wedge/socket to be utilized. After the project was bid, Kiewit/Atkinson, the
successful bidder, proposed using ungrouted stay cables employing the Freyssinet “Iso-tension” stressing method. Implementation of this proposal means that this will be the first US project to use ungrouted stays and the Iso-tension method of stressing. The contractor also successfully proposed using coextruded PE pipe with a spiral bead to reduce stay cable vibration. The CA/T project has opened many doors and advanced the state-of-the-art of stay cable technology. Presently, two of the three stay cable fatigue/tension tests have been performed successfully with the last one underway. 6.6
Cable Anchorage at Towers
The vertical leg at the tower top varies from 3.2 meters square to approximately 4.9 meters square at its base. Because of the limited room to anchor cables, a prefabricated steel anchor box will be built into the tower, acting compositely with the concrete section by means of shear connectors. The cables Figure 7. Tower Head Cable Anchorage will be anchored by bearings at the inner end of structural tube sections built into an anchorage girder (See Figure 7). This detailing offers the following advantages: • Reduced torsional moment due to closer transverse spacing of the cables • Improved geometry control of the cable anchorages • Elimination of complicated forming of the inside walls • Elimination of post-tensioning in the tower cross section However, torsion in the tower leg due to the cantilevered ramp on one side posed a challenge. The east side cables of the main span carry a 30% greater load than the west side cables. This is overcome by using a lightweight concrete deck slab in the cantilever and offsetting the geometric centerline of the back span and main span cables by 76 millimeters. To avoid external cable anchorages and related maintenance issues in the inclined legs of the tower, a non-uniform cable spacing scheme is implemented. This entails gradually increasing vertical spacing from the standard 1.68 meters for the uppermost ten cable pairs up to 2.9 meters for the lowermost cable pair. Additional minor geometric adjustments were also implemented.
6.7
Girder-to-Cable Anchorages The cable anchorages on the main span box edge girders are mounted on the outside and are detailed as a pipe assembly bolted to the side of the girder (See Figure 8). The cables are then passed through the anchor pipe, with the cable anchor bearing against the lower end of the pipe (which also forms a part of the structural system resisting local forces due to the cable anchorage). The pipe will be connected to the base plate with a single web plate.
This detail was selected due to its visual appeal over typical box-type cable anchorages; fabrication and erection considerations; and for allowing easy access for inspecting all critical welds and bolts. Figure 8. Cable-to-Edge Girder Anchorage
7.
Aerodynamic Evaluation
Wind tunnel tests of both the sectional and aeroelastic models were performed for the final structure as well as for intermediate construction stages. Vortex excitation occurred at about 128 kph, within criteria, while flutter speed was measured at 715 kph, well above the requirement of 210 kph. Smoke flow visualization tests also indicated that wind flows were not significantly altered by changes to the deck section, such as deck openings and porous closure panels on the underside. The assessment of the potential for cable vibration, considering the use of coextruded PE pipe with a spiral bead to reduce rain/wind vibration and ungrouted stay cables, resulted in cross-tie requirements to offset galloping. After a study of the Freyssinet viscoelastic dampers was conducted by RWDI and Construction Technology Laboratories, it was concluded that providing dampers at all lower anchorages, coupled with some cross-tie arrangements, would best meet project needs.
8.
Erection Scheme
The cast-in-place back spans will be constructed on falsework concurrent with tower construction. The tension strut at the tower piers will be post-tensioned in stages. Afterwards, the superstructure of the main span will be erected in a cantilever fashion. As sections of the main span are erected, stay cables will be installed and tensioned.
The superstructure of the main span will be erected in stages. Initially, the edge box girders will be cantilevered out, followed by precast slab placement and, finally, cast-in-place closure strip construction. After the superstructure is erected in the main span, barriers and latex-modified concrete overlay will be constructed.
9.
Construction
Construction of the Charles River cable-stayed bridge was started in September 1997 by Kiewit/Atkinson, a joint venture. The low bid price for the bridge was $86.7 million. The drilled shaft foundations for the main piers, back span piers, and walls are nearly complete. The foundation slab of the south tower is complete and work has started on the north tower. The south tower lower inclined legs have also been constructed and work on the tension strut is underway. Bridge completion is scheduled for late 2001.
10.
Conclusion
Boston, in the forefront of the American Revolution over two centuries ago, is now in the forefront of another revolution—in the field of cable-stayed bridge technology. A highly complicated structure, unique in the world, has been successfully designed and is under construction. New technologies and innovations have become hallmarks of the Charles River Crossing.
The Design and Construction of Lockmeadow Footbridge, Maidstone
Ian P.T. FIRTH Partner, Flint & Neill Partnership London, England.
Ian Firth graduated from the University of Bristol in 1979 and obtained a Master’s degree in Structural Steel Design at Imperial College in 1982. He has been responsible for many bridge projects with Flint & Neill Partnership, including the Poole Harbour Bridge in England. He is also responsible for the design of two other footbridges soon to be constructed in Maidstone.
Summary This competition winning design for a cable stayed aluminium footbridge uses aluminium extrusions in an innovative and effective way to reduce both initial construction costs and future maintenance requirements.
1
Introduction
The bridge crosses a bend of the River Medway in the centre of Maidstone in Kent, adjacent to the Grade 1 listed Archbishop’s Palace at a location where historical and archeaological issues predominate. The site has been described as one of the most sensitive sites for a bridge anywhere in England, and after careful analysis the governing visual design criteria of slenderness and lightness evolved. (Figure 1) A mediaeval lock used to occupy the river at this point (hence the name “Lockmeadow”) and more recently a pedestrian ferry boat service operated here, and both of these also had an influence on the design.
Figure 1: Architect’s model image of the finished bridge with the Archbishop’s Palace behind The design was developed in conjunction with Chris Wilkinson Architects and was the winning entry in an invited design competition held by Maidstone Borough Council in early 1997.
Inevitably, any design competition scheme attracts a lot of critical interest from among the architectural and engineering professions, as well as from a wider audience, and the visual quality as well as the elegance of the engineering solution have received and will continue to receive much scrutiny. The contract was let by Maidstone Borough Council to Christiani and Nielsen in July 1998 for a construction cost of £630,000. Their principal sub-contractors are D&B Darke for the fabrication and deck erection, and Nedal Aluminium BV for the aluminium supply. The bridge provides a pedestrian crossing of the river from the town centre to a new leisure development under construction on the west bank adjacent to the Lockmeadow market site.
2
The Conceptual Design
The brief called for a navigation clearance of 4m without intermediate supports in the river, and disabled access requirements dictated a maximum gradient for the approach ramps of 1:20. Due to local constraints at the east bank, where the abutment is set among trees behind an ancient stone river wall, it was however agreed that short lengths of steeper ramp could be tolerated with suitable landings in between. The land behind the river wall on the east bank is a Scheduled Ancient Monument with very difficult access conditions, and the stability of the old stone retaining wall could not be easily determined. The bridge thus needed a very “light touch” on this bank, permitting the use of a small abutment with a minimum of excavation and vertical mini piles in sleeves to prevent any lateral loads on the wall. The river is known to flood regularly, and the west bank is part of a flood plain which was to be kept as clear of obstruction as possible. It thus became necessary for the bridge to span not only the river itself, which at this point is about 40m wide, but also part of the flood plain as well. Access to the west bank was not such a problem, and permitted the construction on the river bank of a substantial pier to compensate for the need for a light touch on the other side. Thus the solution of a twin span cable stayed bridge with one span over the river and the other over the western flood plain began to emerge, with the masts partly hidden in the trees. This also suited the visual and historical references which demanded a strong focus for the bridge on the west bank of the river. This west bank pier is shaped like the bow of a boat to face upstream and act as a “cutwater” under flood conditions, and on its back it carries the access stairs to the bridge from the towpath. (Figure 2) A cable stayed solution enabled the deck depth to be kept to a minimum, owing to the intermediate stay supports, and this not only suited the desired visual lightness and transparency, but also reduced the lengths of the approach ramps. The supporting mast on the west bank was split into two, one each side of the cutwater stairs, and these were inclined forwards and outwards to provide the most effective positions for suspending the deck. The budget set by the Client at the competition stage was extremely tight, and this was partly responsible for the decision to adopt a deck system involving the assembly of simple repeatable components with no added finishes. A lightweight solution was also necessary to minimise
foundation costs. The final bridge solution adopts a unique and very shallow extruded aluminium deck system as a result of these factors.
Figure 2: Plan and elevation Crossing a footbridge such as this is not just a means of getting from one side to the other but also an experience in itself. Indeed part of the interest in a footbridge is the texture, colour and “feel” of the handrail and ballustrade, as well as the visual appearance of the bridge. In this case, the ballustrade also needed to be relatively transparent and permeable to the passage of the flood water. The chosen solution is a stainless steel handrail with black carbon fibre posts and stainless steel “wedge wire” infill panels. These seemingly expensive but attractive materials turned out to be cost effective partly because of their low maintenance costs and partly because their specialist manufacturers were keen to supply components for this high profile project. The bridge has a slight plan curvature which was added at a late stage to tie in with the landscape scheme, to add extra interest, and also to direct the eye away from the rather ugly adjacent leisure building on the west side.
3
The Aluminium Deck
The extruded aluminium sections are placed side by side longitudinally and stressed together transversely with stainless steel bars. The parapet posts are fixed via couplings to the ends of the bars and simultaneously retain the outer edge extrusions. The top flange of the extrusion is ribbed and cross-cut transversely to provide a slip resistant surface, and there is no need for any secondary structure or for any added finishes. This is one of the beauties of the system;- the
aluminium extrusion provides the primary structure, the secondary structure and the finish all in one section, and this provides an elegant and economic solution. This system leads to the formation of a cellular deck cross-section. Early discussions with manufacturers showed that closed section extrusions would be at least twice as expensive as open sections, so a series of back-to-back open channel sections was adopted. We did not wish the soffit to have the same ribbed surface as the top, so a doubly symmetric shape which would have enabled the use of “tongue and groove” type interlocking sections was not possible. Instead we provided small continuous grooves in the section and introduced shear keys to improve transverse rigidity. It was also necessary to introduce inclined webs and a central blocking cell so that when assembled they together formed a pattern of X-bracing. (Figure 3)
Figure 3: Typical Section The maximum cross-section size of extrusion which can be formed is limited by the size of the die through which the aluminium is pushed. In the UK there are no large diameter presses operating, but in other parts of Europe there are several. The limiting size is defined by the circumscribing circle, and it became clear from early discussions with manufacturers that an economic solution would need to fit within a 350-400mm circle. Thus the final section is 300mm deep and 105mm wide. The maximum length of extrusion is governed by the amount of aluminium in the cross-section. An ingot of aluminium pushed through a die will produce a longer length if there is less material in the section. There is also a certain amount of wastage at each end of the section which is cut off after extrusion. In our case, the maximum finished length of extrusion is about 7m, and most finished lengths are approximately 6.4m. The section weighs 15kg/m, so each typical length weighs about 96kg which can easily be handled by two men - another beauty of the system which considerably facilitates deck assembly.
The aluminium alloy selected is 6082 T6 to BS 1474 which gives good material strength properties, although with a slightly lower quality of finish than some of the other architectural grades. The outer edge sections are anodised to give a good uniform finish, but it was decided to leave the remainder as mill finished to reduce costs. The 6082 material contains copper in the alloy, and tends to take on a slightly greenish colour after anodising. The transverse pre-stressing bars are 24mm diameter S316 martensitic stainless steel with a yield strength of 800 N/mm2. The guidance given in the design standard BS8118 regarding isolation of dissimilar metals was followed. This recommends that the stainless steel and aluminium need only be separated when fully immersed in water or where high levels of atmospheric pollution exist. In view of the fact that the bridge would occasionally be immersed in flood water at its lower end, it was decided to place the bars within sleeves and apply a layer of bituminous material under the contact surface at the ends of the bars as an extra safeguard. Friction tests on samples of the extrusions showed a lower than expected coefficient of friction of only about 0.2. This led to the introduction of additional shear keys to assist in transferring transverse and longitudinal shears between the extrusions at points of high shear such as at stay anchor positions and at bearings.
Figure 4: Typical Modal Response Analysis Plot Our analysis of the dynamic behaviour and time history response calculations indicated that the design just failed to meet the criteria contained in the Highways Agency standard BD49/93 for excitation by pedestrians. This analysis integrated the response caused by loads travelling over the bridge in phase with the natural frequencies of the bridge to determine the peak accelerations. (Figure 4) Several options were considered for alleviating this issue, but we found that the simplest was to add mass over the midspan section which improved the response so that peak accelerations were brought back within the specified limits. This extra mass is added in the form of wrapped steel reinforcing bars inserted inside the voids in the deck section over the central 17m at midspan. The calculated fundamental frequency of the finished bridge is 0.98 Hz.
4
The Cable Stay System
The cable stays are 45mm locked coil ropes with cast steel sockets all supplied by Bridon International. Length adjustments are made using externally threaded cylindrical sockets at the deck anchors which are fabricated steel sections fixed to the outside of the deck. The back stays which hold the masts in position are in pairs for added redundancy in the case of damage or wilful vandalism and also so as to facilitate future replacement. These are adjusted by threaded bars at their anchorage beside the cutwater stairs. The top horizontal stays between the mast heads are also paired to permit future replacement one at a time, and the bridge is designed for accidental or planned removal of any one stay.
5
The Steel Masts
Continuing the transparency theme, the 15m long steel masts were designed as skeletal members using 70mm diameter solid legs held apart by special cam-shaped spacers. The masts are cigar shaped for efficiency as a pin ended strut, and this further enhances the appearance of slenderness. The spacers are double 10mm plates in pairs with 6mm webs between to provide sufficient vierendeel stiffness to reduce the buckling length of the individual legs to 1055mm. A solid section at the base discourages vandals from attempting to climb the masts, and a light fitting is contained within it to illuminate the mast head through holes in the cam-shaped spacers. The masts are pinned at their base with a simple spherical bearing surface machined onto a 125mm diameter pin which bears on a slab cast into “ears” on the side of the concrete cutwater, and the stays are attached to flat plates welded to a solid section at the masthead. Each mast weighs about 3.5 tonnes, and was delivered to site in one piece.
6
Aluminium Fabrication
As already mentioned, the aluminium extrusions were machined on their top surface to introduce added roughness to achieve a non-slip surface. The contract required careful control of the finished cross cut pattern, particularly in respect of the regularity of spacing and depth of the cuts, and in the event this presented some difficulties. The equipment available to the specialist sub-contractor and the tolerances in the extrusions meant that they had to be machined individually rather than in pairs as originally planned. However, after the initial difficulties, the necessary quality was achieved with acceptably good results. A trial assembly of a section of the deck was specified under the contract and was carried out at the fabrication works. This enabled the development of a suitable jig for the assembly of the aluminium sections, and allowed the fit up of the aluminium extrusions and the associated processes to be checked. (Figure 5) Particular care had to be taken in the handling of the aluminium sections to avoid damage. Scratches and dents could occur relatively easily with careless handling against unprotected steel rollers or equipment during drilling or machining, and this was unacceptable because of the
desire to achieve a high quality of finish throughout. It was therefore necessary to ensure that extra handling protection was added to prevent such damage, and that all operatives were properly informed about the importance of this factor.
Figure 5: Deck trial assembly
7
Construction
It was originally envisaged that the west bank section would be assembled in situ on temporary trestle supports, and that the river section would be assembled in one 30m long piece on the river bank and then floated out and lifted into place in one operation. However this method required the use of barges which would cause a temporary restriction of the river flow, and this was not permitted by the Environment Agency because of the relatively high risk of flooding. It was therefore decided to erect the bridge by incremental launching from the west bank instead since this only required the installation of a single temporary steel bent at mid-river causing negligible blockage to the flow. The aluminium sections were assembled by hand in a special jig mounted on the west abutment where the working environment and processes could be carefully controlled. The assembled deck was then pushed out along a temporary trestle support and the next section assembled behind it. Thus the deck was in effect “doubly extruded” because this launching process on site reflected the extrusion process in the aluminium manufacture. A king post arrangement was used to enable the deck section to span the distance from the cutwater to the mid-river support and on to the east abutment.
Once the deck was in place, the masts were erected and the stays attached to the deck in a single operation. The deck was then lifted off the temporary supports by stressing the stays, adjusting their lengths to achieve the desired profile. The original design required the aluminium extrusions to be pre-cambered vertically so as to achieve a straight deck in the finished bridge. However, this turned out to be too costly and the pre-cambering had to be omitted. The result of this was that the deck profile could only be adjusted to be what it would naturally adopt between the support positions. The maximum calculated dead load deflection of 43mm over the 16m between the stay positions was considered to be acceptable, although it would have been better if this could have been avoided by precambering. One other consequence of this change was that the bearing at the cutwater had to be fitted prior to lifting the deck by stressing the stays. Originally it had been intended that it should be left out until after stay adjustment so as to achieve higher dead load tensions in the steeper stays. In the event this was not possible, and the stay dead load tensions ended up lower than intended. To compensate for this, some further additional mass was added inside the deck at the side span inner stay anchor position in the same manner as at midspan.
8
Conclusions
As with all innovations, there have been several lessons learnt which would lead to potential improvements next time. Nevertheless, this unique design has worked well and has proved the efficiency and effectiveness of the original concept of assembling the bridge deck from a series of identical aluminium extrusions. The expected economies have been achieved mainly due to the small number of different components, the avoidance of any added finishes, and the ease of assembly and erection. The project proves the effectiveness of aluminium as a structural material for bridges, and the logic of using large section extrusions as the principal structural component. All parties have sought to achieve the desired high quality throughout, and the result should be a bridge which is faithful to the designers’ intentions and in keeping with the Client’s expectations.
A New Model For Cable-Stayed Bridges Control and Adjustment João Sérgio CRUZ Assistant Professor Civil Eng. Depart./IST Lisbon, PORTUGAL
João F. ALMEIDA Associate Professor Civil Eng. Depart./IST Lisbon, PORTUGAL
João Sérgio Cruz, born 1961 Received his civil engineering degree in 1985, the MSC in 1989 and the Ph.D. in 1998 Partner of JSJ-Consult
João F. Almeida, born 1957 Received his civil engineering degree in 1981, the MSC in 1985 and the Ph.D. in 1990 Partner of JSJ-Consult
Summary The present work concerns the analysis and control of cable-stayed bridges during construction. The most currently used construction procedures and adjustment criteria are briefly summarised, illustrating how they can induce important geometrical and stress variations that cannot be neglected. A model for the non-linear incremental analysis during construction is presented. The model is three-dimensional and takes into account all relevant time-dependent and geometrical non-linear effects. Based on the model, new techniques for the adjustment of cable-stayed bridges are formulated. Those techniques simulate the construction sequence, allowing the direct definition, in every phase, of the segments geometric position and the calculation of the forces that should be applied in each cable, in order to achieve an appropriate internal forces distribution and the required longitudinal profile. The procedure is generalised to include the correction of geometrical and cables tensions deviations occurred during or after construction. A practical application concerning a case study of a composite cable-stayed bridge recently built is presented. The results are compared with values obtained from the construction site, showing the adequacy of the proposed models.
1. Introduction Cable-stayed bridges can be built using different construction techniques, which are chosen according to local conditions and bridge characteristics. Therefore, the relevance of the geometric control study increases with the complexity of the erection procedure. Medium span cable-stayed bridges crossing easy obstacles are generally built with simple construction methods. After the towers completion, the common procedure lies on the construction of the whole deck on temporary supports or on scaffoldings, that can be adjusted in order to achieve the correct position for the later cable tensioning. Thereafter, the mounting cable forces are precisely evaluated to balance the vertical deck reactions on the temporary supports, leading to the pretended geometry and stresses distribution [2,3]. Otherwise, cable-stayed bridges over any kind of obstacle can be built by the cantilever method, especially those with long spans. Then, the erection procedure produces deflection and stress histories, which must be carefully evaluated. In this situation, the geometric control becomes an
important aspect of the bridge analysis, in order to obtain the correct geometry and stresses distribution [2,3]. Cable-stayed bridges, enable the design of flexible and slender decks and towers, which allow important adjustments to correct construction differences. Nevertheless, this slenderness, associated to the variability of the material properties, thermal effects, actions and uncontrollable mistakes produced during construction, can lead to sensible deviations relative to the theorectical geometrical profile and stresses distribution. This fact, on itself, implies a detailed geometrical control study, concerning all the erection sequence and relevant actions and effects, in order to support decisions during construction to minimize and correct deviations. Regarding the thermal response behavior of the cables, the study must include a sensibility analysis to thermal effects in terms of structure stresses and displacements.
2. Control and adjustment criteria The geometric control study includes the simulation analysis of the structure erection sequence, allowing the knowledge of the initial mounting segment position of the deck and towers, simultaneously with the initial tensioning cable forces. Among others, this study has the main purpose of evaluating the initial conditions conducting to a pretended final geometric configuration and stress distribution for a determined temporal horizon t. It is currently accepted that cable-stayed bridges adjustment criteria lies on the cable force distribution, for a predefined geometry under dead loads, which minimizes bending moments in towers and deck, corresponding to a certain time instant t. This adjustment criteria, established for the final geometry, leads to permanent loads equilibrium mainly based on axial compression forces in towers and deck, in association with tensions in the stay cables. Small, span independent, permanent bending moments in the deck, between consecutive stay-cables, appear at the end. Another direct consequence of this design condition is the minimizing of the self-induced bending deflections due to creep and non-linear geometric behavior of the compressed members. Fig.2.1 illustrate the static system and the variables used for the establishing of final equilibrium conditions.
Figure 2.1 – Cable-stayed bridge static system
Equations (2.1) and (2.2) express the equilibrium of a central span deck n segment. in 1− in + 1 (2.1) siná c,n + cosá c,n ⋅ in
G + Nn + 1 ⋅ sinâ Tc,n =
c,n
cot gβc , n + 1 G + Nn + 1 ⋅ sin βc , n 1 + α cot g c , n (2.2) Nn = cot gβc , n sin βc , n 1 + cot gαc , n
The recursive nature of these expressions needs a previous estimate of the axial force in the central segment at time t, in order to evaluate all the forces Tc,n and Nc,n, from mid span to the towers. As a remark, these forces applied to the deck only produce bending moments due to the loads in the span (Hc,n) as indicated in Fig 2.2.
Figure 2.2 – Bending moments diagram layout for dead loads in cable-stayed bridge After the evaluation of the central span stay-cable forces Tc,n with equation (2.1), detail B of the Fig 2.1 indicates the towers central and lateral stay-cables connections, from which equilibrium equation (2.3) is derived, providing a null bending moment in the towers above the deck. Tl , n = Tc , n
cos αc , n cos αl , n
(2.3)
Finally, the lateral span equilibrium is established with a symmetrical stay-cable arrangement, and intermediate supports, or even with the help of counterbalance loads distribution.
3. Geometrical and stay-cables forces adjustment model Traditionally, a “backwards analysis” would be applied [2,3], consisting in a logic numerical simulation of the bridge dismounting, from the final state, associated with the design criteria at time t, through all the intermediate phases in the opposite sequence as it was built. Such analysis evaluates all stresses increments, computing the stay-cable tensions at the installation together with the associated position of the structure. Nevertheless, the “backwards analysis” is inadequate for the correct evaluation of time-dependent effects in concrete towers and deck. The nonlinear geometrical effects, sometimes important during construction, become incorrect by the misevaluation of non linear material behavior [2]. The above aspects lead to a successive series of analysis, regarding dismounting and mounting, with correction of the initial conditions, which is an heavy process, even using automatic calculation. This paper presents an alternative adjustment technique based in a convergent iterative process, which lies on a structural analysis simulation model, regarding all the relevant issues, such as [1]: • The structure tridimensional nonlinear geometrical behavior is modeled through the establishment of the equilibrium and compatibility equations on the structure deformed shape.
• The geometrical nonlinear cable effect is evaluated through the tangent Ernst and secant moduli. • Structural system evolution and modification along the time construction is considered. • Loads and action variations are taken into account. • Concrete time-effects like creep, shrinkage, prestress losses due to steel relaxation, are evaluated with a time incremental analysis. Concrete creep is modeled with an association of n reological Kelvin models and one Hooke model. • Bearings are modeled with geometrical and physical nonlinear behavior. The effect of the top plates relative slip displacement with friction is considered. • The prestress cables inside concrete can be considered with or without relative slip friction inside the gains. The iterative process starts with a first bridge mounting simulation analysis, based on initial conditions for the towers, deck geometry and stay-cable forces equal to those predefined at time t. Obviously this first analysis results on a final geometrical profile and cable-stay forces distribution, not coincident with the adjustment design criteria. The differences between the obtained solution and the pretended one, are used to correct the initial conditions of the previous iteration. Hence, there is a new data block ready to simulate again the mounting construction. This method converges to the right solution accordingly with the specified tolerances.
Figure 3.1 – Indicative scheme with the geometric control variables The currently used variables in the adjustment procedure are indicated in Fig.3.1, Robj - Tobj, Rti, Rnfi, Tti and Tn0i. They are, respectively, the final pretended positioning vector and final stay-cable forces, the positioning final vector obtained at iteration i, the positioning vector after mounting the n stay-cable at iteration i, the final stay-cable force at the iteration i and mounting stay-cable force n at the iteration i. The principal static and cinematic differences concerning the towers displacements, deck geometry and stay-cable forces are grouped in ∆R i and ∆T i vectors, indicated in (3.1) and (3.2) equations. ∆Ri = Robj − Rti
(3.1)
∆Ti = Tobj − Tti
(3.2)
It is as well possible to define other static vectors of variables differences, like element action effects ∆Xi and stresses ∆σi, indicated in expressions (3.3) and (3.4).
∆Xi = Xobj − Xti
(3.3)
∆σi = σobj − σti
(3.4)
Based on the fact that the reciprocal influence of the initial segments positioning coordinates, grouped in R0I, can be neglected, the correction in these initial conditions R0i+1 can be done by
simple adding the differences ∆Ri to the previous position vector R0i. Then, for the next iteration, the initial geometric conditions vector is obtained by the expression (3.5). R 0 i + 1 = R 0 i + ∆Ri
(3.5)
This procedure provides the adjustment of current frame bridges, erected by the cantilever method. However, in cable-stayed bridges the stays mounting forces do not remain constant, resulting on final forces quite different from the initial ones. Even in this situation, this convergence process can be enforced in order to obtain an almost correct geometric profile but with wrong stresses. Therefore, concerning cable-stayed bridges it is necessary to correct the stay-cable vector mounting forces T0i, in order to achieve a new initial vector T0i+1, leading to the right final stresses distribution simultaneously with the correct geometrical profile. Similarly to the correction process of the geometrical initial conditions, the stay-cable convergence can be simply obtained by adding the force differences ∆Ti to the initial mounting forces vector T0i, producing a new initial mounting forces vector T0i+1, for the next construction simulation. An important improvement in the convergence efficiency of this process is made by the introduction of a well known influence matricial operator Ci differentiating the stay-cable mounting forces reciprocal influence [1,2]. Nevertheless, in the present technique, the influence matrix concept operator Ci (3.6), has a tangent matrix significance, including all the information concerning the erection sequence, nonlinear physical and geometrical effects and specially the influence of the initial conditions of iteration i. Each column of Ci represents the influence of a stay-cable installation force on the values of the adjustment control variables [4]. The selection of the bridge n stay-cable forces determines the number of matrix columns. The number of lines can be selected, corresponding to n control variables, like n-2 stay-cable anchor deck vertical coordinates and 2 longitudinal towers top coordinates or towers base bending moments. By this way, the obtained subgroup of Ci operator is a square nonsingular matrix Cni. ∂Tf ∂T 10 ∂ Xf Ci = ∂T 10 ∂σ f ∂T 10 ∂ Rf ∂T 10
∂Tf ∂T 20 ∂ Xf ∂T 20 ∂σ f ∂T 20 ∂ Rf ∂T 20
∂Tf (n − lines ) ∂Tn0 ∂Xf . . ( m − lines ) ∂Tn0 ∂σ f . . ( k − lines ) ∂Tn0 ∂ Rf . . ( l − lines ) ∂Tn0 . .
(3.6)
When a stay-cable is installed, for an iteration i, the vector variables Tf, Xf, σf, and Rf, indicated in expressions (3.7) to (3.10), are, respectively, the actual n stay-cable forces, the linear frame element m internal forces, the k stresses and the actual structural position l coordinates. Tf 1 Tf 2 Tf = ⋅ (3.7) ⋅ Tfn
Xf 1 Xf 2 Xf = ⋅ (3.8) ⋅ Xfm
σf 1 f 2 σ σf = ⋅ (3.9) ⋅ σfk
Rf 1 Rf 2 Rf = ⋅ (3.10) ⋅ Rfp
Once the square matrix operator Cni is assembled, it is simple to conceive an evaluation method for the installating stay-cable forces correction vector ∆Ti, accounting for the reciprocal force influence. The differences in the selected adjustment control variables ∆Ri ∆Ti, ∆Xi and ∆σi, are grouped in the ∆Gi vector, allowing the establishment of the linear equation system given by expression (3.11), Cni ⋅ ∆Ti + 1 = ∆Gi
(3.11)
providing a solution vector ∆Ti+1 that is added to the previous initial stay-cable installing forces vector T0i, as indicated in (3.12), in order to improve the convergence for the next iteration. T 0 i + 1 = T 0 i + ∆ Ti + 1
(3.12)
The improved convergence is obtained measuring the different influence that each stay-cable mounting force has on the other adjustment control variables. Another important aspect, is the possibility of mixing static and cinematic control variables. The above procedure can be enlarged to situations where cable forces are installed in multiple steps. The adjustment process can be applied by choosing the last intervention in the stay-cables to calibrate the initial force, in order to obtain the final design conditions. Finally, after the evaluation of the geometrical segments position and mounting or retensioning staycable forces, grouped in the R0 e T0 vectors, it is possible to initiate the construction. All the above adjustment control procedure lies over the assumption of an uniform thermal distribution, a load planning and a rigorous mounting sequence. However, uncertainties during construction are inevitable, having consequences in terms of geometry and stresses deviations. It is common knowledge that cable-stayed bridges are very sensitive to thermal actions, especially due to the cables low thermal inertia. Even the stay-cable exterior protection color influences the thermal behavior. Due to this fact, the mounting stay-cables and retensioning operations must be executed with low thermal gradients, usually in the morning before the sunrise. After the bridge structure completion, all the detectable deviations should be checked in order to permit a final adjustment. That purpose can be performed based on a pre-established stay-cable intervention sequence, on the actual geometric profile and stay-cable stresses distribution, using the presented adjustment technique. In this case, it is necessary to redefine the objective adjustment static and cinematic conditions and simulate the correction sequence iterative process, as explained before.
4. Geometrical and cable-stay adjustment of pereira-dosquebradas bridge The present example refers to the adjustment and geometric control study made for the construction of the new cable-stayed Pereira-Dosquebradas bridge in Colombia. The four lane bridge has a linear plan alignment and a general 1.5% linear profile with small concordances adjustments. The structure is a composite concrete-steel deck, lateral stayed by 36 stay pairs on two diamond shaped towers. The symmetrical span arrangement has two small approach 30.05m spans, two 83.25m lateral spans and a 210.9m central span, in a total of 437.5m between expansion joints. The towers are reinforced and prestressed concrete box girders. The deck is made of a steel structure grid and a reinforced concrete slab, connected by full shear connections. The 0.25m thickness pavement concrete slab was built in a first 0.1m thickness precast slab and a second 0.15m thickness cover concrete cast “in situ”.
Figure 4.1 – General geometry of the Pereira-Dosquebradas bridge 4.1 – Deck erection sequence The deck segment erecting cycle is presented in Fig.4.2. Due to the small weight of the steel structure and equipment, along with the need for reducing the stay-cables interventions, it was necessary to use temporary extraweights during the front steel segment mounting. In that way, it was possible the installation of half of the stay-cable strands with a convenient stress level. In fact, it is important to have a minimum number of strands, with a minimum stress value (0.20fpuk), in all staycables to provide a confortable stiffness during construction, which limits, among other factors, the mounting deck displacements. This fact is strongly associated with the control of the front staycables unload, when a new pair of stays is installed. The mounting sequence of the bridge deck was chosen to achieve, as soon as possible, the maximum dead load, minimizing the stay-cables unload during erection. This objective was reached by concreting the nearest front slab cast “in situ” layer before the stay-cables retensioning and mounting phases. Fig.4.2 illustrates the deck segments erection sequence: 1º Derricks positioning on segment i. 2º Elevation and assembling of the steel segment i, together with an 150KN extraweight. 3º Pre-cast slabs positioning on the segment i-2.
4º Concrete cast “in situ” over the segment i-2 and extraweighs moving to the next segment. 5º Prestress application on segments i-2 and i-3. 6º Retensioning the segment i-2 stay-cables. 7º Installing the segment i stay-cables.
Figure 4.2 – Deck cycle segment construction scheme 4.2 – Final design bridge adjustment The achievement of the correct geometric profile and stresses distribution is based upon the criteria presented in chapter two, consisting in an almost zero bending moment in the towers above the deck and a rigorous dead load balance of the stayed central span, at a 4000 days time. Since stay-cable forces are installed in two steps, the last one was chosen, according to the proposed adjustment technique presented in the third chapter, to define the Gni matricial operator. Therefore, the n stay-cable forces are also the adjustment control variables. The convergence tolerances on the geometrical coordinates and stay-cable forces are, respectively, 10 mm and 0.5%. Fig.4.3 illustrates the comparison between theorectical and measured vertical deck displacements after the T6L and T8C stay-cables mounting at tower 10. As a final remark, the maximum vertical displacement due to the T9 stay-cable last retensioning phase, was about 2 meters. This order of
displacement magnitude value, clearly shows the importance of geometric nonlinear effects during construction.
Figure 4.3 Theorectical and measured vertical deck displacements after the T6L and T8C stay-cables installation
Figure 4.4 - Longitudinal stresses in the deck steel beams and concrete slab
Figure 4.5 - Towers longitudinal bending moments M3 and longitudinal displacements
Figures 4.4, 4.5 and 4.6 show the convergence process in 8 iterations, in terms of, respectively, longitudinal stresses on the deck steel beams and concrete slab, towers longitudinal bending moments M3 and longitudinal displacements, and stay-cable final forces at 4000 days. A effective convergence is obvious on the towers longitudinal deflections and bending moments. In each iteration the final geometric profile is always ensured, but only the last one complies with the aimed stay-cable stresses distribution. A final stay-cable adjustment was done after the central deck connection, in order to minimize the overall deviation on the checked control variables.
Figure 4.6 - Stay-cable final forces after 4000 days
5. Acknowledgment The authors acknowledge Mr. Armando Rito for his valuable suggestions and contributions to this work. To Mr. Jim Curto the acknowledgment for his contribution on the Pereira-Dosquebradas example presentation.
6. References [1] - Cruz, João S. N. D. – Construction Control of Cable-stayed Bridges (in portuguese) - Ph.D thesis, Instituto Superior Técnico, Lisbon-Portugal, August 1997 [2] - Ito, M.; Fujino, Y.; Miyata, T.; Narita, N. – Cable-stayed bridges, Recent developments and their future –Seminar, Yokohama, Japan, December, 1991. [3] - Virlogeux, Michel - Erection of cable-stayed bridges, the control of the desired geometry International Conference A.I.P.C. - F.I.P. - Cable-stayed and suspension bridges, Deauville, October 12-15, 1994 [4] - Fujisawa, Nobumitsu e Nakamura, Nobuhide - Computer system for cable adjustment of cablestayed bridges during erection - International Conference A.I.P.C. - F.I.P. - Cable-stayed and suspension bridges, Deauville, October 12-15, 1994
Cable Finite Element of High Accuracy Michel AUPERIN Special Studies Managing Director BOUYGUES Travaux Publics St Quentin en Y., France
Claude DUMOULIN Civil Engineer BOUYGUES Travaux Publics St Quentin en Y., France
Summary This paper describes a Stay-Cable Finite Element of High Accuracy with only two nodes based on the equilibrium of a string subjected to loads distributed linearly along the cable and taking into account the sag effect. For all static structural analyses, it is convenient to use only one single finite element, whatever its length is. Regarding dynamic analysis, the inertia forces contribute to the stiffness matrix. Assuming that these forces vary linearly between two nodes is sufficient for computing the stiffness. Usually, an important reduction of the node numbers of a finite element model modifies largely the dynamic behaviour. This paper outlines that an appropriate choice of the mass matrix leads to an excellent accuracy regarding dynamic analysis, even with a very small number of nodes. Concerning a stay-cable, a quite exact value of the N first modes of each type (which means a total of 3N modes) could be obtained with only 2N finite elements of high accuracy.
1- Introduction During the eighties, the authors have developed a stay-cable finite element based on the wellknown formula governing the static equilibrium of a string subjected to a uniformly distributed load. This element is defined by two end nodes, whatever its length is. The suppression of all the intermediate nodes is worthwhile to reduce the computation time because the main characteristic of these nodes is their very low stiffness in a plane normal to the cable. The static structural analyses of Pont de Normandie have been carried out using this element for all the construction and service loading cases. Regarding dynamic analysis, this element loss a large part of its advantages, because the distributed loads include the inertia forces, varying along the cable. It is necessary to model a real stay-cable by a succession of a large number of cable finite elements based on a uniform applied load. A new stay-cable finite element was therefore developed taking into account the following objectives: • Regarding static analysis, a real stay-cable must be modelled by only one element if the applied loads are linearly distributed. • The dynamic behaviour of a real stay-cable must be simulated with a minimum number of intermediate nodes. Regarding static analysis, the objective has been reached with no difficulty. Regarding dynamic analysis, if a real stay-cable is modelled by a succession of 2N new cable elements, the frequency value of each of the N first longitudinal modes and transverse modes (in-plane and out-of-plane) is known with a relative error lower than 0.25 %.
2- Stay-Cable Finite Element of High Accuracy 2.1- Static Equilibrium Neglecting the torsion and bending stiffness, the cable is assumed to behave like a taut string. Let us call chord the line joining the two anchorages of the stay-cable and L the distance between them. x is the relative abscissa along the chord, varying from 0 at the first anchorage to 1 at the second one. Let us assume that: • The cable is subjected along its length to a distributed load whose each component varies proportionally to x. • The Hooke’s law is applied to the stay-cable constitutive material. Let us call X1k, X2k and Xck (k varying from 1 to 3) the co-ordinates of the two anchorages and of any ordinary point of the cable expressed in an orthonormal co-ordinate system having one axis parallel to the chord. Let us write the following relationship between these co-ordinates: X ck = (1 − x ) X 1k + x X 2 k + x (1 − x ) Fk [x ; X 1 , X 2 , EA , S 0 , Q ] (1) Fk is a x polynomial whose coefficients are depending on the parameters: • X1 : co-ordinates of the first anchorage. • X2 : co-ordinates of the second anchorage. • EA : product of the material Young’s modulus E by the cable cross-section area A. • S0 : cable length obtained when the cable tension is equal to zero. • Q : set of all the cable linearly applied loads. The distributed load parallel to the chord may be expressed as: p(x ) = (1 − x ) p1 + x p 2 (2) Let us define a force H by writing the projection Tx along the chord of the tension force T as: p + p2 p − p2 Tx (x ) = H + 1 L (1 − 2 x ) + 1 L 1 − 6x + 6x 2 (3) 4 12 Let us then write that the nodal forces, tangent to the cable, equilibrate the tension forces at the anchorages. Having decided to express the functions Fk as polynomials of degree 2 of teh vriable x, three conditions concerning the moments have to be defined: the moments are equal to zero at the anchorages and at the cable mid-span. The polynomial coefficients are then solutions of linear equations whose parameters are the distributed loads and the force H.
(
)
To compute the stay-cable length S, let us assume that the square of the cable slope related to the chord is small versus 1 and let us expand the S formula until the order 4 according to the polynomial coefficients. Let us then write the Hooke’s law, i.e. the average tension Tm along the cable is proportional to the cable length variation: S − S0 Tm = EA (4) S0 Let us define the expressions s and e as: (5) S = sL S 0 = (1 + e ) L (6) and a function h as:
α ( p1 + p 2 ) + β ( p1 − p 2 ) s −1 + s s α and β are expressions a little bit complex according to the polynomial coefficients (and consequently to H) which may be neglected in most of the practical cases. The governing equilibrium may be expressed as: h = EA e This allows computing of: • e and consequently the length S0 if the tension is known at one point of the cable (cable tensioning problem). • H and consequently the tension and the deformed shape of the cable if e is known. h = H − EA
(7)
(8)
2.2- Cable Stiffness Let us define the parameter r by the following formula: dh dh dL 1 = × = (9) r d H c d L c d H c The subscript c denotes that the derivatives are evaluated assuming that the loads are constant according to intensity and direction. This coefficient r plays an essential role in the stay-cable analysis. It is always positive and its value is lower or equal to 1. If the stay-cable is only subjected to its dead load, r may be expressed according to the well-known Irvine’s parameter λ2 as: 12 r = (10) 12 + λ2 It could be easily proved that, if ∆L is the extension of the chord, the total loads along the cable changing neither in intensity nor in direction, the projection ∆Tx of the tension force along the chord truncated to the first order might be expressed as: EA ∆Tx = r ∆L (11) S0 The extension stiffness of a beam where A is the cross-section area, S0 the length and made of an elastic material whose Young’s modulus is E, may be expressed as EA/S0. The expression (11) exhibits that the cable extension stiffness is r times those of the beam. Regarding a stay-cable whose slope versus the horizontal axis is defined by the angle θ and whose applied load is only its own dead load, the tangent stiffness matrix of the cable may be expressed in the vertical plane as: A −A K = (12) −A A where A is a symmetric matrix (2,2) whose coefficients aik are given by: EA H H a11 = r a12 = a 21 = − (1 − r ) tg θ a 22 = (13) S0 S0 L In the previous expression of A, the X-axis is assumed parallel to the chord. 2.3- Mass Matrix There is a complete analogy between the equation of motion of a bar subjected to dynamic axial deformations and a taut string subjected to dynamic transverse deformations. The mass matrix M
of a straight bar element with two nodes, of length l and mass m per unit of length, may be expressed as: a 0.5 − a M = ml (14) 0.5 − a a where a is a coefficient whose value is often taken equal to 1/2 or 1/3. Let us consider a bar of length L, fixed at each end, and let us divide it into N elements of the same length l. Computing the frequencies of this finite element model (N two nodes bar elements) subjected to axial deformations under free-vibration conditions, the following results are exhibited: • To obtain accuracy about 0.25 % on the frequency of the first mode, the bar must be divided into 13 elements. • The error values are the same, except the sign, when the two well-known values of a are used. When N is large versus the mode order k, the convergence towards the exact solution is of order N-2. It is of order N-4 if the value 5/12 is used as a value, i.e. the mean value of the two well – known values. In fact, the objective is a little bit different: what is the most efficient value for the parameter a in order to obtain the first k natural frequencies with the minimum elements number N and for a given accuracy? A detailed analysis shows that the best a value is 0.40733. Then the relative error related to the computed natural frequency is more low than the order of the mode small and is not larger than 0,25 % concerning the mode whose order is equal to the integer part of N/2 (for instance, mode 2 for 4 or 5 elements). A similar analysis, of course more sophisticated, has been developed for straight beams, exhibiting also interesting results. Let us come back to the stay-cable problem. Considering a stay-cable only subjected to its own dead load, it can be demonstrated that the first in-plane natural frequency f1 of the cable with fixed anchorages may be expressed as: 1 H f1 = (15) 2L m r The difference between the result obtained by this formula and that given by the more sophisticated expression proposed by Irvine is insignificant, even when the static sag of the staycable is large. Finally, putting together all these results and assuming that the co-ordinates system is orthonormal with an X-axis parallel to the chord, the mass matrix of the cable finite element may be expressed as: M1 M 2 M = m S0 (16) M 2 M1 where M1 and M2 are two diagonal matrixes (3,3): 1 (1 , 1 , 1) − Diag (M 1 ) (17) 2 The ry and rz coefficients depend on r and on the curvatures in the planes (XY) and (XZ). If the stay-cable is not loaded in the plane (XY) for instance, ry is equal to 1 et rz is equal to r. Diag (M 1 ) = 0.40733 (1 , ry , rz )
Diag (M 2 ) =
Concerning dynamic analyses, the cable element stiffness matrix is that obtained from the static study and the mass matrix is that given by (16) and (17). Modelling a stay-cable with only two elements, the frequencies of the first in-plane mode, of the first out-of-plane mode and of the first axial mode are obtained with a relative error of 0,25 %. The result obtained for the axial vibrations of bars could be generalised. To have a relative error lower than 0,25 % on the
frequencies of the first k in-plane modes, of the first k out-of-plane modes and of the first k axial modes, only 2k cable elements of high accuracy are required.
3- Example Consider a stay-cable with the following characteristics: • Chord length at rest L = 210.50 m • Slope angle versus horizontal θ = 22.3° • Stiffness EA = 2018.25 MN • Tension at upper anchorage T2 = 5.200 MN • Cable mass (not tensioned) m = 95.7 kg/m (total masse: 20094 kg) The e parameter of the stay-cable has a value of 0.25 %. The cable static sag related to the chord is equal to 0.930 m. These static results are obtained whatever the number of cable elements are used (even with one element). The r coefficient, related to the complete stay-cable, is equal to 0.96. The frequency computed for the first in-plane eigenmode depends on the number of elements: • 2 elements: 0.5620 Hz • 4 elements: 0.5641 Hz • 6 elements: 0.5637 Hz The transient analysis of the stay-cable vibrations induced by the lower anchorage moving vertically at the frequency computed for the first in-plane mode and with 2-cm amplitude, has been carried out. The duration of the analysis was 900 seconds. The initial state was at rest i.e. the static equilibrium. The damping viscous ratio was very low (ξ = 0.1 %). The structural analysis software package used was Pont/ARC, which is a Bouygues own developed code. The time integration method is derived from the Bulirsch-Stoer method, which is an extension of the well-known Runge-Kutta method. The stiffness and mass matrixes have been computed at each time step. Figure 1 details the results. One notices that the maximum amplitude of the displacement and the tension decreases when the number of elements increases, stabilising rather quickly: there are only small differences between the responses obtained with four or six elements. The difference is more important concerning the responses obtained with two elements. Nevertheless, a small increase of the excitation frequency (0.001 Hz in our example) modifies largely the amplitude of the response. It is a wellknown phenomenon due to the high non-linearity behaviour of the dynamic stay-cable motion. The amplitudes of the displacements and the tension variations obtained with two elements are close enough to those obtained with four elements with a frequency a little bit increased.
Mid-Span Displacements (unit meters) Figure 1
Tension (unit MN)
Stay-cable response to a vertical excitation with 2-cm amplitude of the lower anchorage. Viscous damping ratio: ξ = 0.1 %. Left column: mid-span displacements, normal to the chord. Right column: tension at the upper anchorage. • (a) and (b) two finite elements model. Excitation frequency: 0.562 Hz • (c) and (d) four finite elements model. Excitation frequency: 0.564 Hz • (e) and (f) four finite elements model. Excitation frequency: 0.565 Hz • (g) and (h) six finite elements model. Excitation frequency: 0.5637 Hz
4- Conclusion The Cable Finite Element of High Accuracy developed in this paper meets to the prescribed objectives. Regarding static analysis, as far as the loads applied on the cable could be assumed to be linearly distributed, one single element is sufficient to model the stay-cable, whatever its length is. Regarding dynamic analysis, the elements number depends on the goal: • If only an estimation of the displacement or tension amplitudes is wanted, only 2N elements are necessary for results till modes of order N. • If a good accuracy of the transient response is expected, then the number of elements has to be increased, for instance by doubling the previous value.
5- References [1]
Irvine, H. Max, 1981, Cable Structures, M.I.T. Press.
[2]
Stoer, J., and Bulirsch, R. 1980, Introduction to Numerical Analysis, New York: SpringerVerlag.
Sunniberg Bridge, Klosters, Switzerland Karl BAUMANN dipl. Ing. ETH Bänziger+Köppel +Brändli+Partner Chur, Switzerland Karl Baumann was born in 1960. He received his Civil Engineering degree in 1984 from the ETH Zürich. 1991 he joined BKB as Project Manager for bridge projects.
Jürg DÄNIKER Bauing. HTL Stahlton AG Zurich, Switzerland Jürg Däniker, born 1946, received his BS in Civil Engineering in 1969. After two years of experience in design of steel structures, he worked in Australia for a Consultant. Since 1974 his activities concentrate on special post-tensioned Structures and QualityManagement
Bridge Concept The Sunniberg Bridge forms part of the main road connection between Landquart and Davos. It crosses the Prättigau valley close to Klosters in a sweeping curve, high above the valley floor. The Bridge is the most visually impressive structure of the Klosters by-pass project.
Fig. 1
View of the finished bridge
In view of the prominent location of the bridge and the importance of the surrounding, still largely unspoiled, alpine landscape, the aesthetic quality of the design was of particular importance. When viewed from the ascending approach road, the bridge appears shorter than it actually is. Span lengths of significantly greater than 100m were therefore desirable. An elegant, modern and original structure was conceived, which convinces the beholder that, in addition to 1
its strengths in farming and tourism, this mountainous region can also contribute to technical and cultural development. The convincing aesthetic appearance justifies the additional costs of about 15%, compared to the least expensive alternative. Given the topography of the site and the chosen route, the desired transparency and longer spans could only be satisfactorily achieved by a cable-stayed bridge. Multi-span cable-stayed bridges present problems with regard to statical behaviour and appearance. The statical problem is that the load-carrying system at each pylon must be stabilised under localised loading. Visually, the ratio of the tall piers to the normally equally tall pylons can be disharmonious and rather unconvincing. The curved form in plan allows for a monolithic structure, fixed at both abutments, without expansion joints. It is thus possible to fix the pierheads at deck level in both the longitudinal and transverse directions. Changes in temperature lead to horizontal deflections perpendicular to the bridge axis, without causing appreciable secondary stresses in the deck cross-section. The piers, however, are subjected to horizontal displacement at the pierhead, and must consequently be designed as slender frame constructions. Viewed from the side, the piers become narrower from top to bottom, corresponding to the force flow in the piers under unbalanced traffic loading. At the upper extremity, the widening pier section is consistently continued into the pylon. This results in a broad, stiff pylon diaphragm, which facilitates a very gentle stay cable gradient. As a result of the fixation of the pierheads by the deck, and the stiff arrangement of the pylons, the deformations under traffic loading over a single span can be kept within acceptable limits, even with very gently inclined stay cables. The combination of pylon, piers, deck and cables results in a balanced structure with impressive architectural qualities.
Fig.2
Pylon model 2
Description of the Bridge General The Sunniberg Bridge crosses the valley at a height of about 60m over the Landquart river, from the Büel plateau to the slope of the Gotschna, close to the Drosbach stream. The bridge is curved in plan, with a radius of 503m, measured to its axis. The deck has a longitudinal inclination of 3.2%, and a transverse inclination of 7%. The span lengths are 59m, 128m, 140m, 134m and 65m, resulting in a total length of 526m.
Fig. 3
Longitudinal section with construction programme
This arrangement of spans is ideally suited to the bridge location. The locations of the Büel and Drostobel abutments were chosen to be as close as reasonably possible to the tops of the valley slopes. The spans are generous and contribute to the transparent appearance of the structure. The usable width of the Sunniberg Bridge is 9.0m. The deck is bounded on either side by a 1m high New Jersey barrier, capped with a steel tube railing. Bridge Deck The bridge deck is formed by a 12.375m wide plate, simply reinforced in the transverse direction, between two edge-beams. The thickness of the plate varies in the transverse direction between 0.40m at the centreline and 0.32m at the edge beam. Outside the New Jersey parapet, at the edges of the deck plate, the thickness varies between 0.4m and 0.5m. For statical reasons, the thickness of the bridge plate is increased close to the pylons. The plate is 0.55m thick at the centreline over the initial 13m length either side of each pylon, before the first stay cable anchors. During the first two balanced-cantilever construction stages, the thickness of the plate at the centreline reduces linearly from 0.55m to 0.40m. 3
Fig. 4
Bridge cross-section
The stressing niche zones, together with the continuous edge beams, form two massive edge reinforcements, each about 1.90m wide. The stressing niches for the stay cables are located outside the edge beams, and are in section slightly asymmetrically positioned. In the mid-span areas, the missing axial force is compensated by longitudinal post-tensioning: 2x3 pcs. 1'900kN cables, pulled in and stressed following the closure of the joint between the two cantilevers. Stay Cables The stay cables are arranged in a harp configuration, with a 6m spacing between the deck anchorages. In view of the radius of the bridge deck, this configuration is required to ensure that the planes of stay cables on either side of the bridge deck give the impression of continuous and reassuring "walls". The average inclination of the cables is 1:5, with variations arising from the longitudinal inclination of the bridge deck. The dominant feature of the system is the stiff pylon. Changes in cable forces on one side of the pylon therefore have practically no effect on the forces in the cables on the other side, but are rather compensated by bending of the pylon. The commonly encountered, and for stay cable systems often crucial, backstay cables can be totally omitted. The maximum working load of the cables was set at a conservative level of 50% of the ultimate capacity. The maximum stay cable forces at the Sunniberg Bridge is 5'000 kN. Pylon and Transverse Beam The pylon rises about 15m above the deck, in the form of two diaphragms outside the deck plate. These two diaphragms are inclined outwards at an inclination of 8:1. The inclined arrangement is prescribed on the one hand by the geometry of the stay cables for the curved structure, and on the other hand by the overall aesthetic appearance of the pier and pylon system.
4
Fig.5
Pier and pylon
With a width of 5.95m - 8.00m in the longitudinal direction, the pylon diaphragm resists the bending forces resulting from non-symmetrical traffic loading. Its thickness of 1.75m allows it to accommodate the bending moments caused by the transverse component of the stay cable forces. The fixed upper anchorages of the stay cables are situated in the central part of the pylon diaphragm. This arrangement leaves the outer parts of the pylon available, unreduced, for the resistance of bending forces. The anchorages are accommodated in two back-to-back steel anchorage boxes which are connected together by steel plates (S355J2G3), each 500x30mm.
5
Fig. 6
Upper cable anchorages
The very massive transverse beam, with a height of about 3.1m and a width of about 2m, transforms the large transverse bending moments of the pylon diaphragms into unequal axial loading on the legs of the pier. The inner leg supports about 60% of the total axial load. Piers In the longitudinal direction, the lines of the edges of the piers are parabola-shaped. Below the deck level, the piers become narrower with decreasing elevation, changing to a slight widening above the foundations, in the case of the tall P2 and P3 piers. The variation in width, from 3.30m to 5.95m, is achieved by varying the flange width and the width of the recessed central part of the pier leg. The edge details and the transverse width of the pylon leg (1.60m) remain constant. In the transverse direction, the transition from the vertical pier legs above the foundations (total width 8.80m) to the 8:1 inclined pylon occurs over a vertical distance of 36m between the lower transverse connector and the pylon transverse beam (total width 13.42m at the base of the pylon). Abutments The abutments are connected monolithically to the bridge deck, and are the anchor locations for the horizontal stabilisation of the bridge system. The size and shape of the abutments have been largely determined by the tensile anchoring forces required at each abutment (at design level: 17'700 kN for the Büel abutment, 14'600 kN for the Drostobel abutment). The abutments consist in principle of earth-filled containers, each with floor, sidewalls and central support wall. Foundations The 3 piers P2, P3 and P4 are each founded on 6 bored piles (dia. 1.50m) between 14m and 16m long. The massive pilecap (11.6m x 7.2m x 3.0m) is offset in plan 0.75m towards the inner side of the curve of the bridge, since the inner leg of the pier supports a considerably larger part of the total vertical load. Pier P2 is situated close to the bank of the river Landquart, and the piers P3 and P4 are situated close to the Drosbach stream. The foundations have been designed to withstand even very severe flooding, with several meters of ground loss. 6
Pier P1, closest to the Büel abutment, is situated on a flat area of ground, adjacent to the steep slope into the Prättigau valley. The foundation is constructed in the form of two pits, about 17m deep. The upper 4m of each pit has a diameter of 4.75m, to suit the dimensions of the foot of the pier. Otherwise the diameter of the pits is 3.5m, due to construction considerations. Finishing Works The bridge deck has been sealed with polymer-bitumen mats and has been paved with 3 layers of asphalt, with a total thickness of 16cm. The edge detail at the New Jersey barrier construction has been sealed with a flexible joint strip. The edge of the deck plate over the stressing niches has been treated with a 4mm thick coat of 2-component epoxy-polyurethane varnish, sprinkled with quartz sand. The drainage of the bridge is achieved by means of drainage gullies spaced at about 30m, connected to a HDPE longitudinal drainage pipe. The drainage pipes and the protection pipes for various services are fixed to the underside of the bridge, between the edge beams. For the purpose of maintenance, a special movable platform, supported at the edges of the deck plate, is foreseen.
Design of the Bridge Gently inclined stay cables Due to the gentle gradient of the stay cables, the vertical deformation of the deck under traffic loading on a single span is a significant design criterion. A maximum allowed vertical deformation of 1/400 the span length was agreed with the client. The design load on a single span is composed of a uniformly distributed load of 2 kN/m2, combined with a point load of 360 kN (including an impact factor of 1.2). The vertical deflection is calculated for the system without cracks, with a Modulus of Elasticity of the concrete (Eco) of 35'000 N/mm2, ignoring the concrete parapets.
Fig. 7
Deformations
7
In the longest span of 140m, the maximum deflection is 225mm, corresponding to 1/600 the span length. The deflection results 40% from the deformation of the pylon and pier and 60% from the elastic deformation of the stay cables. The two neighbouring spans exhibit upward vertical displacements of max. 60mm in this case. It was not considered reasonable to increase the steel section of the cables, just to further restrict the deformations. Is is clearly apparent that the chosen system, with a cable gradient of 1:5, has little in reserve with regard to allowable deformation, and that the fixed connection of the deck to the abutments, with the consequent fixation of the pierheads, was a necessary measure. Curvature The deflected forces resulting from the curvature of the bridge lead to large transverse bending moments in the lower region of the pylon diaphragm. At the foot of the pylon on the outer side of the curve, the bending moment at design level reaches ca. 50 MNm (including secondary effects). This bending moment is taken up by vertical pre-stressing cables in the pylon diaphragm and transformed by the massive transverse beam, pre-stressed by 6 cables of capacity 2'350 kN, into unequal vertical loads on the two pier legs.
Fig.8
Bending moments Myd in pylon and transverse beam
Connection of the deck to the abutments Due to the curvature in plan, with a radius of 503m, the bridge deck can be connected monolithically to the abutments, without causing appreciable secondary stresses in the deck cross-section. The missing axial force in the stage between the last stay and the abutment is provided by 2 x 3 x 1'900 kN cables.
8
Fig. 9 Secondary forces The foregoing diagrams plot the secondary axial force, the concrete stresses at mid-arch, and the horizontal displacement of the bridge deck, as a function of arch length, for a restrained arch. The cross-sectional dimensions of the Sunniberg Bridge and a temperature variation of 10° are assumed. For the system without piers portrayed in the diagrams, the secondary axial force almost disappears, for an arch length of 530m. The horizontal displacement at the crown of the arch is ca. 90mm. In the actual system constructed, with the change in radius being restrained by four piers, the secondary axial force is 2'200 kN, while the horizontal displacement is 50mm.
Construction of the Bridge Construction schedule The client scheduled the construction of the bridge for the period between June 1996 and August 1998, with the deck insulation and paving works being performed in the autumn of 1998, so that the bridge would be ready for hand-over to the contractors performing the construction of the adjacent Gotschna Tunnel in November 1998. Material excavated from the tunnel must be brought over the completed bridge. The time schedule demanded a well planned erection concept from the contractor (see Fig. 3). Working with two major groups, one in charge of the pier and pylon construction and the other in charge of the cantilever construction, a good solution was found, which enabled the works to be performed in a repetitive weekly cycle - an important factor in cantilever construction. The main items of equipment used during the construction were: - two pairs of form travellers, - two large tower cranes, situated close to the pylons, 78 m high and with reaches of 60 m and 70 m, - a smaller tower crane, - a concrete batching plant. Thu.
Concreting of edge beams and deck plate, with simultaneous reduction of ballast.
Fri.
Removal of frontal formwork, positioning of the support rail of the travelling formwork for the next stage, mounting of stressing jacks at the stay cable anchorages, and initial stressing.
9
Mon.
Stressing of stay cables in 4-6 steps, with simultaneous increase in ballast (up to concreting stage 5), lowering of travelling formwork onto the support rail, and moving forward of travelling formwork; positioning of formwork and cable trumpets at one cantilever arm.
Tue.
Positioning of formwork and cable trumpets at the second cantilever arm, placing of reinforcement for the first cantilever arm, preparation of stay cables for installation.
Wed.
Placing of reinforcement for the second cantilever arm, installation of stay cables for next stage. Uncoiling of stay cables for the next stage.
Fig. 10 Weekly cantilever cycle (The weekly cycle for stay cable installation is shown in Fig. 13) An unconventional form traveller concept was proposed and subsequently implemented by the contractor. The form traveller extended over two 6m stages, with the leading edge beams and the trailing deck slab being poured in each concreting cycle. This procedure has the following advantages: - the form traveller is better balanced - the weight of the form traveller (40 tons) can be introduced into the cantilever near the stay cables of the previous stage - installation and stressing of the stay cables can take place at the leading edge beams, before moving the traveller forward into the next stage.
Fig. 11 Travelling Formwork Stay cable fabrication For the stay cables of the Sunniberg Bridge, a parallel wire system with DINA anchorages was chosen. The special features of this system are: - cables are factory-fabricated, and ready for installation upon delivery to site. - cables and anchorages exhibit high fatigue resistance. - the cable has a high, constant modulus of elasticity, corresponding to the modulus of elasticity of the constituent wires. 10
A total of 148 stay cables, each constituted of between 125 and 160 wires, each with diameter 7mm, were fabricated. Cable lengths vary between 11.4m and 67.8m, and the guaranteed breaking loads of the cables vary between 7'695 kN and 9'850 kN. Cold drawn, galvanised wires with a nominal strength of 1'600 N/mm2 and a minimum zinc coating of 280 g/mm2 were cut to a predetermined length. This predetermined length is calculated taking the distance between the anchor plates on the completed bridge structure, as well as the corresponding cable forces, into consideration. The individual wires were bundled together before being pulled through a bath of molten corrosion inhibiting compound, directly into the HDPE stay tube. The corrosion inhibiting compound is a microcrystalline wax with a dropping point of approx. 80°C. The same material was also injected into the HDPE tube, following the fitting of the DINA anchorages to the ends of the cable. This injection of corrosion inhibiting compound fills the spaces between the wire bundle and the duct.
Fig 12 DINA anchorage The wires are anchored in the DINA anchorages by means of button-heads. A special epoxy compound prevents the ingress of oxygen into the anchorage zone, eliminates fretting between wires and the steel anchorage body, and facilitates a smooth introduction of cable forces into the anchorage. The DINA anchorages are designed to withstand fatigue stresses of up to 250 N/mm2 over 2 million load cycles. Coiled on reels, the stay cables were ready for transport to site and installation. The fabrication of the cables in a permanent plant guarantees a high and controllable standard of quality. Cable installation Uncoiling of the 4 cables per stage was performed by means of a reel stand and a winch on the bridge deck. Following the permanent welding of the telescopic joints in the HDPE stay pipe at either cable end, the upper end of the cable was placed on a deviation saddle, which was then lifted to the anchorage location at the pylon. By screwing the lock nut onto the threaded DINA anchor, the upper end of the cable was secured in its final position (see Fig. 6). The lower portion of the cable was then lifted by crane onto a tubular steel scaffolding, equipped with rollers, positioned over the starter reinforcement of the New Jersey barrier, with the lower anchorage being pushed into the mouth of the steel trumpet. On the day following the placing of concrete, the lower anchorages were pulled through the trumpets and temporarily secured.
11
Fig. 13 Stay Cable Erection Stages Cable stressing Three days after concreting, the concrete strength required to allow the tensioning of the cables was reached. Using four 5000 kN hydraulic jacks, the cables were stressed in several stages, determined by work which had to be performed on the form traveller, and by the placing of ballast. These operations had to follow a carefully planned procedure. After each step, various measurements, such as cable forces, deformations of the cantilever, pier and pylon, and cracking of the concrete, were made and compared to the expected values. The regulation of cable forces was very efficient, as increases and reductions of cable forces were easily and accurately possible, by adjusting the position of the lock nut on the continuously threaded anchorage (see Fig. 10). Stability during construction The 70m long cantilever on the 60m high piers had to be stabilised against dynamic wind loads. This was achieved by securing the deck at the quarter-span location to the foundation plate, itself anchored with soil anchors, by means of crossed pre-stressing cables, each made up of four 0.6" strands. These stabilisation cables had to be de-tensioned each time before taking deformation measurements, as they significantly influenced the free movement of the whole structure. 12
Costs The final total cost, including taxes, of the Sunniberg Bridge was SFr. 20 million, corresponding to a unit price of SFr. 3'075/m2 Split up of the Total Costs Site set-up Special foundations Ground works Abutments Piers, pylons incl. foundations Bridge deck, incl. travelling formwork Stay cables Insulation and paving Railings
8.3% 3.0% 1.5% 1.4% 20.6% 33.5% 23.1% 7.4% 1.2%
Credits Outline Design
Detailed Design Site Supervision Main Contractor Stay Cables, Post-Tensioning and Ground Anchors
Tiefbauamt Graubunden Consultant: A. Deplazes, dipl. Arch. ETH Concept: Prof Dr. C. Menn, Chur Bänziger + Köppel + Brändli + Partner, Chur Wüst + Trüb + Partner, Schaffhausen Arge Sunniberg (Vetsch, Klosters; Preiswerk + Cie. AG Brückenbau, Siebnen) Stahlton AG, Zurich
References [1]
Schweizer Ingenieur und Architekt SI+A, Nr 19 and 44/1998
13
Structural Countermeasures for Design of a Very Long-Span Cable-Stayed Bridge under Wind Loads Ken-ichi MAEDA Professor Dr.Eng Tokyo Metropolitan Univ. Hachiouji, Japan
Hitoshi NAKAMURA Research Associate M. Eng Tokyo Metropolitan Univ. Hachiouji, Japan
Yu MOROYAMA Graduate Student Tokyo Metropolitan Univ. Hachiouji, Japan
Makoto ABE Research Engineer Chodai Co. Ltd. Japan
Makoto KONNO Research Engineer M. Eng. Nippon Kokan K.K. Japan
Summary The purpose of this study is to present adequate structural countermeasures for reduction of the stress resultant under design wind loads, which becomes dominant in the static design due to the decreased width-to-span ratio, and for improvement of the static and dynamic aerodynamic stability in the wind-resistant design. In this paper, by using the example of a trial-design bridge with a center span of 1,500 m which is considered the critical span length, the authors clarified the usefulness of the proposed countermeasures from the viewpoint of cost efficiency and windresistant stability, and confirmed the realizability of very long-span cable-stayed bridges in the near future.
1. Introduction The Tatara Bridge being constructed in Japan with a center span of 890m, which is the longest span length of cable-stayed bridges in the world, is scheduled for completion in the spring of 1999. The development of cable-stayed bridges has been rapid, and the class of bridges with a center span of 1,000m is already planned for construction, according to the latest information [1]. The critical span length for cable-stayed bridges is reported to be about 1,500m, mainly because the in-plane buckling stability of main girders is degraded with increasing compressive axial-forces under dead and live loads for the static design [2]. However, with decreasing width-to-span ratios of main girders due to the increased span length, it is predicted that the stress resultant under design wind loads becomes dominant in the static design and influences the cost effectiveness [3]. In addition, it is also predicted that ensuring safety against lateral-torsional buckling instability and coupled flutter under strong winds will become very important. Moreover, to satisfy these requirements, bad influences of the flexibility of stay cables as determined by their own weights and caused by wind actions cannot be neglected [4]. The aim of this study is to present adequate structural countermeasures for reduction of the stress resultant under design wind loads in the static design, and for improvement of the static and dynamic aerodynamic stability in the wind-resistant design. Also, the authors intend to clarify the effectiveness of these structural countermeasures, and to confirm the realizability of very long-span cable-stayed bridges with center spans of 1,000m to 1,500m in the near future. For this purpose, the authors first developed a basic design model based on the trial design of a cable-stayed bridge with A-type towers and a center span of 1,500m, which is considered the critical span length for cable-stayed bridges. Then it was confirmed that the stress resultant due to design wind loads became dominant in a wide region of main girders near each tower. Next, to flexibly change the out-of-plane support conditions between main girders and towers, which are considered to greatly affect the static and dynamic deformation characteristics under
wind loads, the authors produced an alternative design model with three-dimensional (3-D) Atype towers. Cable-stayed bridges with 3-D A-type towers are attracting attention due to their increased in-plane rigidity. The structural countermeasures proposed and investigated by using the above-mentioned basic and alternative design models in this paper are as follows: (1) Application of elastic out-of-plane supports between main girders and 3-D A-type towers, positioned away from the central line of each tower. (2) Application of new auxiliary cable systems for controlling the flexibility of stay cables caused by wind actions in the out-of-plane direction. The analytical modeling was performed so that not only the design conditions peculiar to cablestayed bridges, such as cable prestresses, are satisfied, but also the flexibility of stay cables in all directions is taken into consideration. Then, with respect to the effectiveness of the first countermeasure to reduce the stress resultant under design wind loads, the authors compared the values of out-of-plane bending moments and out-of-plane lateral displacements of main girders, and examined the optimal position of the elastic supports and the optimal spring constant. With regard to the effectiveness of the second countermeasure in improving the static aerodynamic stability, the authors roughly investigated the optimal number of steps of stay cables for which new auxiliary cable systems are installed, and then compared the values of lateral-torsional displacements and critical wind velocities against buckling instability, by applying static aerodynamic forces as a function of the angle of attack. Furthermore, with respect to the effectiveness of the second countermeasures in improving the dynamic aerodynamic stability, the authors carried out multi-mode flutter analyses by applying unsteady aerodynamic forces, and investigated the natural vibration characteristics and the coupled flutter behaviors.
2. Basic Design Model and an Alternative Model To verify the necessity and effects of the structural countermeasures proposed, the authors first performed the trial design of a cable-stayed bridge with A-type towers and a center span of 1,500m, and developed a basic design model, in accordance with the specifications for longspan bridges in Japan [5]. In this process, the in-plane buckling stability of main girders against compressive axial-forces due to dead and live loads for the static design was checked according to the specifications for highway bridges in Japan [6]. Fig.2.1 shows a general diagram of the basic design model, and Table 2.1 lists major crosssectional properties. Fig.2.2 shows a sectional view of a box-shaped main girder and its components (steel type; yielding stress, tensile strength, thickness of web, upper and lower flange plates, according to JIS). In this figure, the hatched region is that in which stresses due to out-of-plane bending moments under design wind loads become dominant in the static design of main girders. In addition, to flexibly change the out-of-plane support conditions between main girders and towers, the authors also produced an alternative design model which has three-dimensional (3D) A-type towers. Because the out-of-plane support conditions of main girders are considered to greatly affect the static and dynamic deformation characteristics under wind loads. Figs.2.3 (a) and (b) show the shapes of towers in the basic and alternative design models, respectively; in the alternative design model, the cross-sectional properties of the region where each tower is three-dimensionally separated into two pillars were set as half those of each tower in the basic design model.
300
C L
40
Girder
Tower 90
20@21=420
4
4
(1)
1.43
6.1
113.7
12.2
(2)
1.82
7.8
144.7
16.7
(3)
2.10
9.1
166.7
19.2
(4)
2.39
10.3
188.7
23.0
Lower
1.79
29.2
45.4
40.4
9.6
9.6
26.5
-
-
-
Member*
12.8
80
20@35=700
550
20
20@35=700
80
20@21=420
90
550
1500
Cable
2
4
A(m ) Iin(m ) Iout(m ) J(m )
Upper 1.54 1st 0.015 36th 0.030
*(1) - (4) : section No. (see Fig.2.2)
Fig.2.1 General diagram of the basic design model
Table2.1 Major properties
C L 23.0 9.0
1.5
9.0 tf tw
4.1
21.8
SM490(3200,5000)
tl 4.1
30.0 (Unit : m)
Grade of material σy*(kgf/cm2)
SM570
SM490
SM570
SM490
4600
3200
4600
3200
σtu*(kgf/cm2) Section No.
5800
5000
5800
5000
(1) (2) (3) tf 12 14 14 Plate thickness 19 19 tw 16 (mm) 16 22 tl 10 * σy: yeileding stress, σtu: tensile strength
(4) (3) (2) (1) 17 14 14 12 22 19 19 16 26 22 16 10 : region where stresses due to wind loads are dominant.
Fig.2.2 Sectional view of main girder and its components
300
300
40
40
(a) Basic model (b) Alternative model
(a) Basic model
(b) Alternative model
Fig.2.4 Skeleton diagrams of both analytical models
Fig.2.3 Shapes of towers in both design models
Next, two analytical models for the basic and alternative models were constructed by modelling box-shaped main girders as fish-bone structures. For these analytical models, to carry out analyses taking into consideration the flexibility of stay cables as determined by their own weights and caused by wind actions, all stay cables were modelled as linked structures by equally dividing each cable into 8 axial-force members. Then the initial conditions of both analytical models were determined so that the design conditions peculiar to cable-stayed bridges, such as cable prestresses, are satisfied [7]. Figs.2.4 (a) and (b) show skeleton diagrams of both analytical models under the equilibrium conditions of completion in which dead loads and cable prestresses are applied.
3. Reduction of Stress Resultant in Static Design 3.1
Countermeasure for Stress-Resultant Reduction
Based on the results of the trial design for producing the basic design model described in the previous chapter, it was confirmed that the magnitude of the stress resultant under design wind loads greatly influences the cost efficiency in the static design, with decreasing width-to-span
ratios of main girders due to the increased span length. Furthermore, it was evident that this is due to the installation of wind-shoes in towers, which fix and support main girders in the out-ofplane direction. Therefore, as a structural countermeasure for reducing out-of-plane bending moments of main girders under design wind loads and consequently increasing the cost efficiency, the authors devised a method for elastically supporting main girders in the out-of-plane direction away from the central line of each tower. Namely, in this proposed method, main girders are elastically supported at optimal positions in 3-D A-type towers in the alternative design model as shown in Fig.3.1; hence, tower-links, which support main girders in the vertical direction, should be displaceable both in the bridge-axis direction and the out-of-plane direction perpendicular to it. Fig.3.2 shows an example of the structure of tower-links in which displacements in the two directions are possible. 3.2
Analytical Results and Optimum Condition
To verify the effects of applying elastic out-of-plane supports between main girders and 3-D Atype towers, finite displacement analyses, based on the approximate updated Lagrangian method (AULD method) [8][9], were carried out by using the basic and alternative design models. Design wind loads were applied to main girders, stay cables and towers in the out-of-plane direction, according to the new specifications for long-span bridges including the aforesaid Tatara Bridge in Japan [10]. Actual values of the design wind loads per unit length with respect to the member-axis are listed in Table 3.1. First, by using the basic design model in which main girders were elastically supported by a provisional support positioned away from the central line of each tower, the authors examined the optimal position of elastic supports and estimated the overall effects of the countermeasure. In the examination, positions of the provisional elastic support were horizontally moved along the bridge-axis, and a spring constant of 2,000tonf/m was set temporarily. As part of the analytical results, Fig.3.3 shows the relationship between the amount of eccentricity at each elastic support position from the central line of each tower and the following factors: out-of-plane bending moments at the elastic support position and out-of-plane lateral displacements at the midpoint of main girders. In the figure, the analytical result for the case when main girders were fixed and supported by wind-shoes at the center of towers is also described for reference. The results in Fig.3.3 indicate that, as a result of applying this method, the absolute value of the minimum out-of-plane bending moment and the maximum out-of-plane lateral displacement are significantly decreased, and that the countermeasure is most effective when the position of elastic supports is far from the central line of each tower and close to the center of bridge. Though the analytical results are not shown, the authors compared the effects of elastic supports at multiple positions near each tower; however, the countermeasure was most effective when there was only one support near each tower. Member Wind load Girder 1.208 (tonf/m) Tower 12.094 (tonf/m/tower) Cable 0.0516 - 0.0816 (tonf/m/cable)
Tower link
Table 3.1 Design wind loads Tower side an e sp Sid
Elastic supports
s ter Cen
pan
Girder side
Fig.3.1 Concept of elastically supported girder Fig.3.2 An example of the structure of tower-links
Out-of-plane lateral displacement at midpoint of center span (by wind-shoe)
-150000
15
Central line of tower
Side span
Center span
10 5
Out-of-plane bending moment at elastic suppot position Out-of-plane lateral displacement at midpoint of center span
-50000
0 -80
-60
-40
-20
0
20
40
60
Amount of eccentricity from central line of tower (m)
Fig.3.3 Examination into the optimal position
-400000
Out-of-plane bending moment at elastic support position
30
With tower-link Without tower-link
Out-of-plane bending moment (tonf . m)
20
-350000
-250000
25
Out-of-plane lateral displacement (m)
Out-of-plane bending moment at fixed support position (by wind-shoe)
Out-of-plane lateral displacement (m)
Out-of-plane bending moment (tonf. m)
-450000
-300000
Out-of-plane lateral displacement With tower-link at elastic support position
20
Without tower-link
-200000
10
-100000
Out-of-plane lateral displacement at midpoint of center span With tower-link
Without tower-link
0 1.0E+02
80
0 1.0E+03
1.0E+04
1.0E+05
Spring constant (tonf/m)
1.0E+06
Fig.3.4 Examination into the optimal spring constant
Next, on the basis of these results, by using the alternative model in which main girders were elastically supported by a one-sided pillar of each 3-D A-type tower close to the center of bridge, the authors examined the optimal spring constant of elastic supports; namely, the amount of eccentricity at each elastic support position from the central line of each tower is 60m. Then, by using the alternative model in which tower-links were temporarily eliminated and main girders were supported directly by a cross beam of each tower in the vertical direction, the authors compared the effects of elastic supports to examine the influence of out-of-plane lateral displacements of tower-links. As part of the analytical results, Fig.3.4 shows the relationship between the spring constant for elastic supports and the following factors: out-of-plane bending moments, out-of-plane lateral displacements at the elastic support position and out-of-plane lateral displacements at the midpoint of main girders for the cases with and without tower-links. In the figure, the analytical result for the case when main girders were fixed and supported by wind-shoes at the center of towers in the basic design model is also described for reference. The results in Fig.3.4 indicate that the absolute value of the minimum out-of-plane bending moment decreases due to the decreased spring constant; however, when the spring constant decreases to below 1,000tonf/m, the out-of-plane displacement at the elastic support position increases and the influence of recovery forces due to the inclination of tower-links becomes apparent. Accordingly, to avoid excessive charges to tower links, a spring constant of 1,000tonf/m is considered to be optimal in this numerical experiment. 3.3
Effect of Structural countermeasure on Economy
Figs.3.5 and 3.6 show the distributions of out-of-plane bending moments and out-of-plane lateral displacements of main girders due to the design wind loads, respectively, for both the analytical models in which fixed supports of wind-shoes or elastic supports with the spring constant of 1,000tonf/m were applied. Both kinds of supports were positioned at the center of
Alternative model
by wind–shoe by elastic support
0 150000
300000
Elastic support position
-150000
Bridge-axis
10
Elastic support position
-300000
20 Central line of tower
by wind–shoe by elastic support
Out-of-plane lateral displacement (m)
Basic model
Central line of tower
Out-of-plane bending moment (tonf . m)
-450000
Bridge-axis Basic model
0 -5
by wind–shoe by elastic support
Alternative model
by wind–shoe by elastic support
Fig.3.5 Out-of-plane bending moments of main girders Fig.3.6 Out-of-plane lateral displacement of main girders
each tower for the basic design model, and on the one-sided pillar of each tower close to the center of bridge for the alternative design model. The results in Fig.3.5 indicate that some effects from the method in which wind-shoes are only replaced by elastic supports, or from the method in which wind-shoes are only moved to a position away from the central line of each tower, can be expected, and that the absolute value of the minimum out-of-plane bending moment can be significantly reduced by combining these methods. In Fig.3.6, we can clearly see that excessive out-of-plane lateral displacements are not generated around the elastic supports, and that the maximum out-of-plane lateral displacement at the midpoint is the largest in the basic design model in which main girders are supported elastically. Based on these results, the structural countermeasure of elastically supporting main girders in the out-of-plane direction at an optimal position away from the central line of each tower is very effective for reducing the out-of-plane bending moments in the region of main girders, where stresses due to the design wind loads become dominant. Therefore, since the additional construction costs due to adopting 3-D A-type towers are not very high, the countermeasure is very useful for increasing the cost efficiency. Moreover, the 3-D A-type towers are expected to increase the in-plane rigidity of cable-stayed bridges and decrease their construction cost.
4. Improvement in Wind-Resistant Design 4.1
Countermeasure against Aerodynamic Instability
As a structural countermeasure against unstable static and dynamic phenomena in the windresistant design, the authors devised a method for controlling the flexibility of stay cables caused by wind actions in the out-of-plane direction. This proposed method aims at improving the wind-resistant stability by installing an auxiliary cable system in which two stay cables in each step are woven together in a twilled-weave manner, as shown in Figs.4.1 (a) and (b) for the basic and alternative design models, respectively. These auxiliary cables, named lacing cables, are installed to avoid the loss of torsional resistance when two stay cables approach each other due to the application of aerodynamic forces. The cross-sectional area of all lacing cables was set at 0.001 m2 in both the analytical models. Because it was previously confirmed that, by installing the lacing cables, the deformation characteristics under live loads and wind loads only negligibly change in the static design, except that torsional deformations under eccentric live loads are slightly decreased. Moreover, in this case, since the diameter is sufficiently small, the landscape wouldn’t be greatly denuded of its picturesqueness, and the driver’s view wouldn’t be seriously troubled due to the installation of lacing cables. In the modeling of lacing cables, dead loads were neglected, and their initial stresses when aerodynamic forces are not applied were also neglected; however, it was assumed that they can resist not only the tension, but also the compression. CD,CL 5.0
CM 0.25
4.0
0.20
3.0
0.15
2.0
0.10
1.0
0.05
0.0
0.00
-1.0
-0.05
-2.0
-0.10 CD CL CM
-3.0 -4.0 -5.0 -15
(a) Basic model with lacing cables (b) Alternative model with lacing cables
Fig.4.1 Image views of both models with lacing cables
-10
-5
0
5
10
Angle of attack α (deg.)
-0.15 -0.20 -0.25 15
Fig.4.2 Static aerodynamic coefficients
4.2
Lateral-Torsional Buckling Stability
4.2.1 Design Model Used and Static Aerodynamic Forces To investigate the effects of controlling the out-of-plane flexibility of stay cables on the lateraltorsional buckling stability, the basic design model was used, in which the lacing cables were installed in steps from the top to the 16th stay cable. Prior to detailed investigations, the authors had developed some analytical models with various numbers of steps installed, and examined the difference in the effects of lacing-cables depending on the number of steps; as a result, it was found that 16 steps are the most effective. By expressing the drag force, lift force and pitching moment coefficients as CD, CL and CM dependent on the angle of attack α, respectively, three components of the static aerodynamic forces per unit length of main girders can be obtained with respect to the wind-axis as follows: D(α ) = 1 2 ρU Z2 An C D (α ) L(α ) = 1 2 ρU Z2 BC L (α ) M (α ) = 1 2 ρU Z2 B 2 C M (α )
1
(1)
Z 7 U Z = U 10 10 α =α 0 +θ x
(2) (3)
where D, L and M are the drag force, the lift force and the pitching moment dependent on α, respectively; ρ is the air density (=0.000125tonf.sec2/m4); An and B are the vertical projected area and the width, respectively. Then the mean wind velocity UZ at the mean height Z corresponds to the design wind velocity, which can be given by eq. (2) expressing U10 as the basic wind velocity at the height of 10 m. In this analysis, the above-mentioned static aerodynamic forces were applied to the main girders, in which An, B and Z were set to 5m2, 30m and 40m, respectively, and CD, CL and CM obtained from a wind-tunnel test were employed as shown in Fig.4.2. Also, the drag forces independent of α were applied to stay cables and towers, in which the drag force coefficients were set to 0.70 and 1.20, respectively. Since the relative evaluation of the values of lateraltorsional displacements and critical wind velocities against buckling instability was the first objective, the authors set the wind-axis in the horizontal direction and the angle of incidence α0 to be 0 degrees. Therefore, the angle of attack α given by eq. (3) was identical to the torsional displacement θx of main girders. 4.2.2 Analytical Results and Effect of Structural Countermeasure In the lateral-torsional buckling analyses, the set values of the basic wind velocity U10 were increased gradually; the numerical calculations were performed until the angle of attack α, namely the torsional displacement θx of main girders, could not converge [11].
6 Torsinal displacement (deg.)
5
With lacing cables
4
(Straight cable model)
99m/s
80m/s
Without lacing cables
86m/s
3 2 1 0 50
60
70
80
90 U10(m/s)100
Fig.4.3 Torsional displacements at the midpoint of man girders
Out-of-plane lateral displacement (m)
As part of the analytical results, Figs.4.3 and 4.4 show the relationships of torsional displacements and out-of-plane lateral displacements at the midpoint of main girders to the basic 60
86m/s 99m/s
50 40 80m/s
30 20
Without lacing cables With lacing cables
10
(Straight cable model)
0 50
60
70
80
90
100 U10(m/s)
Fig.4.4 Out-of-plane lateral displacements at the midpoint of man girders
4
Central line of tower
6
Torsional displacement (deg.)
wind velocity U10, respectively. Fig.4.5 shows the distribution of torsional displacements of main girders when the basic wind velocity U10 is 80m/s. In these figures, the analytical result for the special analytical model, named the straight cable model in which each stay cable was modelled as one straight axial-force member with the purpose of neglecting the effects of flexibility, are also described for reference.
Without lacing cables With lacing cables (Straight cable model)
2 Bridge-axis
0 The results in Figs.4.3 and 4.4 indicate that, as a result of installing lacing cables, the out-of- Fig.4.5 Torsional displacements of man girder plane lateral displacements of main girders increase a little; however, the torsional displacements are fairy reduced due to the control of flexibility of stay cables. Accompanying this phenomenon, in these figures, the critical wind velocity against buckling instability increases from 80m/s to 86m/s. In Fig.4.5, we can clearly see that, at the same wind velocity, the torsional displacements of main girders are greatly reduced by installing lacing cables, and their maximum value is even lower than that of the straight cable model in which the flexibility of stay cables was neglected.
The reason for the difference in torsional displacements of main girders with and without lacing cables can be explained using Fig.4.6, which is a projection figure of the lateral-torsional deformations on the vertical plane at the center of bridge when the basic wind velocity U10 is 80m/s (the same as that in Fig.4.5). Based on the results in Fig.4.6, when lacing cables are not installed, the torsional resistance is Without lacing cables With lacing cables lost because two stay cables approach each other in each step, as predicted; in addition, main girders are pulled in the direction of the Fig.4.6 Lateral-torsional cable-axis. Deformations Accordingly, the structural countermeasure of controlling the flexibility of stay cables in the outof-plane direction is very useful for improving the lateral-torsional buckling stability. The critical wind velocity obtained in this numerical experiment is sufficiently high, even when lacing cables are not installed. However, in cases where the lateral-torsional rigidity becomes weaker due to smaller width-to-span ratios or shallower depths of main girders, critical wind velocities might be lower than the allowable limit [12]. In such cases, the proposed countermeasure is extremely effective without greatly degrading the cost efficiency because of slight design changes. Furthermore, this method can be applied as a temporary countermeasure during construction and as a supplementary measure after completion. 4.3
Coupled Flutter Behavior
4.3.1 Design Models Used and Unsteady Aerodynamic Forces To investigate the effects of controlling the out-of-plane flexibility of stay cables on the coupled flutter behavior, not only the basic design model, but also the alternative design model was used, in which lacing cables are installed in steps from the top to the 16th stay cable. The position of elastic out-of-plane supports and the spring constant in the alternative design model were the same as those evaluated in the previous chapter. As the dynamic aerodynamic forces in this analysis, the lift force and the pitching moment, which are the unsteady aerodynamic forces based on the plate-wing theory, were applied to main girders. Also, the drag force based on the semisteady theory was applied to main girders. For the structural damping, a logarithmic decrement δST was set at 0.02.
4.3.2 Analytical Results and Effects of Structural Countermeasures In the analysis, the authors first obtained natural frequencies and natural vibration modes up to 50 dimensions by means of natural vibration analyses; then, by using these results, multi-mode flutter analyses were carried out on the basis of a modal analysis technique [13]. As part of the analytical results, Fig.4.7 shows the relationship between the wind velocity U at the mean height of main girders and the aerodynamic damping (logarithmic decrement) δ of flutter mode branches. Table 4.1 lists the values of critical wind velocities against coupled flutter evaluated from the U-δ curves. In this table, the values of natural frequencies of the 1-st symmetric and antisymmetric vertical deflection and torsion modes are also listed for reference. The results in Fig.4.7 and Table 4.1 indicate that, due to the control of out-of-plane flexibility of stay cables as a result of installing lacing cables, the flutter critical wind velocity of the basic design model increases by about 23% from 140m/s to 172m/s, and that of the alternative design model with 3-D A-type towers and elastic supports increases by about 16% from 137m/s to 159m/s. In Table 4.1, we can clearly see that, due to this control, frequencies of the 1-st symmetric and antisymmetric torsion modes increase beyond the values, which were expected from the decrement in static torsional deformations under eccentric live loads when the crosssectional area of lacing cables was evaluated.
Logarithmic decrement δ
Therefore, the structural countermeasure of 0.4 Basic model without lacing cables controlling the out-of-plane flexibility of stay Basic model with lacing cables Alternative model without lacing cables cables is extremely effective for improving the Alternative model with lacing cables dynamic wind-resistant stability, and can obtain a significantly high flutter critical wind 0.2 velocity, regardless of the application of elastic out-of-plane supports between main girders and 3-D A-type towers. The critical wind velocity obtained in this numerical experiment is fairly 0 high even without any structural 0 100 countermeasures; however, it is evident that the Wind velocity (m/s) two proposed structural countermeasures can -0.1 indeed increase the safety level against Fig.4.7 U-δ curve dynamic instability due to wind actions.
1-st symm. deflection mode Freq. 1-st antisymm. deflection mode (Hz) 1-st symm. torsion mode 1-st antisymm. torsion mode Flutter critical wind velocity (m/s)
200
Analytical model Without lacing cables With lacing cables Basic model Alternative model Basic model Alternative model 0.1040 0.1309 0.1034 0.1321 0.1102 0.1511 0.1113 0.1522 0.4886 0.4015 0.6321 0.5122 0.8800 0.6058 0.9223 0.6702 139.9 136.8 172.4 159.0
Table 4.1 Natural vibration frequencies and critical wind velocities against flutter
5. Conclusions By using a trial-design bridge with a center span of 1,500m, in this study, the authors investigated the effects of the proposed structural countermeasures on static and dynamic actions due to wind loads, and discussed the cost effectiveness and the wind-resistant stability of very long-span cable-stayed bridges with small width-to-span ratios of main girders. The authors reached the following conclusions based on the analytical results obtained. (1) In the static design of cable-stayed bridges, due to the decreased width-to-span ratios of main girders accompanying the increase in their span length, the stress resultant under design wind loads becomes dominant in a wide region of main girders near each tower, and greatly influences the cost effectiveness. At this time, the proposed structural countermeasure of
applying elastic out-of-plane supports between main girders and 3-D A-type towers is very useful for reducing out-of-plane bending moments of main girders generated by design wind loads, and therefore for increasing the cost efficiency. (2) The countermeasure of applying elastic out-of-plane supports between main girders and 3-D A-type towers increases its effectiveness, if the supports are positioned close to the center of bridge and as far as possible from the central line of each tower. In addition, an optimal spring constant can be evaluated according to not only the degree of stress-resultant reduction, but also the allowable amount of out-of-plane lateral displacement at the elastic support position of main girders under design wind loads. (3) The structural countermeasure of controlling the flexibility of stay cables in the out-of-plane direction is very useful for improving the lateral-torsional buckling stability. For cases in which excessive lateral-torsional displacements occur or critical wind velocities become lower than the allowable limit due to smaller width-to-span ratios of main girders, the proposed countermeasure is extremely effective without greatly degrading the cost efficiency because of slight design changes. Furthermore, this method can be applied as a temporary countermeasure during construction and as a supplementary measure after completion. (4) The critical wind velocities against coupled flutter in cable-stayed bridges are extremely high; they rarely decrease to below the allowable limit, even when their center span length approach the critical value. However, adopting the structural countermeasure of controlling the out-of-plane flexibility of stay cables leads to a higher flutter critical wind velocity, regardless of the application of elastic out-of-plane supports between main girders and 3-D A-type towers; thus it ensures the safety against dynamic instability under strong winds. In this study, a 3-D A-type tower was used, the one-sided pillar of which supports main girders elastically; however, other structures are also possible, in which ordinary plane A-type towers are used and main girders are supported elastically at the edge of extended concrete piers. In addition, as a method for controlling the out-of-plane flexibility of stay cables, an auxiliary cable system was used, in which two stay cables in each step are coupled by lacing cables; however, other methods are also possible. Furthermore, to realize an era of very long-span cable-stayed bridges with 1,000m- 1,500m center spans at an earlier stage, it will be necessary to device more appropriate structural systems and to investigate the efficiency of their construction and maintenance.
References [1] J.M.Muller Very Long Span Bridges - Concepts, Materials and Methods, Proc. of IABSE Symposium on Long-Span and High-Rise Structures, Kobe, 1998. [2] M.Nagai Possibility and Limitations of Long-Span Cable-Stayed Bridges Based on Static and Dynamic Instability analyses, Proc. of International Seminar on Long Span Bridge Aerodynamics Perspective '98, Kobe, 1998. [3] K.Nomura, S.Nakazaki, N.Narita, K.Maeda and H.Nakamura Structural Characteristics and Economy of Cable-Supported Bridges with Long-Span, Journal of Structural Engineering, Vol.41A, 1995. (in Japanese) [4] H.Nakamura, K.Maeda, M.Konno, M.Hayashi and N.Narita Lateral-Torsional Buckling Stability of a Long Span Cable-Stayed Bridge with Flexible Cables under Wind Action, Journal of Constructional Steel, Vo1.5, 1997. (in Japanese) [5] Honshu-Shikoku Bridge Authority Specifications on Superstructure Design, 1989, and Specifications on Wind-Resistant Design, 1976. (in Japanese) [6] Japan Road Association Specifications for Highway Bridges, Part 2 Steel Bridges (English Edition), 1987. [7] K.Maeda, M.Hayashi, H.Setouchi, H.Nakamura and N.Narita Three-Dimensional Finite Displacement Analysis of Long-Span Cable-Stayed Bridges, Journal of Structural Engineering, Vol.41A, 1995. (in Japanese) [8] Y.Maeda and M.Hayashi Finite Displacement Analysis of Space Framed Structures, Journal of Structural Mechanics and Earthquake Engineering, No.253, 1976. (in Japanese) [9] P.Jetteur, S.Cescotto and V.Degoyet Improved Nonlinear Finite Elements for Oriented Bodies Using an Extension of Marguerre's Theory, Computers & Structures, Vo1.17, No.1, 1983. [10] Honshu-Shikoku Bridge Authority Specifications on Wind-Resistant Design of the Onomichi-Imabari Route, 1994. (in Japanese) [11] V.Boonyapinyo, H.Yamada and T.Miyata Nonlinear Buckling Instability Analysis of Long-Span Cable-Stayed Bridges under Displacement-Dependent Wind Load, Journal of Structural Engineering, Vol.39A, 1993. [12] M.Nagai, Xu Xie, H.Yamaguchi and Y.Fujino Static and Dynamic Instability Analyses of 1400-meter LongSpan Cable-Stayed Bridges, Proc. of IABSE Symposium on Long-Span and High-Rise Structures, Kobe, 1998. [13] M.Iwamoto Prediction of Aerodynamic Behavior of Cable Supported Bridges, Ph.D.thesis, University of Tokyo, 1995. (in Japanese)
Aerodynamic Performance of Cable-Supported Bridges with Large Span-to-Width Ratios Søren V. LARSEN. M.Sc., PhD. Danish Maritime Institute, Lyngby, Denmark
Søren V. Larsen, born 1966, obtained his degree in 1991, and his Ph.D. in 1997. He joined DMI in 1995. Project Manager, Hydro- and Aerodynamics
Summary This paper presents some results of an experimental study of three different types of cable supported bridges. A traditional suspension bridge, a traditional cable-stayed bridge and a new concept of a cable-stayed bridge with four inclined cable planes have been studied with the emphasis on the aerodynamic behaviour. All bridges have an identical stiffening girder, which is extremely slender compared with the main span (span-to-width ratio of 100). The paper focuses on the results of full bridge aeroelastic model tests performed at a scale of 1:100.
1. Introduction After the collapse in 1940 of the first Tacoma Narrows Bridge, it became evident for the modern bridge designer that the dynamic effects of the wind are of immense importance. Bridges with tendencies of significant wind-induced movements were modified in the following years. Such modifications included the Golden Gate and the Bronx-Whitestone bridges. In recent years, the spans of erected and/or proposed bridges have become longer and longer. Especially for cable-stayed bridges, an increase of the span over the last 40 years is truly remarkable, from 183 m in 1955 (Strömsund) to a record-holding span of 890 m expected in 1999 (Tatara, Japan). For suspension bridges the increase in span has been more moderate in this period of time from around 1300 m (Golden Gate and Mackinac) to 1624 m (Storebælt, Denmark) and 1991 m (Akashi Kaikyo, Japan) in 1998. Though, studies have been made for spans of 3.3 km (Messina) and even up to 5 km (Gibraltar). A measure of the slenderness in the lateral direction may be defined : the span-to-width ratio is the ratio between the length of the main span and the width of the bridge girder (or deck); this ratio accounts for the lateral slenderness of a bridge system. The bending moment of inertia of the deck is possibly a better parameter to compare with the span length. However, such detailed data as lateral bending stiffness is not readily available for many bridges. Figure 1.1 illustrates the development in the span-to-width ratio for suspension bridges.
100 90 80 Tacoma 1
span-to-width ratio l/B
70 60
Mackinac
50 40 30 20
Brooklyn
Humber Hoga Kusten Akashi Kaikyo Askoey Storebaelt
Golden GateChesapeakeTacoma Tagus 2 VerrazanoSevern Bosporos 1 Fyksesund Minami-Bisan Francisco- Tancarville George WashingtonSanOakland Kita-Bisan Detroit River Emmerich BronxBosporos 2 Forth Whitestone Williamsburg Manhatten
Lillebaelt
10 0 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 year of completion (or expected year of completion)
Figure 1.1 Development in lateral slenderness (span-to-width ratios) for suspension bridges. As seen from Figure 1.1, the suspension bridges were becoming increasingly slender up to the Tacoma Narrows failure, after which bridges were built with more moderate lateral slenderness. However, the lateral slenderness was not decreased to the same extent as the vertical slenderness was. The first Tacoma Narrows Bridge had a span-to-width ratio of 72. Only 17 years later the Mackinac Bridge was completed having a span-to-width ratio of 56. The lateral slenderness of the Mackinac Bridge is similar to that of newly completed long span bridges: the Storebælt and the Akashi Kaikyo bridges For many years, cable-stayed bridges have been somewhat "short and wide" compared to suspension bridges. Cable-stayed bridges were often seen having span-to-width ratios five times less than that of the most slender suspension bridges. The development of the span-to-width ratio for cable-stayed bridges is illustrated in Figure 1.2. For cable-stayed bridges the most critical stage with respect to lateral slenderness is during erection assuming that free-cantilevering method is employed. During erection the free cantilever is prone to lateral deflections. For mono-tower cablestayed bridges during erection, the maximum length of the free cantilever is equal to the length of the main span, whereas for cable-stayed bridges with two towers, the free cantilever is only a half of the main span. Therefore, in Figure 1.2 mono-tower cable-stayed bridges are shown with both a "span-to-width ratio" and a "double span-to-width ratio", where the latter exemplifies the erection stage.
60
Karnali River (erec.)
50
span-to-width ratio l/b
Tatara Skarnsundet Normandie
40
Helgelands Knie (erec.) St. Nazaire
30
20
10
0 1950
Karnali River
Tjorn Wadi Kuf Quincy Ikuchi Tampico Kohlbrand Barrios de LunaBaytown Oresund Brotonne Rande Annacis LulingFaro Maracaibo ReesKnie Rama IX 2nd Severn Bridge Stromsund PascoDuisburg- KennewickDames Sunshine Skyway Severin Neuenkamp Point Erskine Theodor Heuss Friedrich Ebert Nord-Elbe Buchenauer Severin (erec.)
1960
1970 1980 1990 year of completion (or expected year of completion)
2000
2010
Figure 1.2 Development in lateral slenderness (span-to-width ratios) for cable-stayed bridges.
2. Scope and Extent of Study When the span-to-width ratio becomes larger and the bridge consequently becomes more slender in the lateral direction, the demand for additional lateral support becomes more pronounced. As described in [1], three mutually inclined cable planes are required to have a three-dimensional support of the girder, i.e., support against vertical, lateral and torsional loads. This has so far only been used in pipeline bridges and minor pedestrian bridges. Such cable systems consisting of mutually inclined cable planes are referred to as spatial cable-stayed bridges or spatial systems. Three cable planes are, as mentioned, sufficient to establish a spatial system, but based on considerations of symmetry, four cable planes seem reasonable. A spatial cable-stayed system can be obtained with various stay cable configurations and the pylons of a spatial system can be designed in many ways, see [3] and [4] for extensive discussions. The objective of the present study is to investigate bridges with extremely narrow girders with respect to the aerodynamic behaviour. An important part of the study is the examination of a new improved cable-stay system. For comparison, two traditional cable supporting systems are included in the study. The primary study of the three bridges is performed in an extensive three-dimensional aeroelastic wind-tunnel study with full bridge models at a relatively large scale. The project is concerned with bridges having a span-to-width ratio of 100. This is very close to a factor of 2 to what has been seen in suspension bridges, and 2.5 to the extreme in cable-stayed
bridges. The study comprises three cable supported bridges with an assumed full-scale dimensions of 800 m main span and 250 m side spans. The three bridges concerned are: ⋅ Suspension bridge ⋅ Traditional modified fan ("plane") cable-stayed bridge ⋅ Cable-stayed system with four inclined cable planes ("spatial") Traditional cable supported bridges, i.e., suspension bridges and cable-stayed bridges with one or two cable planes, can give only vertical or vertical and torsional support to the bridge deck. Additionally, as a secondary effect, these systems can also give some restraint against lateral loads if the cable system is earth-anchored. So far for major cable supported bridges, only suspension bridges are built as earth-anchored systems. The suspension bridge in the present study is an earth-anchored system, and the two cable-stayed systems are self-anchored. The two cable-stayed bridges will be referred to as plane and spatial systems, respectively. The three bridges are illustrated in Figure 2.1.
Figure 2.1
Illustrations of the three cable-supported bridges studied. Upper: suspension bridge, middle: plane (or traditional) cable-stayed bridge, lower: spatial cablestayed bridge.
For the prototype bridge girder a simplified deck was assumed with a constant cross-section equivalent to a 2N8 m steel box girder, with 16 mm side and bottom flanges and a 20 mm upper flange. The chosen cross-section was intended to represent an idealized deck, hence mass and stiffness contributions from diaphragms, etc., was assumed to be included in the flanges. The bridge deck is studied in two cases: as a rectangular section (bluff) and as a streamlined section, see Figure 2.2. The streamlined section represents a section being aerodynamically preferable to the bluff, but not necessarily an optimized cross-section. The purpose of including two cross-sections in the study was to examine two deck types with significantly different aerodynamic characteristics
Figure 2.2
Illustrations of the two bridge deck configurations. Upper: bluff box girder, lower: streamlined box girder.
3. Section Model Tests Initially, the two cross sections were studied in an extensive section model test programme. The load coefficients were measured for 11 angles of attack of the incoming flow: ±10° in steps of 2°. In Table 3.1, the results for 0° angle of attack are listed. Section flow CD CL CM dCL/dα dCM/dα Table 3.1
Streamlined girder smooth turbulent 0.20 0.20 -0.28 -0.30 -0.054 -0.078 7.59 rad-1 7.40 rad-1 2.83 rad-1 2.71 rad-1
Bluff girder smooth turbulent 0.36 0.36 -0.25 -0.26 -0.010 ~0 3.10 rad-1 5.45 rad-1 -1.01 rad-1 -0.45 rad-1
Static coefficients and slopes, streamlined bluff section. CD = Fdrag/( ρ 1U2Bl), CL = Flift/(½ ρ 2U2Bl) and CM = M/(½ ρ 3U2B2l), where ρ 4 is the air density, U is wind speed, B is a characteristic width of the model (8 m full scale used for both cross sections) and l is the length of the section model.
4. Full Bridge Models The three aeroelastic full bridge models were produced at a geometric scale of 1:100. The two cable-stayed models could be modified into modelling a critical phase of the erection stage. The models were designed using Froude scaling. The models were tested in two flow conditions, namely smooth and turbulent flow. Turbulence intensity in the turbulent flow was about 13% for the u-component at deck level.
The bridge deck was produced with an aluminium spine covered with deck segments of a light foam material. Furthermore, a standard model railing was mounted onto the deck segments. The aluminium spine simulates the structural properties of the deck and the deck segments and the railings simulate the cross-sectional geometry. The deck segments were attached to the spine with small aluminium crossbeams; every second crossbeam was attached to the hangers or stay cables. The bridge deck could be modified from bluff to streamlined cross-section. The sketches in Figure 4.1 show the cross-sections of the bridge deck.
Figure 4.1
Cross-section of bridge deck in full bridge model tests. The upper sketch shows the bluff section and the lower the streamlined section.
Figures 4.2 through 4.4 shows photographs of the full bridge models installed in DMI’s very wide boundary layer wind-tunnel.
Figure 4.2 Suspension Bridge Model
Figure 4.5 Spatial Cable-Stayed Bridge Model Figure 4.4 Plane Cable-Stayed Bridge Model
5. Results of Full Bridge Models It was possible only in two cases to reach the stability limit of the individual systems with the various configurations in turbulent flow. Instability developed for the suspension bridge and the plane system, where the wind speed was increased until the response was found unacceptable. The instability occurred only with the bluff cross-section of the girder. For the spatial system with bluff cross-section, the maximum wind speed of the wind tunnel is believed to be close to the stability limit.
Table 5.1
Bridge
Configuration
Stability limit
Suspension bridge Plane cable-stayed bridge
bluff girder bluff girder
42 m/s 58 m/s
Determined stability limits (turbulent flow) in full-scale.
In the case of the suspension bridge with bluff cross-section, the instability started to develop at approximately 42 m/s in turbulent flow. The instability occurring was in torsion.. Tests performed in smooth flow showed that the stability limits were not different from those measured in turbulent flow. For the plane system mounted with the bluff deck, the instability started to develop around 58 m/s in turbulent flow. Similar to the suspension bridge, the instability has a torsional nature. All systems, where the streamlined section was employed, did not exhibit instability within the range of wind speeds of the tests. Also the spatial system with bluff section was found stable, however, as mentioned, it appeared close to instability. In the case of the erection stage of the plane system, the tests were stopped when the lateral deflections were found unacceptable, therefore aerodynamic instabilities at high wind speeds could not be studied in these cases. The buffeting response was measured in the turbulent flow condition for all bridges in all configurations. These measurements give information about the quasi-static mean and dynamic response in the simulated flow. Figures 5.1 through 5.8 show the buffeting response measured at
RMS vertical displacement (m)
vertical buffeting response - streamlined cross section 0.80 suspension plane 0.70 spatial 0.60 0.50 0.40 0.30 0.20 0.10 0
10
20 30 40 50 60 mean wind speed at deck level (m/s)
70
RMS lateral displacement (m)
Figure 5. 1 lateral buffeting response - streamlined cross section 0.50 suspension 0.45 plane 0.40 spatial 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 50 60 70 mean wind speed at deck level (m/s)
Figure 5. 2
0.40 0.30 0.20 0.10 10
Figure 5. 3
2.00 1.50 1.00 0.50 0.00 0
10 20 30 40 50 60 mean wind speed at deck level (m/s)
70
mean lateral buffeting response - streamlined cross section suspension 12.0 plane spatial 10.0 8.0 6.0 4.0 2.0 0.0
RMS lateral displacement (m)
RMS vertical displacement (m)
0.50
0
2.50
0
10
20 30 40 50 60 mean wind speed at deck level (m/s)
70
Figure 5. 5
vertical buffeting response - bluff cross section 0.80 suspension plane 0.70 spatial 0.60
0.00
torsional buffeting response - streamlined cross section 4.00 suspension 3.50 plane spatial 3.00
Figure 5. 4
mean lateral displacement (m)
0.00
RMS torsional displacement (degrees)
the centre of the span in the completed bridges. However, it should be noticed that the bridge deck with the bluff section was around 10% lighter than with the streamlined section. The mass moment of inertia of the two cross-sections varied more than 30%.
20 30 40 50 60 mean wind speed at deck level (m/s)
70
lateral buffeting response - bluff cross section 0.50 suspension 0.45 plane 0.40 spatial 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 50 60 70 mean wind speed at deck level (m/s)
Figure 5. 6
mean lateral buffeting response - bluff cross section mean lateral displacement (m)
RMS torsional displacement (degrees)
torsional buffeting response - bluff cross section 4.00 suspension 3.50 plane 3.00 spatial 2.50 2.00 1.50 1.00 0.50 0.00 0
10 20 30 40 50 60 mean wind speed at deck level (m/s)
Figure 5. 7
70
12.0suspension plane 10.0 spatial 8.0 6.0 4.0 2.0 0.0 0
10 20 30 40 50 60 mean wind speed at deck level (m/s)
Figure 5. 8
The two cable-stayed systems with streamlined deck exhibit very similar behaviour in dynamic vertical response, whereas the suspension bridge with streamlined deck exhibits a larger response; at 40 m/s the response is approximately 40% larger than that for the cable-stayed systems. The dynamic lateral response of the suspension bridge and the plane system with streamlined deck are both larger and more scattered than that of the spatial system. It is also found that the three systems with streamlined deck all exhibit relatively small dynamic responses in torsion.
6. Conclusions Laterally slender bridges seem to be an area which until now has not had very much attention. Therefore, it was found valuable to carry out a comprehensive study of an important topic related to such bridge structures: the aerodynamic characteristics of cable supported bridges with narrow bridge decks. The study revealed that the proposed spatial cable supported system has a distinct advantage compared to the traditional cable systems in terms of its aerodynamic resistance. This was confirmed in the following aspects. Firstly, a spatial system exhibits a smaller dynamic response than a suspension bridge. Secondly, the lateral deflection, which can be critical for the design of extremely slender bridges, is reduced by approximately a factor of 2. Thirdly, during the critical erection stage, the spatial system is stable at least up to the design wind speed of the completed bridge, even with an extremely slender girder, which will cause large problems during erection for a traditional cable-stayed system. Finally, for the spatial system, the design of the girder cross-section becomes less important because even with a bluff cross-section, the system is still aerodynamically stable, whereas the suspension bridge had only an acceptable stability limit with the streamlined deck. Therefore, the spatial system can be built with a less material-consuming girder than the suspension bridge. Assuming similar flange thicknesses as for the bluff section, a streamlined section will have a cross-sectional area about 30% higher than that of the bluff section. Consequently, the spatial system offers the possibility of saving a significant amount of steel material since a girder with simpler geometry is acceptable. Generally, it may be concluded that a spatial system in terms of aerodynamics may be very advantageous, especially with a slender girder which can cause problems for traditional cable supported systems. It was also found that the observed torsional instabilities were not coupled with
70
the lateral degree of freedom of the deck despite the fact that the bridges were very flexible in this direction.
7. Acknowledgements This study has been supported by the Research Academy, Aarhus and the Danish Maritime Institute. Furthermore, the COWIfoundation has contributed with financial support of the model construction and installation The work has been performed under the supervision of Professor Niels J. Gimsing, Dr. Techn. Claës Dyrbye of Technical University of Denmark and Professor, Dr. Hiroshi Tanaka of University of Ottawa. All are acknowledged for their support. The Danish Maritime Institute and A/S Storebælt are also recognised for making the Very Wide Wind Tunnel available for the tests.
8. References [1] [2] [3] [4]
[5] [6]
Gimsing, N.J. "Cable Supported Bridges with Spatial Cable Systems" - Bulletin of the International Association for Shell and Spatial Structures, Vol. 33 n.1., 1992. Gimsing, N.J.: "Suspended Bridges with Very Long Spans", International Conference on Cable-Stayed and Suspension Bridges, Deauville, France, Proceedings vol. 1, pp. 489-504, 1994. Vejrum, T. & Pedersen, A.: "Bridge with Spatial Cable Systems - Theoretical and Experimental Studies", Proceedings of the IABSE Conference on "Cable Stayed Bridges, past, present, future, Malmö, 1999. Vejrum, T. : "Bridges with Spatial Cable Systems. Theoretical and experimental studies with special emphasis on lateral buckling stability of the girder", Ph.D. thesis, Series R, No. 19, Department of Structural Engineering and Materials, Technical University of Denmark, 1997. Larsen, S.V. & Gimsing, N.J.: "Static and Dynamic Behaviour of Cable Supported bridges With Small Span-to-width Ratios", International Conference on Cable-Stayed and suspension Bridges, Deauville, France, Proceedings vol. 1, pp. 569-576, 1994. Larsen, S.V.: "Long and Narrow Cable Supported Bridges Subjected to Wind Load", Ph.D. thesis, Danish Maritime Institute and Department of Structural Engineering, Technical University of Denmark, 1997.
Cable-stayed Bridge in Bandung, Indonesia Alan SHARPE Halcrow Group Ltd. Senior Bridge Engineer. London, UK
Andrew J YEOWARD Halcrow Group Ltd. Engineering Manager, Bridges Department. London, UK
Roger J BUCKBY Halcrow Group Ltd. Director – Bridge Engineering London, UK
Summary The construction of a 2.1km long elevated road to carry traffic along the Pasteur – Cikapayang – Surapati corridor in Bandung has been authorised by the Government of the Republic of Indonesia. The focal point of the scheme is a 400m long cable-stayed bridge crossing over the Cikapundung valley. The paper describes the general arrangement of the 106m mainspan cable-stayed bridge and key features of the design and construction methods adopted for the bridge
Introduction Bandung is a rapidly expanding city of 3 million inhabitants, located in the West Java province of Indonesia. Studies carried out by the Directorate General of Highways (Bina Marga), as part of the government’s development plan, indicated that priority should be given to providing a new east-west elevated arterial road in the northern part of Bandung. Bina Marga appointed Sir William Halcrow and Partners in association with INCO of Kuwait, INDEC and Associates of Indonesia and LAPIITB to plan and develop a detailed design for the project, and to supervise its construction. Funding for the design and construction of the scheme is being provided under a loan from the Kuwait Government.
Project Description The project consists of: •
A western approach viaduct of 1.35km in length, starting at Junjunan Road in the west, closely following the alignment of the existing Pasteur Road to the Cikapundung valley. Figure 1 illustrates the precast glued segmental structural form of the approach viaduct.
•
A 400metre long elevated bridge across the Cikapundung valley which includes a cable-stayed bridge with a length of 161metres.
•
An eastern approach viaduct of 800m following the existing Cikapayang Road.
The alignment of the scheme is shown in Figure 2.
Figure 1. Western of Approach Viaduct (Pasteur Road). The approach viaducts which carry two lanes of traffic in each direction and have typical spans of 44.5 metres between pier supports, are designed to be erected by the balanced cantilever method. Figure 2. Scheme Layout
The cable-stayed bridge over the valley carries three lanes of traffic in each direction and has a single tower located in the highway median, supporting the main span via a single plane, semiharp arrangement of stay cables. The tower is anchored to the backspan pier by an arrangement of parallel stay cables. The superstructure of the bridge is designed to be constructed using precast, prestressed concrete glued segments, with the main span being erected by cantilevering from the pylon. Intermediate on / off ramps are provided at various locations to allow local traffic to access the elevated road. On either side of the valley, a pair of these ramps is provided with the ramp slip roads forming the third lane in each direction over the cable-stayed bridge.
Cable-stayed Bridge Span arrangement The span arrangement for the cable-stayed bridge was finalised after careful consideration of a number of options. The asymmetrical cable configuration with a single vertical pylon was considered to provide an aesthetically pleasing structure across the valley, with continuity of structural form with the approach viaducts. The resulting asymmetric structure has a main span of 106 m and a back span of 55m. Figure 3 shows computer-generated impression of the bridge. Further details are given in Figure 4.
Figure 3. Cable-stayed bridge.
Figure 4. Elevation and plan of cable-stayed bridge.
Pylon The height of the pylon was restricted by the close proximity of Bandung city airport. This results in the longest cables on the main span being at an unusually low angle of approximately 20 degrees to the horizontal. The pylon shaft rises 53m above the valley floor. Its height above the deck is 37m, which is 0.35 of the main span length. The anchorage region of the pylon shaft has been designed such that the cables pass through the shaft and are anchored on the opposite face. This has the advantage of putting the shaft laterally into compression in the anchorage zone avoids the ‘splitting’ forces frequently associated with this area in of cable-stayed bridge pylons. Figure 5 shows a cross section through the deck at the pylon location and details the cable anchorages at the pylon top.
Figure 5. Pylon Details The pylon shaft is connected monolithically to the superstructure to provide torsional stiffness to the bridge multi cell box girder deck. Below deck level, the pylon remains solid in section. Grade 50/20 concrete is specified for the pylon over the full length of the shaft. Superstructure The superstructure is a three cell precast segmental concrete box girder with an external shape similar to that of the viaducts (Figure 6). Each longitudinal segment is constructed in two sections with an in-situ central stitch enabling the same external formwork moulds as the viaduct to be used. The adoption of an in-situ stitch also facilitates easy construction of the tapered deck sections at each end of the cable-stayed bridge and allows incorporation of the cable anchorages in-situ. The box girder span longitudinally between the pylon diaphragm and the adjacent piers and are partially supported by the cables to enable a shallow depth deck to be maintained. The box is stressed by internal bonded prestress within the top flange.
Figure 6. Precast segment cross sections The segments are all 2.95 metres in length to match that those on the approach viaducts, each having a 500mm deep transverse rib positioned at the centre to support the cantilever slab. The rib also carries the concealed drainage pipe from the gully pots to the longitudinal drainage system, which is situated within the box section. The box has an average web thickness of 450mm, top slab of 250mm and bottom slab of 250mm. The bottom slab is increased to 600mm at pier locations to reduce the compressive stresses due to hogging over the piers. The inner webs are increased to 1250mm as the box approaches the pylon as 90% of the shear was attracted to the pylon through these webs, the remainder being carried via the deck diaphragm. At each pier location special diaphragms segments were required to transmit the forces from the webs into the bearing plates. In each of these diaphragms access holes are provided to allow inspection throughout the box structure. Diaphragms are also incorporated at each cable anchorage to ensure that the support provided by the cables is transmitted into all four webs. A three dimensional analysis was carried out which confirmed that slightly more bending was attracted to the inner webs. The prestress was distributed accordingly. Grade of 50 concrete was required for the main span deck segments to accommodate the high compressive stresses during construction. The profile of the cable-stayed bridge segments was carefully developed to match that of the viaducts. The long cantilever and curved soffit was finally adopted after consideration of many
alterations to produce a section that would reduce the overall visual impact of a very wide superstructure. This was particularly important given the proximity of the existing residential road corridor which the viaduct follows. Stay cables and anchorage positions The main span cables consist of 9 cables along a central single plane spaced at intervals of 8.85metres to coincide with every third deck segment. The back span cables consist of 10 cables in pairs on two central planes and are tied directly back into the backspan pier diaphragm. Cables are made up of galvanized 7-wire strands protected by HDPE sheathing filled with wax after cable tensioning. The cable sizes are of two types, 73T15 in the backspan and 85T15 in the mainspan. During detailed design, consideration was given to providing intermediate anchorages in the backspan but this was found to introduce undesirable hogging moments in that span and increased the main span sagging moments. The design brief specified that the structure should be designed for the effects of any cable being removed with normal loading under the serviceability and ultimate limit states. The cable anchorages are constructed within the central in-situ stitch. These are tied into the precast units by a steel frame which takes the cable forces directly by tension into the concrete deck. The insitu stitch along the centre of the deck allows the incorporation of these steel anchorage frames when the stitch is made thus negating the need for precast segments with pre-positioned anchorages.
Cable-stayed bridge Construction methods Pylon and Piers The pylon and piers are designed to be supported on bored pile foundations with cast-in-situ climbing formwork for the shafts. At the pylon head, formwork tubes will be cast in under carefully controlled geometrical conditions to ensure accurate alignment of the cables. Deck As there are no intermediate stays in the back span and with the varying width it was not appropriate to specify construction by the cantilever method. The backspan was therefore designed to be constructed on falsework supported from the ground and post tensioned with the falsework removed during cantilevering of the mainspan. The main span is built by erecting the two precast segments followed by casting of the in-situ stitch. Temporary prestress is required to hold the boxes in place and permanent prestress is applied only after the in-situ stitch has reached its target strength. This ensures that the in-situ portion is also effective for the prestress design.
At the pylon connection to the deck a cast in-situ length of deck will be constructed to tie into the pylon reinforcement and to create a working platform from which the cantilevered main span boxes will be erected. The length of the cast in-situ deck was chosen at 9.2m projecting approximately 500mm beyond the pylon shaft. As the main span cantilever increases temporary props are specified to support the proportion of the dead load that is later taken by the longitudinal beam action. These props will be removed as subsequent segments are placed relieve the load. The sequence of erection is shown in Figure 7. Cantilever construction continues until it reaches the in-situ stitch joint is located 13.75 metres from the first east pier. The final distribution of loading in the cables and the box girder is achieved by jacking the main span onto the protruding cantilever from the first east pier. This lifts the deck from the remaining support and relieves the cable forces, thereby introducing the desired longitudinal moment distribution into the box girder. The jacking forces relieve the cable tensions and provide the additional capacity in the cables for superimposed and live load effects.
Figure 7. Cable-stayed bridge construction Deck Prestress During construction of the main span, the deck moments vary from predominant hogging during cantilevering to a permanent sagging at the deck completion. The short-term hogging moments are reduced by introducing temporary props during erection. There is also a requirement for temporary prestress in both the bottom and top flanges to maintain the allowable stress range in the concrete box during construction.
The permanent prestress comprises 7-wire strand tendons with tendon sizes of 22T15 and 19T15 chosen to match those in the viaduct. Where possible prestress tendons and anchorages are contained within the top and bottom slab haunches to minimise the web thickness and weight of the segments. At the pylon, where the prestress is at its greatest, some of the tendons are located within the webs. For cable installation and cable replacement the design specifies that stressing takes place from deck level. Sufficient space has been provided for a full size jack to be attached to the anchorage.
Project Implementation Programme The detailed design of the elevated viaducts and cable-stayed bridge, including all tender documents was completed in Bandung by Halcrow – Indec - Inco in the period September 1996 – August 1997. Construction is scheduled to start early in 1999, with a 24-month contract period.
New Developments of Erection Control for Prestressed Concrete CableStayed Bridges L.C. FAN Tongji University Shanghai, China
D.W. CHEN L.G. THAM Tongji University The University of Hong Kong Shanghai, China Hong Kong, China
F.T.K. AU P.K.K. LEE The University of Hong Kong The University of Hong Kong Hong Kong, China Hong Kong, China
Summary In the construction of prestressed concrete cable-stayed bridges, the simultaneous control of geometry and internal forces is one of the most important issues to address. This paper describes the recent developments in construction control of prestressed concrete cable-stayed bridges in China. An adaptive control system has been developed utilizing modern engineering cybernetics theory. The system makes use of the structural parameters identified for the continuous adjustments of the mobile carriages for insitu cantilever construction of the bridge deck. The system has been successfully applied to the construction of several long span prestressed concrete cable-stayed bridges.
1. Introduction With the rapid development in the construction techniques for prestressed concrete cable-stayed bridges in the past two decades, China has become one of the countries having the largest stock of such bridges. From the experience gained so far, the simultaneous control of geometry and internal forces during the cantilever construction of prestressed concrete cable-stayed bridges has been recognized as one of the key problems to address. The importance of construction control has been amply demonstrated by a few mishaps during the construction of a few of such bridges in recent years. Very rigorous numerical simulation of the insitu cantilever construction is usually carried out to estimate the amount of preset in the fixing of the mobile carriage. However in spite of such efforts, it is almost impossible to eliminate the discrepancies between the theoretical predictions and the actual structural responses. Should such discrepancies be not corrected in a timely manner and thus be allowed to accumulate, the geometry and internal forces of the bridge may be out of control. The discrepancies between the theoretical predictions and the actual structural responses can be attributed to the following factors: 1. The assumed structural parameters for the design may be different from the actual values achieved on site. Such parameters include, but are not limited to, moduli of elasticity of concrete, steel reinforcement and prestressing tendons, dead loads, construction live loads, 1
shrinkage and creep of concrete, moments of inertia of the segments as well as the temperature distribution in the bridge deck and tower. 2. The values for the control of geometry and internal forces during cantilever erection are usually given only at certain important milestones such as the beginning of each segment construction cycle. However in reality, the structural responses of the bridge are changing continuously according to the variations of applied loading and environmental conditions. 3. Errors may also be introduced by simplifying assumptions made for the structural model and the method of structural analysis. It is believed that to achieve the designed geometry and internal forces of the bridge within reasonable tolerance, certain parameters need to be continuously monitored in order to determine the appropriate preset in the fixing of the mobile carriage. Factors such as the amount of prestress, alteration of the structural configuration, creep, shrinkage, etc. should all be taken into account. The construction control of cable-stayed bridges has long come to the attention of bridge engineers [1-7]. Three main categories of practical control methods have evolved from the work in the past two decades. They include the Kalman Filter method, relaxation of geometric tolerance and the cybernetics approach. The Kalman Filter method attempts to achieve the intended deck geometry by continuously adjusting the cable tensions. In other words, it tries to achieve the design deck geometry at the expense of the cable tensions. However, apart from significantly increasing the workload on site, this method may also cause adverse distribution of tensile forces among the cables. The second method involves the relaxation of geometric tolerance. The bridge is so designed that ample tolerance is allowed in the levels of the bridge deck and the cable tensions. The profile of the final running surface is then made good by a certain regulating course. Construction control therefore becomes less onerous. This approach may work well for cablestayed bridges with steel or composite bridge decks. However this strategy is not suitable for prestressed concrete as the stress limitations impose a lot of restrictions on the allowable tolerance. Likewise the cables are normally prefabricated to the required lengths and any significant deviations from the design values will cause much inconvenience in construction. The third method works on an adaptive control system utilizing modern engineering cybernetics theory [8]. In essence, the profile of the bridge deck and/or the cable tensions are continuously monitored during the construction stage in order to identify the major design parameters and to predict the discrepancies between the design and the completed structure. Corrective actions are then implemented in order to minimize such discrepancies in respect of both the levels of the bridge deck and the cable tensions. Therefore an adaptive control system is likely to be more suitable for prestressed concrete cablestayed bridges in which a lot of restrictions are imposed by the stress limitations. In the adaptive control system, the identification of the structural parameters is a crucial component. Tomaka and Kamei [2] proposed a least square method of structural system identification whereby the cable tensions could be adjusted. In this method, the structural model together with the discrepancies has to be assumed before hand. Entire magnitudes of the structural parameters are used and it gives rise to certain difficulties in actual practice.
2
This paper describes an adaptive control system, which utilizes the technique of transfer matrices [9, 10] commonly used in structural analysis. Instead of the entire magnitudes of structural parameters, observed increments in various steps of each construction cycle are used to identify the parameters. The method requires less field measurements and hence it is practical but simpler and effective. A package for the adaptive control system has been developed with Visual C++ for use under Windows 95 or Windows NT [11]. The package has also been tested and verified in the construction of a few prestressed concrete cable-stayed bridges.
2. An Adaptive Control System for the Construction of Prestressed Concrete Cable-Stayed Bridges Apart from ensuring the safety during the cantilever construction of a prestressed concrete cablestayed bridge, the construction control system also strives to control the final geometry of the bridge and the cable tensions to be within acceptable tolerances of the design values. Figure 1 shows the flow chart for such a typical system. It consists of numerical simulations of the construction process, the building up and subsequent updating of a database of expected characteristics, field measurements of levels, stresses and cable tensions at selected locations, identification of structural parameters, real-time corrections and adjustments of specifications on site as well as the management, output and storage of data. The success of the system hinges on recent improvements in system identification and the realtime adjustments of the mobile carriages for insitu concreting of bridge segments. Trappl [8] defined cybernetics as the "the science, craft, and art of communication, computation, and control in the machine, the living being, and the organization". In the present system, modern engineering cybernetics theory is used to resolve the problem of inconsistencies between the predicted and measured values of the control variables, and to implement real-time adjustments of the mobile carriages in order to bring the control variables to within acceptable tolerances of the design. 2.1
Correction of Soffit Level of the Mobile Carriage
The surveying and subsequent adjustment of the soffit level of the mobile carriage is the most crucial step in the cantilever construction of bridges. The soffit level requires continuous monitoring round the clock so that corrections or adjustments can be implemented. Such corrections should take into account changes in dead and live loads acting on the cantilever, temperature distribution within the cross section, the actual stiffness of each mobile carriage as well as the effects of construction inaccuracies of the previous segments.
3
Output Measurements on Site • Bearing capacities • Moduli of elasticity • Stresses • Temperatures • Levels of bridge deck • Deflections of tower tops • Cable tensions
Database of Expected Characteristics
Comprehensive Analysis Error Analysis
Adjustment of Expected Characteristics
Adjustment of System Parameters Prediction
Real Time Adjustment on Site Construction Activities on Site Figure 1. Flow chart for the self-correcting control system for the construction of prestressed concrete cable-stayed bridges. Completed segment Design deck profile
Segment to be cast
Node (i-2)
Node (i-1)
δi-2 Constructed deck profile
Node i
∆δi
δi-1
∆δi-2
∆δi-1 li-1
li
Segment (i-1)
Segment i
Figure 2. Real time adjustment of deck Figure 2 shows the relationship between the design deck profile and the constructed deck profile for the completed segment (i-1) and the segment i yet to be cast. The upper solid line denotes the design deck profile. The dash line denotes the expected deck profile taking into account the effects of changes in temporary loading, temperature difference and gradient, as well as the deformation of the mobile carriage. The lower solid line stands for the constructed deck profile with certain construction error. The total amount of preset ∆δi at the tip of the mobile carriage for segment i is given by 4
∆δi = δi + δg + δ∆ in which δi
δg δ∆
(1)
is the adjustment to account for the effects of changes in temporary loading, and temperature difference and gradient; is the required preset of the mobile carriage to account for its deformation; and is the adjustment to account for the construction inaccuracies of the previous completed segments.
Assuming that there is no error due to construction inaccuracies, the adjustment δi to account for the effects of changes in temporary loading, and temperature difference and gradient can be obtained from the geometric relationship of structural deformation [6] as
δi = δi-1 + (δi-1 - δi-2) × li / li-1
(2)
where
δi-1 and δi-2 li and li-1
are the adjustments for segments (i-1) and (i-2) respectively to account for the effects of changes in temporary loading, and temperature difference and gradient; and are the lengths of segments (i-1) and (i-2) respectively.
In actual case, there are discrepancies ∆i-1 and ∆i-2 due to construction inaccuracies for segments (i-1) and (i-2) respectively. The geometric relationship of structural deformation shown in equation (2) can therefore be amended as
δi + δ∆ = (δi-1 + ∆i-1) + [ (δi-1 + ∆i-1) - ( δi-2 + ∆i-2) ] × li / li-1
(3)
When the length of segment is constant, equation (3) can be simplified as
δi + δ∆ = (2δi-1 - δi-2) + (2∆i-1 - ∆i-2)
(4)
In case the mobile carriage is in the form of long suspended falsework [12], the required preset of the mobile carriage is further given by
δg = δa - δb
(5)
in which δa is downward preset to account for the additional inelastic deformation due to the tensioning of stay cables for the mobile carriage and other sources, and δb is upward preset to account for the additional inelastic deformation due to the insitu concreting of the next deck segment and other sources. The equation for real time adjustment can therefore be obtained by substituting equations (4) and (5) into equation (1), i.e.
∆δi = (2δi-1 - δi-2) + (δa - δb) + (2∆i-1 - ∆i-2)
(6)
There are other factors that may affect the correct preset of soffit level of the mobile carriage. They include, for example, the tension and inclination of stay cables for the mobile carriage, and these can be estimated from the database built up from site measurements and the learning process in implementation. It can be observed from equation (6) that the discrepancy ∆i-1 at segment (i-1) will manifest itself at segment i as double of ∆i-1. The importance of timely
5
correction to prevent further accumulation and propagation of errors is therefore amply demonstrated. 2.2
System Identification using Transfer Matrices
An important feature of the adaptive control system as outlined in Figure 1 is the system identification method. This is the essential rationale behind the control system for simultaneous control of both the geometry of and internal forces in the cable-stayed prestressed concrete bridge. Through the site measurements carried out at various stages of each construction cycle and subsequent computational checks, important structural parameters such as the creep coefficients, segment weights, flexural rigidities of the towers and decks, etc. can be estimated and refined. During the cantilever construction of a bridge, each cantilever essentially comprises a chain of segments, and such a configuration favours the use of transfer matrices [9,10] in its analysis and monitoring. v
φ Mi(li)
Mi(0)
u
Ni(0)
Node i
Ni(li)
Node i+1
li
Qi(0)
Qi(li)
Figure 3. Nomenclature of displacements and end forces acting on segment Figure 3 shows the nomenclature of displacements and end forces acting on an existing segment i of the bridge. During a certain step of the construction cycle of the segment at the cantilever tip, the major load increment is not applied on segment i. The state vector Si+1 at node (i+1) is related to the state vector Si at node i through the transfer matrix Gi by Si+1 = Gi Si
(7)
or u i ( l i ) 1 v (l ) 0 i i φ i ( li ) 0 = ( ) N l i i 0 Qi (li ) 0 M i ( li ) 0
0 1 0 0 0 0
0 li li 1 0 0 0
/ Ei Ai 0 0 1 0 0
0 l / 6 Ei I i l / 2 Ei I i 0 1 3 i 2 i
li
0 ui ( 0) l / 2 E i I i v i ( 0) li / Ei I i φi (0) 0 N i (0) Qi (0) 0 1 M i ( 0) 2 i
(8)
where Ei, Ii and Ai ui(0) and ui(li) vi(0) and vi(li) φi(0) and φi(li)
are the modulus of elasticity, second moment of area and cross sectional area, respectively, of segment i; are the axial displacements at the ends of segment i; are the vertical displacements at the ends of segment i; are the rotations at the ends of segment i; 6
Ni(0) and Ni(li) Qi(0) and Qi(li) Mi(0) and Mi(li)
are the axial forces at the ends of segment i; are the shear forces at the ends of segment i; and are the bending moments at the ends of segment i.
In particular, the vertical displacement and rotation at node (i+1) are given respectively by vi (li ) = vi (0) + liφi (0) + li3Qi (0) / 6 Ei I i + li2 M i (0) / 2 Ei I i 2 i
φi (li ) = φi (0) + l Qi (0) / 2 Ei I i + li M i (0) / Ei I i
(9) (10)
At each step of a construction cycle, site measurements are carried out and these can be attributed to certain increment or decrement of loading, such as tensioning of stay cables. On rearrangement, equations (9) and (10) give Ei I i =
li3Qi (0) + 3li2 M i (0) 6 (vi (li ) − vi (0) − liφi (0) )
(11)
v (l ) − vi (0) − liφi (0) φi (li ) = φi (0) + 3 (li2Qi (0) + 2li M i (0) ) i 3 i 2 li Qi (0) + 3li M i (0)
(12)
The loads acting on the cantilever during construction as well as their subsequent variations are closely monitored. For example, the force applied on tensioning each cable is accurately measured. The subsequent variation of cable force is detected by regular monitoring of ambient vibrations. The actual amount of concrete and other construction materials that goes into the bridge deck is also closely monitored and refined. The bending moments Mi and the shear forces Qi can be estimated from information on such loading. The vertical deflections vi can be regularly monitored from precision surveys. The rotation at each node φi can be calculated from equation (12) based on the rotation at the previous node. For symmetrical balance cantilever construction, the rotation φi(0) at the tower-deck junction can be taken to be zero, and hence the rotations at other nodes can be calculated according to equation (12). Equation (11) can also be utilized to estimate the flexural rigidity EiIi. Iterations are carried out until the discrepancies between the predicted values and measured values are eliminated. In most cases, the tensile forces in a few cables are particularly sensitive to concrete creep. Therefore, through continuous monitoring of these cable forces, it is possible to obtain reliable estimates of the creep coefficient [5].
3. System Control Software with Graphical User Interface Advancements in modern computer technology have enabled the implementation of the adaptive construction control of prestressed concrete cable-stayed bridges using a personal computer, in spite of the complexity of the problem. A computer package to realize the strategy outlined in Figure 1 has been developed [11]. The enormous amount of computation for the simulation of the construction process is carried out mainly to confirm the correctness of the design erection sequence and to ensure the safety of the structure during erection. The package was developed using OpenGL for the application programming interface in order to make it user-friendly. The reliability of the package has been tested in the construction of around 10 cable-stayed bridges.
7
4. Case Study The use of the above system in the construction of a real bridge is described below. It is a prestressed concrete cable-stayed bridge that spans over a wide river. The bridge is an asymmetric single-tower cable-stayed bridge with two vertical planes of stay-cables. The main crossing consists of 5 spans, namely 74.5m, 258m, 102m, 83m and 49.5m. The 29.5m wide bridge deck is "floating", comprising two spine box beams of 2.5m depth transversely connected by cross girders at 4m spacing. The 148.4m tall tower is of "H" shape with inclined legs. There are altogether 102 stay-cables arranged in a modified fan pattern. The typical spacing between cable anchorages at deck level is 8m, as shown in Figure 4.
Figure 4. Elevation and section of a prestressed concrete cable-stayed bridge over a wide river. During the construction of segment 11 of the bridge, the levels of segments 9-11 were obtained from precision survey and they are shown in Table 1. Tip of segment no. Design level (m) Measured level (m) Discrepancy (m)
9 37.990 37.903 -0.026
10 37.926 37.816 -0.015
11 37.872 37.784
Table 1. Levels during construction of segment 11 From measurements obtained in previous construction cycles, the required presets δa and δb of the mobile carriage were estimated to be 30mm and 70mm respectively. Substituting these values into equation (6),
∆δi
= (2δi-1 - δi-2) + (δa - δb) + (2∆i-1 - ∆i-2) = [2×(37.926-37.816) - (37.990-37.903)] + (0.03-0.07) + (-2×0.015+0.026) = 0.089m
The corrected soffit level of the mobile carriage should then be (37.872m-0.089m) or 37.783m. The set-up soffit level was 37.784m, implying a discrepancy of 1mm only. An electronic balance on site closely monitored the actual weight of concrete that went into each segment. The average weight of concrete used in each segment was 3390kN. However from the 8
numerical simulation of the erection process taking into account various site measurements, the adjusted weight of concrete in each segment was only 3351kN. It indicated around 1.2% of loss of concrete mainly inside the conveying pipes for concreting. The discrepancies of deck profile when construction reached segment 20, i.e. when the cantilever was 168m long, are shown in Figure 5. The discrepancies of deck profile were within 40mm and the cable tensions were all within 5% of the design values.
0.05
'# 19
'# 17
'# 15
'# 13
#
'# 11
9'
# 7'
# 5'
# 3'
# 1'
0#
2#
4#
6#
8#
# 10
# 12
# 14
# 16
# 18
20
#
0
-0.05
Figure 5. Discrepancies of deck profile in metre when the cantilever was 168m long.
5. Conclusions In the construction of prestressed concrete cable-stayed bridges, simultaneous control of the geometry and internal forces is very important. An adaptive control system has been developed utilizing modern engineering cybernetics theory. The system makes use of the structural parameters identified for the continuous adjustments of the mobile carriages for insitu cantilever construction of the bridge deck. The system was developed utilizing extensive graphical capabilities to make it user-friendlier. The system has also been successfully applied to the construction of several long span prestressed concrete cable-stayed bridges.
6. References [1]. F. Leonhardt, Die Spannbeton-Schrag-Kabel Bruken uber den Columbia River Zwischen Pasco und Kennawich in Etaat Washington, U.S.A., Beton und Stahllelonban, Heft, 1-4, 1980. [2]. H. Tomaka and M. Kamei, Cable Tension Adjustment by Structural System Identification, Proceedings, International Conference on Cable-Stayed Bridges, IABSE, Bangkok, Thailand, Nov., 1987. [3]. Y.P. Lin, The Application of Kalman Filter in the Construction of Cable-Stayed Bridges (in Chinese), Tumu Gongcheng Xuebao (Journal of Civil Engineering), China, Vol. 3, 1983. [4]. D.W. Chen, X.G. Zheng and H.F. Xiang, Construction Control of Concrete Cable-Stayed Bridges (in Chinese), Tumu Gongcheng Xuebao (Journal of Civil Engineering), China, Vol. 26, No. 1, 1993. [5]. D.W. Chen and H.F. Xiang, Application of Construction Control in the Cable-Stayed Bridge over Yong River (in Chinese), Proceedings of the 1992 National Conference on Bridge Structures, Tongji University Press, 1992. [6]. D.W. Chen, L.C. Fan and H.F. Xiang, The Construction Control of the Single-Tower Cable-Stayed Bridge at Sanshui of Guangdong (in Chinese), Journal of Tongji University, Vol. 25, No. 1, 1997.
9
[7]. D.W. Chen, Z.Y. Han, D.J. Huang, Y.L. Qian and L.C. Zhang, The Construction Control of Zhaoboshan Bridge at Ningbo (in Chinese), Annual Conference of Municipal Engineering, Chinese Society of Civil Engineering, Tianjin University Press, 1998. [8]. R. Trappl, Cybernetics Theory and Applications, Hemisphere Publishing Corporation, 1983. [9]. R.K. Livesley, Matrix Methods of Structural Analysis, Pergamon Press, 1975. [10]. S.W. Cai, Matrix Method in Structural Mechanics (in Chinese), China Communication Publisher, 1975. [11]. D.W. Chen, X.T. Wang, W.Y. Chen and L.C. Fan, A Software with Graphical User Interface for Construction Control of Cable-Stayed Bridges (in Chinese), Journal of Tongji University, Vol. 26, No. 5, 1998. [12]. D.W. Chen, D.J. Huang and H.F. Xiang, A New Method for Erecting Cantilevers with Long Suspended Falsework in P.C. Cable-stayed Bridges (in Chinese), Tumu Gongcheng Xuebao (Journal of Civil Engineering), China, Vol. 29, No. 6, 1996.
10
The Lifting, Transport and Placing of the Øresund Pylon Caissons Ferdinand TRENKLER Civil Engineer VSL (Switzerland) Ltd. Lyssach, Switzerland Ferdi Trenkler, born 1941, received his civil engineering degree in 1966 from the Swiss Federal Institute of Technology. Since 1977, he has worked with VSL (Switzerland) Ltd. Presently he is Chief Engineer with Heavy Lifting, one of VSL's worldwide activities.
Dr. Petter SKRIKERUD Civil Engineer Structural Engineering AS Lysaker, Norway Petter Skrikerud, born 1947, received his civil engineering degree in 1970, and the Ph.D. degree in 1982, from the Swiss Federal Institute of Technology. He is presently senior partner of Structural Engineering AS, and is mainly engaged with projects for the offshore oil industry.
Capt. Dan M. VOLL Master Mariner Neptun AS Stavanger, Norway Dan Magne Voll, born 1952, seaman experience since 1968, received his Master Mariner degree in 1974. His experience encompasses master of various marine operations with command of several vessels and equipment. He is presently tow master / salvage master and is involved in offshore oil industry projects.
Summary The two 204 metre tall pylons of the central, cable stayed bridge of the new Øresund crossing between Denmark and Sweden rest on concrete caisson foundations. The caissons have plan dimensions of 35 by 37 metres, are 22.5 (21) metres high and have a dry weight of approximately 20'000 tonnes. The two caissons were transported one by one from the prefabrication site - the Kockums dry dock in Malmö - to their permanent offshore location in Øresund. This operation was accomplished by means of a purpose-built catamaran, suitably equipped with hydraulic lifting/lowering equipment, carrying the partly submerged caissons with high-strength tendons. The present paper describes the caisson LTP operations (Lifting, Transport and Placing) which were successfully carried out in April, 1997.
1
Introduction
1.1
The Fixed Link across Øresund
The 16 km long coast to coast link between Denmark and Sweden consists of two railway tracks and a four-lane motorway, and comprises the following principal elements (Figure 1); a short peninsula at the Danish coast, an immersed tunnel, an artificial island, and a 7.8 km long bridge. The tunnel starts near Copenhagen airport and the bridge ends just south of Malmö. The Øresund Link is scheduled to be opened for public traffic in the year 2000. The bridge part of the Øresund Link consists of two approach bridges leading to a central, 1'092 m long, cable stayed "High Bridge" spanning the new, dredged ship lane Flinterenden. The two 204 metre high pylons on either side of the 490 m long central bridge span rest on two prefabricated concrete caissons.
Figure 1 The Øresund Link 1.2
The Caissons
Although the technique of placing prefabricated concrete structures onto seabed foundations is not new, the Øresund caissons represented a new scale in terms of size, weight and installation accuracy. Each caisson consists of a foundation base, measuring 35 m x 37 m in plan, extending into two base sections for the pylon towers (Figure 2). The total height is 22.5 m for the west caisson and 21 m for the east caisson. After placing of the caissons into pre-dredged trenches (approx. 10 m deep) in the limestone seabed, the two tower sections extended 4.0 m above sea water level, thus allowing concrete casting work to continue. The dry weight of each caisson was about 20'000 tonnes, including temporary fixtures (working platform, crane pedestal, etc.). During transportation to the installation site the caissons were partly submerged (draught about 6.4 metres), and the net design lifting force was specified as 12'200 tonnes. The caisson design included horizontal post-tensioning in both directions as well as vertical posttensioning of the outer walls. The anchors of these vertical post-tensioning cables were utilised as couplers to the tendons of the lifting/ lowering equipment.
Figure 2 Schematic View of Pylon Caisson
1.3
Organisation and Scope of Work
The overall responsibility for the caisson LTP operations (Lifting, Transport and Placing) was with the Main Contractor for the Øresund Bridge, Sundlink Contractors, which is a consortium of Skanska AB (Sweden), Hochtief AG (Germany), Monberg & Thorsen A/S (Denmark) and Højgaard & Schulz a/s (Denmark). Sundlink Contractors engaged Neptun Heavy Lift AS (Norway) for carrying out the marine works, and VSL (Switzerland) Ltd. for the lifting and lowering tasks of the caisson LTP operations. Neptun subcontracted the engineering and design to Structural Engineering AS (Norway), and engaged Gdansk Shiprepair Yard (GSY) Remontowa (Poland) for the necessary conversion of the marine equipment. Due to the substantial weight of the caissons, the possibility of using a conventional crane vessel for their installation was found not feasible. Furthermore, the caissons could hardly be made to float freely, and if so at a draught, which would be larger that the available water depth in Øresund. Hence, an alternative solution had to be established in order to bring the caissons from the prefabrication site in the dry dock of the Kockums yard in Malmö to the installation site in Øresund, and place them safely onto the pre-installed foundation pads in the excavated trench within the given tolerance of ±75 mm. The solution arrived at was to convert (lengthen) and strengthen two existing Neptun heavy lift barges, Goliat 18 and Goliat 19, both having the overall dimensions 80 m length, 17 m breadth and 15.8 m height after conversion. The two barges were then joined by means of two large space truss structures fore and aft, forming a catamaran (Figure 3).
Figure 3 Finite Element Model of Catamaran
2
Catamaran
2.1
Design Resume
The catamaran was designed to carry the 12'200 t net weight of the partly submersed caisson at a common draught of 6.4 m. The response of the catamaran was determined in three different environmental and operational conditions; fully loaded and with the caisson seafastened in transit to the installation site, empty in transit back from the installation site, and for the caisson hanging freely in the tendons during lowering (at several intermediate draughts) with the catamaran moored over the installation trench. The first two analyses, with the catamaran and the caisson modelled as one common body, were used to design the catamaran itself, to check the dynamic load in the lifting tendons, and to design the horizontal seafastening. Thereby the hydrodynamic pressures and accelerations for both the maximum transit and the holding conditions were transferred to the finite element model of Figure 3 for determination of stresses and deflections. For the third hydrodynamic analysis, lowering of the caisson onto the foundation pads, the two structures, catamaran and caisson, were modelled as two separate bodies interconnected by the lifting tendons. The analysis served to verify that both the relative and absolute movements of the caisson were within the tolerances for all stages of the lowering operation. In particular, the analysis served to determine the maximum tolerable sea state at touch-down, for an installation within the given tolerances.
As a result of the design calculations, both barges had to be strengthened. The main areas of strengthening were; the side shell under the load carrying hydraulic jacks and towards the connecting trusses, the deck, and the local area of connection between truss and barge. The two connecting space truss structures were after the LTP operations removed from the barges and used as temporary support for the main bridge girder. 2.2
Hydraulic Lifting / Lowering System
In order to lift the caisson up from the bottom of the flooded dry dock, and to lower it into the cavity at the installation site, each barge of the catamaran was equipped with 20 VSL hydraulic strand lifting/lowering jacks, located on cantilevering supports at the inner side shell (Figure 4). Each hydraulic strand jack had a nominal lifting capacity of 330 t (total for 40 jacks 13'200 t, or 108% of the design load), whereas the nominal breaking load of an individual tendon, made up of 31 high-strength strands, was 930 tonnes (total 37'200 t, or 305% of the design load). All 40 strand jacks were hydraulically coupled to a 3-point, static determinate system during lifting and lowering (20 on one barge and two times 10 on the other). The system was remotely controlled from a single control centre, which also included electronic level and pressure control.
Figure 4 The 20 Strand Jack Assemblies on Goliat 19 During sea transportation, the strands of the tendons were mechanically locked, thus forming a structural entity with the catamaran in the vertical direction. To control the relative motion between the catamaran and the caisson in the two horizontal directions, surge and sway stoppers (seafastening) were installed on the inner side shells of the barges (Figure 5).
The connection between the tendons and the caisson was solved with a specially designed screw on/off type coupler. The anchor heads of the vertical post-tensioning cables in the caisson walls served as mating pieces for the couplers. Whereas the coupling onto the anchor heads was effectuated in the dry dock by closing the gate and lowering the water level (Figure 6), easy and quick uncoupling by divers in 12 m water depth was a main requirement for the design of the couplers.
Figure 5 Surge and Sway Stoppers 2.3
Figure 6 Installing Tendon Couplers
Conversion and Outfitting
The strengthening and conversion of the two barges Goliat 18 and Goliat 19, the fabrication of the two space truss structures, the assembly of the catamaran, and the steel outfitting took place at the conversion yard GSY Remontowa in Gdansk, Poland, in the period mid September, 1996 to mid February, 1997. The final outfitting of the catamaran was carried out in Malmö during March, 1997. The work at GSY Remontowa consisted of; • • • • • • •
lengthening of Goliat 18 by a centre section of 26.6 m to the same length as Goliat 19 (80 m) fabrication of the two space trusses (overall size: 70 x 10 x 16 m, and weighing about 375 t each) fabrication and installation of cantilevering supports for the strand jacks (40 off) fabrication and installation of surge and sway stoppers (for horizontal seafastening) supply and installation of bottom valves, and amendment of ballast tank compartment, to enable fast ballasting of the barges during caisson lowering assembly of the catamaran steel outfitting (various gangways, ladders, platforms, etc.) of the catamaran
For the installation of the supports for the strand jacks, the as-built locations of the posttensioning (coupling) anchors on the caissons (average of the two) were taken into account. Thanks to close co-operation between all involved parties, the entire conversion and outfitting work at GSY Remontowa, from ordering of the first steel until delivery of the catamaran, was completed according to schedule in just over five months.
3
Lifting, Transport and Placing (LTP) Operations
3.1
Lifting of Caissons in Kockums Dry Dock in Malmö
After the final outfitting of the catamaran in Malmö harbour had been completed, and the two caissons were ready for the LTP operations, i.e. complete with work platforms and crane pedestals for the continuation of the construction of the pylons, the Kockums dry dock was filled with water (Figures 7 and 8).
Figure 7 Ingress of Water
Figure 8 Water Filled Dry Dock
The buoyancy reduced the net weight of the caissons to about 9'000 tonnes. After opening of the dock gate the catamaran was manoeuvred into the dock by means of tugs, guides/fenders and winches. In order to avoid clash between the leading space truss of the catamaran and the protruding reinforcing bars of the pylon bases, the catamaran had to be trimmed to about 6 degrees by ballasting the end ballast tanks. When the catamaran was in position over the caisson, it was brought to even keel by deballasting, the dock gate was closed, and the water level was lowered by about 2 metres to allow coupling of the lifting tendons to the post-tensioning anchor heads of the caisson (Figure 6). Then water was again filled into the dock, and the caisson was lifted by means of the strand jacks to a common draught with the catamaran (6.4 m). The net (lifting) weight thereby increased to about 11'800 tonnes (west caisson) and 11'500 tonnes (east caisson). For the first (west) caisson, a test lift was conducted to verify the strength of all lifting and structural elements. This task was effectuated by increasing the lifting height of the caisson (reducing draught and thus buoyancy) by 1 metre, thereby fully utilising the total lifting capacity of the strand jacks, thus achieving a lifting load of about 110% of the actual. After shimming the outer caisson wall against the surge and sway stoppers (Figure 5) to achieve a horizontal seafastening, and fixing the lifting tendons at their current position (mechanical locking of the individual strands), the dock gate was opened and the loaded catamaran was manoeuvred out of the dock by means of winches and tugs, Figure 9. Well outside the dock, but still within the Malmö harbour, the five tugs of the towing fleet were connected to the catamaran, ready to start the tow to the installation site. The operational environmental criteria for leaving Malmö harbour were specified as a 72 hours weather window with forecast Beaufort 5 or less and favourable conditions for the following 2 days. In addition, the 12 km long tow to the installation site in Øresund via the very busy ship
lane Flinterenden, had to be co-ordinated with other ship traffic, because the 70 m wide tow utilised the entire ship lane.
Aft View Figure 9 West Pylon Caisson Leaving the Dry Dock 3.2
Arial View
Tow-out, Transportation and Mooring
The towing fleet for the transport of the loaded catamaran consisted of 5 tugs; one lead tug of about 60 tonnes bollard pull, and four assisting tractor tugs hooked up to the catamaran of about 35 tonnes each (Figure 10). The towing fleet was dimensioned to safely manoeuvre the catamaran in the strong currents of the Øresund (design value 1m/s, holding condition 1.75 m/s).
Figure 10 Towing Configuration
The towing route had to be carefully selected due to the large draught (6.4 m) and the generally shallow waters of Øresund. As primary navigation and positioning aid, satellite navigation (GPS system) was used. Prior to starting the LTP operations, the tugs and vessels of the Neptun fleet had installed and tested the mooring spread for the catamaran for the west pylon location. The pre-laid mooring spread consisted of 8 legs, each of which made up of a 12 tonnes Stevprice anchor and ø76 mm chain (length between 150 and 200 m), which were picked up via surface buoys and coupled to the catamaran mooring wires. In east-west direction, the latter were tensioned by four mooring winches on board the catamaran itself. In north-south direction, the mooring legs were connected to two of the tractor tugs on one side, and to a common anchor vessel connected to the towing bridle on the other side. The north-south mooring legs were tensioned by means of the winches on board the tugs and the anchor vessel, respectively. Figure 11 gives an overview of this mooring configuration.
Figure 11 Mooring Configuration During the lifting of the east pylon in the dry dock, the mooring spread was re-located to the installation site of the east pylon and tested. 3.3
Placing on Pre-Installed Foundation Pads
The operational weather window for releasing the seafastening and lowering the caisson onto the pre-installed foundation pads in the cavity was specified as 20 hours of Beaufort 3 or less.
During lowering of the caisson, the catamaran was concurrently filled with ballast water in order to avoid unnecessary lowering distance. The ballasting was effectuated by opening the bottom valves of the barges and redistribution of the ballast water to other ballast tanks as required using portable pumps. Thus the catamaran was kept on constant draught 6.4 m throughout the lowering operation. At the end of the 12 m lowering distance the net weight of the caisson was reduced to about 3'000 tonnes. Just before touch-down, the position of the caisson was checked and any corrections made by means of the mooring lines, and, if necessary, with four tugger winches with wires attached to the caisson. The achieved installation accuracy was well within the given tolerance of ±75 mm: 42 mm for the west and 24 mm for the east caisson. Immediately following touch-down, the tendons were paid out by several full strokes of the strand jacks and the barges were flooded by opening the bottom valves, in order to quickly slacken the lifting tendons and thus stabilising the caisson. The couplers between the lifting tendons and the post-tensioning anchor heads were released by divers. Due to the strong currents experienced in Øresund, the divers had to tie themselves to the tendons to be able to release the coupler. When a coupler had been released the lifting tendon was retracted to surface and subsequently prepared for the next lift.
4
Conclusions
The described LTP operations for the two pylon caisson of the High Bridge of the Øresund Link took place in April 1997. Weather conditions, as usual at this time of the year, were sometimes quite rough. Picking the right weather window became one of the most difficult tasks of the operation. The fact that the whole operation was a real success is the result of a great teamwork of specialists from not less than 7 nations.
The Val-Benoit Cable-Stayed Bridge Jean-Marie CREMER Civil Engineer Engineering Office Greisch, Liège, Belgium
Jean-Marie CREMER, born 1945, received his Civil Engineer’s diploma at the University of Liège, 1968. He presently carries on the function of managing director at the ENGINEERING OFFICE GREISCH. He performs the direction of the bridges department. Professor at the bridges chair of the University of Liège.
1. Situation The city of Liège in Belgium is located at the intersection of 7 highways leading to important European cities. A connecting highway goes round Liège on the south-west, along a very important railway axis. Along this 4,1 km long connection, there are among others a double tunnel under the hill adjoining the city, a bridge to cross the river and a tunnel under an important railway junction.
Figure 1.
2. Choice Of The Type Of Bridge
Figure 2. The site constraints and the transportation requirements over and underneath the bridge are numerous and contradictory. Squeezed between two tunnels, the bridge crosses the river and roads on both banks. The grade profile on the bridge does not allow slopes over 6,5 % to enter or exit the tunnels. Under the bridge, the road clearance, mainly on the left bank, and the navigation clearance allow a maximal thickness of 2,50 m for the deck. The river, over 140 m wide, has to be navigated in the future by pushed convoys of 9.000 tons. There is a sharp curve in the river at that place. Just below the new bridge, two older ones, with two piles each in the river, are already considered as security obstacles for the navigation. For the new bridge, piles in the river had obviously to be avoided, if it was possible.
Figure 3.
Various types of bridges have been studied, a classical one with a variable height girder and a support in the river, a arch-tied bridge, a cable-stayed bridge with a pylon on each bank and a cable-stayed bridge with a single pylon. In addition to the sharp curvature of the river, the site is characterised by a sharp housing dissimetry. On the right bank, the outer side of the curve, the quite flat ground is mainly occupied by industrial constructions, dominated by the important railway junction. On the left bank, the inner side of the curve, the urbanistic texture is mainly made of habitations, squeezed between the river and the hill. The numerous technical requirements and the site constraints have led to the choice of a cable-stayed bridge with a single pylon on the right bank. Its particularity of highway bridge in urban site has also led to the need to combine simplicity, impeccable appearance and high quality finishing materials.
Figure 4 The esthetical quality of the bridge is related to the following particularities : - The necessary readability of the structure has led us to choose a single cable plane, located on the axis of the bridge. - The search for thin structural elements bordered by more monumental abutments is satisfied by the stays and the very thin circular pylon, which slenderness is accentuated by the truncated cone shape.
On the contrary, the choice of a single cable plane thwarts this search for slenderness for the deck. Indeed, the height of the deck box-girder, required by the torsional stiffness, does not match this objective. However, the design of the cross-section allows to limit its visual impact. The deck slab is located around mid-height of the box-girder and is supported by very sloping lower steel tubes which improve the lower part and accentuate the impression of slenderness, as the upper part is hidden by the lateral security barriers. - The balancing span replaced by a balancing abutment which, on the one hand, points out the entrance portal of the tunnel and, on the other hand, acts as an acoustical protection for the near by habitations. The visible concrete facings are concreted on site in plank-structured formworks; the lower face of the deck is particularly being taken care of as it is very closely perceived by the walkers.
Figure 5. - The faces of the abutments are realised with country natural stone as the roof of the balancing abutment is entirely covered with vegetation. - The pylon, shaped as a slightly truncated cone, is covered with glazed glass, fixed with bolts. - The sheathes of the stays as well as the external sleeve of the steel tubes supporting the deck slab are made of stainless steel. - A specific lightning device points out the bridge and respects the habitation neighbourhood. - Absorbent coverings are widely used to limit at best the acoustical nuisances. - Landscaped arrangements such as pedestrian and cycle tracks, rest zones, street furniture and vegetation complete the urbanisation of the site, strongly perturbed by the monumental bridge.
- An esplanade, widely open on the river, clears the base of the pylon.
Figure 6.
3. Technical description
Figure 7. The main span of the bridge over the river is 162 m long, in continuity with a short 31.5 m long span above the left embankment and a very short 12 m long span between the pylon and the balancing abutment. This abutment is 122 m long and is the first part of a tunnel that goes on under the railway junction.
The whole structure bears through bored piles on a gritty shistous foundation rock of good quality, however crossed by thin coal veins. The left bank abutment is founded on φ 1,28 m vertical and inclined piles. The other bearings, that means the pile P1, the pylon and the balancing abutment, are founded on φ 1,50 m vertical piles.
Figure 8. The prestressed concrete deck, 25,90 m wide, has a rather uncommon cross-section, with a small central box-girder, 3,75 m high and 4,50 m wide, and two cantilever slabs, located 1,25 m beneath the upper level of the box-girder. The prolongation of the box-girder above the cantilever slabs is necessary to obtain a torsion rigidity sufficient to resist to the transversal loads of balances. The cantilever slabs are supported every 3 m by steel tubes, they are also transversally prestressed by 4T15 cables every 50 cm. On most of its length, the deck is longitudinally centrally prestressed. The end span which is not cablestayed and the zone around the bearing on left bank have to be fitted with 16 complementary undulated cables 19T15. The whole prestressing is located inside the concrete and is injected with a cement grouting.
Figure 9.
The pylon, located on the axis of the bridge, has a total height of 82 m. It is rigidly restrained to the deck. It is covered with glazed glass. Its double foundation sole allows a slight longitudinal translation due to the effects of shrinkage, creep and temperature variation in the part of bridge that separates the pylon from the fix point around the middle of the balancing abutment. The deck is supported, above the river, by 22 stays, balanced on the pylon by 22 other stays which are anchored in the balancing abutment. The 44 stays are made of sheathed greased galvanised strands in an external 2 mm thick stainless steel sleeve. The sections of the cables vary from 81 cm² (54T15) to 137 cm² (91T15). The external diameters of the sleeves are 219 and 254 mm. At the lower part of the stays, a 5 m long double sheath, filled with wax, insures an excellent dumping towards parasitic vibrations. Figure 10.
4. Execution
The deck is positioned by incremental launching and here are the main stages : - foundation of the pylon and temporary supports for the launching, - construction of the deck on the right bank and incremental launching in 18 stages, - construction of the pylon and the balancing abutment, - fitting of the stays and adjustment of the geometry, - removal of the temporary supports and fitting of the bridge equipment's,
Figure 11.
a) Foundations The design of the pylon foundation and the construction method have mainly been dictated by the level of the Meuse river (60,0), influencing directly the level of the water-table in the gravel's behind the embankment walls. The difficulty to realise a water-tight cofferdam and the need of the foundation slab to be concreted out of the water have dictated a lower level of the foundation slab above level 55,5. Since the foundation rock is crossed by a 50 cm thick coal vein of weak mechanical characteristics, the use of φ 1,50 m bored piles has allowed, on the one hand, to bridge locally the coal vein and, on the other hand, to build the foundation slab out of the water. Figure 12.
b) Deck The deck is made of 18 pieces, out of which 16 ones are 12 m long, and is built on a fix site located on the right bank and positioned by incremental launching 12 m at a time. The site is divided in five 12 m long working zones : - zone 0, assembly of the reinforcement steel for the floor of the box-girder, - zone 1, formwork fitting and concreting of the central box-girder and tightening of the launching longitudinal prestressing, - zone 2, free zone, - zone 3, formwork fitting and concreting of the cantilever slabs and tightening of the longitudinal prestressing of the slabs, - zone 4, fitting of the lower steel tubes and tightening of the transversal prestressing of the slabs. To allow the launching, three temporary supports are placed in the bed of the river, one temporary support on the left bank, two on the right bank, plus the launching abutment, where are placed the jacks, able to produce the 600 tons horizontal effort, necessary for the launching. The front end of the boxgirder is prolonged by a 32 m long steel nose. The succession of the operations is such than in a cycle of one week, a 12 m long piece is realised and launched, as the tightening of the longitudinal prestressing, the removal of the formworks and the launching are realised each Monday morning.
c) Pylon The pylon, culminating 70 m above the deck, is built once the deck has reached its definitive position. The pylon has a circular cross-section, shaped as a slightly truncated cone. It is concreted with climbing formworks, about 4 m at a time. A 38 m high steel structure is incorporated in the concrete, in order to facilitate the fitting of the stays. The glazed glass facing is planned for the end of the works, once most of the contractions in the pylon have occurred.
Figure 13. d) Balancing abutment
Figure 14. The balancing abutment is a classical reinforced concrete structure, founded on φ 1,50 m bored piles. Started at the beginning of the works, the construction goes on during the erection of the pylon. e) Stays As soon as the construction of the pylon and the balancing abutment is finished, the stays are placed, starting with the shortest ones and symmetrically with regard to the pylon.
The first adjustment, as the stays are being placed, allows to make up for 70 % of the lengthening under permanent loads. The definitive adjustment is relaxed as all the stays are placed, the temporary supports are removed and all the equipment's are fitted.
5. Studies The design of this cable-stayed bridge is unconventional and the implantation site has some particular characteristics. It has required important specific studies. In addition to the difficulties related to the particular shape of the deck and to the tridimensional behaviour of the balancing abutment, some uncommon problems have been met. Figure 15. A railway bridge is located 80 m down the construction site. The important wind turbulences, provoked by the very angular shapes of this bridge, risked to have a negative effect on the aerodynamical behaviour of the new bridge. An analysis of this behaviour, in situ measures and wind-tunnel tests have shown that the turbulences created by the railway bridge risked not to cause tangible disagreements for the cable-stayed bridge. A 50 cm thick coal vein goes askew in the foundation rock under the pylon. A very detailed simulation of the foundation soil behaviour has been realised in collaboration with the University of Liège. This study has allowed to precise the effect of the coal vein and to determine the settlements (millimetres) to be considered in the calculation of the superstructure.
Construction Control Practice for Panyu Cable-stayed Bridge Dajian HAN Prof. Dr. Soth China Univ. Technology Guangzhou, China
Quansheng YAN Assoc. Prof. Dr. South Cina Univ. Technology Guangzhou, China
D.J.Han, born 1940, received her B.S. 1963 Peking Univ. China M.S. 1982, Ph. D. 1984 Purdue Univ. USA
Q.S.Yan, born 1968, received his B.S. 1985, M.S. 1988, Ph. D 1994 Changsha Railway Univ China
Summary This paper presents the methods used to simulate the erection process, to monitor and adjust the geometry and cable tensions of Panyu cable-stayed bridge. The bridge with 380 meters long of the main span is built using the balanced cantilever construction method. Bridge segments are cast in-situ with traveler form. Due to the flexibility of deck, cable-supported carriages are used. It brings more difficulty into the construction control. Thus it is important to carry out careful and detailed simulation of the construction processes. It shows that detailed calculation and continuous monitoring of the erection process can lead to high precision and give good knowledge of the static behavior of the actual bridge. Such a method makes it possible to achieve a high level of accuracy for construction of PC cable-stayed bridges.
1.
Introduction
The general view of Panyu cable-stayed bridge is shown in Fig.1. The cable-stayed portion of the bridge has a total length of 702.0 meters. The main span between towers is 380.0 meters and the side anchor spans are 161.0 meters. The side anchor spans consist of two spans of 90.0 and 71.0 meters long. An auxiliary pier is in between. The deck is composed with two edge girders and a deck plate. The edge girders are laterally stiffened by a T-shape PC girder with 6 meter spacing. The edge girder is a solid section whose height is 2.2 meter and width varies from 2.6 meter at intersection of girder and pylon to 2.0 meter at middle span. The deck plate is 28cm thick. The width of the deck is 37.70 meter out to out with 8 traffic lanes. Spatial 264 stay cables are arranged in a semi-fan configuration. The pylon shape like a diamond with an extension mast. All the cable stays are anchored in the mast part of the pylon. The stay cables are attached to the edge girders at 6.0 meter spacing. At the side anchor span an auxiliary pier is arranged to increase the stiffness of the bridge. Two anchorage segments of deck at both ends of the bridge are set up to balance the lifting forces from anchorage cables. For a bridge with multiple cable systems, the girder with lower height becomes more flexible and make it more difficult to control the geometry and stay tensions properly. And due to inevitable errors between design values and actual ones at the construction stage, it is
necessary to carry out a detailed simulation analysis and a continuous monitoring throughout the erection process [1][2]. Thus the real state of the structure can be obtained in order to determine the most suitable adjustment of cable tensions and of the elevation of the given segment. In this paper the detailed simulation analysis of the erection process, the methods used in the control and adjust the deck profile and the stay of Panyu cable-stayed bridge are discussed.
Photo 1. The general view of PanYu cable-stayed bridge after completion
2.
Erection Process and Simulation Analysis
2.1 Erection process The deck of the bridge is erected by the balanced cantilever method utilizing cable-stayed form carriages. Due to its large width of 37.7 meters, each segment is nearly 4200.0 kN weight. But the thickness of deck plate is only 28.0 cm. It is necessary to provide more rigid form carriages in order to reduce local deformations. And the weight of a form carriage is about 2500.0 kN. The construction process is briefly described as follows: . To build the towers . To cast in-place the first segment on timbering support . To erect the No. 1 cable and stress to its final length . To hoist the traveling carriages and locate their positions. . To erect the girder segments one by one on the two sides of the pylons . To connect the cantilever ends of the side span with the anchorage parts at two ends. . To continue to erect the remaining girder segments in center span . To connect the cantilever ends of the center span . To remove traveling carriages and temporary supports . To connect the girder with the auxiliary piers. . To cast pavement and set up fence etc. A typical erection stage of one segment is described as follows: . To move the traveling carriage forward and set up the form at proper elevations.
. To erect the stay cables, connect them with the traveler and partially stress them. . To place reinforcement, post-tensioning bars and couple the stressed bars with those of the previously completed segment. . To cast in-situ the concrete . To stress the stay cables and adjust the girder segments to proper elevations . To cure the concrete of segment and stress the longitudinal and lateral bars and strands. . To loosen the connection between the stay cables and the traveling carriages . To stress the cable stays to their final length The above erection step are repeated until the bridge is closed at middle span. 2.2 Detailed Construction Simulation in Site Design final state of cable-stayed bridge under permanent loads In the Panyu cable-stayed bridge, the final situation is defined as such a state that the geometry of deck and pylons is a prescribed profile by designer and there is no or a little bending forces in the pylons and the deck under permanent loads (including self-weight of structure, pavement, fence etc.). Such a situation will reduce the second-order effects as well as the time-dependent effects, such as creep and shrinkage of concrete etc.[1] From the final bridge situation, the erection situations can be evaluated by a precise structural analysis. Software for simulation analysis The erection analysis can be performed by using a conventional step-by-step method, such as the forward assemblage analysis according to the construction process or inversely, the backward dismantling analysis[3]. But for the cable-stayed bridges erected utilized cablesupported form carriages, the installation, remove and movement of carriages must be carefully considered. A software which implement for the monitoring and adjustment of construction procedure of Panyu bridge is specifically developed. In this software the carriages are simulated as a part of the constructed structure and the behavior of carriage can modeled efficiently and automatically. Primary factors on construction such as the construction loads (weight of equipment and traveling carriages, temporary loads etc.), effects of concrete creep and shrinkage, are considered in detail. The software also implements the methods of forward assemblage and the backward dismantling analysis. Simulation of Erection Scheme for Panyu Cable-Stayed Bridge The construction procedure described in Section 2.1 has been simulated stage by stage. Since the creep and shrinkage of concrete occurs and the second part of the dead weight is loaded on the bridge girder after completion of the structure, a downward displacement is induced. Therefore, as the erection is just finished the elevation of the girder profile is set higher than that of the design profile and the pylons is leaning toward the side spans. As for Panyu bridge, the maximum value which is set higher than the designed profile in the middle of the bridge is about 35.4cm, while the displacement of pylon top leaning to anchorage span is about 7.8 cm. Through the simulation of construction process, a theoretical reference for each construction stage is established. They include the information about elevations for laying form and for cable tensions etc.
To give a precise modeling of all site operations, the volumes of concrete actually implemented, and the temporary loads on the deck etc. need to be available. Then theoretical calculations are performed at site for every stage. Creep effects are also taken into account. And when there a need for slight modifications of the actual construction, the simulation of actual construction process also provides the information on the adjustment of cable tensions and laying forms.
3.
Monitoring and Adjustment
There are four sets of instrument installed on Panyu bridge to measure parameters as listed below: - elevations of the deck and displacement of the pylons. - tensions of the cables - stresses of the concerned section in the deck and pylons - temperatures and gradients in the deck, pylons and cables. 3.1 Elevations of the deck and displacements of the pylons Usually the elevations are measured at the previous three segments to monitor the configuration of deck during the concrete casting. After the longitudinal strands and bars are stressed and the stays are stressed to their final length in each segment, the elevations of deck are measured at five previous segments of the front deck ends. And the displacements of pylon ends are also measured. For every 5 segments have been completed, the geometry of the completed structure are monitored. In order to eliminate the thermal effects as much as possible, the measurement have been done at 6:30-7:00 a.m. before the sun rises. Using the careful measurement can guarantee the geometry of bridge under the control of engineers in site. 3.2 Cable Tensions At Panyu bridge, the semi parallel wire cables (SPWC) with Hi-am anchorage are used. The cable tensions are measured by frequency method. First the lowest 10 natural frequencies of the cable are measured, then using the calibrating coefficient to evaluate the cable tension. Each cable is calibrated after it is just installed and partially stressed. Measurement sensors fixed on the five pairs of previous stays near the carriage enable to establish the actual stay tension precisely correspond to those predicted by the design model. Before and after the closure of side spans and main span, tensions of all the installed cables are measured. 3.3 Temperature There are six thermocouples in different parts of segments, eight thermocouples distributed over the pylons, two thermocouples inserted in the cables. The average temperature measurements are used in monitoring and the calculation of adjustment. 3.4 Stresses in pylons and deck In several concerned sections of the deck and pylons, strain gauges are embedded into and the strains of the structure are measured during the whole construction period. All strain measurements, including the collection, storage and processing of measured data, are finished
by PC computers automatically. Generally the measurement was done once every 1 hours. Thus the stress of the structure can be monitored. 3.5 Supplementary measurement of structural parameters In an actual cable-stayed bridge, the discrepancies of parameter values between designed and actual values such as the modulus of elasticity of concrete, the mass density of concrete, the weight of girder segments may give rise to disagreements between the actual structural response and the theoretical prediction. At Panyu bridge, when the traveler carriage is lifted upon the deck, the reactions of each form carriage are measured. Thus the weight of each carriage is obtained. At each stage the mass density of concrete and the elasticity modulus of concrete are tested in laboratory in situ. And the quantity of concrete and steel bar used in each segment are recorded and measured. All the measured parameters are used in the calculation of construction and adjustment. Thus the actual weight of deck are quite precise. The uncertainties of loads are diminished as much as possible.
4.
Results of the Panyu cable-stayed bridge
4.1 Excellent agreement of the theoretical prediction and actual measurement With the software described in Section 2 and the structural parameters evaluated by measurement, detailed analyses are carried out during the construction processes. For every segment, many plans to tension the stays which link with the form carriages temporarily are calculated, and every concerned factors, such as the stresses in the deck and form carriage, the cable tensions and the displacements of deck and pylons etc., are obtained. Thus the engineers in site select an optimum scheme. Table 1 shows the results from the theoretical prediction and measurement of actual structure when the 14th deck segment is competed. The result of comparison shows good agreement. In the practice, the agreement for every segment is very well. These provide with a solid foundation to ensure the safety and smoothness of construction. Cable Cable’s Tension(kN) Elevation of deck(m) Number Tm Tp Tm-Tp Hm Hp Hm-Hp S10 2865.0 2793.0 72.0 34.703 34.703 0.000 S11 2980.0 2948.0 32.0 34.518 34.519 0.001 S12 3241.0 3230.0 11.0 34.344 34.349 0.005 S13 3489.0 3503.0 -14.0 34.187 34.186 -0.001 S14 3681.0 3657.0 24.0 33.983 33.994 0.011 Cable Cable’s Tension(kN) Elevation of deck(m) Number Tm Tp Tm-Tp Hm Hp Hm-Hp M10 2634.0 2742.0 -98.0 37.408 37.407 -0.001 M11 2788.0 2862.0 -74.0 37.491 37.487 -0.004 M12 3072.0 3116.0 -44.0 37.552 37.551 -0.001 M13 3368.0 3308.0 60.0 37.617 37.623 0.006 M14 3506.0 3532.0 -26.0 37.693 37.702 0.009 In Table 1, “T” represents cable tension, “H” represents elevation. sub-index “m” represents measured value, “p” does theoretical predicted ones. Table 1.Comparison of the measured and predicted values (at 14th segment)
4.2 Final geometry within 4 cm of theoretical figures After ten-month long erection of deck segments, the two ends of the cantilever parts meet at the middle within only 3.9cm deviation in elevation. The errors in the axis of the deck are limited to 1.5cm. The two ends of cantilever before the closure of side spans is well agreed with the design requirement within error less than 2.0 cm. The spatial position of a deck segment is given by reference to the previous segment; namely by the relative geometry, there are no great errors in the successive segments. At every segment the errors of laying form are limited at the prescribed construction tolerances. The final profile of the deck is smooth in elevation. At each stage the position of the deck is in good agreement with the design requirement (within 3.0 cm variation). 4.3 Cable tensions under control (<7%) The problem of cable tension is more than just the accuracy of the readings of a pressure sensor of the jack. When a cable is stressed to its final length, the tension of the cable is obtained from the reading of the jacks which are calibrated every two months and from the tension measurement system by frequency method. These results of tensions are corrected each other and an exact tension value of a cable can be obtained. As construction proceeded, the geometry of deck is monitored and the forecast final geometry is compared with the final designed geometry. In every phase, the standard deviation of the differences in each segment is less than 3.0 cm. The convergence of the results from geometry monitoring and cable tension measurement substantiates the conclusion that tension is correct to within better than 7%.
5.
Conclusion
During the erection of Panyu cable-stayed bridge, detailed simulation and continuous monitoring of construction process has been carried out. These made it possible to achieve high precision of construction. From the results of construction control practice of Panyu cable-stayed bridge, some conclusion can be induced as follows: 1. In cable-stayed bridges, and particularly in PC cable-stayed bridge with relatively flexible deck, the construction of the concrete cantilevers is complicated due to the use of the cablestayed form carriages, continuous geometrical monitoring is absolutely necessary in order to obtain acceptable geometry and tension conditions for the structure. 2. This type of continuous monitoring enables the engineers to treat any errors that may arise during the construction process and can make more suitable decision for the adjustment in site. 3. Since there are many deviation in parameters, such as the mass density, elasticity modulus of concrete etc., must be measured in the erection of each segment of deck. And the practice of construction control for Panyu cable-stayed bridge shows that it is very important and necessary to carry out a detailed simulation of construction process. 4. The good adjustment of the Panyu cable-stayed bridge is made possible by the co-operation of all those involved. Such continuous monitoring and detailed simulation of erection process make it possible to reach a high level of accuracy of construction in PC cable-stayed bridges.
References [1] Virlogeux,M. Erection of cable-stayed bridges: the control of the desired geometry. Proc. of the Seminar on cable-stayed and suspension bridges, Oct. 1994. [2] Tang,M.C. The 40-Year Evolution of Cable-Stayed Bridges, in 1994 International Symposium on Cable-Stayed Bridges, Lin Yuanpei et. al.(Editors) pp30-11,Shanghai. [3] Walther,R., Houriet,B., Lsler,W., and Moia,P., Cable-stayed Bridges, Thomas Telford, London, 1988.
Elevation
Plane Fig.1 General View of Panyu Cable-Stayed
Some Aspects of The Design of Martwa Wisla River Bridge in Gdansk
Krzysztof WACHALSKI Chief Engineer, Bridges BPBK S.A. Gdansk, Poland
Jacek KAMINSKI Civil Engineer BPBK S.A. Gdansk, Poland
Marek SUDAK Civil Engineer BPBK S.A. Gdansk, Poland
Computer visualisation
Summary The intention of paper is to impart same of specific problems as regards designing cable-stayed bridge in Gdansk, and also especially with seeking own computational methods and construction details adequate to the Polish reality. We would like to pay special attention to the method of concrete pylon computation and computational model of foundations as well as constructional solutions of such details as support of vertical load variable sign (pressure and anchor) with considerable horizontal displacement.
1.
Introduction
Polish economic changes of last years have caused the necessity of development of, among other things, seaports. As far, goods’ transport out of The Seaport in Gdansk to the country interior has been executed by train. In the current circumstances, a reconstruction of the port is connected with the necessity of the road network reconstruction. In 1994 a project was started the aim of which was efficiency increase of the communication system in the area of The Seaport in
Gdansk. The first element of the reconstruction is Crossing over the Martwa Wisla River. The crossing of about 1 km length is to connect the port areas with the national road Warszawa – Gdansk. Assumptions concerning the new route localisation are based on the its connection with highway A1 (European highway) to be executed in the future - the connection shall perfectly pass by the city. Additionally, the designed crossing shall constitute an element of the north-western ring of Gdansk. As it has been presented, the investment, necessary for the port, appears profitable for the whole agglomeration of Gdansk. The basic element of the designed crossing is a bridge over the Martwa Wisla River. Various variants of the river crossing were considered, such as a typical bridge with supports in the river current, drawbridge, cable - stayed bridge and tunnel. During evaluation of the above - mentioned conceptions, a cable-stayed bridge was chosen. Advantages of the conception were, among others, significant technical attractiveness, a challenge for Polish engineers (it is one of the first bridges of that type to be built in Poland), and finally economic justification, as the most important factor. Cable-stayed bridge enabled, due to its small constructional height, shortening of the access roads to the bridge and elimination of inclusion lanes within the bridge, which shall diminish its width. This is the reason why the total cost of the whole investment with a cable - stayed bridge is not bigger than, and in some circumstances it may appear smaller in relation to, a bridge of typical construction. A very important factor as regards the advantages of a cable-stayed bridge is its foundation. Because of significantly high costs of supports in the river current and very inconvenient geologic conditions, it was advisable to use a construction of as few supports in the river current as possible. Apart from the factor, whose importance should be evaluated and classified as equal to that of economy (if not as more important), there are also aesthetic advantages. In the localisation, in the area of entry to the city, a cable-stayed bridge, with its architecture, fits in with the city panorama very well, constituting its characteristic element. The executed study of architecture and landscape confirmed the conclusions. Finally, General Directorate of Public Roads, as the representative of Polish Government (Client), decided in favour of construction of a cable-stayed bridge over the Martwa Wisla River in Gdansk. The project is financed by Polish Government and supported by financial credit from World Bank. The technical and bidding documentation has been prepared in Municipal Design Office (BPBK S.A.) in Gdansk. The beginning of the bridge construction is planned to be in the middle of 1999 and its completion and putting the whole crossing into service at the end of 2001.
2.
General characteristics of bridge
The designed bridge is one-pylon construction of the main span length equal 230 m. Total length of the bridge equals about 380 m. In cross-section, an composite bridge deck consists of two girders and a reinforced concrete bridge deck slab of 23 cm thickness. The height of bridge deck construction equals 2,39 m. Each steel girder consists of two welded plate girders. Crosswise, the bridge deck is braced by steel cross-beam spaced every 4,0 and 4,33 m. Total width of the bridge deck equals 20,31 m. The width includes two carriageways, two traffic lanes each, (2 x 7,0 m), a reserve lane (median strip) and service footways, 0,75m each. Cable stays’ system has been designed as semi-harp pattern, of dense type with two-sided outside stays (two-planed). As stays, cables of parallel 7-wire strands, 15,5-mm diameter each strand, are used. In the longer span, 15 stays have been used, spaced every 12 m. In the back span 8 stays have been used, spaced every 13 m. Stays’ passive anchorage is placed in the pylon and active anchorage in the bridge deck. The anchorage in the bridge deck has been designed in girder’s axis (plane), which prevents from its torsion. Bridge supports are founded on reinforced concrete drilling piles of 1500 and 1600 diameters. The piles’ lengths equal from 25 to 30 m. The bridge main support - pylon, has been designed
with its total height of about 100 m and inside service. The pylon is A-shaped. In cross-section, the pylon is a reinforced concrete box of 3,60 x 5,0 m dimensions. In the areas of stays’ anchorage in the pylon, additional strengthening has been applied by means of steel frames, which are to transfer great tensile forces. The pylon has been put on a concrete block - footing of variable thickness from 3,5 to 7,0 m, founded on 59 piles of 1600 mm diameter and 30 m length. Bridge abutments have been designed as box abutments. The abutment on the side of the back span has been fixed to the bridge deck and constitutes a fixed bridge support. The abutment on the side of the main span is loaded with variable vertical reaction (lift up and pressure) and considerable deck horizontal displacements. Additionally, the back span has been stabilised with 3 anchoring supports, spaced every 26 m. The bridge assembly as regards the ground part has been designed as assembly on scaffolding and as regards the water part as using the cantilever erection method. Assembly segments to be subsequently fixed using the cantilever method shall be transported by waterway on pontoons. They consist of full composite section (steel girders and reinforced concrete deck slab). The assembly segments length equals 12 m, and total weight of a single segment equals about 200 T. Characteristic indexes of the bridge construction are : • • •
ratio of the bridge construction height and the main span length 1:96 ratio of the pylon height and the bridge stays’ length 0,46 ratio of the bridge deck width and the main span length 1:11,3
SCAFFOLDING ER ECTION
Figure no. 1 – Side view
CANTILEVER ERECTION
SCAFFOLDING ER ECTION
Figure no. 2 – Cross section of deck
A
A
A-A
B
B
B-B
Figure no. 3 – View of pylon
3.
Computational model of pylon foundation
The bridge foundation geotechical parameters are not advantageous. In the vicinity, there are poor grounds depositing to the depth of about 20 m below the area level. They are constituted by interbedded aggregated mud and fine sands of loose consolidation. Only below the sands are there consolidated medium and coarse sands. Because of the possibility of the base displacement under the bridge main support, the pylon foundation flexibility was taken into consideration in the computational analysis. The bridge computational model includes substitute resultant elastic reactions, calculated for each direction in space (3D) co-ordinate system and imposed at the place of the pylon rest on the foundation block. Calculation of the substitute elastic reactions-springs was executed according to the following algorithm: • A single pile was modelled in an elastic space defined by elastic reactions. The reactions are equivalents of ground layers of thickness above 0,25 m in the pile upper part to layers of 1 m thickness at a pile base. The reactions corresponded to the vertical component - friction on a side surface, and to two horizontal components - lateral passive earth pressure. Elastic reactions also occurred as support in a pile base. • Loads of unit forces and moments on a pile head in all directions (two horizontal loads, one vertical, three rotations) and the displacements obtained were the basis of rigidity determination : 1 Ki =
where :
∆i
i – degree of freedom (X, Y, Z, RX, RY, RZ) ∆i - displacements from a unit load
In such a way, substitute rigidities of each pile for all the other degrees of freedom (3D) in elastic geometric space were obtained. • A model (3D) of the pylon base was created. It consisted of a concrete block supported by elastic supports that corresponded to each foundation pile. • Unit loads were executed at the place where ‘legs’ are rested on the base and the corresponding displacements, according to the principle described above, were the basis of calculation of substitute rigidities of the whole support in all directions (3D).
Figure no. 4 – Model of pile and footing
The obtained substitute (resultant) rigidities of foundation enabled active consideration of support displacement. The basis of estimation of ground elastic reactions-springs parameters (as regards the pile model) were formulas specified by Polish Standards and Polish publications concerning geotechnics. The elastic reactions’ envelope obtained out of a static and dynamic analysis was used to load the described models of a base and a pile and to calculate inner forces in them.
4.
Computation of stresses in pylon
The state of stresses in the pylon reinforced concrete construction, constituted by two-way eccentric compression, conditions of Polish Standards, which require execution of strength calculations according to the Linear Stresses Method, as well as the fact that pylon construction is of extreme importance for the whole bridge resulted in preparation of special software for computation of stresses in concrete and reinforcement steel for optionally shaped sections. A principle was assumed that section modelling should consist in division into minute concrete elements and particular reinforcement bars. For such an assumption, the problem was described theoretically, an algorithm was made, and finally, a computer program was prepared. Popular software for PCs, such as EXCEL 7,0 for WINDOWS’95, with elements of VISUAL BASIC, was applied here. Preparation of the algorithm was executed in co-operation with Prof. K. Wysiatycki from Technical University of Gdansk. In the following lines, we present theoretical bases and exemplary computational results.
Figure no. 5 – Theoretical model
∆x
We have 3 equations of equilibrium :
∑w ∑x ∑y
ij
wij
= F
Y
(1)
ij
⋅ w ij = F ⋅ x o
(2)
ij
⋅ w ij = F ⋅ y o
(3)
∆y
yr
F
Zij
yj
Z
X
c xi
xr
X
β
α
Zij = a ⋅ xi + b ⋅ yi + c
xr y b = 2r 2 r r 2 2 2 r = xr + yr
Y
The plane
(4)
a =
Z = ax + by + c
(5)
a=tgα b=tgβ Conditions for points (xi , yj) : if if
Zij > 0 Zij ≤ 0
then then
Zij : = Zij Zij : = 0
(6) (7)
We assume comparative stress σp and
wij = ∆x ⋅ ∆x ⋅ zij ⋅ σp (8)
Then we find equations solution (1) (2) (3) by use (4) and (8). Searching solution (1) (2) (3) needs check below conditions : if Σ wij > F if Σ wij ⋅xi> F ⋅ xr if Σ wij ⋅yj> F ⋅ yr
then then then
reduce “c” parameter reduce “xr” parameter reduce “yr” parameter
The iteration method of change xr and yr parameters helps us to find solution automatically.
Figure no. 6 – Stresses of lower part of pylon
Figure no. 7 – Stresses of upper pylon part
5.
Analysis of horizontal force transfer from stay onto bridge deck
The analysis of horizontal forces distribution from stays, at the place of their anchors in the bridge deck, was carried out by means of programme Robot V6, applying Finite Element Method. Shell model was applied for the elements such as upper flanges, bottom flanges and webs of the main girders and cross-beams. Plate model was applied for the reinforced concrete slab. Connectors of the slab integration to upper flanges were assumed as strips, modelled also as a shell. The conclusions drawn from the stress results analysis were used for dimensioning of bridge deck elements. The most significant fact is that normal stresses, in the slab, in the nearest area of a stay anchor, turned out to be about twice as big as uniformly imposed stresses. Such
assumptions were confirmed as regards angle of force distribution in the bridge deck slab, which approximately equals 45o. Additionally, introduction of an axial force into the slab takes place (by means of connectors) mainly in the nearest area, which totally takes up about 6 m (in front and behind the point of application of the stay force).
Figure no. 8 – MES model of deck
7.
Detail of bearing of variable reaction and great horizontal displacements
In order to transfer horizontal forces (reactions) of variable sign from the superstructure onto the abutment on the main span side, a special bearing was constructed. The bearing consists of two standard pot bearings and prestressing bars. Additionally, the bearing must ensure the possibility of the bridge deck horizontal displacement, whose shift absolute value equals 450 mm. Because of additional vertical tensioning of the pack of two pot bearings, the bearing is free from knocking effect during a change of reaction sign. Optionally, a variant with a single pot bearing and prestressing bars was considered. However, load capacity of such a bearing would be almost twice as high, due to additional tensioning of the bearing against the whole tensing force. Because of the above-mentioned great horizontal shift on support and relatively short prestressing bars possible, the solution was rejected.
Figure no. 9 – Abutment anchor bearing
8.
Conclusions
In this article, we wanted to popularise the project of cable-stayed bridge, the building of which shall be soon started. The discussed issues constitute a small part of the solved designing problems. These are, most probably, standard issues solved in the case of constructions of that type. However, we aimed at explanation of the methods used in Polish reality. Among interesting issues, there are : 1. Pylon foundation estimation method influence on static operation of the bridge superstructure Support model with about 25000 freedom nodes, substituted by resultant rigidities during superstructure analysis, enabled optimum (time and software) determination of inner forces and stresses in the construction. 2. Computation of stresses in pylon concrete and reinforcement steel. A special computer programme, based on popular and available personal computer (PC) software, was prepared. 3. Computation of stays anchorage details, by means of MES, enabled determination of precise distribution of forces near anchorage.
9.
References
[1].
Detailed technical project of cable-stayed bridge over Martwa Wisla River, prepared by BPBK S.A. Gdansk 1998.
[2].
“Bridge over Martwa Wisla River in Gdansk” – Scientific Conference Gdansk-Jurata, September 3-5, 1997.
[3].
“Bridge over Martwa Wisla River in Gdansk” – Magazine “Inzynieria i Budownictwo”, 6/1998.
Rain/Wind Induced Vibrations of Parallel Stay Cables Guy L. LAROSE Technical Manager Danish Maritime Institute Lyngby, Denmark Guy L. Larose, born 1961, graduated in mech. eng. from Laval Univ., Québec, MESc from Univ. of Western Ontario and PhD from Tech. Univ. of Denmark. He joined DMI in 1992 where he is a wind engineering specialist.
Leif WAGNER SMITT Chief Naval Architect Danish Maritime Institute Lyngby, Denmark Leif Wagner Smitt, born 1939, graduated in naval architect., MSc, from the Tech. Univ. of Denmark. He joined DMI in 1964 where he is a renowned specialist of physical modelling of fluid-structure interactions.
Summary The main findings of a series of wind-tunnel experiments focusing on the rain/wind induced vibration phenomenon of stay cables of a large cable-stayed bridge are presented in this paper. In particular, the phenomenon is studied for stay cables in tandem arrangement, one cable on top of the other, where the effectiveness of an aerodynamic means to mitigate the excitation has been verified.
1.
Introduction
Cable vibrations associated with a combination of wind and rain have been reported on several occasions since the middle of the 1980’s [1,2,3]. The lightly damped stay cables of large cablestayed bridge are particularly susceptible to these oscillations, especially when the steel strands forming the stays are covered by a smooth synthetic tube, often polyethylene high-density (PEHD), and when the cables form an angle of 20° to 30° with the horizontal plane. Remedial measures have been devised, experimented and implemented on many structures, most of them with great success and relatively low cost [2,4]. The excitation is, in general, weak and needs the simultaneous combination of several parameters to occur. Some prefer to increase the modal damping by a factor of five or so to damp out the vibrations [e.g. Erasmus Bridge [6]), others prefer to mitigate the excitation at its source by aerodynamic means (e.g. several Japanese bridges [4]) and others select a combination of both approaches (e.g. Pont de Normandie [7]). The conditions at which these oscillations can occur for a cable-stayed bridge are well determined and were pointed out as early as 1984 by the late Hikami [1]: smooth stay cable, cable inclination of +20° to +45°, wind yaw angle 20° to 40° directed towards the decreasing cable height, cable natural frequencies between 0.4 and 3 Hz, mean wind speed between 8 to 15 m/s, light rain or mist, and high wettability of the cable surface. The vibrations are thought to be caused mainly by the formation of water rivulets on the upper and lower surfaces of the cable. The rivulets change the aerodynamic shape of the cable to an unstable shape, inducing acrosswind vibrations (lift) due to variations of the mean pressure distribution on the cable. The problem is also amplified by the fact that the rivulet changes position as a function of wind speed
and with the cable motion. Also, the presence of secondary axial flows has also been observed for inclined cables [5]. These axial flows can also create mean pressure distribution changes that can induce vibrations for inclined cables (30° to 45° or so), even without rain. A final element that adds a bit more complexity to an already complex problem is that, for the majority of the stay cables of cable-stayed bridges, the transition between sub-critical to critical Reynolds numbers occurs in the 8-15 m/s range of wind speed, depending on the cable surface roughness and turbulence intensity. This transition corresponds to an abrupt reduction of drag force (50% or so) and a reduction of the strength of the shedding of vortices in the wake. The latter is equivalent to a reduction of the loading mechanism associated with fluctuating pressure. This reduction leaves room for weaker excitation to dominate the loading such as the excitation encountered during the rain/wind-induced vibration process. The presence of the water rivulet or a slight change of surface roughness can trigger this transition from sub-critical to critical Reynolds number. The Öresund High Bridge is a cable-stayed bridge with a main span of 490 m flanked by Figure 1: View of the cable system of the side spans of 301 m each. The two-level Öresund High Bridge during construction. truss-girder bridge deck will carry vehicles and train traffic and will be supported by two vertical cable planes anchored to two 204 m high H-shaped pylons. The cable system has a harp configuration, each cable forming an angle of 30° with the bridge deck. The bridge has 40 stays per cable plane, each stay being composed of two parallel cables placed one on top of the other with a 670 mm centre-to-centre spacing. The steel strands of the stay cables are covered with a polyethylene high-density (PEHD) tube, 250 mm in diameter. Fundamental natural frequencies of the stay cables will range from 0.5 Hz to 2.5 Hz. Figure 1 shows a view of the cable system arrangement for the partially constructed bridge.
Figure 2: The 2.1 mm thick double helical fillet fitted to the PEHD tubes of the Öresund Bridge
The combination of cable angle, polyethylene surface, low natural frequencies and high probability of occurrence of light rain with moderate winds at the bridge site set the stage for possible rain/wind-induced vibrations of the stay cables. Based on experience, it was decided at an early stage in the detailed design of the superstructure to fit the PEHD tube with an aerodynamic countermeasure to prevent rain/wind-induced vibrations, namely a double helical fillet, 2.1 mm high (see Figure 2),
similar to the fillet used for the stay cables of the Pont de Normandie in France, with the same pitch but the fillet is 0.7 mm higher. To verify the effectiveness of the proposed countermeasure for 250 mm diameter cables (the Pont de Normandie cables have a diameter of 160 mm) in a tandem configuration, a series of wind-tunnel tests was initiated by Sundlink Contractors and carried out by the Danish Maritime Institute (DMI).
2.
Experimental Procedures
2.1
Dynamic Test Rig
A 6 m long section model of a stay was built at a geometric scale of 1:1 and was mounted in a purposely designed test rig fitted with suspension springs. The rig was designed such that only one of the cables of a pair could oscillate while the other, when present, was kept fixed and only acted as a dummy to simulate adequately the surrounding flow field. All windtunnel tests were carried out in the Velux Wind Tunnel in Østbirk, Denmark, which has a 4 m x 4 m open jet cross-section, a Figure 3: Test rig in A/S Velux Wind Tunnel 30 m/s maximum wind speed and a rain facility. A view of the test rig in the wind tunnel is shown in Figure 3 and a sketch of the rig general arrangement and sign convention is given in Figure 4. 2.2
Scope of Wind Tunnel Tests
The parameters investigated during the rain/wind vibration tests were: • • • •
the influence of the tandem cable configuration on the vibrations; the influence of wind incidence, ±40° in the horizontal plane; the influence of wind speed and rain intensity; and, the influence of structural damping and frequency of oscillations.
Initially, the test programme focused on the reproduction of rain/wind-induced vibrations observed elsewhere for an isolated smooth PEHD tube forming an angle of 30º with the horizontal plane in yawed winds and light
Figure 4: Sketch of test rig and sign convention
rain. This was followed by a series of tests aimed at defining a systematic test procedure including surface treatment of the PEHD tube. The test procedure was applied for a series of exploratory tests where the worst case conditions were sought for the cable fitted with the helical fillet. Finally, tests aimed at comparing the level of aerodynamic damping between a dry and a wet cable with rivulet were performed for various cable configurations and various levels of structural damping. 2.3
Cable Surface Treatment
Past experience with the simulation of rain/wind-induced vibrations in wind tunnels had shown that the wettability of the cable specimen was an important test parameter. In nature, a combination of dust accumulation, saline deposit, acid rain or the like, and sunlight increases the wettability of the PEHD tube surface with time. It was also observed that the more wettable the cables are, the larger the possibility of formation of a water rivulet (upper and / or lower) on the cable and therefore possible rain/wind-induced vibrations. Based on this it can be conclude that black PEHD tube are more susceptible to rain/wind excitation than white tubes since they have a larger proportion of carbon, an element that happens to increase the wettability. Since the PEHD tube supplied for the experiments were brand new, a wetting agent had to be applied to the surface to simulate the prototype conditions. For the Pont de Normandie experiments, soot from an oil furnace mixed with water proved to be a very effective wetting agent. For the present investigations a different approach was used. Firstly, the PEHD tubes were lightly sanded with a fine grade sandpaper to simulate natural erosion and dust particles. Subsequently, the cable surface was treated with a thin coat of polyvinyl alcohol simulating a rise in surface energy of the cable equivalent to oxidation. This surface treatment increased the apparent wetting characteristics of the PEHD tube, helping the formation of the upper rivulet. Figure 5 compares the flow patterns on a smooth untreated PEHD tube to the flow patterns on a treated tube. The polyvinyl alcohol used in this study was Gosenol KP-06 from Nippon Gosei applied with a brush from a 5% solution in ethanol. The polyvinyl alcohol coating was applied systematically after about two hours of testing. 2.4
Figure 5: View of lower rivulet on a new PEHD tube (top) compared to flow pattern for a PEHD tube after treatment with polyvinyl alcohol (bottom)
Scaling Parameters
The aerodynamic phenomena studied here is due to a combination of rain running down on the PEHD tube covering the stay cables and wind with low turbulence intensity in the 8 to 15 m/s range. The difficulty in scaling rain droplets and the complexity of the phenomenon, which is surely dependent on Reynolds number, suggests that the only advisable scale for geometrical scaling is 1:1. The same remark prevailed for the choice of the velocity scaling, the water patterns on the cable being a function of the volume of rain droplets being carried by the wind. A velocity scale of 1:1 was thus selected, implying a frequency scale of 1:1 also.
An advantage of the 1:1 geometrical scale is that the PEHD tubes fabricated for the prototype structure could directly be used for the model cable. However, to ensure an adequate aspect ratio of the model (length of the model divided by its diameter) a cable model of at least 6 m (6 / 0.25 = 24) should be used. This forced the wind-tunnel tests to be conducted in a very large wind tunnel, namely the 4 m x 4 m Open Jet Wind Tunnel of the window manufacturer Velux A/S in Østbirk, Denmark. The mass per unit length of the prototype cables is on average 80 kg/m. For a 6 m long model cable this would mean a mass of 480 kg. For practical reasons, the mass scaling could not be kept at 1:1. The model cable, including the springs and the diverse fixing components had a total mass of 84 kg, resulting in a mass scaling of 1:5.7. It can be assumed that the mass damping parameter: 4 π mζ , ρ D2
(1)
where ρ =air density, D = cable diameter, m = cable mass per unit length and ζ = cable damping as a fraction of critical, governs the dynamic modelling of wind-induced vibrations of cables. Based on this parameter, the lower mass of the cable model can thus be compensated for by a higher modal structural damping in comparison with the expected structural damping of the prototype cable. This links directly the mass scaling, 1:5.7, to the damping scaling, 5.7:1. However, to take into account unavoidable three-dimensional effects due to the flow passing by the extremities of the finite length model cable, the damping scaling was corrected. Since, the 3D effects are likely to render things better in the wind-tunnel than for the prototype cables, a damping scaling of 3.8:1 was adopted. This means that a model structural damping of 0.6% of critical would be equivalent for the prototype to a structural damping of approximately 0.16% of critical. The main scaling parameters were thus as follows: geometry, velocity, frequency and density, 1:1; mass, 1:5.7 and damping, 3.8:1. 2.5
Modelling of the Wind and Rain
The 4 m x 4 m open-jet of the Velux Wind Tunnel provided a relatively smooth air flow with a mean turbulence intensity of 1% measured 0.2 m downstream of the inlet. Zones of higher turbulence intensity (approximately 2%) are found at the edges of the inlet while the lowest turbulence zones are near the centre of the cross-section. The turbulence intensity increased further downstream but was believed to be in the lower range of turbulence intensity expected for prototype cables. The room
Figure 6: View of medium intensity rain and rain rig in the Velux Wind Tunnel.
around the jet is 7.5 m wide by 7.5 m high. These flow features made the Velux Wind Tunnel well suited for rain/wind induced vibration experiments. The wind tunnel is also equipped with a rain generation facility, where demineralised water is supplied under pressure to an array of adjustable nozzles to provide a wide variety of rain intensity and droplet sizes. For the present experiments, a rain rig was purposely built by DMI to provide a medium to light rain in a plane following the cable inclination of 30° and parallel to the cable. At first, the rain rig was composed of two tubes with 10 nozzles each. This proved to provide rain with too high intensity (see Figure 6), even though the water supply pressure was reduced to a minimum (flow rate of 3.5 litre/min). After several iterations, the optimum rain rig was composed of only one tube with 8 spray nozzles (Figure 7).
3.
Main Findings
3.1
Smooth Cable
Figure 7: View of the light rain rig in the wind tunnel.
Rain/wind-induced vibrations of a smooth PEHD tube, 250 mm in diameter were observed for an angle of wind incidence of +30º and wind speeds varying between 9 and 12 m/s. The vibrations developed rapidly, within a few cycles, up to ±250 mm, after the formation a small coherent rivulet on the upper and lower surfaces of the tube. There was no apparent along-wind motion of the rivulets. The large vibrations started after an equivalent medium intensity rainfall had wet the cable and was stopped for approximately one minute. The structural damping of the cable was very low, 0.025% of critical. Large rain/wind vibrations (up to ±250 mm) were also observed for smooth cables in a tandem configuration (670 mm cable spacing). The damping level was adjusted so that the amount of energy dissipated per cycle for the experiments was equivalent to the prototype conditions, assuming a prototype structural damping of 0.16% of critical. Subsequently, it was observed that an increase of structural damping up to an equivalent prototype damping of 0.58% of critical was not sufficient to damp out completely the rain/wind-induced vibrations for smooth cables in tandem configuration as seen in Figure 8.
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Figure 8: Time histories of lower cable displacements due to rain/wind excitation for smooth cables in tandem configuration and structural damping of 0.58% of critical. 3.2
Cable With Helical Fillet
The tests conducted with the PEHD tube with a double helical fillet, 2.1 mm thick, showed a strong reduction of the rain/wind-induced vibrations observed with the smooth tube. The helical fillet disrupted the formation of a coherent upper rivulet, therefore mitigating the excitation at its source. These observations are in accordance with the results of the wind tunnel investigations made for the stay cables of the Pont de Normandie. The helical fillet proved to be effective in reducing the large rain/wind induced oscillations even for the cases where the structural damping of the model was as low as 0.025% of critical. Exploratory tests indicated that the helical fillet was as efficient for a wind angle of +30º as for its mirror image configuration at -30º. The tests indicated also that the process was only slightly affected by the frequency of oscillations of the cable, the helical fillet being as effective at 1.2 Hz as at 0.66 Hz. For some conditions, the rain/wind-induced excitation persisted even with the cable fitted with the helical fillets. The amplitudes of vibrations were limited, however, when compared to the results of the smooth PEHD tube tests. The worst cases observed were: 1) +30º, 12 m/s; and 2) +20º, 11 m/s, (see Figure 9). In both cases, the cable was in its tandem configuration and oscillated at a frequency of 0.66 Hz. It is believed that the lower rivulet, which remains coherent even with the helical fillet in place, causes these oscillations.
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Figure 9: Comparisons between time histories of vertical displacement of a dry cable versus a wet cable at 11 m/s for a wind yawed angle of +20°, in tandem configuration, with helical fillet. It was observed that the cable immersed in a steady-state rain field of light to medium intensity had a tendency to lift. This lift was combined with an apparent damping of the buffeting vibrations when the intensity of the rain reached medium level. This can be observed in Figure 10 where a mean cable lift of 20 mm was recorded at a 12 m/s wind speed. 40 20 0 -20 -40 -60
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Figure 10: Effect of rain on vertical displacement of the cable configuration for the Öresund High Bridge, 12 m/s and wind angle of +30°, in tandem configuration, with helical fillet. Figure 11 compares decay traces at 12 m/s wind speed for a dry cable to a slowly drying cable where a distinct lower rivulet is present. For these tests, the cables were excited by hand and
released. It clearly indicates that the total damping is reduced when the cable has been exposed to rain, the decay traces being shorter for a dry cable. 100
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Figure 11: Comparisons between decay traces of a dry cable versus a slowly drying cable with lower rivulet and helical fillet, 12 m/s and wind angle of +30°. 3.3
Effect of Added Structural Damping on the Rain/Wind-Induced Vibrations
A damping device composed of a plunger oscillating in a silicone oil bath was built and fitted to the rain/wind cable vibration rig (see Figure 12). An extremity of the plunger was fixed directly to the moving cable while the other extremity was fitted with an array of 2 to 6 pins; the number of pins being varied to change the level of damping. A damping device was fitted at each end of the cable. Figure 12: Silicon oil damper In addition to the inherent damping level of the rig without damper (0.49% of critical), three other levels of damping were achieved, namely 1.31%, 1.62% and 1.94%. The damping referred to here and later on in this text is the mean damping value of the model cable for oscillations between 60 mm and 20 mm in amplitude. While the damping was found to vary only slightly with amplitude for the tests in still air without rain, the tests with wind and rain showed an important variation of total damping with amplitude. The effect of increasing the damping from 0.49% to 1.31% of critical in model scale is depicted in Figure 13 for the cable with helical fillet, at 12 m/s wind speed, with rain. In general, the amplitudes of vibrations were slightly less than halved by this 2.6 increase of damping. For all the tests with increased structural damping, no self-induced vibrations due to the rain/wind combination were observed. Based on mass damping similitude, 1.31% of critical in model scale is equivalent to 0.33% of critical in full-scale.
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Figure 13: Comparisons between time histories of vertical displacements of cables in tandem for two levels of structural damping, with rain and 12 m/s wind speed. To study the influence of the structural damping on the rain/wind-induced vibration phenomenon, aerodynamic damping tests were carried out. The tests were performed systematically for four levels of structural damping for the cable with helical fillet, in tandem arrangement, with a +30° azimuth angle, with and without rain.
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The results are summarised in Figure 14. -1.2 At 12 m/s without rain, an important -1.6 contribution to the total damping was 0 0.5 1 1.5 2 Structural damping (% of critical) attributed to the aerodynamic damping. The decay tests with 12 m/s wind speed Figure 14: Variations of aerodynamic damping for and rain showed a drop of total damping dry and slowly drying cables for four levels of generally 2 or 3 minutes after the rain had structural damping. been stopped. This drop in total damping typically corresponded to the level of aerodynamic damping at 12 m/s for a dry cable. From this observation, it can be concluded that the presence of the lower rivulet transforms the aerodynamic shape of the cable so that a lift force (upward) is created. This lift force varies as a function of the apparent angle of attack of the wind when the cable is oscillating vertically. This variation of lift appears to annihilate the drag-induced lift that is the source of the aerodynamic damping.
4.
Conclusions
Rain/ wind–induced vibrations of a stay cable were reproduced in the laboratory for a single cable and for cables in tandem configuration. The vibrations were mitigated either by using an aerodynamic appendage to the cable, namely a 2.1 mm double helical fillet, or by increasing the level of modal damping. No marked differences were observed between the single and tandem cable configuration with regards to rain/wind vibrations. If anything, the propensity of developing axial flow might be larger for the tandem configuration, increasing the possibility of vibrations.
Acknowledgements Sundlink Contractors, the constructors of the Öresund Bridges, commissioned this wind-tunnel study. Their support and permission to write this paper is greatly acknowledged.
References [1] Hikami Y. & N. Shiraishi, “Rain-wind vibrations of cables in cable-stayed bridges”, J. of Wind Engineering. and Industrial Aerodynamics, 29 (1988), 409-419. [2] Langsoe H. E. & O.D. Larsen, “Generating mechanisms for cable stay oscillations at the Faroe Bridges”, in Proc. of Intl’l Conference on Cable-stayed Bridges, Bangkok, Nov. 1987, pp. 1023-1033. [3] Yoshimura T., T. Tanaka, N. Sasaki, S. Nakatani and S. Higa, “Rain-wind induced vibration of the cables of the Aratsu Bridge”, in Proc. of 10th Japanese National Conf. On Wind Engineering, Tokyo 1988, pp 127-132. [4] Matsumoto M., K. Yokoyama, T. Miyata, Y. Fujino and H. Yamaguchi, “Wind-induced vibrations of cable-stayed bridges in Japan”, in Proc. of Canada-Japan Workshop on Bridge Aerodynamics, Ottawa, Sept. 1989, pp. 101-110. [5] Matsumoto M, C.W. Knisely, N. Shiraishi, M. Kitazawa and T. Saito, “Inclined cable aerodynamics”, in Proc. of 1989 Structures Congress, San Francisco, May, pp. 81-90. [6] Geurts C.P.W., A.C.W.M. Vrouwenvelder, P.C. van Staalduinen & J.H. Reusink, “Numerical modelling of rain-wind induced vibrations: Erasmus Bridge in Rotterdam”, Structural Engineering International, Vol. 8, No. 2, May 1998. [7] Flammand O., “Rain-wind induced vibration of cables”, J. of Wind Engineering. and Industrial Aerodynamics, 57 (1995), 353-362.
Swietokrzyski Bridge, Warsaw Pekka PULKKINEN M.Sc. Civil Eng. MESTRA Engineering Ltd Helsinki, Finland
Pekka Pulkkinen, born 1955, received his Civil Eng. degree at the University of Oulu 1980.
Summary A bridge competition was organised 1997 to find technically the most innovative and progressive bridge solution over the river Wisla in Warsaw. A single pylon cable-stayed bridge proposed by Finnish and Polish designers was the winner of the competition. Many modern technical solutions were proposed in this bridge. The cable anchorage structures as well as the cross section of the superstructure have been designed in most economic and effective way. The aesthetics of the bridge was investigated very thoroughly.
1.
Introduction
The bridge is located in the heart of the city of Warsaw. The new bridge will be built just beside the existing bridge named Syreny bridge. The old bridge will be demolished after the new bridge is opened. The bridge will give a new outlook for the city and river banks. The building of the new bridge is a part of the bigger building project to improve the traffic conditions in Warsaw. The bridge is a cable stayed bridge of composite construction. The cable spans are 180 and 140 metres in length. The total length of the bridge is 448 metres. The total effective width of the bridge deck is 29.8 metres, consisting of four traffic lanes and bicycle and pedestrian lanes on both sides of the bridge deck. The bridge will be constructed in extremely short time, during 1998-2000.
Fig 1. Elevation
2. Aesthetics of the bridge During the competition phase many bridge types were studied. In order to fulfill all technical and aesthetic requirements set in competition documents a cable stayed bridge with single pylon was chosen as a final bridge type. Raising of the street level at bridge site was limited because the new bridge is a part of existing street connection. On the other hand the size of the navigation channel was determined to be relatively large. These reasons caused that the bridge should have quite a long main span and a slender superstructure. When considering the type of the pylon A-shape seemed to be superior. It gave good possibilities to design the shape of the pylon to be a land mark of the river crossing. At the top of the pylon there is a black cover plate which illustrates a key of piano. This reminds people of the remarkable musical background of Warsaw. The colour of the pylon will be light or natural white. The cable anchorages on the deck level are placed between the traffic and bicycle lanes. When approaching the bridge the passengers have a possibility to see the cables and the pylon fluently. Close to the pylon legs there are extensions of the deck designed to be places for rest and viewing the river banks. The rest stops are equipped with benches and they are covered by shelters made of steel.
Fig 2. The pylon
3.
Superstructure
The superstructure of the main bridge is a composite steel - concrete girder. In cable spans the cross section has two main longitudinal steel beams at the distance of 19.0 metres. The deck slab is a
reinforced cast in situ concrete slab. The distance between cross beams is 5.0 metres. The cross beams have cantilevers outside the main girders. The aerodynamic behaviour of the bridge was analysed in the conceptual design phase. The ratio between height and width of the cross section is only 0.08. In order to improve the ratio of natural frequencies of bending and torsion the weight of the cantilever slab and the height of the edge beam were reduced. In order to get more stiffness to the cross section outside the cable-stayed part two additional beams have been placed to the cross section. Four beams are also used at the negative moment area at the ballast abutment. The total amount of structural steel in cross section is only 180 kg/ m2, which is a relatively small amount. The superstructure is fixed to the ballast abutment. The uplift force at the abutment is balanced by a foundation slab and earth filling. There is only one expansion joint in the main bridge. The steel superstructure will be installed by launching. Launching will be carried out by using temporary supports at the main spans. The launching is proposed to be executed from both sides of the pylon. The concrete deck slab will be cast in 20 metres long sections.
Fig 3. Cross section of cable spans The cable forces are anchored directly to the webs of the main steel girders. The anchorage structure is simple and consists of stiffened steel web and guide pipe. The locations of cable anchorages don’t affect the spacing of cross beams. The stressing of cables will be carried out at the pylon top, therefore the space needed for cable anchors is minimised on the deck level. Forces due to eccentricities of guide pipes are eliminated by using short external centring pipes, which are installed after the stressing of cables.
Fig 4. Cable anchorage to the main girders
4.
Pylon and cables
The A-pylon is a 87.5 metres high concrete tower. The cross section of tower legs is hollow with a hole of φ 1.25 metres for maintenance purposes. In order to get smaller inclination in legs they are forced to penetrate the deck slab at the pylon. The bearings of superstructure have been placed on external cantilevers. The cable anchorages at the pylon top will be fixed to the concrete structure, there will be no steel boxes inside the tower. The cables are anchored to the concrete tower by penetrating cable guide pipes through the tower. In the crossing area the cables from Warsaw city side are placed to the inner side of the pylon. The pylons will be constructed by using climbing formwork. Each casting section will be about 4.2 metres in height. The stay cables consist of high quality parallel wires, which are protected against corrosion with hot-dip galvanising, grease and HDPE pipes. The colour of cables is white or light colour. The cable installation and stressing work will be made after the casting of the deck slab. The cables will be stressed at the pylon top.
Fig 5. The principle of cable anchorage at the pylon
5.
Foundations
The ground conditions of the bridge site are interesting. At first there are fills on both sides of the river. The filling material is mainly coarse; sand, gravel, concrete etc. Under the fills and the river base there is a sedimentary layer of sand. The material varies from fine sand to gravelly sand. The layer thickness changes a lot. The base layer consists of hard plastic cohesive material down to 100 metres depth. The soil is mainly clay and sandy clay. All supports are founded on cast in situ bored piles. The piles act partly as end-bearing and partly as cohesion piles. The diameter of piles is 1.5 metres, except at ballast abutment where the diameter is 1.2 metres. Raked piles are used for ballast forces, collision loadings and for launching forces during construction. Vertical piles are used only at pylon and abutment S1. Because of the soil conditions, a lot of attention has been given to the settlements of the pile foundations. FEM-analyses have been made to determine total settlements and deformations during the construction period. Full scale test loading of piles will be implemented during the piling works.
Fig 6. Swietokrzyski Bridge
The Design of the Zwolle Cable-stayed Bridge - Integrating Engineering with Aesthetics Robin SHAM Technical Director Maunsell Ltd Beckenham, UK Robin Sham, born 1954, received his BSc in 1978 (Birmingham) and PhD (Structural Engineering) in 1989 (Imperial College). He is Technical Director responsible for Bridges & Special Structures and was Maunsell’s Project Engineer for Zwolle Bridge.
Arie MONSTER Grontmij Consul.Eng. De Bilt, The Netherlands Arie Monster, born 1946, BSc in Civil Engineering. He works for the Structures for Roads & Waterways Department and is an experienced Project Manager for all types of bridges, viaducts and tunnels. He was Project Manager for the Zwolle Bridge
Introduction Between Stadshagen and Zwolle in the Netherlands, a landmark bridge now graces the environs of Zwarte Water and forms a subject for study on bridge aesthetics. As construction progressed the striking profile of the Zwolle Bridge emerged from Zwarte Water and captivated the admiration of the local residents and visitors alike. At dawn and in the golden sunset, the scene was one of the most spectacular of all bridge sites.
Fig 1 Zwolle Bridge, The Netherlands The Zwolle Bridge is an asymmetrical cable-stayed bridge with a single main span of some 56m and a continuous east approach span of 25m. The project also consists of a west approach viaduct and a bascule bridge. The steel bascule span closes the 18m gap between the cable-stayed main bridge and the west approach viaduct. The superstructure of the cable-stayed bridge consists of twin longitudinal spine beams 1000mm deep, with a concrete slab varying in depth from 250mm to 330mm, and cross girders at typically 4375mm centres. Longitudinal bending, shear and axial compression are primarily resisted by the twin spine beams and top flange. Transverse actions between the cable planes are resisted by the stiffening cross girders. The superstructure is monolithic with the bascule chamber, which forms the substructure to the pylon, and is continuous over the intermediate pier in the east approach span. The unique elegance of the Zwolle Bridge has been instrumental in the marketing of the Stadshagen development area. It has received extensive coverage in the regional and national press which has increased the profile of the development area. Local residents have shown great interest and pride in their new structure, especially as it is the first asymmetrical cable-stay structure in the whole of the Netherlands.
Design Consideration of bridge architecture dictates that the pylons are located as close to the Stadshagen side of Zwarte Water as possible, to compliment two apartment development areas. Clarity, light, space and water are the key elements considered in the architectural design of the structure. The shape of the pylons is architecturally unique and brilliant. The flow of forces are well communicated by the shape and form. The rationale for the overall aesthetics is motivated by the desire to maximise the intensity of light that can be cast on the pylons - leaf shafts which represent masts are therefore adopted to maximise the surface area while providing a sufficient horizontal cross section to enable column action. Careful consideration has been given to the projection of light on the structure, including shadow during Fig 2 - Effect of Light & daylight and illumination at night. Each leaf shaft is 17 metres wide, tapering to a knife blade-like point at the top. A number of Shadow options for the curved profile would be feasible - circular, polygonal and parabolic. A parabolic profile was adopted by virtue of the smooth flow which it introduces to the system. To improve the stability of the asymmetrical cable-stayed superstructure, the weight of the main span is counterbalanced by inclining the pylons backwards. This combines structural efficiency and aesthetics. The self weight of the pylons are not sufficient to balance the overturning moment from the deck. To compliment this and thereby to control the tension in the near face, each pylon shaft is prestressed vertically from the base of the Bascule chamber to a height of 22.5m above deck level. The cellar was designed such that the cables could be drawn up the pylons from within the Bascule chamber. Prior to cable installation the prestress in the pylons are inefficiently positioned. The prestress adds to the tension on the front face. The centre of action of the forces on the bascule chamber lies outside and behind the footprint of the bascule chamber. The leaf Fig 3 - Stillness versus shafts would normally have been continued down to pile cap level Motion had it not been for the need for a bascule chamber for accommodating the electrical and mechanical installations for the adjacent bascule bridge. The pylon shafts are cast monolithically with the bascule chamber which thereby reduces their effective buckling length. The need for a bascule chamber is therefore exploited in the design to optimise functional requirements and structural efficiency. If the pylons lean forwards, they will still be aesthetically interesting although structurally inefficient in terms of the counterbalance which they provide for the weight of the main span. In the conceptual development of Zwolle Bridge, it is logical to consider rotating the pylons backwards, away from the navigation span. As the pylons become vertical, the centroid of the pylon stems shift longitudinally outside the main span. Further rotation backwards instigates a counterweight action whereby the self-weight of the pylons assists in stabilising the superstructure system. A ground investigation showed that the site consists primarily of wellcompacted sands. However, layers of soft silt are found in the river channel. During the design, the possibility of adopting a spread footing for the foundation of the bascule chamber was examined. It was judged and then proven by analysis that the behaviour of the cable-stayed
bridge would be sensitive to stiffness of the foundation. A piled foundation was therefore chosen. The piles are in tension during construction and this condition determines their length. In order to achieve a clean profile, the twin leaf shafts are designed to remain stable without the need for cross bracing. The pylon shafts are at a maximum height of 43.35m above deck level and 50m above mean water level. The rear face of each pylon shaft is notched to accommodate the bascule steel span in its opened position, thus completing a smooth pylon outline whenever the bascule span is raised. The notches add further character to the profile and provide visual relief where it is warranted. The cross section of the superstructure, as well as the highway layout over the deck, are asymmetrical. The design allows for future widening of the deck Fig 4 - Rear Face of on one side to accommodate a revised Pylon Shaft Notched to highway cross section. (Should this be Fit Bascule Span required with further development of the Stadshagen area). The lateral position of the pylon shafts has been configured to permit deck widening. The final concept is one in which the shafts are inboard of the edges of the running deck. If the shafts were located outboard of the deck, the need for additional clearance to allow for deck widening would have resulted in an increased horizontal separation of the shafts. This would risk the introduction of horizontal bracing for stability against buckling and thereby ruin the clean aesthetics of the pylon design. Fig 5 - Tour de Force There are five cables to each pylon shaft and each cable is threaded obliquely through, in deviator pipes, and anchored at recesses in the rear face to permit access to cable anchors for inspection, maintenance and potential re-stressing. At the lower end access would be more difficult as the anchorages will be over Zwarte Water. Here the cables are anchored on the underside of the deck slab, outside the longitudinal spine beam girders, at every second cross girder. The in situ concrete anchorages are functional as well as being a deliberate architectural statement. They are integrated with the grillage beam system, thus accommodating the geometric variation and injecting the cable loads directly into the main beams.
Construction Construction of the 17m-long by 15m wide bascule chamber commenced through pouring a 1m-thick concrete slab under water.
Fig 6 - Variation of Geometry with Viewpoint
Fig 7 - Cable Anchorage - A Deliberate Statement Fig 8 - The Bascule Chamber under Construction
A further 2.3m was added to form the reinforced concrete base slab. The bascule camber is some 10.5m high, with side walls rising to form the monolithic base of the pylon shafts. Pylon construction commenced in September 1997 and was completed by the end of the year. The pylon shafts were constructed in 4.5m lifts at an average rate of one pour per pylon per week. Once construction had reached 22.5m above deck level each shaft was prestressed. Pylon construction was completed after grouting of the prestressing tendons. The lift size was influenced by the architectural imprint which appears on the pylon leaves. Aesthetics considerations also dictated the layout of the shuttering boards - to ensure that the pylon faces are embossed with a particular quilt like pattern. The pylon was constructed using climbing falsework which moved up the pylons as the construction progressed. All the cable stays appear to be the same size despite the actual number of strands they contain. The visually smooth appearance of the cables is enhanced by providing protective casings over cable correction details, which eliminate sharp changes Fig 9 - Construction of Pylon Shafts in profile.
Fig 10 - Embossed Pylon Face
The construction of the superstructure was investigated and carefully controlled by an erection sequence analysis. Over half of the 56m cable-stayed span, to a point just beyond the third cable, was constructed on falsework. After three cables were fixed from each pylon shaft to the edge of the deck, the falsework was then removed.
Zwolle bridge was officially opened on 19 September 1998 and it has added to the worlds repertoire of landmark structures.
Fig 11 Superstructure under Construction
Fig 12 - Maximising the Intensity of Light
Acknowledgement Client: Consultant:
City of Zwolle, the Netherlands Grontmij Traffic & Infrastructure, The Netherlands Cable-Stayed Bridge Sub-Consultant: Maunsell Limited, United Kingdom Architect: Maarten Struijs, Gemeentewerken Rotterdam, The Netherlands
Fig 13 - Combining Functionality with Aesthetics
Accuracy Control On the Construction of Tatara Bridge Yasuhito MANABE Mukaishima Office, HonshuShikoku Bridge Authority, Hiroshima, Japan
Nobuyuki HIRAHARA Tokyo Office, HonshuShikoku Bridge Authority Tokyo, Japan
Nobuo MUKASA Mitsubishi Heavy Ind. Co.Ltd Hiroshima, Japan
Masashi YABUNO Ishikawajima-Harima Heavy Ind. Hiroshima, Japan
Summary Tatara Bridge is a world’s longest steel-concrete hybrid cable stayed bridge, constructed by Honshu-Shikoku Bridge Authority on the “Onomichi- Imabari” root. The center span is 890m long, and a part of side span is concrete . Deck girder section is structured by 3-chambers. This bridge is much flexible because not only by it’s length but also the low girder- depth (the girder-depth / span-length ratio is about 1/300). This flexibility cause a large deformation while the erection of girder. The largest vertical deformation at the edge of girder caused by the loading of deck-block while erection was more 2 m. Such a flexibility of structure, it was difficult to complete the bridge accurately with controlling cable tension as used on general sized cable stayed bridges. Because the geometric error would be large with only controlling the tensions. So, for the accurately erection of Tatara Bridge, we gave account on the geometrical controlling included length of each member. By those controlling, Tatara Bridge was completed accurately.
Fig-1 General view of the Tatara Bridge
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Fig-2 The procedure of erection of superstructure
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1. Outline of erection of superstructure Fig-2 shows the procedure of erection of superstructure. At first, the lower part of tower and inclined support were erected by floating crane(F.C.), and then large block of deck around tower was erected. Upper part of tower was erected block by block. The side span was consisted by steel and PC deck. Immediately after the completion of the tower, steel deck between P2 to 2P was erected by F.C. by large block, because the length of steel section was shorter than 3P side. For the erection of side span of 3P side, the span was long that it was impossible erected by a large block. So, at the first stage of the erection near the tower, balancing erection method was applied. It was the method erecting deck by each short block alternatively adjusting the balance between center and side span. When the distance from the edge of erected deck to the PC deck became 100 m then large steel deck block was erected by F.C. The deck of center span was erected by traveler crane in short block. The deck was jointed by welding in upper flange, bolted by high tensile bolt in web and lower flange.
2. Basic philosophy for accuracy control 2.1 Structural characteristics of Tatara Bridge For the controlling of accuracy of this bridge, the structural characteristics should be cleared. So, the calculation considering some error factor was carried out. a) Tolerance of member length The error of deck length effect for the geometrical accuracy. If the deck was 2mm longer in 10m length block, the deck level came to be 320mm higher at the center of span. The effect for the cable tension is few, so negligible. The error of stay cable length also much effective for the geometrical accuracy of the deck. The cable tension is insensible, so the controlling of cable tension is not applicable for the accuracy controlling. b) Tolerance of straightness The deck structure shows high convergency. While if the each deck block have same tolerance of angle, geometrical tolerance of whole of deck is negligible it expected making large curvature. Local tolerance of angle remain after completion and it is hard to be collect. But the effect also locally and negligible in whole structure. c) Tolerance of Dead weight If considering the 5% error in dead weight, vertical 170mm deformation will be caused at the center of middle span. Then the tension change about 18 ton. The dead weight of PC deck is large but they were supported themselves, so the effect for the whole structure was few and negligible. d) Tolerance of cable tension The effect of dead weight of deck for the cable tension is few. If the dead weight changed 5%, the tension changed only 2 - 3% . So, the tolerance of cable tension caused by the dead weight is negligible for the geometry of the deck. But if the cable tension is controlled satisfying the design value without considering the error of dead weight, large deformation of deck would be caused
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(in order of meter). Because the tension not correspond to the dead weight play as the prestressing. So the tension controlling was not suitable by the effect to geometrical accuracy. e) Tolerance of deck closing work The structure is so flexible that the force pulling the deck for closing is small and easy to do. But the tolerance caused by the closing work remain locally around the closing joint. f) Tolerance of stiffness Calculation considering the 5% tolerance of bending and elongation stiffness for deck and tower was done. The result shows that the effects for sectional force and deformation were few and negligible. Calculation considering the 1% tolerance for the elongation stiffness for stay cable also done, and the effect was negligible. g) Geometrical tolerance of PC deck The PC deck of side span have high bending stiffness because of it’s short span. So the controlling of geometry is difficult by it’s rigidity. The characteristics of structure got by calculations are summarized as follows; • the effects of tolerances of dead weight and stiffness are few for the geometrical accuracy. The change of stress also in the range of margin considered at design. • the tolerance of member length effect for the geometrical accuracy, but few for the tension of stay cable and sectional forces of deck and tower. • a large deformation would be caused by the controlling the cable tension, adjusting for the design value without the consideration of tolerance of dead weight . So such a usual and traditional method was not suitable for this bridge. • controlling of the globally geometric of structure effect few for the sectional forces (the change of them are in the range of margin considered at design) . 2.2 Basic philosophy for accuracy control By the result of the study for the characteristics of structure, we decided the basic philosophy for accuracy control of erection of deck. a) at site, geometric of deck are mainly controlled, but cable stresses are not. The tension of stay cables are observed for the references only but not for the controlling. b) the controlling of length of member are emphasized. c) controlling of member length is based on the fabrication data observed in workshops because of the accuracy of data itself. Also the observed value at site considered supplementary. Off cause, the data of PC deck was given only in site. d) the measuring and controlling were done when a same level of stays of center and side span were erected. e) if the controlling by spacer plate at anchor of stay cable was required, it was planed to be done only a stay cable at edge block. (actually, only measurement work done in night, but such a installing work never done because the controlling at daytime satisfied the requirement.) f) geometrical data were measured while night time, under constant temperature state. g) controlling of length of stay cable by spacer plate were done for collecting the geometry of deck, because the structural characteristics and for the performance of the road. h) controlling of geometry of PC deck is impossible. So the setting direction of jointing girder was decided to be not effective for whole structure. Also, the coordinate of stay anchor in PC deck was measured before erection of stay, and the error in them are collected by spacer plate. i) effect of deformation by creep is negligible, so it never considered in controlling in each step.
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The distinction of geometrical accuracy controlling of Tatara Bridge is given by the controlling of length of the member fabricated in workshops. The measurement in site is only a checking of erected geometry. By such a controlling, the works in site for accuracy controlling would be reduced. pre-measuring data in workshops the height of tower (accumulated),steel deck length (accumulated), PC deck length (measured in site),length of stay cables (the length of gage wire)
definition of thickness of spacer plate
erection of cable
measurement for controlling (at each erection step) lean of tower camber of deck tension of stay cable temperature of bridge controlling by spacer plate
measurement for tolerance factor axial force of inclined support straightness of deck the length of deck shrinkage by site welding weight of deck block (in workshops) weight of stay cable
calculation of tolerance collection for temperature
NO judgment YES next erection step
Fig-3 Flow chart of accuracy control
3. Target of accuracy control in erection Target allowable range of accuracy in erection is; sectional forces: in a range of margin equal 5% of design sectional forces geometry of deck: allowable range decided for the completed state are applied for erection
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-110
+110
+110
-110
[unit:mm]
+235 +55
+80
-55 1A P1 P2 2P 50m 50m 170m
-235
-80 3P
890m 1480m
270m
P3 4P 50m
Fig- 4 Target value of accuracy control
4. Measuring system Whole construction work of superstructure was divided into two joint venture, 2P and 3P side. Each of them had own measuring system, but the logic of calculation and the basic method for accuracy controlling were same. Table-1 shows the characteristics of measuring system of both.
lean of tower
2P JV optical range finder (measure 2 point automatically)
camber of deck
3P JV vertical collimator (collimate directory with CCD camera) water gage (pressure sensor system :measuring the difference of pressure)
water gage (magnetic strain system :measuring the water level by magnetized float ) tension of stay accelerometer cable (calculate the tension by natural frequency) temperature thermocouple (automatically ) calculation non-linear calculation (systematized by EWS) others automatically measuring for all data automatically except for the lean of tower Table-1 Comparison of characteristics of measuring system
5. Actual result of accuracy control 5.1 Workshops In workshops, the length of each member was measured and controlled with cumulated tolerance. The cumulated tolerance were under 10 mm in total length of tower and deck, it means the each parts were fabricated with few tolerances. 6
The tower blocks’ jointing edge were faced by facing (cutting) machine. The deck blocks were welded under temperature control, the difference of temperature of upper and bottom flange is less than 2 degrees. The accuracy of data itself got at workshops were high, so the reliability of the accumulated data also high. The measuring of length of stay cable were impossible because of it’s length, the longest one is about 460m. So they were controlled by the length of gage wire. The actual measuring of length of stay cables were impossible. But, as mentioned below, it was estimated that the major uncertainty factor was originated by this tolerance of stay length because the tower and deck were measured accurately. 5.2 Result of measurement for accuracy control in erection In balancing erection of 3P side, the edge of deck of center span deformed downward, side span upward and the tower top leftward (2P side). They means the total structure leaning leftward. It was caused by the weight of traveler crane on the edge of deck of center span. The state in balancing erection was easily deform by small load, so the estimation of factor cause the tolerance
Fig-5 The geometrical tolerance and the cable tension tolerance (when the center span was closed) 7
was difficult. Considered such a situations, the controlling of length of stay cable were never done in balancing erection. In cantilever erection state, after the side span was jointed with PC girder, edge of deck of center span deformed upward, side span downward and the tower top lean outer side of bridge, both 2P and 3P. Such a tendency was shown clearly after the erection of stay cable anchored in PC deck. If they were left without any control, the deck level at the center estimated was over allowable range, 235 mm when the bridge completed. So the length of stay cable were controlled by the erection of stays anchored in PC deck, installing the spacer plate. The thickness of spacer plate were calculated based on the tolerance of deck level. The tolerance of deck level at the edge of deck of center span was 150mm upward than design. By the result of measuring of them after closing of span, the decreased of tolerance was about 100 - 150 mm locally around the center. Fig-5 shows the geometrical tolerance when the deck was closed
6. Analysis of tolerance factors 6.1 Outline of tolerances As mentioned above, in cantilever erection state, the structure lean outer side of bridge, both 2P and 3P. Such a tendency was shown clearly with the progress of erection. The deck near the center of main span deformed upward just before the closing. And it was decreased 100 - 150 mm by closing locally around the center. The factor of tolerance after the closing of deck, was needed to be considerate special local condition. So the analysis of the tolerance factor was done individually, before closing and after closing. 6.2 The analysis of tolerance factor at cantilever erection In cantilever erection state, edge of deck of center span deformed upward, both 2P and 3P. This tolerance grew with the progress of erection. This tendency shown clearly after the erection of stay cable anchored in PC deck. So the analysis of tolerance factor was done at the erection step12(2P) and step-14(3P). The number 12 and 14 means that the stay cable number counted from the lower, so the step-12 means the erection of 12th stay cable. By the analysis, the half of tolerance was caused by these 4 factors; dead weight of steel deck, temperature of bridge, weight of erection facility and creep of PC deck. The factor cause another half’s was assumed as uncertain factor. Uncertain factor was conversed for the thickness of spacer collecting the length of stay cable. After those steps, the thickness of spacer (it means the effect of uncertain factor) was controlled. The tolerance caused by the factor already had been cleared were left without any controlling. By the calculation considering those effects, the deck would be deformed upward about 150mm at just before the closing. Actually this tolerance was measured for such situation.
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Fig-6 Chart of analysis of tolerance factor 6.3 The analysis of tolerance factor after the closing The tolerance of deck level at the edge of erection of center span was 150mm upward than design. This value equal to the analysis of tolerance factor mentioned above. But, by the measurement after closing of span, the tolerance was decreased about 100 - 150 mm locally around the center. The tolerance factor of such behaviors was analyzed. The closing work was done in summer, the hottest season. For the welding work, the root-gap was set as 3mm, but it became narrow by the elongation of deck caused by the high temperature. The decks touched each other and welding work came to be difficult. So the gap was recreated by gas cutting for easy welding. It was assumed this gas cutting done in site cause the error of angle of welding face, and it cause the deformation to downward at center block. So calculation considering such deformation angle was done. By the result of calculation, the angle of joint welding face changed 6mm, then the deck of center would be deformed about 100mm locally. This result explains the actual situation. This 6 mm is appropriate consider the original 3 mm + gas cutting 3 mm. Another calculations, considering the error of length of center block, or another factor, never explain actual situation. So the factor cause this local tolerance is the change of face angle of welding.
Conclusions and acknowledges Tatara Bridge is the world’s longest cable stayed bridge not only the 890m center span, but also the length of cantilever erection. The structure is much flexible and this flexibility cause the large deformation. The accuracy control was difficult by this flexibility. From the phase of fabrication in workshops, the length of every member were measured and the tolerance was controlled severely. Also in the phase of erection at site, worked for the reproduce of the accuracy of fabrication in workshops. By those endeavors, Tatara Bridge was completed with high accuracy. Everyone relate for this work pride this result. This result and experiences, construct with the controlling the member length geometrical, will help the construction of long span cable stayed bridge in future. We thank everyone who related this work for the completion with high accuracy, and no accident.
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References [1].
Yukikazu Yanaka, Tsutomu Takazawa and Nobuyuki Hirahara ; Erection of the Tatara Bridg’s Superstructure, Proceedings of the IABSE Symposium Kobe ,1998
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Bridges with Multiple Cable-Stayed Spans Michel VIRLOGEUX Consulting Engineer and Designer President of fib Bonnelles, France
Michel Virlogeux, born 1946, worked as civil servant in Tunisia (1970-1974) and then in France at the SETRA. Head of the large bridge division (1980-1994), he designed many bridges among which the Normandie Bridge and the Ré Island Bridge. Now Consulting engineer, he worked as consultant for the Portuguese Administration for the Vasco de Gama bridge.
Summary This paper is devoted to a very important development of cable-stayed bridges, bridges with multiple cable-stayed spans. Beginning with historical reference to pioneer bridges by Ricardo Morandi, it evokes the very few bridges built with several cable-stayed spans and the projects which were proposed without success. It ends with the presentation of recent and important projects which evidence the possibilities of this new concept for wide river and sea crossings. 1.
Historical background
As everyone knows, the first attempts to erect cable-stayed bridges in the beginning of the 19th century were unsuccessful with the collapse of the Tweed and Saale bridges; engineers ignored at the time the real flow of forces and did not seriously consider wind effects even with a simplified and purely static approach. The famous French scientist Navier "demonstrated" that cable-stayed bridges were unsafe and that suspension bridges were to be preferred. This stopped the development during a very long time, and cable-stays were only used in some suspension bridges close to the pylons to stiffen the system; the best example is the Brooklyn Bridge, but many others could be cited. In France, at the turn of the century, Gisclard increased the role of cable-stays in his personal composite design associating suspension and cable-staying. The first very pure cable-stayed bridge has been built in Spain by Eduardo Torroja in 1925, in concrete, a cable just replacing a pier which could not be installed due to the site. But the real and scientific development of cable-stayed bridges came with the ideas and the papers by Franz Dischinger in the late thirties and beginning forties. Surprisingly, the first application was in France by Albert Caquot, in 1952 and in reinforced concrete, for the bridge over the Donzère Canal, some years before the well-known Stromsund bridge in Sweden. Everyone knows the fantastic development of cable-stayed bridges which followed, in Germany in a first step and in the whole world later. But in the same time as the concept of modern cable-stayed bridges was being developed, with "flexible" pylons and a continuous deck - and later with multiple cable-stays following Helmut Homberg, total suspension initiated by Fritz Leonhardt and very flexible decks developed by René Walther and Jorg Schlaich - Ricardo Morandi developed his own concept in a different direction, with extremely rigid pylons (inverted V shape longitudinally, with an additional V to support the deck), rigidly connected to a deck section cantilevering on both sides, and with simply supported spans to close bays between the different cantilevers tied to their pylons. The first application of this concept was the Maracaibo Bridge, designed by Morandi and completed in 1962, with six pylons and five main cable-stayed spans 235 metres
long (figure 1). The same principle was used by Morandi, but with two pylons only, for the Wadi Kuf Bridge in Libya (main span 282 metres in 1971), and for the Polcevera Creek viaduct near Genoa in Italy, with three pylons and two main cable-stayed spans (208 metres in 1964). It has been reproduced only once by another designer for the Chaco Corrientes Bridge in Argentina with two pylons (245 metres in 1973).
Figure 1 - Structural concept of the Maracaibo Bridge 2.
The specific problem of multiple cable-stayed spans
As we shall see, the concept of Morandi's bridges is perfectly adapted to the specific problem of bridges with multiple cable-stayed spans. Though evident, these problems must be evoked. 2.1 In a classical cable-stayed bridge with three spans, loading the main span produces its downwards deflection and due to the tension variation in cable-stays the pylons bend towards the loaded span; the cable-stays which suspend side-spans receive a tension variation to balance horizontal forces in the pylons but due to the limited rigidity of the deck it deflects upwards and tension variations are concentrated in the backstays, anchored at the abutment and which have anchorages fixed vertically due
Figure 2 - Structural behaviour of a classical three-span cable-stayed bridge
to their position (figure 2). This unequal distribution of tension variations in the cable-stays which suspend the side-spans produces important bending forces in the pylons: the backstays, anchored on top, balance alone the tension variations in the cable-stays suspending the main span. This is why it is necessary to concentrate cable anchorages when the cable-stayed bridge has this classical configuration: the reduction of the distances between anchorages in the pylons reduces the bending moments. When a side-span is loaded, it deflects downwards, and due to the tension variation in the corresponding cable-stays, the adjacent pylon deflects towards the loaded span; thus the tension decreases in the backstays and in the same time the main span deflects upwards. The backstays have a very specific role to stabilize the pylons, and receive the largest tension variations in the bridge. We have the same situation with cable-stayed bridges continuously extended by access spans on both sides, where the group of cable-stays anchored close to the first pier on each side acts as backstays; and with cable-stayed bridges having two spans, one shorter with the backstays anchored at the corresponding abutment. As demonstrated in many occasions, for example for the Seyssel Bridge (Travaux, October, 1988), 2.2 the design of classical cable-stayed bridges can be improved by the installation of intermediate supports in the side-spans: when the main span is loaded, all cable-stays anchored in the side-spans act as backstays since they are tied to an almost fixed deck at their lower anchorage; the deflection of pylons towards the loaded span is thus reduced and the efficiency of cable-staying increased; even the downwards deflections of the main span is reduced by the greater rigidity of the system. And when side-spans are loaded, the load directly passes in the intermediate supports and there is practically no effect in pylons and main span. The same of course applies to a cable-stayed bridge with two spans, when intermediate piers are installed in the shorter one. If we consider now a bridge with multiple cable-stayed spans, the situation is very different. 2.3 When one span is loaded, it deflects downwards; the corresponding cable-stays receive an increased tension; the adjacent pylons deflect towards the loaded span and the adjacent spans upwards without any other restraint than their own rigidity. There is no more any backstaying effect (figure 3). Deflections can be only limited by the rigidity of pylons or deck, or of pylons and deck.
Figure 3 – Structural behaviour of a bridge with multiple cable-stayed spans
The situation appears even more critical with the effects obtained when loading one of the adjacent spans: the span which was deflecting downwards with the load now deflects upwards with large bending moments, and the adjacent pylons deflect in the opposite directions. The design must produce the necessary rigidity. One of the possible solutions consists in rigidly 2.4 connecting the pier below the pylon, the deck and the pylon, so that the pier rigidity takes part in the restriction of deflections. But this immediately produces a new problem: the structural system must adapt to the length variations in the deck due to the elastic shortening produced by prestressing forces installed after span closure, to temperature variations and also to concrete creep and shrinkage. 3.
The Morandi's concept
Clearly the concept developed by Ricardo Morandi perfectly answers the different questions: the 3.1 pylons are extremely rigid and can directly balance the effects of live loads on either sides; and with the simply supported spans between the cantilevers supported by the pylons, length variations can freely develop. The single drawback of this solution is its high cost and weight; this is why - though it must be considered as the pioneer one for multiple cable-stayed spans - it has not been reproduced. 3.2 But it inspired many designs, though none of them received an application. - We can mention the project proposed in 1967 by Ulrich Finsterwalder for the Great Belt Bridge, with solid and rigid pylons suspending a series of spans 350 metres long, with a very flexible deck and expansion joints at mid-span in each bay ([5] p. 38; [7] pp. 17-20-33; [9] p. 142). - And also the project for a bridge across the river Ganges in India, designed by Fritz Leonhardt with ten pylons and nine central spans 159 metres long. Pylons were also solid and rigid, allowing for a limitation in the number of expansion joints, only in some spans ([4] pp. 28-42-45; [7] pp. 33-34). More recently, the Grands Travaux de Marseille - GTM- developed two important projects which had no more success than the previous ones for the Great Belt and the River Ganges. - The first one is part of the GTM Channel Project prepared in the early eighties, which comprised a bridge on each side of the Channel to give access to a central immersed tunnel. Each of these bridges was made of a series of complete cable-stayed cantilevers - composite deck rigidly connected to the concrete pylon, and cable-stays -, totally prefabricated and installed with the help of heavy floating cranes on the corresponding piers; the cantilevers were joined by drop-in spans to constitute a series of typical spans 520 metres long. This project was in the same time a prefiguration of the Rion-Antirion conceptual design, and one of the first attempts to develop heavy prefabrication techniques which received large applications later with the Storebelt Western Bridge, the Second Severn Crossing and the Confederation Bridge in Canada. - The second one, very much inspired from the Channel project, has been jointly proposed by GTM and Campenon-Bernard for the Ré Island Bridge in 1986. The same concept was used of complete cablestayed cantilevers - totally in prestressed concrete this time -, prefabricated and installed on the piers. But with spans limited to 140 metres, the cantilevers were only joined by expansion joints at mid-span in each bay. The cross-section of the deck, proposed by Jean Muller and inspired from a previous idea by Pierre Xercavins, consisted in a flat slab stiffened by multiple floor-beams and with side walks at a lower level to produce the desired rigidity; we developed and applied this concept for the Burgundy Bridge at Chalonsur-Saône (Travaux, October, 1991 and July-August, 1992). - GTM came back to these principles and very close to Morandi's ideas with the conceptual design of the Rion- Antirion bridge, developed in the late eighties by Jean-Paul Teyssandier, François Lempérière and Yves Maury's team. The bridge is made of four cable-stayed cantilevers, each resting on a large foundation caisson which constitutes a pier in the same time, and of simple spans between the cantilevers. Each cantilever consists in a four-legged pylon, rigidly connected to the composite deck, and of two cantilever arms, 255 metres long from the pier axis. Each central span, 560 metres long, is made of two cantilever arms - coming from the two adjacent pylons - and of a simple span 50 metres long. Each sidespan is made of one cable-stayed cantilever hanging from the corresponding pylon, also 255 metres long,
Figure 4 – The peliminary design of the Rion-Antirion Bridge
and of a single span 50 metres long to join the cantilever with the end support (figure 4). The sole difference with Morandi's design is that the cantilever - with its pylon - is not rigidly connected to the pier below; to reduce seismic forces, the cantilever is installed on sliding bearings with a system of large dampers in both directions - longitudinal and transverse - to limit seismic movements. We shall see later how this initial concept has been amended and improved for a much better design. 4.
Typical solutions
4.1 Some other solutions than the Morandi's concept can be considered, though many of them are not extremely elegant (figure 5). 4.2 One consists in introducing an intermediate support at mid-span in every second span. Of course this is not always possible, and this is certainly the weakest way to introduce the necessary rigidity. Fortunately, nobody dared doing it. 4.3 The second solution is inspired from suspension bridges, which are even less adapted to the concept of multiple spans than cable-stayed bridges. To prevent pylons from bending towards the loaded spans, they are connected from head to head by horizontal cables, headcables ("câbles de tête" in French). Several French bridges built in the first half of the century have several suspended spans with such headcables ; we can cite the bridges at Châteauneuf-sur-Loire, Langeais … The same could be done for cable-stayed bridges, though this solution is probably not so efficient as for suspension bridges since the structural rigidity of cable-stays is greater ; the additional effects of headcables may be more limited. In addition this does not look so elegant, with the introduction of a new line in the structure, reducing the architectural simplicity. A unique project referred to this technique, the winning design of the Poole Harbour competition, but construction is not yet decided. 4.4 A third solution consists in introducing, in addition to the classical cable-stays distributed to carry the deck loads, diagonal cable-stays which are only installed to stiffen the pylons; a typical diagonal cable is anchored on top of a pylon and at the deck level in one of the two adjacent pylons. Once again, this solution introduces a new line in the structure, reducing the architectural simplicity. It has been adopted by Jorg Schlaich for the design of the Ting Kau Bridge in Hong Kong. Since it has only three pylons and two central cable-stayed spans, only the central pylon had to be stabilized by diagonal cables of this type.
The composite deck is supported on the piers by classical bearings so that length variations can easily develop. Almost the same idea consists in installing cable-stays from each pylon beyond the mid-span section of the two adjacent spans; the central part of each bay is thus suspended from both adjacent pylons. But this can be efficient only if the deck has a rather large rigidity. 4.5 Fritz Leonhardt proposed a last solution many years ago ; it consists in amending the distribution of spans with a longer and a shorter one for each group of two. With a ratio of about 0.90 to 1.10 or 0.85 to 1.15, the shorter span stiffens the longer one. But this system also has serious drawbacks ; the differences in span lengths and in the distribution of stays, is not so elegant, and in addition the distribution of permanent loads is not well balanced, calling for serious amendments. The Macau Bridge - designed by José Luis Cancio Martins with two central cable-stayed spans 112 metres long - can be related to this concept ; with two pylons and a very short span between the two main spans, it works like two successive and independent cable-stayed bridges and cannot be considered as a real reference for bridges with multiple cable-stayed spans. It has been completed in 1994 ([11] p. 52; [12]).
Figure 5 – A series of more or less acceptable solutions for multiple cable-stayed spans
5.
Distribution of rigidities
5.1 Finally, the best solution appears to be the research of an adapted distribution of rigidities between deck, piers and pylons to resist bending forces and limit deflections (figure 6). From one extreme to the other, several solutions can be considered :
- on the one hand, we can have a very rigid deck and flexible pylons on condition that spans are not too long. Then the deck can be simply supported on the piers with pylons rigidly connected to the deck for simplicity. - Rigidity can be distributed between piers, deck and pylons with a careful attention to the deck length variations. - And on the other hand, we can have a very flexible deck on condition to have rigid pylons, either by their shape (an inverted V, longitudinally) or their dimensions. Of course, bending moments must pass from pylons to piers, either through two lines of bearings to adapt to length variations or with a rigid connection between pylon and pier on condition that the design of piers adapts to the deck length variations.
Figure 6 – Distribution of rigidity between piers, deck and pylons 5.2 As already mentioned, length variations are produced in the deck by the elastic shortening induced by prestressing forces installed in the structure after the span closure, by temperature variations and by concrete shrinkage and creep. The design must be such that they can develop almost freely. Three solutions can be proposed (figure 7). - The first one consists in installing between piers and deck special bearings, sliding except on one, two or three central piers - the number depending on the piers flexibility - where fixed bearings can be introduced. There may be only one line of bearings on each pier if the deck is extremely rigid as already shown (paragraph 5. 1) but there must be two lines of bearings to take advantage of the piers rigidity. This solution is not so simple due to two different problems: if the bridge is very long, the displacements produced by length variations produce load eccentricity (the deck and pylons move on the piers and receive excentered reactions) ; and due to the heavy loads on the supports, friction on sliding bearings can produce important bending forces in high piers. - The second solution is more efficient and more elegant. It consists in producing a rigid connection between the deck - which may be rather flexible - and piers made of two flexible parallel shafts. Such piers are extremely rigid as regards rotations, but rather flexible as regards length variations in the deck. This concept of twin flexible shafts was developed by Jacques Mathivat in the early sixties.
Figure 7 – Solutions to allow for length variations with rigid piers - The last solution consists in introducing an expansion joint in some - few - spans. But to avoid an increase in vertical deflections, the continuity of bending moments can be restored by introducing a steel continuity beam in the deck (figure 8) ; as done for example by Jean Muller for the Rogerville viaduct, a rather classical prestressed concrete box-girder bridge. But this is possible only with a box-girder deck of rather large dimensions, just to leave the necessary place.
Figure 8 – A continuity beam to transfer bending moments through a joint 5.3 Though some of these ideas already appeared in one or two early projects, such as twin flexible shafts, no real application was made of this global concept. 5.4 We can only mention that after the first competition for the Storebelt crossing another project was proposed in Denmark for the Samso Belt, in 1972, this time with a continuous deck ; the project had four spans 264 - 624 - 624 and 264 metres long ([5] pp. 313-314). The lateral pylons were stabilized by backstays but the central one had to receive a very large rigidity. Of course - and as for almost all the other bridges which will be evoked in this paragraph - the situation is extremely favourable with only four spans. 5.5 Since this time some medium-span cable-stayed bridges have been built, almost unnoticed, with several cable-stayed spans.
The first one is the Kwang Fu bridge in Taiwan, designed by T.Y Lin and completed in 1978 ([11] p. 10). It has three pylons and two central cable-stayed spans, 134 metres long ; pylons have classical shapes and a limited rigidity ; the effects of traffic loads are balanced by bending forces in pylons and deck - which has a rather large flexural rigidity as compared to the span - and also by the side-spans with cables acting as backstays due to the high deck rigidity. These backstays control the deflection in the lateral pylons, only the central pylon being really flexible. Such a design has been reproduced in Spain for the Colindres Bridge completed in 1993 with three pylons again and two central spans 125 metres long ([11] p. 49). But the most important application has been for the construction of the Mezcala Bridge in Mexico, still with three pylons and two main spans 312 metres long, completed in 1993 ([11] p. 44). Due to some specific site conditions controlling the distribution of spans, the central pylon is taller than the lateral ones, as in the Ting Kau Bridge. We must insist on the favourable situation of these bridges with only three pylons and two central cablestayed spans. This is only an intermediate step between classical cable-stayed bridges with two pylons and a central span and the real multispan cable-stayed bridges. The single application of really multiple cablestayed spans is the Arena viaduct in Spain, designed by Juan José Arenas and completed in 1993, with six pylons and five central spans, 105 metres long ([11] p. 48). But the reduced span length limits the rigidity problems in this bridge and prevents learning much from its design: the classical rigidity of deck and pylons is perfectly adapted to the forces in such spans. We must add that in all these bridges - Kwang Fu, Colindres, Mezcala and Arena - the deck is supported on the piers with classical bearings to adapt to length variations. 6.
Geneva and Millau
6.1 Two very large projects developed in the nineties produced a gigantic step forward, for the Millau viaduct over the River Tarn valley, and to cross the Lake of Geneva. We developed the concept for the Millau viaduct in 1990-1991 but the design remained preliminary until 1993, due to the many obstacles met by the project. Jean- François Klein and Pierre Moia took inspiration from it to design a bridge across the Lake of Geneva in a project competition which they won ; they developed in 1993-1994 an excellent project with a completely detailed design. Being in the jury of this competition, we have taken inspiration from their project for the later development of the design of the Millau viaduct so that these projects helped each other as it happens frequently.
Figure 9 – The bridge designed to cross the Lake of Geneva
6.2 The Pont de la Rade in Geneva has four pylons and three central spans 350 metres long. It has a slightly curved alignment for the bridge elegance (R = 900 metres). The deck is extremely wide, 33.46 metres. Its design is specially elegant, balancing rigidity between a relatively slender deck (an elegant streamlined box-girder, 3.50 metres deep) and rather rigid piers and pylons (figure 9). Length variations, produced by temperature, shrinkage and creep are permitted by the relatively limited distance between the central point and the extreme pylon but also by soil conditions. Unfortunately a general votation is necessary in Switzerland to build very large structures and the Geneva population voted against the project for financial reasons. 6.3 The Millau viaduct is even more ambitious; almost 2.5 kilometres long, it comprises seven pylons and six central spans 342 metres long with two piers about 240 metres tall. The development of the project has been extremely complex, with an initial design by the SETRA and two design competitions, a rather informal one in 1993 and a more formal one in 1995-1996. Five teams of engineers and architects were constituted for this second competition, from the result of the first one and each in charge of developing a different type of solution. The cable-stayed solution with multiple spans, developed from our conceptual design by SOGELERG - Europe Etudes Gecti - SERF and the British architect Sir Norman Foster, was selected in July, 1996 and we developed the project with this team between the end of 1996 and September, 1998.
Figure 10 – The Millau viaduct (prestressed concrete solution)
Two alternatives are proposed, the deck being either in prestressed concrete or in steel with almost the same design adapted to the specific conditions of multiple cable-stayed spans and to the extreme wind forces due to the high position of the bridge in the valley. The rigidity is distributed between the deck, piers and pylons. The deck is a trapezoidal box-girder with a rather narrow bottom flange so that it is almost triangular; it is about 4.50 metres deep. The pylons, 90 metres tall, have the shape of inverted V for a very high rigidity. The design of piers is more complex since the taller ones have to resist important forces due to wind and to second order effects ; and the extreme ones - about 90 metres high - must adapt to very important length variations due to the bridge size (about ± 0.80 metres). As soon as in 1992-1993,
with Emmanuel Bouchon we decided to have these extreme piers made of two parallel, flexible shafts with a unique line of fixed bearings on top of each to increase their flexibility. The architect later preferred to have the same design for all the piers; this led to the final design of solid piers which divide into twin shafts in the upper part, 90 metres high (figure 10). This very elegant bridge will be built - if decisions taken are applied - in the years to come with a concession.
Figure 11 - The four pylons of the Rion-Antirion Bridge
7.
Total suspension
7.1 A last idea must be evoked to complete this overview : the total suspension concept. It has been initiated with the Pasco Kennewick bridge and soon after for the Alex Frazer Bridge in Canada. It must be clear that it adapts very well to the concept of multiple cable-stayed spans since it allows for free length variations without any interference with the rigidity of piers and pylons. This concept has been proposed by Bouygues and Pierre Richard for the Ré Island Bridge in 1986. They proposed a cable-stayed bridge with a continuous deck, almost 2800 metres long and with a series of central spans 210 metres long. Unfortunately, just after the successful construction of the Bubiyan Bridge and at a time when the Syllans and Glacières viaducts were to be built, Pierre Richard preferred for the deck an expensive three-dimensional prestressed concrete truss the cost of which eliminated the solution. The deck was totally suspended from the pylons to adapt to longitudinal length variations - concrete creep and shrinkage, elastic shortening produced by prestressing tendons installed after span closure and effects of temperature - in complete opposition with the solution proposed for Millau and Geneva. Traffic loads were perfectly balanced by the large flexural inertia of the three dimensional truss which constituted the deck, and very classical, almost slender pylons could be designed in this situation. 7.2 This is why, when Jacques Combault asked for our opinion on the design of the Rion-Antirion Bridge, we suggested to have a continuous deck, totally suspended from the four pylons. The concept has been immediately adopted and developed with many advantages as compared to the initial design : continuity, a regular distribution of cable-stays in the spans to perfectly balance loads... Rigidity this time
comes from the pylons, made of four legs with an inverted V-shape in both directions ; the composite deck is rather flexible. The final project, now being detailed by GTM and Ingerop, has a continuous deck with five spans, 286 - 3 x 560 and 286 metres long; and pylons are rigidly connected to the piers, a much more comfortable situation than installing a cantilever on sliding bearings and dampers (figure 11).
Figure 12 – The final design of the Rion-Antirion Bridge
8.
Conclusion
As evidenced by this survey, cable-stayed bridges with multiple spans might develop rapidly in the coming years, specially if the Millau viaduct and the Rion-Antirion bridge are erected as expected, evidencing the enormous capacities of this new structural type.
Literature [1] [2] [31 [4]
The bridge spanning Lake Maracaibo in Venezuela. Bauverlag. Berlin. 1963 Boaga G. and G. Boni. The concrete architecture of Ricardo Morandi. Alec Tiranti. London. 1965. Wittfoht H. Triumph der Spannweite. BetonVerlag. Düsseldorf. 1972. Podolny W. and J. Scalzi. Construction and design of cable-stayed bridges. John Wiley and Sons. New York. 1976. [5] Gimsing N.J. Cable-supported bridges. Concept and design. John Wiley and Sons. Chichester. 1983. [6] Wittfoht H. Bridges. BetonVerlag. Düsseldorf. 1984. [7] Walther R. and als. Ponts haubanés. Presses polytechniques romandes. 1985. [8] Leonhardt F. Ponts. Puentes. Presses polytechniques romandes. 1986. [91 Troitsky M.S. Cable-stayed bridges (second edition). BSP Professional Books. Oxford. 1988. [10] Ricardo Morandi. Innovazione, tecnologia, proggetto. Gangemi. Roma. 1991. [11] Freyssinet. Cable-stayed bridges. 1994. [121 The new Macau-Taija Bridge. The friendship bridge. Port and Bridge office. 1994.
The Development of Composite Cable-Stayed Bridges Holger Svensson, born 1945 received his Diplom-Ingenieur (M.Sc.) degree in 1969 He specialised in all aspects of the design and construction of long-span, mainly cable-stayed bridges all over the world.
Holger S. SVENSSON Managing Director Leonhardt, Andrä und Partner Stuttgart, Germany
Summary Although the first modern cable-stayed bridge (Strömsund / Sweden, 1955) used a composite deck, this bridge system really became successful in the mid-eighties. Currently 44 major composite cable-stayed bridges are completed or under construction, including a twin bridge (Baytown) and two double deck bridges (Kap Shui Mun, Øresund). Composite cable-stayed bridges will remain the dominant system for medium and longer spans.
1.
Introduction
For the last few years, composite cable-stayed bridges have been much more common worldwide than all-concrete or all-steel ones. The main reasons are economy in materials and ease of construction. By using concrete rather than steel in compression, and by using a concrete roadway slab rather than an orthotropic deck, substantial savings against all-steel bridges are realised. A composite deck can use small parts - main girders, floor beams, precast slabs - which can easily be lifted. They can be joined simply by bolting the steel girders together and connecting the precast slabs with cast-in-place joints. Thus, smaller lifting equipment and the absence of match-cast joints together with savings in cable steel favour composite decks against all-concrete ones. This trend was already pointed out by us in 1984 [44]. In order to distinguish the different types of composite decks we split them into four groups, see Tables 1 to 4: -
Main girders having a concrete roadway slab on top of a steel grid or deck. Main all-steel (or composite) girders in the centre span combined with all-concrete side spans. Concrete main girders with a concrete floor slab supported by steel floor beams.
1
-
Composite roadway slabs are orthotropic steel decks stiffened by a substantial layer of concrete.
Composite bridges are currently not only more numerous, but they include the last three record span holders: the Yang Pu Bridge [22] with 602 m in 1993, the Normandy Bridge [37] with 856 m in 1995 and the Tatara Bridge [38] with 890 m in 1999, see Fig. 1.
Main Span Length [m]
1000
[38] [37]
900
symmetric configuration
800
Composite main girders
700 [22]
600 500 400 300
(not built) [4] Design completed [28]
[29]
[9] Steel main and concrete side pans
200 [1]
(not built)
100 0 1950
1960
1970 1980 1990 2000 Year of Completion
2010
Figure 1. Development of span lengths, from Tables 1 and 2
2. Historical Development 2.1
Composite main girders (Table 1)
The first modern cable-stayed bridge - the Strömsund Bridge [1] - has a concrete slab on top of a steel grid. The concrete roadway, however, distributes only the wheel loads and does not ostensibly act composite for primary forces, unlike the other bridges listed in Tables 1 to 3. The first and - curiously - the only composite cable-stayed bridge in Germany is the one in Büchenau [2], built in 1956. The reason is that the German codes at that time did not permit tensile stresses in the concrete slab [40]. This would have required post-tensioning the slab (together with the steel deck) which would have been uneconomical. A major step forward took place with the design of the Hooghly River Bridge [4] with a 457 m (1500 ft) main span. In order to suit local Indian fabrication methods a concrete slab was chosen to avoid the welded orthotropic deck which would have been chosen elsewhere. All steel connections are actually riveted, and a design requirement was that the concrete deck be without stress under permanent loads. Had it been completed in 1980 as originally planned, the bridge would have held the span record (Figure 1). However, design changes and construction problems delayed the bridge opening until 1992, by which time a longer span had been constructed elsewhere.
2
Ref. Name No. Location
Slab Type Tower Type Post-Tension Cable Planes
1
CIP, 0,20 m
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Completed Deck Main Span Width Deck Depth Strömsund Bridge 1955 14,30 m Sweden (not composite) 183 m 3,00 m Büchenauer Bridge 1956 20,80 m Bruchsal, Germany 58,80 m 1,40 m Pont des Iles 1967 28,65 m Expo 67, Canada 2 x 105 m 2,82 m 2nd Hooghly River Br.* (1980)1992 25,00 m India 457 m 2,33 m Sitka Harbor Bridge 1972 11,00 m Alaska, USA 157 m 1,80 m Heer-Agimont Bridge 1975 14,50 m Belgium 123 m 2,05 m Steyregger Donau Br. 1979 24,86 m Linz, Austria 161,2 m 4,07 m Sunshine Skyway Br.* (1982) 27,50 m Florida, USA: Design 366 m 2,34 m Annacis Bridge 1986 28,00 m Vancouver, Canada 465 m 2,10 m Saint Maurice 1986 2 x 11,75 m Switzerland 105 m 1,01 m Quincy Bridge 1987 13,80 m Mississippi River, USA 274 m 2,10 m Kemjoki Bridge 1989 25,50 m Finland 126 m Weirton-Steubenville Br 1990 28,00 m Ohio River, USA 250 m 2,74 m Nan Pu Bridge 1991 25,00 m Shanghai, China 423 m 2,10 m Burlington Bridge* 1993 25,70 m Ohio River, USA 195 m 1,85 m Tähtiniemi (Heinola)Br.* 1993 22,00 m Finland 165 m 3,20 m Utsjoki Bridge 1993 12,00 m Finland 155 m 1,76 m Karnali River Bridge 1993 11,30 m Nepal 325 m 3,00 m Mezcala Bridge 1993 18,10 m Mexico 300/311 m 2,79 m El Canon 1993 21,00 m Mexico 166 2,11 m El Zapote 1993 21,00 m Mexico 176 2,11 m Yang Pu Bridge** 1993 32,50 m Shanghai, China 602 m 3,00 m Clark Bridge 1994 30,50 m Mississippi River, USA 230 m 1,90 m Baytown Bridge* 1995 2 x 23,83 m Texas, USA 381 m 1,83 m 2nd Severn Bridge 1996 34,60 m UK 456 m 2,70 m Kap Shui Mun Br.*
1996
35,20 m
3
2 H inclined 2 CIP, 0,25 m 2 H w/o struts longitudinal 2 CIP, 0,19 m 1 H w/ struts none 2 CIP, 0,23 m 2 H inclined none 2 CIP, 0,20 m 2 H w/o struts none 2 CIP, 0,19 m 2 H w/ 2 struts none 2 CIP, 0,20 m 2 A, unsym. longitudinal 2 PC, 0,23 m 2 Diamond none 2 PC, 0,27 m 2 H inclined none 2 CIP, 0,22 m 1 A incl. longit. none 2 PC, 0,23 m 2 H inclined longitudinal 2 CIP, varies 1 centre mast transverse 2 CIP, 0,22 m 2 A, unsym. none 2 PC, 0,26 m 2 H inclined longitudinal 2 PC, 0,25 m 2 H inclined longitudinal 2 CIP, varies 2 H, 1 strut transverse 2 PC, 0,26 m 2 H, inclined none 2 PC, 0,23 m 1 H, unsym. none 2 CIP, 0,20 m 3 H towers none 2 0,20 m 1 H inclined 2 0,20 m 1 H inclined 2 PC, 0,26-0,40 2 inverted Y long. + transv. 2 PC, 0,27 m 2 centre masts longitudinal 2 PC, 0,20 m 2 twin diamond none 4 PC onto grid, 2 H w/ 2 struts 0,25 2 none PC onto grid, 2 H inclined
Ref. Name No. Location Hong Kong 27 28 29 30 31
Ting Kau Bridge Hong Kong Raippaluoto Bridge, Finland Øresund Bridge ** Sweden / Denmark Sunningesund Bridge ** Uddevalla, Sweden Kolbäcksbro ** Ume Älv, Sweden
Completed Deck Slab Type Main Span Width Post-Tension Deck Depth 430 m 7,46 m 0,25 none 1997 43,00 m PC, 0,23 m 448/475 m 1,75 m none 1998 15 m PC, 0,27 m 250 m 2,8 m none 2000 30,50 m CIP 490 m 10,20 m transverse 2000 26,5 m PC, 024 m 414 m 2,20 m none 2001 17,65 m CIP, 0,27 m 130 m 2,59 m none
Tower Type Cable Planes 2 3 centre masts 4 2 diamond 2 2 H w/o strut. 2 2 diamond 2 1 H inclined 2
Table 1: Cable-stayed bridges with composite main girders * Co-designed by Leonhardt, Andrä und Partner GmbH ** Reviewed by Leonhardt, Andrä und Partner GmbH The next important step forward came with the design of the Sunshine Skyway Bridge [8] in 1982. It has the main characteristics of modern composite stayed decks: - open steel grid from I-girders as shown in Fig. 2 - outside main girders to which the stay cables are directly connected - precast concrete slab elements, spanning longitudinally between floor beams, connected by lap spliced reinforcement in CIP joints. - erection in small elements possible: main girders, cross-girders, precast slabs. - crack control in the slab by rebar only, without post-tensioning. Although this composite alternate lost by a small margin in competitive bidding against the concrete alternate, similar design principles were successfully applied to the Annacis Bridge [9], which captured the span record in 1986. This initiated a series of cable-stayed bridges with composite decks all over the world. In the US five cable-stayed bridges of composite construction [11, 13, 15, 23, 24, 28] have been completed since 1987. In Finland 4 cable-stayed bridges [12, 16, 17] were built differently. Their steel decks were launched into position and supported by temporary piers. The concrete slabs for the Kemjoki [12] and Heinola Bridge [16] were then cast-in-place. They span transversely with cantilevers and are, consequently, posttensioned transversely. The Utsjoki Bridge deck [17], however, uses the principles outlined for the Skyway design. The Raippaluoto Bridge [28] was built by free cantilevering. The single-tower Karnali River Bridge [18] is remarkable as it would have a span of more than 600 m, if doubled to a symmetric configuration, and because it was built in a very remote location at the foothills of the Himalayas. Since from 1975 China has built more than 30 cable-stayed bridges [46], most of them from concrete. With the composite Nan Pu [14] and Yang Pu [22] bridges (once a record holder) China became a front-runner in this type of construction. The Baytown Bridge [24] across the Houston Ship Channel is a twin bridge with two independent decks supported by 4 cable planes from double diamond towers. 4
The Kap Shui Mun Bridge [26] has the first composite double deck with highway traffic running on the top slab and road + rail traffic on the bottom slab, similar for the Øresund Bridge [29]. The Ting Kau Bridge [27] has two main spans and 3 towers. The 43 m wide deck is also supported by 4 cable planes like the Baytown Bridge, but the two decks are connected by crossgirders. 2.2
Steel or composite main span and concrete side spans (Table 2)
In order to use a concrete deck as counterweight for a steel main span it must be possible to place piers in the sidespan. Under permanent load conditions these piers support the additional weight of the concrete required for safety against uplift. Savings can be achieved against a balanced steel side span. This system was first used for the Mannheim North Bridge ,[32] in 1972, and again for the Flehe Bridge [33] in 1979. If doubled to a symmetric configuration, the Flehe span would come to about 700 m, Fig. 1. The former record holder for all types of cable-stayed bridges, the Normandy Bridge [37], has a steel main span and concrete side spans. An additional economic advantage was realised by incrementally launching the concrete approach bridges. In order to stiffen the 856 m main span for aerodynamic stability, the concrete approach span is extended into the main span by 116 m on each side, so that only the remaining 624 m utilise an all-steel cross-section. In Section 4 it is shown that such a reduced steel deck length is economically advantageous. The double-deck Kap Shui Mun Bridge [26] not only has a composite deck in the centre span as mentioned under Section 2.1, but has also concrete side spans. It is currently the only bridge of that type. The concrete approach spans were also incrementally launched to cantilever 21,5 m each side into the main span. The first three steel sections of the main spans were used as a launching nose with some modifications because the water underneath was too shallow for barges. The current record holder, the Tatara Bridge [38] in Japan has an all-steel deck which extends far into the side spans and uses concrete counterweight beams only for the backstay cables. Ref. Name No. Location
Tower Type Cable Planes
32
1 A, unsym. (2) 1 inverted Y 1 2 H vertical 2 2 centre masts 1 2 diamond 2
33 34 35 36
Completed Deck Width Steel Deck Main Span Deck Depth Length % of Main Span Mannheim North* 1972 36,90 m 287 m Rhine River,Germany 287 m 4,50 m 100 % Flehe Bridge* 1979 41,70 m 368 m Rhine River,Germany 368 m 3,80 m 100 % Tjörn Bridge 1982 15,75 m 386 m Sweden 366 m 3,0/3,0 m 105 % Emscher Bridge 1990 41,00 m 310 m Rhine River,Germany 310 m 3,68 m 100 % Ikuchi Bridge 1991 24,10 m 490 m Japan 490 2,48 m 100 %
5
37 26 38
Normandy Bridge Seine River, France Kap Shui Mun Br.* Hong Kong Tatara Bridge Inland Sea, Japan
1995 856 m 1997 430 m 1999 890 m
22,30 m 3,05 m 35,20 m 7,46 m 30,8 m 2,7 m
624 m 73 % 387 m composite 90 % 1312 m 147 %
2 inverted Y 2 2 H inclined 2 2 diamond 2
Table 2: Cable-stayed bridges with steel composite main and concrete side spans * Co-designed by Leonhardt, Andrä und Partner GmbH 2.3 Composite cross girders (Table 3) The foundations for the East Huntington Bridge [39] were already built for a steel superstructure when it was decided to consider a concrete alternate for competition. We thus had the task of designing a rather light, "mostly concrete" alternate. We did that by using high-strength concrete and steel floor beams. This combination was bid considerably lower than the original steel design. The Vasco da Gama Bridge [40] also uses this deck design. Ref. Name No. Location
Cross-Gird.,h Distance
Tower Type Cable Planes
39
I-deck 0,91 m 2,73 m I-Section, 2,0 m 4,41 m
1 A unsym. 2 2 H inclined 2
40
Completed Deck Main Span Width Deck Depth East Huntington Bridge* 1985 12,20 m Ohio River, USA 274 m 1,52 m Vasco da Gama Bridge 1998 31,20 m Lisboa, Portugal 420 m 2,50 m
Table 3: Cable-stayed bridges with composite cross girders * Co-designed by Leonhardt, Andrä und Partner GmbH 2.4
Composite roadway slab (Table 4)
Orthotropic steel decks have two disadvantages (besides high cost): the asphaltic wearing surface may not adhere well to the steel plate, and the steel deck may permit the forming of ice faster than a concrete deck slab. These potential problems may be mitigated by using a concrete wearing surface. In 1969 a 0,22 m thick layer of concrete was cast onto the orthotropic deck of the Massená Bridge [41]. Because this arrangement gave a very satisfactory service, it was used again with a 0,12 m thick concrete layer for the Dartford Bridge [43] in 1991. The two Zárate Bridges [42] use a 0,10 m thick concrete layer. Its stiffening effect permitted the distance between the longitudinal ribs to be increased from the usual 300 mm to 400 mm. Due to the possibility of extensive repairs, the concrete wearing surface was not considered to carry the global deck forces. On the other hand, sufficient shear studs and reinforcement were provided to assure the integrity of the steel-concrete roadway slab under all load conditions.
6
Ref. Name No. Location 41 Massená Bridge Paris, France 42 2 Zárate Bridges* Rio Paraná,Argentina 43 Dartford Bridge London, UK
Completed Main Span 1969 161 m 1976/77 330 m 1991 450 m
Deck Width Deck Depth 36,30 m 4,35 m 22,60 m 2,60 m 19,00 m 2,00 m
Concrete Slab Thickness 0,22 m 0,10 m 0,12 m
Tower Type Cable Planes 2 Centre masts 1 2 H with crosses 2 2 H w/o struts 2
Table 4: Cable-stayed bridges with composite roadway slab * Co-designed by Leonhardt, Andrä und Partner GmbH
3. Roadway Slab For composite main girders it is of overriding concern to keep tensile stresses away from the deck slab. Transversely this is achieved by using two external cable planes which provide compression in the slab which acts as the top flange of a simply supported girder. Table 1 - Cable Planes - thus shows no exception to this rule. In the longitudinal direction, the slab receives little bending stress because the neutral plane is located close to its underside, Fig. 2. Negative moments caused by load positions away from the section under consideration are relatively small, and the corresponding tensile stresses are generally overcome by the normal forces from the inclined cables. In the centre of the bridge where these normal forces decrease to zero, sufficient compression in the roadway slab can be created by cambering the deck, i.e. by introducing a positive moment.
Figure 2. Typical composite cross-section [15]
4. Economic Comparison For this investigation we have consistently used the following average unit prices: concrete: 500 Euro/m³, structural steel: 1.750 Euro/t, orthotropic deck steel: 3.000 Euro/t, stay cable steel: 6.000 Euro/t.
7
To resist a normal force thus costs about 65 % more if steel is used instead of concrete. Therefore, towers are generally concrete. An orthotropic deck (180 kg/m²) costs about four times as much as a 0,25 m thick concrete slab. Therefore, orthotropic decks are used in relatively few cases. The bridge costs per m² as a function of main span length are shown in Fig. 4. When neglecting the steel main and concrete side span decks, concrete decks are most economical up to a main span of 400 m; above that composite decks govern up to 1000 m where steel takes over. Steel main concrete and sidespan decks reach their minimum costs if the concrete approach bridges protrude about 100 m constant into the main span. Fig. 4 indicates that a combination of concrete approach with composite centre deck then governs from 350 m to 600 m. Above that, a combination of concrete approaches and all-steel main spans becomes more economical. The results confirm the concept of the latest steel concrete bridges: Kap Shui Mun Bridge [26] with a composite centre span of 430 m and Normandy Bridge [37] with an all-steel centre part for a main span of 856 m. The individual unit prices may, however, vary considerably for different locations and competition conditions, so that the intersections of the various curves may shift. 8000
7000
6000
Cost DM/m²
All-concrete deck All-steel deck Composite deck
5000
Longit. conc/steel Longit. conc/comp
4000
3000
2000 200
300
400
500
600
700
800
900
1000
Mainspan Length [m] Figure 3. Unit costs for different types of cable-stayed bridges
8
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
Wenk, H.: Die Strömsundbrücke - Ein Großbrücken-Auftrag der Königl. Wege- und Wasserbauverwaltung in Stockholm. Der Stahlbau 23 (1954), p. 73 - 76. Kunz, R., Trappmann, H., and Tröndle, E.: Die Büchenauer Brücke, eine neue Schrägkabelbrücke der Bundesstraße 35 in Bruchsal. Der Stahlbau 26 (1957), p. 98 - 102. N.N.: Stayed Girder in the Dry. Engineering News-Record, August 5, 1965. Schlaich, J.: On the Detailing of Cable-Stayed Bridges. Cable-Stayed Bridges - Recent Developments and their Future. M. Ito et al. 1991 Elsevier Science Publishers B.V., p. 57 76. Gute, W.: First Vehicular Cable-Stayed Bridge in the U.S. Civil Engineering-ASCE, November 1973, p. 50 - 55. Mahieu, L. and Wouters, M.: Pont Haubané sur la Meuse a Heer-Agimont. Burgholzer, L.: Die Steyregger Donaubrücke in Linz. IABSE Structures C-12/80, p. 24 25. Svensson, H., Christopher, B., and Saul, R.: Design of a Cable-Stayed Steel Composite Bridge. Journal of Structural Engineering, Vol. 112, No. 3, March, 1986, p. 489 - 504. Taylor, P.: Hybrid Design for the World’s Longest Span Cable-Stayed Bridge. Proceedings of the IABSE Conference 1984, p. 319 - 324. Ponts sur le Rhône à Saint-Maurice. Tunnels de l’Arzilier et Ponts sur le Rhône. Department des Travaux Publics du Canton de Vaud, p. 14 - 23. Kulicki, J., Waldner, E., and Prickett, J.: Design of the Cable-Stayed Mississippi River Bridge at Quincy, Illinois. Transportation Research Record 950, Second Bridge Engineering Conference, Volume 2, p. 34 - 50. Kettunen, A., and Järvenpää, E.: Kemijoki River Bridge at Rovaniemi (Finland). IABSE Structures C-44/88, p. 6 - 7. Kozy, W., and Kolmus III, R.: Design of the Cable-Stayed Girder Weirton-Steubenville Bridge. Transportation Research Record 950, Second Bridge Engineering Conference, Volume 2, p. 23 - 33. Quinghua, Z.: Shanghai Builds World’s Second Largest Cable-Stayed Bridge. Stahlbau 61 (1992), p. 26 - 27. Svensson, H., and Petzold, E.: The Cable-Stayed Bridge over the Mississippi at Burlington, USA. Proceedings of the Third Symposium on Strait Crossing, Ålesund, Norway, June 1994. Balkema, Rotterdam (1994) p. 239 - 246. Pulkkinen, P., Saul, R., and Kettunen, A.: Tähtiniemi Bridge. Proceedings of the 1994 International Symposium on Cable-Stayed Bridges, Shanghai, p. 153 - 157. Järvenpää, E., Lunabba, T., and Kettunen, A.: Utsjoki Bridge - The Northernmost CableStayed Bridge in the World. Proceedings of the 1994 International Symposium on CableStayed Bridges, Shanghai, p. 148 - 152. Arzoumanidis, S., and Kunihiro, M.: The Karnali River Bridge. Proceedings of the IABSE/FIP Conference on Cable-Stayed and Suspension Bridges, Deauville, October 1994, p. 395 - 403. King Revelo, C., Alvarez Guillen, C., Chavin, A .et al: The Four CableStayed Bridges of the Mexico-Acapulco Highway. Proceedings of the IABSE/FIP Conference on Cable-Stayed and Suspension Bridges, Deauville, October 1994, Vol. 1, p. 351 - 360. Lin Yuan-pei et al.: Yangpu Bridge. Shanghai Scientific and Technological Education Publishing House, 1994. McManamy, R.: Still Tall in the Saddle, Project Survives Flood - Mississippi Span Bends Cables over Single Pylons. ENR, November 8, 1993, p. 35. 9
[24] Svensson, H., and Lovett, T.: The Twin Cable-Stayed Baytown Bridge. Proceedings of the IABSE/FIP Conference on Cable-Stayed and Suspension Bridges, Deauville, October 1994, Volume 1, p. 361 - 368. [25] Maury, Y. et al: Some Aspects of the Design of Second Severn Crossing Cable-Stayed Bridge. p. 369 - 279. [26] Saul, R., Lovett, T., and Hopf, S.: The Kap Shui Mun Bridge at Hong Kong. Proceedings of the IABSE/FIP Conference on Cable-Stayed and Suspension Bridges, Deauville, October 1994, Volume 1, p. 405 - 412. [27] Highways Department Hong Kong Government, Ting Kau Contractors Joint Venture: Project Information, Issue 1 – September 1995 [28] Esko Järvenpää, Pekka Pulkkinen: Raippaluoto Bridge. Finnish Civil Engineering, 1/97, p. 7-10. [29] ASO Group: The Øresund Bridge, May 1996 [30] Vägverket: Sunningeleden – the loveliest short cut! [31] Aas, Jakobsen: Tender Documents for Kolbäk Bridge, 1998 [32] Volke, E., and Rademacher, C.-H.,: Nordbrücke Mannheim-Ludwigshafen (Kurt-Schumacher-Brücke). Der Stahlbau 42 (1973), p. 97 - 105, 138 - 152, 161 - 172. [33] Modemann, J., and Thönnissen, K.: Die neue Rheinbrücke Düsseldorf-Flehe / NeussUedesheim. Bauingenieur 54 (1979), p. 1 - 12. [34] Kahmann, R., Koger, E.: Die neue Tjörnbrücke - Konstruktion, Statik und Montage der Stahlkonstruktion. Bauingenieur 57 (1982), p. 379 - 388. [35] Schmackpfeffer, H.: Rheinbrücke Emscherschnellweg - Bauausführung der Strombrücke in Stahl. Bauingenieur 65 (1990) p. 453 - 462. [36] Ohasi, M. et al: Design of Complex Cable-Stayed Bridge. International Conference on Cable-Stayed Bridges, Bangkok, November 1987. [37] Virlogeux, M. et al: Design of the Normandie Bridge.Proceedings of the IABSE/FIP Conference on Cable-Stayed and Suspension Bridges, Deauville, October 1994, Volume 1, p. 605 - 630. [38] Housku-Shikohu Bridge Authority: Tatara Bridge. Structural Engineering International 1/98, p. 12, 13. [39] Grant, A.: The East Huntington Bridge - Design and Construction Highlights. PCI Journal, vol. 32, no. 1 (1987), p. 20 - 29. [40] Prime Piling. New Civil Engineer 17 November 1994, p. 38 - 42. [41] Dussart, R.: Le Pont Massená à Paris. TRAVAUX - Mars/Septembre 1970 [42] Leonhardt, F., Zellner, W., and Saul, R.: Zwei Schrägkabelbrücken für Eisenbahn- und Straßenverkehr über den Rio Paraná (Argentinien). Der Stahlbau 48 (1979), p. 225 - 236, 272 - 277. [43] Knox, H.S.G., and Walther, F.: The Open Steel Deck Cable-Stayed Bridge. Strait Crossings 94, Krokeborg (ed.), 1994 Balkema, Rotterdam, p. 123 - 131. [44] Zellner, W., Saul, R., and Svensson, H.: Recent Trend in the Design of Cable-Stayed Bridges. Proceedings of the 12th IABSE Congress in Vancouver, B.C., September 1984, p. 279 - 284. [45] Saul, R.: Schrägseilbrücken im Verbund für das Ausland. Stahlverbund-Brückenbau. Tagungsband des Stahl-Informations-Zentrums, p. 75 - 84. [46] Bridges in China. Editor: Xiang Haifan, Tongji University Press, A & U Publication (HK) Ltd., 1994.
10
Comparison of Slab Participation: Assumed for Design vs. FEA David D. BYERS
Steven T. HAGUE
Project Engineer, HNTB Corporation Kansas City, MO, USA
Project Engineer, HNTB Corporation Kansas City, MO, USA
Steven L. McCABE
David M. ROGOWSKI. Manager, Highway Bridge Design HNTB Corporation Kansas City, MO, USA
Professor The University of Kansas, Lawrence, KS, USA
Summary Results of a study in slab participation and resulting stress distribution in the concrete deck of composite cable-stayed bridge systems are presented. Analytical models developed using the ANSYS finite element analysis package have been investigated for typical span arrangements, similar to those being designed and constructed in the United States. Particular attention is given to the longitudinal stress distribution across the deck section and the resulting effective slab width. Recommendations for the implementation of a modified effective slab width procedure are referenced. Finally, stress results are compared for a fullscale cable-stayed bridge model using both the current method of practice as well as the proposed modified method.
Problem Description Bridge design has developed through the centuries in a fashion that continues to improve upon the types of materials being used, as well as to use existing materials in a more efficient manner. Thus, as new materials, analysis methods, design concepts and construction methods are developed, they are frequently employed in bridges because of society's need for longer, more durable spans that can be built within ever-tightening public budgets. However, with new technologies such as the cable-stayed bridge, the rush to implement the concept frequently does not permit the answering of all the important engineering questions prior to implementation. To date, no information has been recorded in the literature that sheds light on the actual longitudinal stress distribution in the concrete deck portion of any of the composite steel and concrete cable-stayed bridges that have been constructed. Without this information, determining the extent to which the concrete deck is participating in the resistance of external force is unknown. The use of Finite Element Methods (FEM) for design in civil-structural applications has been slow in evolving, primarily due to the cost associated with engineering design time and the general simplicity of most of the models encountered. In addition, proper modeling of structures as large as a typical cable-stayed bridge structure requires modern software to be pushed to its maximum capacity for operation. Consequently, modeling of structures of this nature for design is generally performed using a two-dimensional (2-D) or three-dimensional (3-D) direct stiffness model, making use of three degree of freedom (DOF) or six DOF nodes respectively. Cable-stayed bridge design is no exception and makes almost exclusive use of these less complex, direct stiffness analysis methods.
The focus of this paper is to investigate the issue of slab participation in composite steel and concrete cable-stayed bridges and to determine the proper assumptions and guidelines that should be adhered to by designers of these structures. Specifically, a comparison is presented between the current method of practice for determining effective flange width and a proposed modified method developed by the author.
Current Method for Determining Effective Slab Width The analysis of any deck and beam system where a flanged compression region acts as a "wide" compression element requires assumptions for design purposes as to the actual width of the flange that can be assumed as acting together with the beam or girder. The problem for composite concrete deck-steel girder systems is the notable difference in elastic moduli between the two materials. For example, to obtain equilibrium when subjected to positive bending, the steel girder resists tensile stress that must be reacted in compression by the relatively flexible concrete. Additionally, as you moves away from the girder the compressive stress distribution in the slab drops quickly due to shearing deformation of the flange elements near the web. There is a great deal of data in the literature regarding the performance of “conventional” flanged concrete systems under flexural load on rigid supports. These studies have been utilized in developing guidelines for bridge structures through AASHTO (1994) as well as foreign bridge codes such as the German Deutsche Norm (DIN 1075), (1981). The basic concept is one of identifying the effective portion of the deck slab that can be realistically considered to resist external force. Attempting to apply these code provisions to a “real” design process for a cable-stayed bridge creates a great deal of latitude for interpretation on the part of the designer. The current state of the art method of implementation involves applying the above methods for determining effective slab width for both axial and bending forces separately, thereby making use of two distinct values of effective width for use in stress computations on the composite member.
Axial Force Effective Slab Width One important issue that is not adequately addressed in the literature or design codes, but is directly related to the total involvement of the slab, is the participation of the slab in resisting axial forces that are present in the composite cable-stayed deck system. Effective width or "cooperating slab width" for concentrated axial forces, similar to those introduced into the deck system through the cables, is addressed as a separate issue in the codes. The AASHTO LRFD (1994) Design Specifications, in dealing with segmental concrete box girder construction with “normal forces” present, recommends an effective width of flange generated by intersecting 30 degree lines drawn from the edge of the concrete girder stem. This is shown in Fig. 4.6.2.6.2-4 of AASHTO (1994). The DIN 1075 specification offers a similar recommendation, however with an angle of only 26 degrees. Note that each of the longitudinal edge girder members will contain an effective width that varies linearly with the distance from the point of application of the load. In design, it is generally assumed that the portions of the deck located at a sufficient distance from the anchorage point of the outer-most cable possesses an effective slab width equal to one-half the total bridge deck width. That is to say; if the assumed linear stress distribution given by Fig. 4.6.2.6.2-4 of AASHTO (1994) exceeds one-half the bridge deck, the entire deck is assumed to be effective in resisting axial force.
Variations on this simplifying assumption require that the force influence from individual cables near the point of interest be continuously monitored so that the proper portion of the total axial force be applied to a different cross-sectional property. Modeling of this nature is impractical, especially when considering moving loads such as those encountered for typical truck loading.
Bending Effective Slab Width Effective slab width for bending of beam sections with wide flanges presents the designer with a greater difficulty. Although the code provisions outlined in both the AASHTO and German DIN 1075 are nearly identical, the extent to which they can be accurately applied to structures of this type is more uncertain. Using the abbreviations given by the AASHTO LRFD code provisions, the effective slab width for bending, bmf or bms is computed as follows. From the geometry of the preliminary cross-section, the constant, b can be determined by the use of Fig. 4.6.2.6.2-3 of AASHTO (1994). Depending on the width of overhang, engineering judgement is required to determine to what extent the overhang portion of the slab should be considered. Generally speaking, the difficulty of engaging this small portion of the deck, which is often physically separated from the main deck by the cable connection plates, and the relative size of the overhang in proportion to the overall bridge deck excludes it from consideration as part of the “effective” slab. Having established the available flange width, b, the “notional span length”, Li, is required for each member. This parameter is not clearly defined in the code for beam structures supported on elastic supports, such as cable-stayed bridges. However the AASHTO LRFD code, section 4.6.2.6.1, offers the following guidance for beams supported on rigid supports: The effective span length used in calculating effective flange width may be taken as the actual span for simply supported spans and the distance between points of permanent load inflection for continuous spans, as appropriate for either positive or negative moments.
Taking this statement to its logical conclusion, the points of moment inflection due to a unit load located at the point of interest can be used to establish the notional length, Li for all points of interest along the length of the deck. Initially an estimate is made with regard to the relative stiffness of the deck members in the stiffness model. Vertical unit nodal loads are applied in sequence over the entire length of the bridge structure. After application of the unit load at each location, the moment diagram is analyzed and the length of positive moment adjacent to the point of interest is established, thus giving Li. Having established the notional length, Li, for each of the edge girder members, Fig. 4.6.2.6.24 of AASHTO (1994) can be used to determine the effective flange coefficients, bf and bs, depending on the location being considered. The coefficient bf is to be used for all interior portions of the span as defined by Fig. 4.6.2.6.2-1 of AASHTO (1994)6 while bs is used at or near rigid vertical support locations such as at the tower or anchor pier location. Again, the codes fall short in determining the boundaries of such regions and engineering judgement is required to complete the task.
Once the initial effective width is established, the notional length should be re-computed to verify the original assumptions of the relative stiffness of the girder section. Generally, a single iteration is all that is required to converge on a satisfactory value for effective width that will not change the notional length significantly. Now, the effective width for both bending and axial force has been computed and the model is ready for analysis for all the various load combinations required in the code. Once the member end forces have been determined for each of the required load combinations, stresses are computed by applying the member end forces separately to both the “axial” composite member and the “bending” composite member. Stresses caused by both axial and bending forces are superimposed and compared to the code allowable values for strength and serviceability. These assumptions combine a great deal of information that is borrowed from various related analysis methods. For example, the original material contained in section 4.6.2 of the AASHTO LRFD code for “Approximate Methods of Analysis” appeared in the Guide Specifications for Design and Construction of Segmental Concrete Bridges, (1989) as does the German DIN specification. It is of particular interest to note that structures supported on elastic restraints with combined axial and bending forces present are not addressed explicitly anywhere in any of these design codes. Addressing this issue was one of the primary focuses of this research
Modified Method for Effective Flange Width Finite elements are used to investigate the interaction of the slab and steel girder system and its influence on the deck behavior under immediate loading. Studies using the Finite Element Method have been conducted by Byers (1999) to establish an effective representation of the composite girder and slab system that is consistent with the known behavior. This study includes three-dimensional modeling of the major components within the composite deck system including the slab, edge girders and floor beams shown in Figs. 1 and 2.
Figure 1 Floor Beams and Edge Girder
Figure 2 Model with Tower and Back Span
Particular attention is given in the finite element analysis to the longitudinal stress distribution across the section and the resulting effective slab width. Linear assumptions in typical composite member design, using transformed sections, assumes that plane sections remain
plane during bending. Near the edge girder, analysis has indicated that a nonlinear strain distribution exists across the deck section. A typical example is shown in Fig. 3.
Figure 3 Sample Longitudinal Slab Stress from Finite Element Analysis 18 full-scale models were developed to encompass the desired span and deck widths for structures similar in size to those being constructed in the United States. Specifically, main span lengths of 240 m, 300 m and 360 m were evaluated, each having accompanying deck widths of 8 m, 12 m and 15 m. Along with these variable dimensions, all of the models contain the following constant properties: Slab Thickness Floor Beam Spacing Cable Spacing Edge Girder Web
250 mm 5000 mm 15 000 mm PL 28 x 1800 mm
Edge Girder Top Flange
PL 25 x 600 mm
Edge Girder Bottom Flange
PL 55 x 800 mm
Floor Beam Web
PL 12 x 1800 mm
Floor Beam Top Flange
PL 25 x 600 mm
Floor Beam Bottom Flange
PL 38 x 600 mm
Cable Modulus
200 000 Mpa
Steel Elastic Modulus
200 000 Mpa
Concrete Elastic Modulus
29 914 Mpa
Poisson’s Ratio, ν
0.30
The shear modulus for each material was computed using the usual equation for homogeneous, isotropic materials given in Eq. (1).
G=
E 2(1 + ν )
For each of the models indicated, a series of calculations was performed. First of all, each model was analyzed using the ANSYS finite element software. In the post-processing portion of the analysis, sections were cut through the slab elements at each floor beam location and 1/3 points between edges of floor beams. Stresses were recorded at the top and bottom of the slab and imported into an Excel spreadsheet developed by the author. Here, the stresses across the section, such as those shown in Fig. 3, were summed per Eq. (2) to give the total force resisted by the slab at each section. Next, the effective slab width is computed in accordance with Eq. (3). n
Q = ∑σ i t s bi i =1
b eff =
Q
σ max t s
!
Effective slab width was then plotted over the span length for each of the models. From the onset, the goal of this research was to establish what effective width of slab should be used to accurately determine stress and deflection. In an attempt to locate any general trends or consistencies between the various spans and slab widths being investigated, the computed effective slab widths were normalized with respect to span length (x/L) and with respect to deck width (beff/b). Good correlation between the models appeared to exist which allowed for a beginning point in establishing a modified effective width formulation. Next, the task of determining if a generalized or modified solution could be found and what form that solution might take was undertaken. Various shapes were attempted for use in both the back span and main span models. Each attempt consisted of the following steps: 1. An effective slab width curve was assumed for the deck system 2. A two-dimensional plane frame model was assembled using 6-DOF composite beam elements 3. The stick model was loaded and analyzed and the stress and deflection values stripped and compared with those obtained in the finite element solution This process was repeated until satisfactory correlation of the results between the modified method and the finite element solution was obtained. Good correlation of the results was obtained for all of the models analyzed by using the proposed modified effective slab width shown in Fig. 4.
Figure 4 Proposed Modified Effective Slab Width
Comparison of Methods The largest of the models analyzed in the finite element portion of this research was singled out to make a comparison between the current method described above and the proposed modified method. The center span is made up of symmetrical 12 cable spans of 15 000 mm each and one additional 15 000-mm span between the outer-most cables (375 m tower to tower). The laborious task of computing effective slab width using the current method was performed. It should be emphasized that this step required over 100 separate analyses of the same structure using an assumed value for the effective slab width along with computation of the “effective span length” for each member. Effective slab width for bending was then computed using spreadsheets that make use of curve-fit approximations for values in Fig. 4.6.2.6.2-2 of AASHTO (1994). This process takes several days to complete. Effective slab widths for axial load between the cables using the current method were computed as described above. Effective slab width was then computed using the proposed modified method indicated in Fig. 4. Again, the available width of slab, b, is equal to 15 000 mm and the thickness of the slab, ts, is equal to 250 mm. This process, ignoring the two years of research, took less that ten minutes to complete. Combined results of the effective slab widths used in the comparison are shown in Fig. 5 showing the proper orientation with respect to the structure.
Figure 5 Effective Slab Width for Comparison Model Findings from this comparison show that the methodology currently being employed gives good results throughout the middle portion of both the back and main span of the structure. The greatest area of inconsistency with the finite element model occurs in the slab stress near the anchor pier support of the back span and the center portion of the main span near the closure area. These variations are largely due to the manner in which the axial portion of the load and the effective slab width for axial load are dealt with in the current method of design. In the region near the center of the main span, a reduced effective slab width is used for both axial force and bending by the current method as can be seen in Fig. 5. A comparison of the top of steel stress for the main span is shown in Fig. 6. Note that the results labeled T187Modified b_eff represent the stresses obtained using the proposed modified method in a conventional direct stiffness “stick” model. It should be noted that in both of these regions, the stress values obtained by the current method are conservative in nature, but raise questions as to the appropriateness of the methods used for an economic design solution.
Figure 6 Top Flange Stress Comparison
Conclusions In an age of ever-increasing complexity for the field of structural engineering, designers are asked to perform more rigorous detailed investigations on atypical structures such as the cable-stayed bridge. Therefore, the need to simplify broad categories of assumptions into a more direct solution method is greater than ever. In the early development of composite design methods for simple structures, generalizing mathematical models were developed to explain such phenomena as shear lag and effective breadth. These theoretical solutions, though exact, were dependent on multiple variables that change with virtually every problem such as beam depth, flange width, span length, slab thickness etc… Given the intricacy of the solution methods presented, simplifying assumptions were needed to allow engineers to perform repetitive design tasks on “typical” structure types without being burdened by the complexity of the intermediate solutions. Thus, design codes were established that provided a vehicle for the engineer to safely establish intermediate computations, such as effective flange width, so that more time and effort could be given to the more important “big-picture” items in the design. Because of the high degree of indeterminacy presented by complex bridge structures like cable-stayed bridges, direct mathematical theory becomes too complex to offer any practical consideration for solution. Finite elements of an elastic continuum, such as the ones used in this research, offer approximate solutions that can be used in a fashion similar to the early mathematical models mentioned above. This research has provided a “first attempt” at establishing a simplified method of analysis for determining the effective slab width to be used in the design of composite cable-stayed bridges comprised of steel and concrete sections. At the present time, no research of this kind has been previously recorded in the literature.
Using the modified effective slab width described above, good correlation of the results are obtained when comparing both stress and displacement between the simplified direct stiffness models and the full finite element models. In addition, little difference exists in the results when comparing the current method to that of the proposed modified method except as noted above. Therefore, it appears the modified effective slab width method proposed provides a suitable tool that can be expediently used by designers to predict both stress and deflection of composite cable-stayed bridges. Based on the results of this research, it is recommended that the effective slab width for composite cable-stayed bridges meeting the parameters and limitations described by Byers (1999) may be accurately estimated using the guidelines presented in Fig. 4. Further research into localized areas near the cable to deck connection and the portion of the deck between the cables at the center of the main span will provide additional insight into design parameters that can be implemented by engineers.
References [1].
AASHTO (1994), LRFD Bridge Design Specification, American Association of State Highway and Transportation Officials, First Edition.
[2].
D.D. Byers, “Evaluation of Effective Slab Width for Composite Cable-Stayed Bridge Design”, Ph.D. Dissertation, The University of Kansas, 1999
[3].
DEUTSCHE NORM, German DIN 1075, April, 1981, DIN 1072, Din 1076, Current.
Yamuna Cable Stayed Bridge at Allahabad/Naini, India Ejgil VEJE M.Sc. Civil Engineer COWI AS Lyngby, Denmark
Poul Møller NIELSEN M.Sc. Civil Engineer COWI AS Lyngby, Denmark
Flemming PEDERSEN M.Sc. Civil Engineer COWI AS Lyngby, Denmark
Kent FUGLSANG M.Sc. Civil Engineer COWI AS Lyngby, Denmark
1 Introduction Yamuna is a tributary of Ganga River. Very near the holy site at the confluence of Yamuna and Ganga a new bridge will be built across Yamuna between the cities Allahabad and Naini. The new river crossing has to cater for a large volume of traffic between Allahabad and Naini, due to the industrial growth of Naini. It will also provide an important intra-state link to the cities of Mirzapur and Varanasi. The existing road which links Allahabad to National Highway 27 crosses Yamuna on a combined railway and road bridge, built about 100 years ago. This old bridge has inadequate capacity in regard to traffic and structural strength. Initially the project preparation was carried out by Consulting Engineering Services (India) Ltd., New Delhi (CES) based on a solution with haunched box girders of 120m spans constructed by free cantilevering for the deep channel portion of the river. Subsequently, the Ministry of Surface Transport (MOST) received a loan from OECF, Japan and engaged COWI-SPAN JV for a supplementary feasibility study and detailed design.
2 Feasibility Study The objective of the supplementary feasibility study was to investigate larger cable stayed span alternatives in concrete or steel. Since the crossing is near a historic site, aesthetic qualities of the bridge were also considered to be important. Moreover a large span alternative could be a guide for future bridges crossing wide rivers in India.
2.1 Bridge Alternatives The river is notionally divided into a deep channel portion (approximately 600m wide) and a shallow channel portion to include flood plains. Concrete Alternatives: Span Arrangement: 60-115-260-116-60m a) Deck section A with different arrangements of the pylons, on one or two wells under each pylon with double plane semifan or harp cable stay arrangement b) Deck section B or C with pylons on one or two wells with double plane semifan cable stay arrangement c) Deck section D with twin pylons on single wells with four planes semifan cable stay arrangement d) Deck section E with two vertical cable stay planes e) Deck section F with one leg pylons on single wells and with a single central plane harp cable stay arrangement
Figure 1 Alternative Cross Sections, Feasibility Study
The requirement of 260m as minimum of the central span arose to accommodate the horizontal navigational clearance of 240m corresponding with two 120m spans of the initial haunched box girder solution. Two 60m end spans are introduced, because the anchor stays are distributed on both sides of the anchor piers to reduce bending moments in the critical parts of the 115m spans. Furthermore, the weight of the 60m spans results in avoiding upward forces in the anchor piers. Finally, the southern 60m span gives a good transition to the following approach spans (the part of the bridge crossing the shallow channel portion of the river). Concrete Alternative: Span Arrangement: 145-320-145m f)
Deck section C with double plane semifan cable stay arrangement.
The larger span alternative proved to be approximately 20% more expensive than the smaller span alternative b with deck section C.
Steel alternative: Span Arrangement 60-115-260-115-60m A solution with orthotropic steel deck was considered. This solution proved to be approximately 25% more expensive than the concrete alternative b, with deck section C. Composite Deck alternative: Span Arrangement: 60-115-260-115-60m A composite solution with concrete deck and longitudinal girders and cross girders of steel was considered. This solution proved to be approximately 20% more expensive than the concrete, alternative b, with deck section C.
Figure 2. Alternative Pylon Solutions 2.2 Optional Solution The harp cable stay system and the semifan cable stay system were compared and the semifan cable stay arrangement proved to be 15% cheaper than the harp cable stay arrangement. The weight of the bridge deck was a deciding factor for selection of the optimum cross section, because increase in weight would increase the cable stay cost, which was estimated to be in the order of 40% of the total costs. Cross section C was most advantageous. The ratio of the permanent load of the different deck solutions as compared to deck solution C was found to be 1.38, 1.17, 1.30, 1.22 and 1.38 for deck solution A, B, D, E and F, respectively. Also the pylons for deck solution C have better proportions than the pylons for solutions with a larger distance between the cable stay planes. The pylon legs below the deck level are inclined to minimise dimensions of the well foundations. A single well for each pylon was preferred, as one well below each pylon leg could result in extra stresses in the pylon frame in case of differential settlements. Therefore, this type of pylon with semifan arrangement of cable stays in two vertical planes with deck section C was recommended to be adopted for the detailed design. For feasibility investigations, a cost comparison for the two bridge options, cable stayed versus haunched girders, has been worked out considering unit prices from similar works recently executed in India.
The costs for the bridge modules exclusive contingencies etc. were (April 1996) estimated to: Cost of the cable stayed solution
:
Cost of the haunched concrete girder solution:
792 Million Rupies 869 Million Rupies
The main reason for the lower cost of the cable stayed solution was that the length of the viaduct on the Allahabad side could be reduced, because the small depth of the cable stayed deck above the navigation channel allowed for a lowering of the longitudinal road profile. The lower longitudinal profile also results in lower running cost for vehicles passing the bridge and less pollution. Figure 3 shows the general arrangement of the two above-mentioned alternatives.
Figure 3. General Arrangement of Cable Stayed Solution and Box Girder Solution
3 Design Criteria The design of the concrete structures has been based on the CEB-FIP Model Code 1990, while for foundation design Indian Standards and Codes have been used. 3.1 Loads Traffic loads are in accordance with current Indian Codes, i.e. 2 lanes of Class 70R or 4 lanes of class A according to IRC:6-1966. As a special case an accidental crowd loading of 5 kN/m2 has been considered to act on the entire bridge deck due to religious festivals where millions of pilgrims gather at the confluence of Yamuna and Ganga river near the bridge site.
Cable stays are examined for fatigue load of 0.5 x class A traffic load with 2 x 106 stress cycles. Wind loads are based on IS 875 (Part 3) - 1987. The basic wind speed (peak gust velocity for 100 years return period averaged over about 3 sec in 10m height) is 47m/sec. Flutter is checked for a wind speed of 1.45 times the hourly mean wind speed at the girder level. Water current forces are based on a maximum velocity of 3.0 m/s. Ship impact forces of 10 MN and 5 MN perpendicular to and parallel to the bridge alignment, respectively have been considered for the design of he pylon foundations. Horizontal forces from earthquake of 4.5% of gravity have been considered in accordance with the seismic zone defined in IRC:6-1966. 3.2 Concrete Structures In accordance with CEB-FIP Model Code 1990, exposure class 2a, the maximum allowed crack widths are 0.30mm for reinforced concrete and 0.20mm for pre-stressed concrete. The loads combinations in SLS for frequent situations are used for check of crack widths, see figure 4. The design is based on a characteristic compression strength of fck = 40 Mpa (cylinder strength) for the pylons and the bridge girder. The partial material factors for ULS (Accidental load cases) γm are: Concrete: γm,c = 1.5 (1.2) Reinforcement: γm,s = 1.15 (1.0) Concrete compression stress limitations in serviceability state are:
σc ≤ 0.6 f ck , rare combinations σc ≤ 0.4 f ck , quasi permanent situation The load combinations considered are shown in Figure 4. Figure 4. Load Combinations 3.3 Cable Stays The cable stay force for permanent load + full live load • 0.45 times the minimum breaking load.
It is possible to remove the cable stay one at a time for replacement without restrictions for the traffic. During cable replacement, all normal requirements for ULS and SLS are fulfilled, except that 25% increase in cable stay forces in stays next to the stay being replaced is allowed. A sudden rupture of a cable stay is assumed to act in combination with full live load. For this situation 50% increase in cable stay forces are allowed.
4 Final Design The bridge is divided into tree modules, see figure 3. Module 1: From pier P15 to pier P20 (the cable stayed module): Span arrangement: 60-115-260-115-60m Module 2: From pier P20 to abutment A2 on the Naini side: Span arrangement: 9x60+45m Module3: From abutment A1 on the Allahabad side to pier P15: Span arrangement: 30+13x25+20m 4.1 Superstructure The 260m main span and the 115m side spans have two longitudinal girders (18.2m apart), 1.37m deep and 1.4m wide supported by cable stays per 10m. The side span girder in module 2 has the same principle arrangement as the girder in the cable stayed module except that the girder depth is 3.5m instead of 1.37m. The 26m wide and 250mm thick deck slab is supported on cross beams per 5m as shown in figure 5. The cross beams are pre-stressed by two tendons having 12 ø15.7mm strands tensioned from one end. In the central part of the main span each longitudinal girder is provided with 12 tendons consisting of 19 ø15.7mm strands. They are tensioned after the closure joint at mid span is cast. In the side spans near the anchor piers each longitudinal girder is provided with 10 tendons consisting of 19 ø15.7mm strands. They are tensioned after the closure joint at the anchorage piers are cast.
Figure 5. Section in Main Span, Module 1
4.2 Pylons The pylons have slender solid legs above the deck with dimensions as shown in figure 6. In the longitudinal direction of the bridge the thickness of the legs varies from 2.50m at the top of the pylon to 4.00m just above the lower cross beam. The lower part of the pylon legs is hexagonal in shape. The upper cross beam of the pylon is solid while the lower cross beam is hollow with a provision for access. Both cross beams are post tensioned. The upper cross beam is provided with 6 tendons, and the lower with 20 tendons of 19 No. 15.7mm strands. 4.3 Cable Stays The cable stays are galvanised locked coil ropes with diameters between 76mm and 116mm. The minimum breaking load varies between 5.77 MN and 13.60 MN. The wire material has σ u = 1570 MPa and E-modulus = 160000 MPa. The outer 3 layers of the wirer in the cable stays have a Z-shaped cross section.
Figure 6. Section Through Pylon
At the lower anchorage, the cable stays have sockets with thread and nut. The cable stay forces are transferred to the longitudinal girders through steel plates. The cable stays pass through the girders in steel pipes projecting 1.8m above the girders. At the top of the steel pipes neoprene dampers and neoprene covers are arranged. At the top of the pylons, the stay cables are anchored by fork sockets to thick steel plates protruding from the pylon legs, see figure 7. 4.4 Foundation The pylon foundations are double Dshaped open wells of 10x20m size which shall be sunk approximately 40m below the river bed by dredging inside the well. After sinking to the required depth an underwater concrete bottom plug will be cast. The foundation for the piers in module 1 and module 2 are circular wells with 7.5m outer diameter. Bridge module 3 piers are founded on 1.2m diameter bored piles.
5 Construction Aspects The anticipated construction method is illustrated in figure 8. In stage 1, the spans P15-P16 and P19P29 are cast and posttensioned. 15m bridge deck at each pylon (supported on the lower pylon cross beam), is cast and the first stays are erected and partly tensioned.
Figure 7. Steel Anchorage at Pylon Top In stage 2, cantilever equipment for construction of 10m sections of the deck is erected. Part of the deck sections are anticipated to be pre-cast elements, which are transported by barge to the site, lifted in position and supported on the cantilever equipment.
A stabilising system consisting of all four permanent cable stays 13' (see figure 8) is established and the cable stays partly tensioned. The sliding bearings on all 4 pier shafts of P19 and P20 are locked, so that longitudinal forces can be transferred. In stage 3 the erection/casting of the 10m sections and the erection and tensioning of cable stays are continued (first a part in the main span and then a part in each of the side spans). One section on each side of a pylon will be erected/cast per 14 days. After casting the closure joints at P16 an P19 side spans will be pre-stressed and the temporary fixing of the girder at the pylons removed.
Figure 8. Construction Method for the Cable Stayed Bridge Deck of Module 1. In stage 4, the erection/casting of 10m sections in the main span and erection and tensioning of cable stays will be continued. Before casting of the closure joint at mid main span, the cantilever equipment is removed, the two ends of the cantilevers are temporarily connected, and bearings on P19 and P20 are made movable. After casting of the closure joint, the main span is pre-stressed. Then cantilever slabs,
footways, edge beams and verges are cast, railings, safety barriers and expansion joint structures installed, and surfacing executed. The total period of construction is assumed to be 40 months.
6 Conclusion The feasibility study carried out for a new major bridge crossing of the Yamuna River at Allahabad, India has revealed that the introduction of larger cable stayed spans are more cost effective than smaller spans of typically 120m for cantilever concrete box girders traditionally used for major river bridge in India. Design criteria for the cable stayed bridge has been based on CEB-FIP Model Code 1990, as the Indian Codes are not suitable for design of the this type of structure. The design of the bridge has focused on simplicity and consideration to local conditions and technology. At the same time considerable effort to achieve a light and elegant impression of the bridge has been aimed at. It is expected that the developed design may form the basis for several new cable stayed bridges across the numerous rivers in India in he coming years.
Probabilistic FE analysis of a cable stayed composite bridge A. de BOER
P.H. WAARTS
M.Sc. Civ. Eng. Div of RWS, Utrecht, The Netherlands
M.Sc. TU Delft & TNO, Delft, The Netherlands
Ane de Boer, born in 1951, graduated as a Civil Engineer from TU Delft in 1988. At present he is senior structural research engineer in the civil engineering division of the Dutch Ministry of Transport, Public Works and Water Management.
Paul Waarts, born in 1961, got his civil engineering degree at TU Delft in 1988. At present he is a senior project engineer in the department of structural dynamics and reliability engineering at TNO and research assistant at TU Delft, faculty of civil engineering.
Summary This paper describes the design of a new cable stayed composite bridge near Kampen in the Netherlands. In the design process, the safety of bridges is insured by means of partial safety factors for both strength and load parameters. As a result it is generally accepted that the structure as a whole matches the desired probability of failure. In this paper another method is followed. A full probabilistic analysis on the complete composite structure is performed using FE analysis. The paper described the design of the Kampen bridge and the full probabilistic study. It is concluded that the computed safety of the bridge is well above the required safety.
1.
Introduction
In 1998 a new cable stayed bridge was designed near the city of Kampen in the Netherlands. Figure 1 shows an artist impression of the cable stayed bridge to be built. The bridge has been designed by the civil engineering division of the Dutch Ministry of Transport, Public Works and Water Management. The cross-section of the main span has a composite character. The main span is built up out of a beam grid of steel. The concrete slab on top of the beam grid is initially used as compression zone in the total cross section of the bridge deck. In the design process, the safety of bridges is insured by means of partial safety factors for both strength and load parameters. As a result it is generally accepted that the structure as a whole matches the desired probability of failure. The safety factor was often based on common practice developed over a long term of experience of successful design. For new designs and new materials or loads, the experience only partly exist.
1
Figure 1: Artist impression of the Kampen bridge The combination of materials (composite structures) is an example of such a new design. Johnson and Zhang [1,2] for example have analysed this behaviour. They derived safety factors for the composite structure. For structures different from the ones analysed by Johnson and Zhang, other safety factors have to be derived to insure the bridge safety. In this paper another method is followed. A full probabilistic analysis on the complete composite structure is performed using FE analysis. A full probabilistic analysis used to be a too much computational effort. As computers become faster and faster and alternative computational methods of probabilistic analysis are used, it becomes feasible to carry out probabilistic computations within a design office. This makes it possible to directly analyse (bridge) structures in a probabilistic way. In cooperation with TNO, Delft University of Technology has written a computer code to calculate the failure probability of structures. The civil engineering division of the Ministry of Public Works is a sponsor of this project, within the framework of safety aspects of structures. Probabilistic methods have been implemented in a pilot version of the existing TNO Finite Element code DIANA [3], which already includes physically and geometrically non-linear behaviour of the structure. In the probabilistic finite element code, all variables like material properties, geometrical dimensions and loads can be treated as random variables. The probabilistic method used in this case is based on the principle of adaptive conditional directional sampling [4].
2. Cable stayed bridge structure A side view of the cable-stayed structure is given in Figure 2. The bridge was designed in 1998 with use of partial safety factors. The figure shows a main span of 148.4 m, a side span of 92.5 m, while the height of the pylon reaches 70 m above the bridge deck. The netto width of the bridge deck is 17 m, four traffic lanes of 3.25 m each and two maintenance lanes with a width of 2 m each. The bridge is supported at the both ends, the pylon and in the middle of the 2
left side span. All supports are assumed to be springs, representing the soil’s stiffness. This paper concentrates on the main span and its probabilistic behaviour of the composite structure. 70 m
92.5 m
148.4 m
Figure 2: Side view of the cable-stayed bridge. Side span The concrete side span has a post-tensioned pre-stressed character. The cross-section of the side span is given in Figure 3 and shows a middle rectangular part with 8 holes. Each hole has a diameter of 0.9 m. The side parts have a trapezoid shape and do not contain holes. The middle rectangular part of the cross section accommodates 9 groups, with in total 30 posttensioned pre-stressed cables. 0.22 m
1.25 m 2.6 m
2.6 m
13.5 m
Figure 3: Cross section of the concrete side span Main span The cross-section of the main span has a composite character. The 148.4 m main span is build up with a beam grid of steel and is subdivided in sections with a length of 14.5 meter. Each bridge deck section contains two main girders and four cross beam girders (see Figure 4). On top of the beam grid lies a concrete slab with a thickness of 0.25 m. The concrete slab is initially used as compression zone in the total cross section of the bridge deck. The main girders have a centre to centre distance of 13 meter. The cross beam girders on both sides of the connection between the stay cable and the bridge deck are heavier then the other two cross beam girders of the section. The connection of the cable stay centre is 1 m outside the centre of the main girder. At this point also a rather rigid grid has been used to distribute the stay cable force into the bridge deck. A top view of the FE mesh of a connection section is shown in Figure 4.
3
14.5 m
2m main girder
cross beam
stay cables 13 m
main girder 2m 5 * 3.625 m
Figure 4: Top view steel section of the beam grid The main girders of the steel beam grid have a rigid connection with the side span. The connection between the concrete bridge deck and the beam grid is designed with a so-called stud connection (see Figure 6 for FE mesh) which is typical for steel concrete composite structures. Studs are small pins welded on the upper flanges of the main girder and the cross beam girders of the grid of steel. The main and cross girders of the beam grid are welded profiles. Near the connection of the stay cable and the deck the lower flange of the cross girder on both sides are heavier then the other cross girders (see Figure 7). The measures are given in Table 1. 0.25 m
2m
13 m
2m
Figure 5: Cross section main span Profile
Height
main girder 1.5 light cross girder 1.1 heavy cross girder 1.1
Upper flange 2.2 0.5 0.5
Width Lower flange 1.0 0.5 0.75
Web 0.020 0.014 0.014
Table 1: Measures of the beam grid under main span [m]
4
Thickness Upper Lower flange flange 0.020 0.040 0.020 0.030 0.020 0.040
concrete interface plane with studs cross beam girder
Z Y X
main girder
Figure 6 : FE mesh of half steel section main span Concrete deck
stay cable
cross beam girder
Z Y
X
main girder
Figure 7: FE mesh near the connection with the stay cables Pylon and anchor block The pylon is made from concrete and has an oval cross-section. The top of the pylon measures about 8.6 times 13.0 m2 and anchors the 2 times 9 stay cables in the top of the pylon. The base of both pylon near the foundation has a width of 25 m centre to centre. The anchor block support on the side span has rough dimensions of 17 times 13 m2, with a height of 5 m. The length of the support block (17 m) is divided into 5 rooms, each room has a length of 2.8 m.
5
Stay cables Typical in the process of the cable stayed bridge design, is the finding of the prestress of the 24 stay cables. Within the bridge module of the FE code, these prestress of all different stay cables is easily found by balancing the vertical deflections of the bridge deck and the horizontal deflection of the top of the pylon at the connection point of the stay cables to these structure parts. Within this probabilistic study, only the linear static analysis option of balancing is used, however a nonlinear can be used as well. The balancing load case is selfweight of the bridge structure. A view of the total 3-D model is presented in Figure 8.
Z
Y X
Figure 8: Iso view 3-D model cable stay bridge
3.
Probabilistic method
Reliability methods compute the probability of failure given a limit state model and stochastic parameters. Limit states might be for instance exceedance of yield stress in a member, exceedance of maximum deformation or global collapse. Well-known methods for computing the reliability are Monte Carlo simulation (MC) [7] and the First Order Reliability Method (FORM) [5]. In this paper an unusual method is applied: Directional Sampling [6]. Most structural reliability problems have many stochastic variables. Up to 100 or 1000 stochastic variables is common place. For standard directional sampling about 20000 samples are necessary [4]. For every sample several FE computations have to be carried out. The adaptive conditional direction sampling (ACDS) is introduced to speed up the computations. In short the improvement to the standard directional sampling lies in the use of FE for the important directions and a response surface for less important directions. In practise this means that after the response surface is constructed, only a few FE computations have to be carried out. For the construction of the response surface all variables are varied individually and increased or decreased until failure. A FE model with n stochastic variables gives 2n (directional) samples in the principal directions. Consequently a quadratic response surface is fitted to 6
these results. Following this starting procedure the random directional sampling takes place. The response surface is used in case of a large distance from the origin to the response surface. FE computations are used to calculate the real distance in case of a small distance from the origin to the response surface. In that case the response surface is updated (adapted). Influence factors give insight on the importance of stochastic variables on the limit state. After finishing the directional sampling procedure, the influence factors α are computed by means of a FORM analysis on the response surface.
4.
Stochastic properties of the 2-D and 3-D model
The probabilistic analysis is first performed on a 2-D bridge model. The analysis on such a model is much faster then on the full 3-D model. The results of the 2-D model are checked by means of an analysis on a 3-D model. The (stochastic) properties of the 3-D model are the same as the 2-D model. Additional to the 2-D model, the probabilistic analysis of the 3-D model gives more information over the width of the structure. Also the torsion behaviour of the bridge deck is taken into account in this analysis. Variable Deck side span Econcrete A I q (load) Deck main span Econcrete Esteel Thickness q (load) Footing pylon Econcrete Pylon Econcrete Stay cables E Prestress σu Supports (springs) Vertical translation side span Rotation under pylon foot
µ
σ
lower bound
Unit
38500 0.2252 0.1991 45.
0.48 0.002252 0.01991 4
1 0 0.01 0
N/mm2 m2 m4 kN/m
38500 2.1 105 0.25 45
0.48 8.4 103 0.005 4
1 1 0.10 0
N/mm2 N/mm2 m kN/m
38500
0.48
1
N/mm2
38500
0.48
1
N/mm2
1.95 105 7.8 103 nom. val. 0.1*nom. val. 1800 100
0.1 0. 700
N/mm2 N/mm2 N/mm2
nom. val. 0.1* nom. val. nom. val. 0.1* nom. val.
0.5 * nom val. 0.5 * nom.val
N/mm2 N/mm2
Table 2: Input of probabilistic properties The traffic loads in the bridge are derived from [8]. The lifetime of the structure has been set equal to 100 years. For this period a reliability index β = 3.6 has been chosen according to the Dutch Building regulations (NEN 6700). In [8], according to ISO 2394, a design value of the load is found at a probability of exceedance of Φ(-αβ) =Φ(-0.7 *3.6) = Φ(-2.5)=0.0062 in 100 year. If the load process is ergodic, this corresponds to a load effect with a return period of 7
100/0.0062 = 16000 year. For a span length of 100 m and 4 lanes, [8] gives a distributed load of 45 kN/m for a return period of 100 years. For a return period of 16000 years the distributed load is equal to 55 kN/m. Assuming a normal distribution this means a mean load of 45 kN/m and a standard deviation of 4 kN/m for the 100 year maximum. The thickness of the concrete deck and Young’s moduli of steel and concrete are random variables. Stochastic parameters are the prestress force of the cables and material properties of the concrete pylon and pylon footing. Stochastic properties are summarised in table 2. Most geometric and material parameters are derived from [9]. The ultimate limit state is overstressing of either the cables or concrete-steel deck. The ultimate strength of the cables is supposed to be random as well. The ultimate strength in the 24 cables is supposed to be uncorrelated. All variables presented in table 1 have a truncated normal distribution. The 2-D and 3-D models have in total respectively 27 and 58 independent stochastic variables.
5.
Results of the 2-D and 3-D analysis.
The probability of failure of the bridge structure is computed by means of the ACDS procedure. The 2-D model results is an expected reliability index β = 5.7, with 95 % confidence intervals: 5.5 < β < 6.0. The reliability index corresponds with a probability of failure Pf = 6 10-9. This reliability index is well above the required reliability according to the Dutch building code (β=3.6). The main influence to the probability of failure is found in the thickness of the concrete deck (an influence factor α=0.8 is found). Next the prestress of the cables connected to the bridge deck (α=0.4) is of importance. The ultimate stress of the cables connected to the bridge deck is very important as well (α=0.3). The cumulative influence of the prestress of all cables is equal to α = 0.55. Most other variables have an influence factor α < 0.10. The randomness of traffic load has little influence on the reliability index. The 3-D model results in a reliability index β = 5.05 (intervals 4.8 < β < 5.4). The reliability index corresponds with a probability of failure Pf = 4 10-7. The probability of failure of the 3D model is higher compared to the 2-D model because of the fact that more variables are taken into account and more limit states can occur in the 3-D model. The main influence factors are found in the prestress of the cables, α = 0.7 and ultimate stress of some cables (α=0.6). Next the thickness of the concrete deck (α = 0.5) and traffic load (α=0.2) are of importance. For the 2-D and 3-D model 476 and 274 FE computations were carried out respectively. The total computational time for the 2-D and 3-D model on a HP 9000 130 MHz UNIX machine is 27 minutes and 4:10 hours respectively.
6.
Conclusions
The paper shows the possibility to perform a probabilistic analysis in the design environment. A 2-D model takes half an hour computational time, which is acceptable in this environment. In the definite design process, the elapse time of a 3-D model (4 hours) is also acceptable. 8
A 3-D model results in a lower reliability index β compared to the 2-D analysis. The 3-D model shows that there is an additional safety compared to the safety required by the building codes. It may be concluded that this bridge, designed by using partial safety factors, is much safer then required, at least for the limit states considered. The partial safety factors are mostly based on an assumption that the influence factors on the loading are α = 0.8 and α =0.7 for strength parameters. The results show that the traffic load has only an influence factor 0.2. This explains some of the difference between the required and computed safety. Another influence may be a conservative assumption of the systems behaviour by the designers.
Acknowledgement We like to thank the members of the steel and concrete design offices of the civil engineering division of the Ministry of Public Works, Transport and Water Management for the support at the several FE models used in this paper.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Johnson, R.P., D.J. Huang, ‘Partial safety factors for composite beams in bending found from test data’, University of Warwick, Research report CE38, 1991 Johnson, R.P., D.J. Huang, ‘Calibration of safety factors for composite steel and concrete beams in bending’, Proc. Engrs Structs & Bldgs, Aug. 1995 Diana User’s Manuals, release 7.1, 1998 Waarts, P.H., ‘Directional sampling and FORM in structural reliability by means of an adapted response surface’, TNO–Report 98-CON-R0483, 1998 Hasofer, A.M., N.C. Lind, ‘An exact and invariant first order reliability format’, J. Eng. Mech. Div., ASCE, Vol. 100, 1974, p. 111-121. Bjerager, P., ‘Probability integration by directional simulation’, J. of Eng. Mech., Vol. 114, No. 8, 1988 Rubinstein, ‘Simulation and the Monte Carlo method’, John Wiley and Sons, New York, 1981. Vrouwenvelder, A.C.W.M, P.H. Waarts, ‘Traffic loads on bridges’, Structural Engineering International, no. 3, IABSE, 1993 Vrouwenvelder, A.C.W.M, A.J.M. Siemes, ‘Probabilistic calibration procedure for the derivation of partial safety factors for the Netherlands building codes’, Heron, vol. 32.
9
A Method For The Creep Analysis Of Composite Cable-Stayed Bridges
Gan XIA Civil Engineer Ruhr-Universität Bochum, Germany
Rolf KINDMANN Professor Dr. -Ing. Ruhr-Universität Bochum, Germany
Gan Xia, born 1963, received his Master degree in civil engineering from Southeast Univ., Nanjing, P.R. China. He is currently a research assistant at Ruhr-University Bochum. His research interests include the time-dependent behaviour of composite structures.
Rolf Kindmann, born 1947, worked for one of the greatest German companies for 10 years. He was head of the technical departments for the design and construction of structures. Since 1990 he is professor for steel and composite structures at the University in Bochum.
Summary This paper proposes a method for the time-dependent analysis of composite cable-stayed bridges. Using this method creep analysis can be performed by applying finite element method in only one time step and therefore it is useful for practical design. A fictitious transformed section for creep analysis is introduced and equivalent loading vectors are derived from the newly obtained results of creep analysis of generic composite sections. A numerical example of application is given for a composite cable-stayed bridge.
1.
Introduction
Due to creep of concrete, redistribution of stresses and/or stress resultants, loss of prestress and additional displacement in a composite structure made of steel and concrete may be occurred. Therefore, the time-dependent analysis is unavoidable for designing composite structures. For the creep analysis of complex composite structures by applying finite element method there are two types of analysis methods with regard to time discretization, namely step-by-step [1] and onestep method [2,3]. As an internally heterogenous structure with external elastic restraints the ‘exact’ creep analysis of composite cable-stayed bridges has to be performed by using numerical step-bystep techniques with more than 100 calculation steps [1]. One-step method is apparently applicable for most practical designs. Klement [2] proposed an approach which is based on some solutions by using dischinger method (or rate of creep method) to analyse composite structures, while the method proposed by Schade [3] is based on the age-adjusted effective modulus (AAEM). It should be noted that the solutions for composite cross sections obtained by using dischinger method and the usual AAEM method inevitably have errors, which in some cases are negligible, but in other cases unnegligible. A new method has been in [4] developed for the creep analysis of generic composite sections, which was direct based on the integral-type creep law (i.e. the superposition equation) of concrete and mathematically exact on the usual hypotheses. Therefore, the accuracy of the results by using the new method is better than ones by using the AAEM method or the dischinger method.
1
Based on the new results, this paper proposes a one-step method for the creep analysis of complex composite structures including composite cable-stayed bridges. The basic assumptions of this paper are: (1). Instantaneous strain and creep of concrete are linearly proportional to the applied stress, so that the principle of superposition is applicable; (2). Plane sections remain plane so that the total strain distribution is linear; (3). Time development of internal forces due to creep and shrinkage in interval (t0,t) in a statically indeterminate composite structure depends linearly on the creep coefficient ϕ(t,t0); (4). Internal forces after creep are distributed longitudinally linearly along a finite beam element.
2.
Section properties
2.1
Properties of transformed section for elastic analysis
Elastic analysis of a composite section at the time t0 can be easily performed by using so-called transformed cross section properties, which is illustrated in Fig. 1. The properties of the transformed section can be calculated by the following formular: Ec,Ac,Ic
Es,Acϕ,Icϕ
Es,Acr,Icr Gc ac
⇒
a
as
ac Gi0
aϕ Es,As,Is Gs
Es,As,Is a)
b)
Giϕ
Es,As,Is
c)
Fig. 1 a) Original cross section b) Fictitious cross section for elastic analysis c) Fictitious cross section for creep analysis Ac I ; I cr = c n0 n0 Ai 0 = As + Acr I i 0 = I s + I cr + S i 0 ⋅ a Acr =
Si 0 = As ⋅ a s = Acr ⋅ a c =
(1) As Acr ⋅ a Ai 0
where n0 =
Es E c0
= ratio of elasitic moduli,
2
Es, Ec0 As, Is Ac, Acr Ic, Icr Ai0, Ii0 Si0 a, ac, as 2.2
= Young’s modulus of steel and of concrete at time t0, = area and inertia moment of steel parts, = area and reduced area of concrete part, = inertia moment and reduced inertia moment of concrete part, = area and inertia moment of transformed cross section, = static moment for elastic analysis, = distance between the centroids of steel, concrete part and transformed cross section according to Fig. 1.
Properties of fictitious transformed section for creep analysis
Differing from the famous aging coefficients χ of the AAEM method, two corrected aging coefficients χN and χM for a composite section were in [4] derived, which are the aging coefficients with respect to the axial force Nc and bending moment Mc of concrete respectively and make an exact description of the creep behaviour of concrete in composite sections possible. The creep analysis of composite sections by using the method with the two aging coefficients χN and χM developed in [4] is similar to that of the famous AAEM method, but the results are exact under usual assumptions. For the purpose of the creep analysis of complex composite structures, we can define the following two corrected age-adjusted effective moduli for concrete in a composite section: E c0 1 + χ N ⋅ ϕ (t , t 0 ) E c0 = 1 + χ M ⋅ ϕ (t , t 0 )
E cχN = E cχM
(2)
By means of the corrected age-adjusted effective modulus EcχN and EcχM, a fictitious transformed section can also be introduced for creep analysis, which is similar to the above mentioned transformed section for elastic analysis and illustrated in Fig. 1c). The properties of the fictitious transformed section for creep analysis may be similarly determined with: Ac I ; I cϕ = c nA nI Aiϕ = As + Acϕ
Acϕ =
I iϕ = I s + I cϕ + S iϕ ⋅ a S iϕ = aϕ = (
(3)
As Acϕ ⋅ a Aiϕ 1 1 − ) As ⋅ a Aiϕ Ai 0
and
3
Es = n0 (1 + χ N ϕ t ) E cχN
nA =
Es nI = = n0 (1 + χ M ϕ t ) E cχM
(4)
In equation (3) and (4) ϕt=ϕ(t,t0) nA, nI Acϕ, Icϕ Aiϕ, Iiϕ Siϕ aϕ
= creep coefficient, = ratio of moduli for reduced area and reduced inertia moment of concrete part, respectively, = reduced area and reduced inertia moment of concrete part, = area and inertia moment of transformed cross section for creep analysis, = static moment for creep analysis, = distance between the centroids of the transformed cross sections for elastic analysis and for creep analysis (see Fig. 1c).
The aging coefficients χN and χM have to be previously found out in order to determine the properties of the transformed section for creep analysis. It should be explained that χN and χM for a generic composite section depend not only on the material properties of steel and concrete on the one hand and on the section geometrical properties on the other hand, but also on the type of loads [4]. For the purpose of determining the change of internal forces in a statically indeterminate structure due to creep and shrinkage, only the aging coefficients χN and χM for the loads which increase from 0 to its end value in interval (t0,t) linearly with respect to the creep coefficient ϕt (basic assumption 3) are of interest. For the determination of the fictitious section properties it is assumed that the aging coefficients for the varying axial force and varying bending moment have the same value. The calculation of χN and χM for the varying bending moment will be therefore discussed in the following. There are two ways to determine the corrected aging coefficients χN and χM. The first way is based on exact creep analysis of composite sections in which the integral-type creep law (i.e. the superposition equation) of concrete and a step-by-step procedure are used [4]. The extensive results according to the CEB MC 90 model [5] were reported in [4]. In this case, exact results for the creep analysis of composite sections are given by adopting the corrected aging coefficients χN and χM. The another way to determine χN and χM is approximate, nevertheless, in most cases excellent results can be obtained by using the approximate χN and χM if the formula proposed by Trost in [6] is used and the variation of elastic modulus of concrete can be neglected. The expressions for the corrected aging coefficients χN and χM in this case are as follows [4]:
χN =
1 I i 0 Acr ⋅ a 1 − ( β 1 − ω 1 ) µ M c1 − ( β 1 − ω 2 )(1 − µ M )c2 1 ⋅ − ] [ ⋅ ϕ t Is α Si 0 µ M c1 + (1 − µ M )c2
Ii0 Si 0 ⋅ a 1 I cr Si 0 ⋅ a 1 = − [ ⋅ ] M M ϕ t Is I i 0 − ( β 1 − ω 1 ) µ c1 − ( β 1 − ω 2 )(1 − µ )c2 α M
µ M c1 + (1 − µ M )c2 −
χM
(5)
4
where
α=
µM
As I s Is αM = ; Ai 0 ( I i 0 − I cr ) I s + I cr I ( β 1 − cr ) − ω 2 Ii0 ( I + I cr ) As β1 = s = ; ω1 −ω 2 I i 0 Ai 0
ω 1,2 =
I i 0 Ai 0 + I s As − I cr Acr I A + I s As − I cr Acr 2 I s As ± ( i0 i0 ) − 2 I i 0 Ai 0 2 I i 0 Ai 0 I i 0 Ai 0 −
c1 =
ω 1ϕ t 1+ 0 , 4 k vω 1
−
1− e ω 1ϕ t
;
c2 =
(6)
ω 2ϕ t 1+ 0 , 4 k vω 2
1− e ω 2ϕ t
1 1 +ϕt k v = − + with 2 4 k =1 v
für ϕ t < 2 für ϕ t ≥ 2
It is to be noted that the use of the Eqs. (5) and (6) is not restricted to the CEB MC 90 model and these expressions are also applicable to other creep models, e.g. ACI 82 model.
3.
Creep analysis of statically indeterminate structures
The change of the internal forces due to creep in a statically indeterminate structure consisting of heterogeneous sections may be calculated by using usual finite element program for elastic analysis. But the matrix of stiffness has to be determined by using properties of the fictitious transformed section for creep analysis (Eq.(3)) and for a usual beam element we have the following matrix of stiffness:
[k ]
e
ij
E s Aiϕ l 0 0 = − E s Aiϕ l 0 0
−
0
0
12 E s I iϕ
6 E s I iϕ
l3 6 E s I iϕ
l2 4 E s I iϕ
l2
l
0
0
−
12 E s I iϕ l
3
−
0
l
12 E s I iϕ
0
−
0
−
E s Aiϕ
6 E s I iϕ l
E s Aiϕ
2
6 E s I iϕ
2 E s I iϕ
l2
l
l 0 0
l3 6 E s I iϕ l2 0
12 E s I iϕ −
l3 6 E s I iϕ l2
6 E s I iϕ l2 2 E s I iϕ l 0 6 E s I iϕ − l2 4 E s I iϕ l 0
(7)
where l is the length of the element ij.
5
The equivalent loading vectors can be derived from the results which were obtained in [4]. For constant sustained load, for example, the axial force and bending moment increment of steel part of every section ∆Ns(t) and ∆Ms(t) can be obtained, namely ∆N s ( t ) 1 = ∆M s ( t ) − a s
0 1 0 T − ⋅ 1 − a 1 T
B nn B mn
Acr T Ai 0 ⋅ T 0
Si 0 As I i 0 Ai 0 − I cr 0 I i 0
−
B nm B mm
Si 0 I i 0 N (t 0 ) I s M (t 0 ) I i 0
(8)
where ω 1ϕ t
ω 2ϕ t
− − 1 T = [( β 1 − ω 2 )e 1+ 0,4 kvω 1 − ( β 1 − ω 1 )e 1+ 0 ,4 kvω 2 ] ω1 −ω 2 B nn
ωϕ
B nm
T
ω ϕ
1 t 2 t − − Si 0 I i 0 1+ 0 , 4 k vω 1 1+ 0 , 4 k vω 2 (e ) = −e ω1 −ω2
TmnB =
( β 1 − ω 1 )( β 1 − ω 2 ) (e (ω 1 − ω 2 ) ⋅ Si 0 I i 0
−
ω 2ϕ t 1+ 0 , 4 k vω 2
−e
−
ω 1ϕ t 1+ 0 , 4 k vω 1
(9) )
ω 2ϕ t
B mm
T
ω 1ϕ t
− − 1 [( β 1 − ω 2 )e 1+ 0,4 k vω 2 − ( β 1 − ω 1 )e 1+ 0,4 kvω 1 ] = ω1 −ω 2
The change of the strain and curvature ∆ε(t) and ∆κ(t) at the centroid Gϕ of the transformed cross sections for creep analysis can be easily found out because of the linear elastic property of steel (see Fig. 2): 1 ∆ε (t ) E s As = ∆κ ( t ) 0
aϕ − a s E s I s ∆N s ( t ) 1 ∆M s (t ) E s I s
The equivalent loading vector for constant sustained load can be then determined by
{P}e
∆ε i + ∆ ε j − E s Aiϕ ⋅ 2 6E I − s iϕ ⋅ ( ∆κ − ∆κ ) i j l − E s I iϕ ⋅ (4 ∆κ i − 2 ∆κ j ) = ∆ε + ∆ε j E s Aiϕ ⋅ i 2 6 E s I iϕ ⋅ ( ∆κ i − ∆κ j ) E I l ⋅ ( 4 ∆κ − 2 ∆ κ ) j i s iϕ
(10)
Gc G Gϕ (11)
Gs
∆ε
aϕ
x as
∆ε s
Fig. 2 Strain distribution in a cross section
6
where ∆εi, ∆κi ∆εj, ∆κj
4.
= strain and curvature increment of the left node i of a beam element, = strain and curvature increment of the right node j of a beam element.
Calculation procedure and numerical example
The creep analysis of statically indeterminate composite structures using the here presented method is divided into the following steps: 1. Calculation of the properties of the fictitious transformed section for elastic analysis and for creep analysis according to Eqs. (1) and (3); 2. Elastic analysis of the structure for various loads by using usual finite element program, in which the properties of the fictitious transformed section for elastic analysis (Ai0, Ii0) are used; 3. Creep analysis of the structure for sustained loads using the same finite element program but by means of the fictitious matrix of stiffness Eq.(7) and the equivalent loading vectors e.g. for constant sustained load according to Eq. (11), in which the internal forces N(t0) and M(t0) are the results of the elastic analysis (step 2). It should be noted that the structure for creep analysis has a system line which is different from that for elastic analysis(i.e. a remove of aϕ); 4. The results from step 2 together with that from step 3 as basis of the proof and design. To show its application, redistribution of internal forces due to creep in a cablestayed bridge (see Fig. 4) with composite cross section shown in Fig. 3 is evaluated by using the presented method. The properties of the cross section, the fictitious transformed section for elastic analysis and for creep analysis are shown in Table 1. The elastic internal forces N(t0), M(t0) and the change of internal forces Nϕ, Mϕ due to creep for sustained load g=300 kN/m, which are the results of first order analysis by using a finite element program, are illustrated in Fig. 4.
4000mm 250mm 400×20
2000×14
600×80
Fig. 3 Cross section
It should be said that the influence of geometric non-linearity in the stiffening girder (second order effect) has to be taken into account if higher precision is required. Ac cm2 10,000
Ic cm4 5.21×105
As Is cm2 cm4 840 4.86×106
a cm 164.3
Ai0 cm2 2745
Ii0 cm4 2.07×107
Si0 cm3 9.58×104
as cm 114.0
Aiϕ cm2 1626
Iiϕ cm4 1.59×107
aϕ cm 50.3
Tabel 1. Properties of cross section and fictitious transformed sections
7
5.
Concluding Remarks
In order to perform the creep analysis of statically indeterminate composite structures by applying the presented method, only the properties of the fictitious transformed sections and equivalent loading vectors have to be implemented in a usual finite element program for the elastic analysis of structures. The creep effects can be then evaluated in only one time step and therefore the presented method is useful for practical design.
aϕ=0 for elastic analysis aϕ=34.6 cm for creep analysis
24.0 m
aϕ
aϕ 20.0 m
20.0 m
20.0 m
M(t 0)
48037 kNm 19463 kNm
-3622 kN
-19427 kNm
-9004 kN N(t 0)
-19104 kNm -27287 kNm -26772 kNm Mϕ -934 kN
-2425 kN Nϕ
Fig. 4 Example
References [1]
Jurkiewiez, B. ; Destrebecq, J.-F.: A Global Approach to Account for Time Effects in Composite Structures. Composite Construction-Conventional and Innovative (Conference Report), Innsbruck, pp 229-234, 1997.
[2]
Klement, P.: Die Berechnung komplizierter Verbundstabwerke unter Verwendung üblicher Programme. Der Bauingenieur 60 (1985).
[3]
Schade, D.: Zur Berechnung der Schnittkraftumlagerungen infolge von Kriechen und Schwinden des Betons bei statisch unbestimmten Stabwerken mit Verbundquerschnitten. Der Stahlbau 49 (1980). 8
[4]
Xia, G.: Zur wirklichkeitsnahen Berechnung von Verbundkonstruktionen unter Berücksichtigung des zeitabhängigen Betonverhaltens. Dissertation, Ruhr-Universität Bochum, Oktober 1998.
[5]
CEB: CEB-FIP Model Code 1990. Final Draft, Bulletin D’Information No. 203, Lausanne, Juli 1991.
[6]
Trost, H.: Dischingers grundlegende Arbeiten und neuere Erkenntnisse über die Auswirkungen des zeitabhängigen Werkstoffverhaltens in vorgespannten und nicht vorgespannten Stahlbetonkonstruktionen. Spannweite der Gedanken, Springer-Verlag, Berlin, 1987.
9
Composite Structures in the Øresund Bridge
Henrik CHRISTENSEN Civil Engineer MSc Design Manager Øresundskonsortiet Malmö, Sweden Henrik Christensen received his degree from the Technical University of Denmark in 1987. He joined Øresundskonsortiet in 1994 and is Design Manager for the bridge.
1.
Kaj MADSEN Civil Engineer MSc Director Gimsing & Madsen A/S Horsens, Denmark Kaj Madsen received his degree from the Technical University of Denmark in 1959. He is a technical advisor to the ASO Group, the bridge consultant to Øresundskonsortiet.
Christian Riis PETERSEN Civil Engineer MSc Chief Engineer ISC Consulting Engineers A/S Copenhagen, Denmark Christian Riis Petersen received his degree from the Technical University of Denmark in 1978. He is technical advisor to the ASO Group, the bridge consultant to Øresundskonsortiet..
Introduction
The Øresund Bridge was developed for a design competition in 1993 by the ASO Group (Ove Arup & Partners, SETEC TPI, Gimsing & Madsen and ISC). The design was subsequently modified to a conceptual design and the ASO Group was appointed as the Owner's bridge consultant for carrying the concept to the tender stage. The bridge was tendered in 1995 as a "Detailed Design and Construct" contract, where the main visible dimensions were fixed by the Owner through contractual Definition Drawings. The bridge contract was in November 1995 awarded to Sundlink Contractors HB (Skanska, Hochtief, Monberg & Thorsen and Højgaard & Schultz). The detailed design for the Contractor is by CV Joint Venture (COWI and VBB). The bridge is 7.8 km long. The 1.1 km long cable-stayed High Bridge consists of a central navigation span with two side spans each side. Minimum vertical navigational clearance of the main span is 57 m. The High Bridge is connected to the artificial island, Pepperholm, and the Swedish coast at Lernacken via in all 6.7 km long Approach Bridges. The bridge deck is in two levels with a dual two-lane motorway at the top and a two-track railway at the bottom. The two levels are connected by two parallel Warren type steel trusses. The 20 m bay length of the truss is constant along the bridge. The conceptual design included both an upper road deck in concrete and a lower railway deck in concrete, but the tenderers were free to choose steel decks instead of concrete decks. The final solution was, however, that the concrete decks were preferred for the Approach Bridges and a lower steel deck was chosen for the High Bridge, where the weight saving was found more important than the otherwise cost effective composite solution. Road and railway bridges are to an increasing extent constructed as composite structures. In some of the most recent composite bridges a ‘double composite’ concept has been introduced, as the bottom chord has been strengthened by a concrete slab in regions at the inner supports. In this context the Approach Bridges of the Øresund Bridge are ‘double composite’ over the entire length. As extensive use of the composite principle was expected, a number of studies and investigations for the composite solution were carried out in the pre-tender stage along with the development of the design criteria to be used in the detailed design of the bridge structure.
2.
The Concrete Decks
2.1
The Road Deck
The upper concrete road deck is made both in the conceptual design and in the final design with bonded transverse prestressing tendons and normal reinforcement in the longitudinal direction. This solution can be classified as well known technology, which will lead to satisfactory behaviour of the concrete deck with regard to strength, rigidity and durability. The Contractor preferred to omit the prestressing and increase the thickness of the deck slab in regions adjacent to the in-situ stitches above the piers.
Cross section approach spans
20m truss module
Permanently unbonded tendons as an alternative to bonded tendons are widely used in building structures, but has only recently been introduced in bridge building. Long time experience with this solution under fatigue loading is thus not available. The use of unbonded tendons at the Øresund Bridge was restricted by the requirement, that the design of members should accord with a recognised code of practice, subject to the Owner's approval, but it turned out that this technology was not brought into play. The connection between the concrete deck and the steel top chord transfers a longitudinal shear force through a great number of relatively short 22 mm diameter headed studs. The transverse bending moments in the deck are partly taken up by the torsionally stiff steel chords. This transfer of stresses is secured by a smaller number of long studs over the webs of the chords, loaded in tension. The shear and bending connectors are placed along the entire length of the steel chords with a concentration at the 7 m length of the truss girder nodes. Full scale laboratory tests, carried out at the Danish Technical University, with a similar connection combining short shear studs and long tension studs designed for a non-realised proposal for the Great Belt West Bridge have shown a satisfactory behaviour. 2.2
The Railway Deck
The lower railway deck on the Approach Bridges is a containment structure comprising two parallel trough sections supported on cross beams spanning between the lower truss girder nodes. The trough sections are prefabricated and stitched above the cross beams and fixed at the same place to the steel structure. According to the ASO investigations it would be possible to apply longitudinal posttensioning after connecting the concrete deck to the steel structure. This solution was, however, found to be uneconomic, as a major part of the prestress force would be transferred to the steel structure. The lower deck is consequently made of reinforced concrete. ASO Group carried out analyses of alternative solutions, among others a separation of the concrete troughs from the steel structure. This would
eliminate tensile stresses due to global sagging moments. As a large number of bearings and joints would be involved the solution was, however, not considered feasible due to maintenance costs. Headed shear studs are used in a similar way as at the upper deck for the connection between the lower concrete deck and the steel cross beams. Short studs are mainly placed at the outer trough webs to transfer the longitudinal shear between concrete and steel, while long tension studs are placed at all webs of the troughs to transfer part of the local hogging moments in the troughs to torsion in the cross beams. The transfer of longitudinal shear leads to bending of the cross beams in a horizontal plane and thereby a certain rotation of the top plate of the cross beams relative to the bottom slab of the troughs and a non-uniform distribution of the stud shear forces in this area. A thorough calculation turned out to be necessary to demonstrate, that the stud forces were suitably limited in the serviceability limit state.
Cross section cable-stayed spans
3.
Structural Analysis
Elastic behaviour of the structure without moment re-distribution shall be assumed according to the Design Requirements for global static analysis at both the ultimate limit state and the serviceability state. The distribution of the internal forces between steel and concrete parts of the structure depends then on the stiffness of the concrete, which will be influenced essentially by formation of cracks in the concrete. Cracked sections are defined as sections where the maximum tensile concrete stress has reached the mean tensile strength fctm in the serviceability limit state. The stiffness of concrete cross sections may be based on gross-sections, and the modulus of elasticity shall be taken as Ecm for uncracked sections and 0.6Ecm for cracked sections.The use of simple rules of this kind is clearly convenient in large calculations, but it can be claimed, that the effect of a complicated process like crack formation, including tension stiffening, hardly can be covered by a single factor. In the present case it was realised during the design process, that the factor 0.6 may be unrealistic high in some situations.
4.
Shear Connections
Headed studs are used as already mentioned to connect the concrete deck structures with the steel truss girder. The basic codes of practice for the design of the Øresund Bridge were the Eurocodes, including EC4: Design of composite steel and concrete structures. Only Part 1-1 of this code comprising general rules and rules for buildings was available, and a comprehensive literature study of shear connections between concrete and steel was therefore carried out by the ASO Group, partly to assess the viability of alternatives to headed studs and partly to determine the fatigue characteristics of shear connections.
4.1
Type of Shear Connection
The result of the investigation regarding different types of shear connections was that the only realistic alternative to headed studs seemed to be the so-called PERFOBOND strip, developed by H.-P. Andrä, to be used especially in fatigue sensitive composite structures, eg. railway bridges. The basic idea behind this solution is to limit the contact pressure between concrete and steel and thus avoid premature crushing of the concrete and slip between concrete and steel in the state of serviceability. The practical solution is to introduce a roughness by welding a simple perforated steel plate to the flange plate of the beam. The perforated plate acts as an anchor as well, if it is placed in an upright position. Other measures to prevent uplift of the concrete plate are then superfluous. It has been demonstrated that it is possible to maintain a high static strength and plasticity during the complete fatigue life of this connection, even if it is set in a fully cracked concrete. Another point is that the perforated plate is connected to the steel flange by longitudinal fillets welds, which belong to a higher fatigue strength category than the weld of a shear stud or the transverse welds of other types of shear connections. The PERFOBOND strip shear connection has been applied in the road and railway bridge over the river Caroni, Venezuela. It is allowed at the Øresund Bridge according to the Design Requirements if a suitable test programme is set up and supported by a conceptual model. A test programme is not required for the headed stud solution, which is commonly used in modern road and railway bridges and thereby can be classified as well known technology. Headed shear studs were selected finally for the Øresund Bridge. 4.2
Static Strength of Headed Shear Studs
The ASO investigation showed that a proper model for the behaviour of headed studs is missing. The static resistance according to EC4 and several other codes of practice is given by two empirical expressions, one comprising the yield stress or the tensile strength of the stud material and another comprising the concrete strength and stiffness. Using high concrete strengths as in bridges, the expression based on the characteristics of the steel is governing. The failure mechanism of studs is normally described in the following manner: The shear effect leads to a concentrated pressure against the concrete at the root of the stud; this causes local failure (crushing or softening) of the concrete. The compression moves subsequently away from the root of the stud, which leads to the stud being gradually more and more subject to bending and tension. Based on this description it may be questioned, if a better value of the carrying capacity of the stud can be obtained by an expression involving the characteristics of concrete and steel at the same time. Research is made at present at the Danish Technical University in order to establish a theoretical clarification of possible failure mechanisms for headed studs and thereby an improved basis for predicting the resistance of such shear connections. The current formulas for the resistance of shear stud connections are mainly based on tests of the pushout type. Such tests have been criticised for being over-simplified compared to the conditions in composite beams. The push-out test specimen consist of a short length of a rolled steel I-section connected to two parallel, reinforced concrete slabs by means of the shear connection to be tested. The specimen is supported at the ends of the concrete slabs and a load is applied to the steel section. F. Leonhardt states that the studs are subject to compression and shear in the push-out tests, whereas the studs are subject to shear and tension in real structures. The push-out tests lead thus to an overestimated resistance. Research has been made to reveal if the shear capacity is influenced by crack formation in the concrete. The test results are contradictory, but it is believed that a 20% reduction of the stud shear capacity in concrete subject to tension is a very conservative estimate. The unfactored shear resistance of headed studs is according to EC4 equal to 0.8Asfu. As is the nominal stud shank section area and fu is the specified ultimate tensile strength of the stud material, limited to 500 N/mm2. The ASO investigation showed that the resulting safety level using this resistance is
considerably lower than according to the corresponding Danish and German rules. Especially the latter have been extensively used in major bridges with a satisfying result. Considering the above mentioned situation regarding the understanding of the behaviour of studs, it was decided to change the EC4 formula to 0.7Asfu and to introduce a further reduction by a factor 0.8 for studs set in concrete in tension. The rules are valid for studs of diameter 22 mm or less. 4.3
Fatigue Resistance Of Headed Shear Studs
The Eurocode requirements regarding fatigue resistance of headed studs are found in Eurocode 3, Design of Steel Structures, Part 1-1. The verification is based on nominal stresses corresponding to two failure modes: •
failure in the weld between stud and steel flange or in the heat affected zone under the weld; the detail is classified as a welded joint with load carrying weld; the nominal stress is the shear stress ∆τ on the cross section of the stud, and the fatigue strength at 2⋅106 cycles (equal to the detail category) is ∆τC = 80 MPa, • failure in the tension flange caused by the effect of attaching the stud; the detail is classified as a welded attachment with non-load carrying weld; the nominal stress is the normal stress ∆σ in the flange, and the fatigue strength at 2⋅106 cycles is ∆σC = 80 MPa.
A study of recent literature indicated that an interaction between failure of the stud and failure of the flange is possible if the steel flange is subject to tension. As for the static strength it is questioned by some authors if the push-out test specimen are sufficiently representative for composite beams. The outcome of the ASO investigation was, that the following verification procedure for the fatigue resistance of headed shear studs was decided: • •
the fatigue strength of headed studs in shear welded to a steel flange in compression shall be assessed in accordance with EC3, but using a lower detail category, 60 in stead of 80, the fatigue strength of headed studs welded to a steel flange in tension shall be assessed according to the following requirement for combined shear and flange tension when using constant amplitude stress ranges:
∆ τ E .2 ∆τ C
3 2
∆ σ E .2 + ∆σ C
3 2
≤ 1
where ∆τC = 60 MPa and ∆σC = 80 MPa are the fatigue strengths, while ∆τE.2 and ∆σE.2 are the equivalent constant amplitude stress ranges corresponding to 2⋅106 cycles, calculated from the basic fatigue strength curves for ∆τ and ∆σ according to the rules given by EC3. Partial safety factors shall be applied to the load effects and the materials strengths according to the Design Requirements. The interaction criterion is based on experimental evidence considering available beam test results but avoiding push-out tests in order to obtain a conservative rule.
Build a Link - Goals, principles, strategies and results Peter LUNDHUS Civil Engineer, M. Sc Technical Director Øresundskonsortiet Copenhagen Denmark
Peter Lundhus graduated in 1965 from the Technical University of Denmark as M.Sc in civil engineering. From 1965 to 1988 he worked for an international contractor, covering all aspects of design, bidding and construction of civil engineering works. From 1988 he joined the owner organisation responsible for the construction of the Great Belt Link. In 1992 he was appointed Technical Director for the Øresund Link
Introduction Scandinavians have a tradition for building bridges – which, of course, is quite natural for countries surrounded by water – or characterised by large lakes and fjords. But a bridge is not just a bridge. In the case of the Øresund Link, we're talking about one of the largest infrastructure projects in European history. Its dimensions and position are both unique, as are the technical challenges confronting the builders. In addition, there were significant psychological barriers to be overcome before Denmark and Sweden decided to build the link in 1991. Building a bridge between two nations, Denmark and Sweden – in an area of 3 million inhabitants - is an enormous undertaking. Yes, our two countries have a great deal in common in terms of their past history and future interest. Yet we have different traditions, different systems and, in many ways, a different approach to things. The bridge, therefore, will have large impact on the surrounding region – culturally and economically as well as in terms of development. Technically, too, we have had to find common ground. In one country for instance, the railway runs on the left, in the other on the right. The Øresund Fixed Link is a combined rail and motorway link extending 16 km between Kastrup on the Danish side to Lernacken on the Swedish side. From the project's earliest days, it has attracted enormous interest from political circles, from the authorities, from future users and from the local residents. Where should the link be sited? What should it look like? How will it affect the environment? These are just some of the many questions raised in the media – questions which have added to the pressure on decision-makers, authorities and the project's owners on both sides of Øresund. The populations demanded to be heard on issues relating to traffic, the environment and finance. The environment played a particularly major role in the debate in advance of the decision to build the Øresund link – a relatively new item on the agenda. As late as the mid 1970s, Danish and Swedish authorities seriously
considered building a new airport on the island of Saltholm in Øresund. 10-15 years later, as the 80s drew to a close, Saltholm had become a protected area. The effect of the Fixed Link on the environment, therefore, became a subject for heated debate at all levels. In Scandinavia, debates of this type are unlikely to be quiet affairs and, true to form, our democratic traditions gave rise to extensive discussion among all interested parties. The project was taken very seriously indeed - by organisations and interest groups, by future users and by its neighbours. By tradition, Scandinavians are inclined to be critical. They put questions to political leaders and they demand answers. And they're not satisfied with easy solutions. In this respect, too, Øresundskonsortiet has earned the title of "bridge builder." What distinguishes this project from many other projects, however, is its surrounding community and the many factors that needed to be taken into account: -
The project is politically sensitive and has been highly affected by the political decision processes relating to other infrastructure projects (Øresund's landworks, the City Tunnel, etc.
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Although its framework was laid down from the outset, the project had to define its own standards and ascertain whether they worked.
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In view of the attention given to local as well as global environmental issues, the environmental impact of the construction process, as well as that of the completed traffic facility, has had to be considered very carefully.
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The professional demands on those involved have been very high. A contributory factor has been the strong emphasis on quality and transparency in recent years.
The Decision to build the Bridge The decision to build the Øresund Fixed link was taken by the Danish and Swedish governments in 1991, when the two parties each agreed to establish a state-owned limited company for the purpose of forming Øresundskonsortiet which would be responsible for constructing the Øresund link. In addition, the government agreement assigned Øresundskonsortiet the task of operating and maintaining the link following its completion in the year 2000 – partly by levying toll fees on the link's users. Some considerable time elapsed, however, before the detailed planning, let alone the construction phase, could commence. On the Danish side, a number of hearings on the assessment of the effects on the environment as well as on the control and monitoring programme for the coast-coast section and near-lying areas were held.
Final permission In Sweden, the establishment of the Øresund Fixed Link was tested under the terms of the Natural Resources Act, the Water Act and the Environmental Protection Act. On June 16, 1994 the Swedish Government approved the construction of the Øresund Link under the terms of the Natural Resources Act and the Water Act and in 1995, the Licensing Board for Environmental Protection gave its permission to build and operate the fixed link on Swedish territory under the terms of the Environmental Protection Act. Then, in a verdict in July, the Swedish Water Court gave permission to construct the Fixed Link under the terms of the Water Act. At the same time, the Water Court set out the environmental requirements which Øresundskonsortiet had to meet in connection with construction activities in Swedish territorial waters. On July 8, 1994, the Danish Government approved the project. In March 1995, the Danish Minister of Transport approved the Øresund project's environmental quality objectives as well as the criteria and requirements for the control and monitoring programme for the link's Danish sections. The period prior to the decision The extensive investigations and verifications generated considerable uncertainty among the populations of the two countries. In particular, the environmental impact of the Øresund Fixed Link was, as I said, the subject of enormous public interest and debate. Economic and technical issues as well as future expectations were widely discussed. These debates, however, did not deter Øresundskonsortiet. The time was spent laying down the strategy – how best to proceed? The dual-nationality of the project, for instance, necessitated a detailed examination of the different legislation in the two countries. In fact, for each decision concerning the facility's design and construction, Øresundskonsortiet had to examine the legislation of both countries – a task which was not made any easier by the fact that, at this stage, Sweden had not yet become a member of the EU. Consequently, a number of EU laws and regulations had to be considered. In each individual case, Øresundskonsortiet had to decide whether a joint platform could be established (the lowest common denominator), whether EU regulations applied or whether Øresundskonsortiet was able to set its own standards and norms. With regard to norms, it became clear that a number of problems were bound to arise. Since Denmark and Sweden do not apply the same norms and regulations, Øresundskonsortiet was faced with the choice of either co-ordinating the existing norms of the two countries or coming up with an alternative solution. Consequently, the consortium decided to apply the future EU regulations or, in cases where norms had not yet been defined, to work actively towards making them applicable to the project. In this way, Øresundskonsortiet solved both the project's own technical norm problems and acted as a catalyst for the definition of a series of technical EU norms. In fact in several instances, this marked the initial introduction of a number of EU
norms. Since then, such norms have been applied at several other projects, including the Metro project in Copenhagen. Within the field of the working environment, Øresundskonsortiet was also faced with certain choices. Here too, both countries have different norms – but in accordance with Øresundskonsortiet's objective of keeping the number of work-related accidents to less than half the national average (in Sweden and Denmark as well as in Spain where the bridge girders are built), the working environment requirements were written into the contracts which stipulate that all planning must incorporate the environment.. In addition, an extensive safety-at-work campaign has been focused on the employees throughout the construction period. One aspect of the safety-at-work campaign is that it has continuously emphasised the individual employee's personal responsibility as far as safety issues is concerned. In the light of the political requirements from the two countries, Øresundskonsortiet adjusted the original alignment as well as the link's technical design. The objective was to optimise the link - technically, economically and environmentally - in order to reduce any harmful effects on the environment. The new project Following international tender, Øresundskonsortiet invited Øresund Link Consultants and the ASO Group to put forward proposals for the link's design. The results from these proposals formed part of the ongoing planning of the project for, for instance, the purpose of ensuring that the facility's blocking effect on the water flow in Øresund was reduced. Øresundskonsortiet also decided to split the coast-coast section into five large projects: -
Dredging & reclamation work (6 contractors tendered) The immersed tunnel under the Drogden Channel (5 tenders) The low and approach bridges (6 contractors took part in the competition) The high bridge across the Flinte Channel (5 contractors tendered) The railway engineering system and installations
Organisation Øresundskonsortiet's main aims are: -
The design and construction of the Fixed Link to Sweden Ownership Operation and maintenance of the Fixed Link the organisation has two key functions – to establish the link and to operate and maintain it
Organisation diagram Management Joint functions
Staff
Technical Department
Operations
Management principles Øresundskonsortiet's management principles are not static. Flexibility is an important component in the whole process and Øresundskonsortiet is conscious of its responsibility to initiate and motivate change within its own organisation as well as within its partners and the world beyond. For all this to happen, two pre-conditions must be met: -
Everyone should know the objectives Everyone should know how we achieve them
The vision Øresundskonsortiet's basic management principles can be summarised as management by objectives, delegation and pro-activity. Consequently, from the earliest stage, Øresundskonsortiet defined clear goals within the vision and business concepts. As such goals should be measurable, a strategy for their achievement was developed. Once the goals and strategy are in the place, Øresundskonsortiet determines the organisational structure which will eventually realise the goals and business concepts. At regular intervals (approximately every six months), the objectives and strategies are reviewed. Wherever necessary, Øresundskonsortiet adjusts the organisation to ensure that sufficient resources are available for the tasks in hand – and that those in charge of individual tasks have the authority to act accordingly. This "controlled process" serves to emphasise the concept of pro-activity – that Øresundskonsortiet is ready to act before events force us to and that any change of direction has been carefully considered. The successful implementation of a project the size of the Øresund Link – and within such a short time span – requires the existence of a company culture which
continually and naturally adapts to new demands and requirements, internally as well as externally. No less importantly, it also requires an acceptance of openness, a willingness to listen to suggestions and to adapt to ideas from partners as well as from the world at large. Only in this way will Øresundskonsortiet be able to bring the project to its successful conclusion and thereby lay the foundation for strengthened links between Sweden and Denmark. The bridge as the Øresund region's focal point The Øresund Fixed Link is intended to bring Denmark and Sweden together – two countries which are each other's largest trading partner. It will also draw Europe closer together. Once the link is completed, there will be fixed rail and motorway connections from the North Cape in Northern Norway to Southern Italy for the first time ever. In the process, Copenhagen and Malmø will become one city – a new metropolis with a highly skilled workforce of nearly 2 million – offering the best from the two nations, economically, technologically and culturally. Linking two of Europe's most developed societies, the link represents a huge advance in terms of public transport. Both Denmark and Sweden are, of course, members of the European Union and both countries enjoy long traditions for political stability, stable economies and high educational standards. It should also be noted that this huge investment in public transport is a consequence of the region's endeavours to create environmentally sound growth. This philosophy for growth is a natural extension of the whole concept of the Scandinavian model. The Øresund region will become Northern Europe's political and economic centre – a centre which will attract large numbers of businesses, organisations, scientists and researchers as well as tourists. With 3.2 million inhabitants, the region will, in fact, be Northern Europe's largest domestic market, equalling Berlin, Hamburg and Amsterdam. The region will also become a natural centre for inward and outward economic activity in the Baltic area and parts of central Europe. Our biggest ports already handle very large quantities of freight and Copenhagen Airport in Kastrup is Northern Europe's largest and most modern. Significant investments are also being channelled into railways and motorways on both sides of the Fixed Link. In a number of contexts, the region will be at the cutting edge of international developments – not least within the field of biochemistry, pharmaceutical production, medical equipment, IT, environmental technology and food processing. In these areas, a number of companies and research institutions rank among the foremost in the world, at least partly because of the exemplary collaboration between the public and private sectors in creating the optimum conditions for development environments.
Design and industrial production also have a high profile, with a number of world class designers and architects living and working in the area. As a conference destination, the region is the foremost in Northern Europe. The level of education, too, is second to none. The population of the Øresund region is open, socially responsible and internationally-oriented. To most Scandinavians, English is the second language and many are familiar with German, French, Spanish or Russian from their senior school classes. The quality of life in the region is among the highest in the world and its inhabitants benefit from unparalleled personal safety, freedom and excellent public systems – including free education and an extensive and free health system. Vision and strategy In 1994, Øresundskonsortiet invited tenders for the link's main contracts – the tunnel, the dredging works, the high bridge and the approach bridges - based on the principles in the EU Directive 93/37/EEC concerning public agreements. This was despite the fact that the directive did not yet apply to the Øresund Link. The tender process itself did not follow traditional methods either. Due to the dualnational aspect, Øresundskonsortiet was able to lay down its own tendering strategy. In a traditional tendering process, the client undertakes the detailed planning and then invites tenders for a number of contracts in international tendering. You could say that the architect designs the house and the contractor prices and builds it. In the background, the client manages the entire process with a firm hand. Øresundskonsortiet wished to handle the process differently. For instance, the consortium wanted to avoid the discussions, confrontations and arbitrations which are often inherent in conventional client-contractor relationships. The aim, of course, was to build the facility at the agreed price and at the agreed time – and also to create a working relationship which ensured fair and constructive collaboration between the many parties involved. The basic concept was "partnership." A survey of Øresundskonsortiet's "stakeholders" revealed that no fewer than 150 organisations were involved in the project, all of which all exercised a degree of influence. Unless this was tackled in a new way, it could easily lead to a large number of confrontations.
Stakeholder diagram Companies Organizations Media Citizens
Parliament
Municipalities Neighbors
Government Øresundskonsortiet
Transport authorities
Expropriated
Fixed link
Road-and-rail-users
Contractors Consultants
Øresundskonsortiet's basic concept, therefore, was to be a client that valued a constructive partnership with all parties involved, including, of course, the contractors. In contrast to the conventional methods, the consortium did not wish to manage in detail, but to delegate responsibility and power while, at the same time, maintaining an constant overall view. The contract philosophy One consequence of this was the introduction of the Design+Construct philosophy which provided the contractors with strong draft proposals – and, not least, a free hand to improve the project. The concept is that responsibility for detailed planning and execution should be clearly assigned. This limits the conventional working relationship's potential for confrontation and provides the individual contractor with greater opportunity for solving his task efficiently. This again creates committed contractors who become involved in the detailed planning, initiating improvements and who feel total responsibility for the execution. This involves considerable freedom for the contractor – a freedom which the client must be continually aware of and respect.
The basic premise for Design+Construct is the illustrative design where the client has developed one or more designs which meet all specifications set out by, for instance, the authorities and the client. You could say that it's the client's "homework" that provides the contractor with the parameters for the execution of the task: this is how it can be if the regulations are adhered to. Since, however, the contractor possesses considerable knowledge, the project will inevitably be improved once the contractors have examined it. With the illustrative designs, Øresundskonsortiet provided constructive groundwork which was made available to the bidding contractors, guiding them in the right direction while not tying them down. At this stage, a number of requirements from the authorities, approval of worksites as well as a series of obvious questions which always crop up at the detailed planning stage, had been taken care of. Quality All contracts comprise descriptions of the fundamental quality management philosophy of "own control". This means that the contractors have been assigned responsibility for the design and administration of the quality management systems and the quality control of their own work. The contractors must therefore establish/implement and maintain an extensive quality management programme based on the EN 29001 standards. The programme must comprise the construction works (temporary as well as permanent), the external environment and the working environment (health & safety). KKSURR As part of the consortium's preparatory work on safety, accidents, rescue and clearance, close working relationships have been established with a number of individuals representing the authorities (police and emergency authorities) on both sides of Øresund. This aimed at involving the authorities in an advisory capacity in relation to Øresundskonsortiet's draft proposal to the contractors, thus ensuring that the regulations laid down by the authorities of both countries as well as their professional and technical knowledge contributed to the quality of the completed facility. These joint efforts have meant, for instance, that general agreement on the facility's safety systems was achieved - for example on possible sprinklers in the tunnel. In this case, the KKSURR members agreed that the disadvantages outweighed the advantages of sprinklers because they would make the smoke wet, heavy and more difficult for the rescue teams to work in. The involvement of these representatives, however, in no way undermined the authorities' role as the final arbiter of the facility. In the example mentioned above, the authorities subsequently approved the KKSURR members' recommendation concerning the sprinkler system. Assessment of risks A natural consequence of this model is that the contractor has full responsibility for risks over which he has control, ie. detailed planning, the workforce, permissions from the authorities. On his part, the client is responsible for other risks: currencies, political aspects, the overall granting of approvals by the authorities, i.e. areas in
which contractors traditionally calculate a risk premium and which often become subject to dispute following the completion of a project. Dispute Review Board The Design+Construct working relationship also reduces the number of potential conflicts compared to conventional methods. By establishing a Dispute Review Board, Øresundskonsortiet has further reduced the likelihood of a dispute. The principle is that a Dispute Review Board – a panel of three experienced, independent and internationally respected engineers – is set up for all contracts. They take no nonsense In the event of a dispute, the Dispute Review Board functions as chief arbiter. The Board convenes every second month when contractors give a briefing on the status of the contracts and bring up possible problems. The aim is to solve such problems as quickly as possible – preferably before they affect the running of the construction sites. The experience with the Dispute Review Board shows that problems are rarely allowed to come this far – if ever. Firstly, there are few potential areas for conflict (these have been pre-empted in the contracts). Secondly, the preparatory work for Dispute Review Board meetings reveals problems at an early stage, thus enabling them to be resolved before the matter is brought before the Board. The Board's decisions are not binding, but can be referred to arbitration. In the contracts, however, the parties have agreed to accept the Board's decisions until the arbitration process has been completed. The facility The aesthetic aspects of the Øresund Link have been subject to extensive considerations. The intention throughout has been for the link to appear as a whole with an architectural and aesthetic expression which reflects Nordic architectural traditions. The link should express a cohesive, rythmic harmony in which the individual components fit effortlessly into each other and where the details are subordinate to the project as a whole. The link should also complement the open landscape on each side of Øresund. The aesthetics of the Øresund Link have been comprehensively discussed at an international reference group with participation from international experts. The environment The governments of the two countries and their environmental authorities have laid down rigorous regulations for the acceptable environmental impact of the link. In many areas, Øresundskonsortiet has, therefore, had to develop new strategies and methods in order to limit the effects on the marine environment in Øresund and the Baltic Sea. The fact that the project extends across national borders has played a special role, too. In many instances, the project has had to obtain double approval
from the authorities. Consequently, due to the judicial, traditional and political differences between the two countries, variations in the definitions of the prescribed environmental requirements have occurred. A key element in the national hearing procedures has been the need to optimise environmental planning. The Øresund Fixed Link may not impact on the Baltic Sea (the physical/chemical marine environment and the biological marine environment in the Baltic). The construction works must only temporarily affect the environment surrounding the facility. This resulted in a number of changes, including: -
The blocking effect of the Øresund Fixed Link on the water flow may not exceed 0.5%. Compensation dredgings in the Drogden Channel will even reduce the blocking effect to 0%.
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Sediment spill from dredging works must be limited to 5% of the dredged material. The spill must be limited in intensity, time and space.
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Total dredging works for the entire Øresund Fixed Link must be limited to m3 7 million.
The changed conditions necessitated a change to the facility's design. A more northern alignment was chosen and the Danish land facility at the Kastrup peninsula was modified. Compensation dredgings were carried out in the Drogden Channel while the immersed tunnel was extended and its alignment altered. The design of the artificial island was also changed and realignment and dredging of the Flinte Channel were carried out. The stipulated requirements also incurred further costs, particularly as a result of the new tunnel solution and the compensation dredgings. Control and monitoring programme – an example of good co-operation The Design+Construct partnership has also resulted in a novel solution within the field of the environment. The authorities' demand for a control and monitoring programme resulted in the setting up of the On-line system, EAGLE, which enables the authorities, the client and the contractor to monitor the environmental impact of the construction works on an ongoing basis. The EAGLE system is operated by the contractor who, as part of the contract, has assumed responsibility for meeting the authorities' requirements. The point is that the system makes it possible for both authorities and client to follow developments. In practice this means that only one environmental monitoring vessel – the contractor's is permitted to sail in the area. It is not necessary for the authorities or the client to operate their own vessels as both are kept informed via the EAGLE system. This is one example of Øresundskonsortiet's delegation of responsibility to the contractor and its confidence in the fact that the contractor will fulfil his contractual obligations.
In order to check that the prescribed environmental requirements and conditions are met, a number of control and monitoring programmes have been established and implemented. These must ensure that no unexpected short or long-term impact on the environment occurs during the construction period. A further aim is to document that the stipulated environmental requirments and conditions are maintained. Execution and economy The project's economy has developed steadily – and as expected. The extensive cooperation with the contractors has meant that the Consortium has maintained a clear overview of all activities. Only in one instance has it been necessary to revise the budget. The only major item to impact on the budget has been the so-called zero-solution designed to ensure an unchanged water flow through Øresund. This meant that the budget had to be increased by approximately DKK 1.5 billion. The experiences The Øresund Fixed Link must be ready by the summer of the year 2000. This is the overall objective which Øresundskonsortiet and the contractors are working towards. The secret behind the new time schedule is a "parallel works" approach on various sections of the project. The purpose of "parallel works" is improved utilization of time. Thus, any surplus time on one project is transferred to another contractor who lacks time. It's obvious, for instance, that the bridge has to be welded together before rail tracks are laid. But the rail contractor can begin preparations before the high bridge is ready. Øresundskonsortiet could not have operated the Parallel Works method over the last two years unless co-operation procedures had allowed for planning across the contracts. Conventionally, each contractor has completed the task assigned to him as quickly as possible – irrespective of whether his neighbour might benefit from using, for instance, some of his scaffolding overnight in order to finish more quickly, too. With the parallel works method, we created a common understanding of the project's time schedule – and an openness and knowledge of time schedules etc., which has made it possible for everyone to "pull together" in the final months. Such co-operation means that the individual contractor doesn't have to accelerate his pace of work in order to be finished on time – rather, that he has more time and scope to complete on time – and thus achieve the bonus offered by us. Of course, the client doesn't give a bonus to the contractor just because he's completed his task, but because he has co-operated with others so that everyone can finish on time.
The Øresund Bridge: Project Development from Competition to Construction Klaus FALBE-HANSEN Civil Engineer MSc Director Ove Arup & Partners DK Copenhagen, Denmark
Örjan LARSSON Civil Engineer MSc Contract Director Øresundskonsortiet Malmö, Sweden
Klaus Falbe-Hansen is Project Director of the ASO Group, the bridge consultant to Øresundskonsortiet.
Örjan Larsson is Contract Director responsible for the Øresund Bridge Contract.
Summary Øresundskonsortiet, formed January 1992, is owned jointly by the two states Denmark and Sweden and is the Owner of the Øresund Link. Øresundskonsortiet is responsible for planning, designing, financing, constructing, and after completion of the road and rail Link of its operation and maintenance. ASO Group is the bridge consultant and was engaged by Øresundskonsortiet in 1993 after an international design competition. ASO Group is responsible for the bridge concept and is presently integrated in the Owner organisation with particular responsibility for monitoring the construction works of the bridge. The paper describes the project development that took place for the bridge from the design competition to the construction. Also described are the Owner’s construction contract strategy, the quality management policy and the Owner’s active role through cooperation with the Contractor in achieving the earliest possible opening of the Link.
1.
Introduction
Øresundskonsortiet invited, towards the end of 1992, engineers and architects to take part in a competition for the design of the Link. In response to the invitation the ASO Group was formed by Ove Arup & Partners of the UK with SETEC of France and Gimsing & Madsen and ISC of Denmark. Georg Rotne of Denmark is architect to the group. The group was selected for the competition together with five other international groups. The competition led to two teams, ASO and ØLC, being chosen to develop their designs further. As a result of this ASO later became consultant for the bridge and ØLC became consultant for the tunnel and reclamation works. The basic principle of the construction contract is the design & build concept. It means that the Contract specifies a number of requirements that the finished product shall fulfil. The Contractor has undertaken to design and construct works that fulfil the requirements. The Owner has undertaken to pay the contract price. The undertaking of the Contractor includes everything required for the total completion of the “Portion of the Link” to a state in which it is “fit for its intended purpose”. Excluded from the Contractor’s undertaking are only those items that are expressly excluded by the Contract. This runs contrary to the principles of a traditional construction contract. Basically the Owner specifies what the Contractor shall achieve, and the Contractor determines how to achieve it. As a logical consequence of the design & build concept the Owner has adopted the basic quality assurance principle of self-control. The Owner is monitoring the Contractor’s compliance with his Quality System and the requirements of the Contract. Although only Denmark was a member of the EEC at the time of signing the Contract, the Council Directive 93/37 EEC, restricted procedure including prequalification, has been applied in the procurement process throughout.
2.
From Competition to Tender
The design competition took place over a few months in the early part of 1993 and the result was announced in July that year when two group’s proposals were chosen as joint winners. They included two very different bridge designs: ASO Group’s two-level predominantly steel structure with the road placed above the railway and ØLC’s proposal for a single-level concrete bridge with the railway placed in between the two road carriageways. Øresundskonsortiet decided to develop both designs further in parallel before choosing between them. In the following only the two-level solution is described in any detail as that in the end proved the successful concept.
The two-level bridge The detailed concepts were developed during the later half of 1993. The two-level bridge concept as developed during the short competition phase proved a robust design and fundamental changes to the concept were not required. Early 1994 it was decided that both bridge solutions should be taken forward to bidding stage on a common alignment. A number of alternatives for the layout of the whole Link were prepared and evaluated at this stage. The main issues were the environmental impact of the Link and the economic consequences of alleviating the impact. The critical factor was the blocking of the water flow through Øresund due to the physical obstruction of the Link. The main parameters in these investigations were, the extent of the artificial peninsula at Kastrup, the length of the tunnel and artificial island, and also whether the island should be split in two with the opening being bridged by a low level structure. Number of and shape of bridge piers were also considered in these studies. A value of the blocking effect of the Link at around 2 to 3% had been assumed acceptable by the governments at the time of the Øresund Treaty in 1991. However, it soon became apparent that a much lower value had to be achieved if the project were to gain the necessary environmental permits. The environmental investigations carried out by Øresundskonsortiet and their consultants proved that a ‘zero solution’ could be achieved without serious economic consequences, and on this basis the two governments gave their approval in the summer of 1994 to constructing the Link. However, the Swedish environmental legislation requires that the Swedish Water Court, which is independent of the Swedish government, must rule on the effect on the water regime of constructing the Link as a prerequisite of giving the permission to construct the Swedish part of the Link.
In July 1995 the Water Court gave its ruling on the construction of the Swedish part of the Link, which constitutes approx. 80% of the bridge. The Link itself should be designed so as to limit the blocking effect to 0.5%. To achieve the ‘zero solution’ compensation dredging should be carried out. A maximum of 7 million m3 could be excavated in connection with the construction of the Link of which the excavation in Swedish water was limited to 2 million m3. Another important part of the ruling was that the sediment spill during dredging activities for the whole Link must not exceed an average maximum of 5% of the total dredged volume. The Concession Board, another independent Swedish authority, at the same time ruled that it would not put any restrictions on the traffic on the bridge, thus giving Øresundskonsortiet the right to construct and operate the Swedish part of the Link.
The Øresund and the Baltic
With these approvals the main legal obstacles for the construction of the Link had been cleared. The timing and content of the rulings were critical considering that the tender documents, the so-called Enquiry Documents, had been issued to the prequalified bidders in December 1994 and their bids received in June 1995 i.e. before the ruling of the Water Court. 2.1
Contract Strategy
At an early stage Øresundskonsortiet had decided to let the works in the form of design & build contracts based on the following principles: • • • • • • •
Owner’s defined requirements on function, aesthetics, safety and environmental protection, everything included in Contractor’s scope of work unless expressly excluded, only specified duties of the Owner, specified division of risks attributable to geotechnology, weather and permits, Contractor’s self-control within QA system, Owner is monitoring the Contractor’s performance and review/inspection/approval does not relieve the Contractor.
Øresundskonsortiet also decided not to follow any standard general conditions. In stead a tailor made document, General Conditions of Contract containing all general and legal provisions, was produced for the project. Under the form of contract chosen the Contractor has considerable freedom regarding the means and methods for carrying out the works. The Contractor is responsible for the detailed design as well as the physical works. He is supervising his own work and is responsible for providing documentation to prove that he is doing so, and that as a result the work he is doing is of the quality required by the Contract. This means that the Contractor is approving his own work. However, the Owner is monitoring the Contractor’s performance. The contract strategy led to the inclusion of a number of particular documents within the Enquiry Documents issued to the bidders: • • •
Definition Drawings and Illustrative Design Reference Conditions Quality System Requirements
2.1.1 Definition Drawings and Illustrative Design The design & build type of contract has some obvious advantages, but clients have little direct influence on designs as long as the functional requirements formulated in tender documents are met and the design conforms to the design basis. In the case of the Øresund Bridge, extensive consultations had been held with authorities in the two countries on matters like aesthetics, environment, road and railway operation, navigation, safety, etc. The designs prepared by the Owner’s consultants were markedly influenced by these activities and included many features over which the Owner wished to maintain control. Some of these could be expressed as functional requirements but some important design features could not. The Enquiry Documents therefore included not only the usual design and construction requirements but also Definition Drawings, which described the design features, geometry, and materials that should be retained in the Contractor's design. The Definition Drawings were only concerned with the visible geometry, foundation types and sizes were not shown. The Illustrative Design drawings were included as an example of a design, which fulfilled the Owner's requirements. The Illustrative Design was included in the Enquiry Documents for information only and would not become part of the Contract, while the Definition Drawings were contractual documents, which the Contractor was obliged to follow in order to fulfil the requirements of the Contract. 2.1.2 Reference Conditions Reference Conditions refer to geotechnical conditions and weather conditions, and define benchmark values above or below which as the case may be the Contractor is entitled to compensation. The purpose is to avoid the Contractor having to unnecessarily add contingencies to his lump sum price. Regarding the geotechnical reference conditions the Owner had, prior to issuing the Enquiry Documents, carried out his own site investigations in the bridge line and he had also carried out detailed testing on shore of in particular the predominant Copenhagen Limestone. The geotechnical conditions contained the ground stratigraphy and a summary of the strength and deformation properties for the ground. Bands of uncertainty were provided within the Reference Conditions and the Contractor must accept these as ‘foreseen’ ground conditions. Where the ground conditions were outside the Reference Conditions, the Owner accepted the risk, and the Contractor would be compensated for proven extra cost. However, he was not required to ‘compensate’ the Owner if conditions were better than assumed. 2.1.3 Quality System Requirements The basis for the Owner’s monitoring of the Contractor’s work is the Contractor’s Quality System and the Owner’s requirements to this system were laid down in the document, Quality System Requirements. The Contractor was required to establish, maintain and adhere to a Project Quality Programme, specifically adapted to the Contract. The PQP may adopt routines and procedures developed for the Contractor’s internal quality system, if applicable to the Contract. The PQP had to be based upon the contract document, Quality System Requirements, which in turn is based on the EN ISO 9001 standard, 1st edition. The PQP should be documented by a Quality Manual including General Procedures and a number of Quality Plans. The Quality Manual and the General Procedures (typical administrative procedures) are meant to set out the overall systems and principles governing for all activities under the Contract. The Quality Plans with method statements and work procedures are intended to be the Contractor’s operative instruments for his planning, execution and control of the numerous work activities.
2.2
Tender
Øresundskonsortiet decided to split the bridge into two contracts, one called the High Bridge, containing the cable-stayed main span and the flanking side spans and one called the Approach Bridges containing the eastern and western approach bridges leading to the High Bridge. By tendering the bridge in two separate contracts the Owner could combine the lowest bid for each package, which could lead to a lower total price than one price for the whole project. The Enquiry Documents were issued to the prequalified contractor groups in December 1994. In all six groups competed for the Approach Bridges contract and five groups for the High Bridge contract. Both the one-level and the two-level bridge concepts were offered to the bidders.
3
Approach Bridges and High Bridge
Tender Evaluation and Award
The tenderers’ bids were returned on 1st of June 1995. All tenderers had put in bids for the twolevel solution. Two tenderers also put in bids for the one-level bridge. The lowest bids for both the Approach Bridges and the High Bridge contracts were for the two-level concept. The tender evaluation was carried out strictly on the basis of the submitted bids, the competition had ceased. The actual process of tender evaluation followed a number of procedures prepared by the Owner. The purpose of the evaluation was to identify the economically most advantageous tender to the Owner. The evaluation was in two stages, a preliminary evaluation shortlisting two to three bidders followed by a detailed evaluation of the shortlisted bids. In both stages the evaluation was carried out under separate headings: technical, financial, quality & planning systems and contractual. No cross communication was allowed between the groups. The technical group was again subdivided into a number of subgroups concerned with: design, construction, environment/authorities and aesthetics (this subgroup was only established at the detailed evaluation stage) In case clarification was required at the detailed evaluation stage the necessary communication was strictly controlled by the Owner with clearly defined and specific questions with no possibility for the bidder to improve their bid or attempt to negotiate. Deviations were identified and the assessed costs were added to the tender sum. The evaluation led to the award of a single combined contract for the High Bridge and the Approach Bridges to an international group of contractors, Sundlink Contractors HB on 27th November 1995. Sundlink consists of Skanska of Sweden, Hochtief of Germany and Monberg & Thorsen and Højgaard & Schultz of Denmark. The Contractor’s designer is a Joint Venture of COWI of Denmark and VBB of Sweden. Sundlink’s successful tender design followed ASO Group’s two-level concept without any deviation from the requirements of the Definition Drawings.
4.
The Construction Phase
The Contractor’s bid was based on the principle of large scale onshore prefabrication, with finished elements being installed by heavy lifting equipment. The most important centres of production have been: Malmö and Karlskrona in southern Sweden and Cadiz in southern Spain. The two pylons, and the onshore structures are the only major elements constructed in situ.
Malmö North Harbour: substructure
Cadiz: approach spans
Karlskrona: high bridge steel
Bridge Site: installation by ‘Svanen’
4.1
The Owner’s Monitoring during the Construction Phase
The Contract is based on the principle of self-control. In general the Owner does not need to nor does he want to approve materials, which are to be incorporated in the works. The Owner does not get involved in the day-to-day inspection and approval of construction work. It is tempting to do so, and the tradition of detailed inspection by the Owner’s representatives dies hard. In fact it often suits the Contractor to have inspections by the Owner; it makes his work easier, can reduce his staffing level, and may reduce his responsibility for his work. The Owner is of course present at the sites and may from time to time test materials or inspect the works. However, it is vitally important that the Contractor sees the Owner’s monitoring as a supplement to and not a replacement of his own supervision and QC function. The Contractor must know not only what the Owner will do but also what he will not do as part of his monitoring.
The Owner will • • • • •
approve the basic design assumptions, the Project Quality Programme documentation, and the basic planning for the works, visit, observe, meet, discuss, witness, review quality records, audit, comment (all hands-off activities) and may carry out random sampling, review and if required comment/approve actions in connection with site questions, review and approve non-conformity reports, effectively approve the physical work when Payment Milestones are authorised for payment.
The Owner will NOT • • • • • • •
get involved in day-to-day supervision, inspection and approval of construction, inspect setting-out, inspect construction joints, re-bars, formwork etc., inspect every radiograph of welds, watch every batch of concrete being placed, be present all day, every day at each construction site, produce quality records.
An important part of the Owner’s strategy has been to stay a comparatively small and proactive organisation. The Consultant ASO Group has since the start of the construction phase been totally integrated in the Owner’s organisation. This has created a non-bureaucratic organisation with fast and direct lines of command and communication. Only a total of 12 to 15 people have been involved in the Owner’s monitoring activities on the many and geographically widely spread production sites. 4.1.1 Review and Approval of Documentation Owner’s approval is only applied to certain forms of basic documentation and never to the actual physical works produced by the Contractor. Areas requiring approval are limited in order to maintain a clear division of responsibility. The Contractor’s design assumptions, his so-called basic design is submitted to the Owner for approval and has been checked for adherence with the design requirements including the Definition Drawings. The detailed design on the other hand is not subject to the Owner’s approval, it has been submitted for the Owner’s review and possible comments. The detailed design is part of the permanent works and therefore the Contractor’s responsibility. The most important approval by the Owner is the approval of the Contractor’s Project Quality Programme, which forms the basis for the Owner’s monitoring. The Quality Plans are crucial for the planning, execution and control of the works and are therefore subject to scrutiny by the Owner. No work activity is allowed to commence until the Quality Plan covering that particular activity has been approved by the Owner. The Quality Plans are the proof that the Contractor has understood the specified requirements and knows how he will achieve them. The Owner’s approval is also required for the Contractor’s basic planning and for plan revisions. The Owner may require revisions if delays on any activity affect the critical path. 4.2
Parallel Works
In addition to the major civil contracts that physically make up the Link: the tunnel, the reclamation works and the bridge, there are a number of coast-to-coast contracts. These contracts cover the installation of the railway, the communications and SCADA and traffic control systems. The coastto-coast contracts basically have continuous interfaces with each other and with the civil contracts, Although a large number of interface milestones for providing access are identified in the various contract documents, this is not a guarantee for the Link to be completed on time as planned. A Contractor might be delayed in a certain area denying access to the Contractor following on and
thus delaying the completion. In order to alleviate the effects of unforeseen delays the Owner has taken an active role in the coordination and planning optimisation of the so-called Parallel Works. The clear objectives are to have the Link structurally completed, comprehensively tested and opened for traffic as early as possible and within budget. The Parallel Works procedure was established, in the autumn of 1997, by the Owner preparing an integrated timetable where all the coast-to-coast contractors’ planning was incorporated in the civil contractors’ planning. This became the Reference Timetable and was the basis for an optimisation towards a Target Timetable. The Target Timetable required rescheduling of different activities within the timetables but it also opened up for several activities to happen in parallel despite being performed by different contractors. Prior to implementation, the Target Timetable was discussed and refined with the respective contractors; with the Owner acting as the coordinator between the contracts. The system would not have worked without the cooperation of the contractors, and in order to achieve this an award was identified for finishing on the target date. The Owner’s ‘award’ being the extra revenue for opening the Link early.
The cable-stayed bridge nearing completion
5. Conclusions The bridge is not yet complete but it is not too early to state that the Owner’s strategy of cooperation, trust and openness has been a success. The bridge Contract is almost 80% complete and is as the other Link contracts on time and on budget. The quality of the permanent works is to the Owner’s satisfaction. There have been no disputes so far and therefore no significant claims against the Owner, and none are expected either. This is not usual for a project of this size and complexity and can to a large degree be attributed to the spirit of partnership between Contractor and Owner, which has been allowed to develop throughout this truly international project soon to connect the two countries Denmark and Sweden.
Getting the Balance Right The Øresund Bridge - Design Concept Jørgen NISSEN Civil Engineer, MSc Director Ove Arup & Partners London, United Kingdom
Georg ROTNE Architect MAA Associate Professor Royal Academy of Fine Arts Copenhagen, Denmark
Jørgen Nissen is Director of the ASO Group, the bridge consultant to Øresundskonsortiet.
Georg Rotne is the ASO Group’s architect.
1. Introduction Vitruvius set the agenda: good architecture is about the proper balance of Firmitas, Utilitas and Venustas - or firmness, commodity and delight. And so during the Renaissance designs for bridges, as for buildings, aimed to meet this ideal. With the invention of industrialised processes and new materials and technology, a new profession was created: the engineer. The new materials and technology were used in the building of bridges and other structures. Firmness in particular was the domain of the engineer; commodity was interpreted as function but more interest was shown in inventiveness and efficiency than in delight. The first engineers built remarkable bridges of iron, and later of steel and reinforced concrete. They used a rational and economic design approach – form follows function – which worked hand in hand with the current belief in progress. Following the end of the Second World War, an urgent need for new infrastructure meant that bridges, like other structures, became more and more mass-produced. Efficiency dominated; which left little room for inventiveness and experimentation. Sometimes architects were involved in the design of the more prestigious bridges, but mostly in a secondary role. This has now changed. Architectural competitions are increasingly being held for bridges. Delight is firmly back on the agenda.
Antonio da Ponte: Rialto Bridge, Venice 1597
Gustave Eiffel: Viaduc de Garabit, Truyére, 1889
2. The Øresund Bridge The Øresund Bridge is very long. Technical, functional and economic issues are critical. It includes approaches, where shorter spans are suitable and a much longer span over the navigation channel. The structure should appear as a whole and not a collection of parts; it should be economic for the approach spans as well as for the main span. A small team of designers developed the design concept. A larger team, which also included the client and various public authorities, developed the tender design, and the contractor’s team carried out the detailed design within a design and construct contract. And because it is very large, the client had divided the project into a number of contracts to be handled by different contractors, and different teams might therefore handle the final design. The continuity of the design process would thus be broken. In these circumstances, how is it possible to ensure unity and the proper balance of firmness, commodity and delight? The right design would ideally be functional, economic and beautiful. Given the huge scale of the project, emphasis should be put on developing a consistent and robust design befitting the unique site. It is often this relationship to its site that gives a bridge its special character. This bridge would stand in a seascape without any dramatic natural forms to set it against. The landscape on both sides is gentle and friendly, with small and rolling hills and curved coastlines where the land merges with the sea. The bridge rises gradually from the tunnel at the artificial island like from a hole in the sea. The Link would often be seen at a distance: from the shores, the sea and the air. Those travelling on the bridge would mostly see it at speed, but they could, given a suitable design, have exceptional views of the sea, the islands, the coastlines and the cities of Copenhagen and Malmö.
View from the Danish coast at Dragør south of Copenhagen Airport. In the distance the artificial island Pepperholm and the bridge
3. Design Objectives The design concept was developed in a design competition for the whole Link: an artificial peninsula, a tunnel, an artificial island and the bridge. The two Governments had decided on the overall functional and technical requirements and described these in a Reference Project that was part of the Agreement between them. Under the Treaty the Link should be designed and constructed with due consideration of “what is ecologically motivated, technically feasible and economically reasonable in order to prevent any detrimental impact on the environment”. The competition brief was simply to improve on the reference project if possible; to propose “the best scheme - the most beautiful, the best technical and the best environmental solution - within the budget costs that has been agreed by the two Governments”. Three independent panels would judge the competition: an aesthetic, an environmental, and a technical and cost panel, which indicated that the client would attach equal importance to these factors: the client clearly wanted a balanced design. Our design strategy was to use a simple and straightforward design: to express function and structure in a direct way without unnecessary detail. We used well proven design concepts, materials and construction methods to create a strong and robust form, capable of safely being divided into smaller parts, which could be detailed by different contractors and still make a harmonious and coherent whole. As it would be for a design and construct contract, the design should allow the contractor some choice of construction methods and materials to suit his particular skills and techniques. The design, the materials and the methods of construction should be well proven to minimise the risk of changes being necessary during the detailed design and construction and, given the difficult site conditions, allow for repetition and for minimum on-site construction for better quality and reduced risks.
Aerial view of the Link. Copenhagen is to the left and Malmö to the right. The 4km tunnel under the Drogden channel is adjacent to Copenhagen Airport, the 4km artificial island Pepperholm is south of the bird protection area on Saltholm island and the 8km bridge arrives at Lernacken south of Malmö.
4. Design Concept Just two months were granted for the competition, which made the concept stage even more crucial than usual. The main features of the design had to be settled very early, since there would be little time to make fundamental changes later on as the design was developed and refined, if the basic concept was then found to be unsuitable. A small team of engineers and an architect, working alongside each other, created the competition design. They shared an approach to design that had been formed over some years as they worked together on a number of other bridge projects. They had learnt to understand what each of the team members could contribute to the whole and knew how to combine the contributions of their many different skills and experience. No solution was taken for granted, every suggestion was examined and challenged, and nothing was accepted until the proposal was not only technically and functionally sound and efficient but also delightful. The form of the alignment is important for the experience of the journey across the bridge. We chose to alter the reference project’s straight alignment to a curved alignment to give a more interesting journey across the Øresund. We also decided to separate the road and the railway traffic on the whole Link, a decision that meant that the bridge would have two levels. The Link should provide a dual two-lane motorway and two tracks for high-speed passenger trains and heavy goods trains. In the reference project the road and railway were placed side by side on the bridge, but separating the traffic gives obvious operational advantages and flexibility. During lane closures, whether caused by accidents or maintenance, road traffic can be directed onto the other carriageway, and on the railway, crossovers can be placed freely. With the motorway carried at the upper level and the railway below it, users are also given ample comfort and security. Cars are separated from the high-speed trains and travellers can have free and excellent views of the Øresund. We decided finally that the high bridge would be cable-stayed. For a two-level bridge, the most economical structure is to use steel trusses with diagonals connecting the upper and lower decks. The deep girders naturally lead to longer approach spans, which has environmental advantages and gives a lighter and more elegant appearance. They are also rigid enough for a cable-stayed bridge to comfortably span longer than the reference project’s 330m and 290m spans over Flintrännan and Trindelrännan. We therefore proposed a single navigation span of 490m over Flintrännan alone.
5. The Journey across the Øresund The main attraction of the journey across the Øresund will be the unique views from the bridge: views of the ever-changing sky and sea with a remarkable play of light including every shade of grey and blue, and views towards the gently curved coastlines, to the island of Saltholm and to the cities of Copenhagen and Malmö. With the curved alignment, a drive across the bridge will be a continually changing experience and the cable-stayed bridge, which is the visual peak of the journey, will be seen from changing angles, whether one is driving from Sweden or from Denmark. We proposed an S-curve for the competition design, as this would give the best views of the high bridge whether it is approached from east or from west. It would also give a nearly perpendicular crossing of the Flintrännan navigation channel, and the straight cablestayed bridge could be accommodated between the two curves of the S. Later, however, the alignment was altered from an S-curve to a C-curve when changes were made to the alignment at Copenhagen Airport in order to simplify construction through the airport and also improve the water flow through the Link. Although the changes were made 8 km from the start of the bridge they altered the bearing of the alignment at the artificial island and this, in combination with bird sanctuary restrictions south of Saltholm, made the S-curve impractical. The motorway is on the upper level and the cars are separated from the high-speed trains, which means that motorists have a free view of the Øresund. The railway runs inside the structure. To give railway passengers a clearer view, the trusses have been given a more open bracing than is usual. This in turn helps to make the bridge appear lighter and more transparent. Changing views from the S-curve
Roads - and railways in particular – come with a great deal of ‘furniture’: barriers, signs, signals, power supplies, surveillance cameras, and lights, windshields etc. All are necessary but all distract and obstruct the views from the bridge, and more so if all traffic is at the same level. On a two-level bridge, the railway furniture can be attached to the inside of the structure, and the road furniture alone obstructs the view from the road.
S-curve (viewed towards Sweden)
C-curve
6. The Girder as a unifying Element The Øresund Bridge is not just a structure that extends from bank to bank with a distinct beginning and a distinct end. It is part of a much larger link; - a road and a railway that wind their way as continuous bands across the water; rising from the tunnel, passing over the island and onto the bridge and up and over the navigation channel. In these circumstances, and given that the journey across the bridge is made at the high speed, monumental end pieces or abutments would seem inappropriate. Unity and continuity are fundamental, and the approach bridges and the high bridge should merge together rather than conflict with each other. Most of the competition entries for the high bridge were cable-stayed, but two were arch bridges. The arch is a famous structural form with great symbolic value and an easily understood flow of forces. The cable-stayed bridge has not yet acquired the same standing. It looks more rigid and the flow of forces is often less clear. At Øresund, however, where the high bridge is part of a longer sequence, a cable-stayed high bridge joins readily with the approach bridges; - a strong continuous bridge girder of uniform and consistent design ties the whole length together. The bridge is continuous from Sweden to Pepperholm, the artificial island. The simple but strong horizontal bridge girder is the principal element that gives the design a sense of unity. The overall effect is a clear statement of structural purpose: the strong horizontal girder is supported on concrete piers in the approaches and, at the main span by cables which continue the line of the truss diagonals to the two high free-standing towers.
7. Beacons in the Sea The towers stand out like beacons, rising from the sea, aspiring towards the sky, marking the summit of the journey and the border between Denmark and Sweden and announcing that here is the crossing of the navigation channel. All rising lines are straight without kinks. All visible planes reduce in size from the sea towards the sky, expressing strength and stability. The inner faces of the towers are slightly inclined outwards, sufficient for the towers not to appear to be leaning inwards. The stiffness of the truss deck was a factor in choosing the harp pattern for the cables. The repeating geometry of the truss has a natural affinity with the harp, which was highlighted by matching the slopes of diagonals and cables. The cables are arranged in completely vertical planes, with the cables symmetric about the pylons. All cables have the same inclination. Whereas the cables under certain light and weather conditions will seem to vanish, the towers will always be a prominent part of the Link. The cable planes on cable-stayed bridges are often slightly twisted. This becomes particularly apparent when the cables are viewed under a very acute angle, such as from the bridge, and tends to lead to an awkward and uncomfortable appearance. The visual formality of the harp system is particularly impressive when the cable planes are vertical. Straight towers together with outrigger brackets at the deck make it possible to arrange the cables in vertical planes. The centres of gravity at all cross sections of the towers are on a vertical axis, which is also the cable plane and vertical loads induce only axial forces in the towers. The centroid is at the third point of the cross sections so as to minimise the separation of the two cable planes and reduce the reach required for the outrigger brackets. However, the cables are at a safe distance from the roadway and well protected from accidental damage. The towers are high to give a good inclination of even the longest cables, and therefore smaller cable forces and an increased stiffness of the whole system, which is useful as the bridge carries a high-speed railway. The towers are connected by a substantial crossbeam immediately below the deck and by their shared foundation below water level, but they are free-standing above the deck. The pylons are slightly higher than is strictly necessary. The extra height accommodates a working platform and railings on top of the towers are avoided.
8. A Structure tied tightly together The trusses are uniform throughout the bridge with the diagonals on a constant 20m module. The regular pattern in the approaches is modified at the cable-stayed main span so that every other diagonal has the same direction as the cables. At the deck, the cables are anchored to large sloping outrigger brackets that transfer the cable forces from the anchorages to the bottom chords and through the upper deck. The outrigger brackets lie in the same inclined plane as the long diagonals and continue the line of the cables in elevation, in an easily understood structurally efficient way. The modified truss pattern, the parallel cables, the outrigger brackets and the vertical cable planes bind the structure so closely together that it is difficult to alter. Changing one part would lead to changes everywhere else. Because all the main components of the cable-stayed bridge are interconnected the design has an overall coherence.
9. Some Details In developing the design we intended the details to support and enhance the overall design concept. The outrigger brackets are a good example. They are an harmonious part of the continuous girder but at the same time stand out in their own right demonstrating their special function. All angles are rounded in the steel girder to stress the unity and the continuity of the girder. And the structural steel is painted black. Since the girder is the unifying element in the bridge it needs to stand out from the other parts of the bridge, which are predominantly in grey concrete. Black also suits the natural setting as it acts a neutral background to the subtle shades of grey and blue in the sky and the sea. All the concrete parts of the bridge; the pylons, piers and decks have simple and strong forms. The finishes are fair faced and horizontal lines between formwork panels have been made as small as is technically reasonable so as not to conflict with the verticality of pylons and piers. The two abutments, at Lernacken where the railway carries through in a tunnel and on Pepperholm where it continues within an open viaduct structure, are designed to express the continuity of the journey rather than emphasise the two ends of the bridge. Much of the equipment added to the bridge; barriers, stairs, supports for lights and signs etc. are made from grey galvanised steel showing their subordinate role to the main structure. Some of the furniture such as the safety barriers on the motorway is in harmony with the straightforward design of the main structure. Other, such as the outside emergency stairs, drainpipes and the railings on the lower chord of the girder looks awkwardly out of place at close quarters. However, the main structure with its the huge scale and simple and robust design seems to accept and cope with this. The road is lit. The lights are carried by a row of 12m high masts placed in the central reserve, which will produce an evenly lit road surface and a continuous string of light in the air like a luminous pearl necklace. Navigation lights are attached to the towers and the main span girder and the towers are floodlit. Spotlights are placed at the outrigger brackets nearest the towers. The floodlighting is aimed at the cable anchorages at the tower and the shadows of the cables will form a distinct vertical line on the upper part of the towers.
10. Getting the Balance Right Bridges are structures just as buildings are, but engineering considerations have a much stronger influence on bridge design. Engineering is presumed to be rational and objective and some claim that it provides a unique solution to all problems. Everything else being equal, all engineering works would then be much the same with little variety or room for surprise. And if one also believes that pure rational forms are inherently beautiful, what role is then left for imagination let alone for involving architects? Everything is never equal. Design has a rational and an irrational part. Understanding is as important as knowledge. When knowledge does not suffice, the designer must use intuition and synthesis to reach a balanced design. Technology is necessary, as help and a tool but also as an inspiration. Ove Arup put it well: "Engineering is not a science. Science studies particular events to find general laws. Engineering design makes use of these laws to solve particular problems. In this it is more closely related to art or craft; as in art, its problems are under-defined, there are many solutions, good, bad or indifferent. The art is, by a synthesis of ends and means, to arrive at a good solution. This is a creative activity, involving imagination, intuition and deliberate choice.”
The Øresund Bridge: The Tender Project Jørgen Gimsing is Technical Director of the ASO Group, the bridge consultant to Øresundskonsortiet
Jørgen GIMSING Director Gimsing & Madsen A/S Horsens, Denmark
Summary In 1991 the Danish and Swedish Governments signed a Treaty for establishing a fixed Link across the Øresund. The Treaty laid down the main principles for the Link: A combined 4-lane motorway and a 2-track railway for both passenger trains and freight trains, a tunnel under Drogden, an artificial island south of the natural island Saltholm and a bridge from here to Sweden. In 1993 ASO Group presented a solution for the bridge in an international design competition. This solution was refined to a Tender Design, which formed the basis for the bridge Contract with the successful tenderer. The paper describes the design process and the Tender Design. The emphasis is placed on demonstrating the robustness of the Tender Design by highlighting the very few and minor modifications, both compared to the original competition design and to the Bridge actually being constructed.
1.
Introduction
The design process for the Øresund Bridge has consisted in a larger number of steps than usual, mainly due to the selected form of tendering as “Design and Construction” contracts for two separate bridge contracts, one for the High Bridge and one for the Approach Bridges. The main steps in the process were: • • • • • • • •
Competition Design Conceptual Design Tender Design Contractor’s Tender designs Design Evaluation of Contractor’s Tender designs Basic Design Detailed Design Changes to Basic and Detailed Design during construction and due to changed wishes from the Owner.
During the conceptual and tender design phases, the Design and Construction Requirements were worked out. The Design Requirements are based on the Eurocode system, as far as known for the first time for a major bridge project.
1
2.
The Design Process
2.1
The Competition Design
In November 1992 the Owner, Øresundskonsortiet, invited consulting engineers to seek prequalification for a design competition for the Øresund Link. Each group had to present a design (“Reference Project”) conforming to the agreement between the Danish and the Swedish governments and could present one or more designs (“Open Proposals”) which deviated in specific instances from this agreement. The main restrictions imposed on the conforming design were: • • •
a fixed alignment fixed navigation spans of 330 m and 230 m for the bridge a one level bridge with the railway at the centre in the cross section.
The outcome of the competition was that the Owner selected two Open Proposals, a two level bridge from ASO Group and a one level bridge from ØLC, for further investigations.
The Competition Design 2.2
The Conceptual Design
The Conceptual Design
During the first half year after the announcement of the result of the competition the two consultants refined their designs for the total link in order to arrive at realistic cost estimates and time schedules for construction. At the end of this period the Owner decided to continue with the bridge designs from both ØLC and ASO Group and to let ØLC design the tunnel and dredging/reclamation. 2.3
The Tender Design
The tender design period, from November 1993 to November 1994, involved a large number of technical investigations both in relation to the bridge designs and to the Design and Construction Requirements. Both due to the decision to tender for two separate Bridge Contractors and to the Owner’s wish to have a strong influence on the aesthetical design of the Bridge, all visible dimensions in the Bridges were fixed by so called “Definition Drawings”. At the same time it had to be ensured that the fixed dimensions were realistic and even nearly optimal, as deviations proposed by one Tenderer leading to major savings would complicate the evaluation of the tenders. Some of the investigations carried out by ASO Group for the two level bridge are described in the next chapter. 2
2.4
Contractor’s Tender Designs and Evaluation
All 5 pre-qualified Tenderers for the High Bridge, 6 for the Approach Bridges submitted tenders on the two level bridge. All tenders were conforming to the Definition Drawings, although some tenderers indicated that they had investigated alternative pylons, cable stay arrangements etc., which might lead to some savings in construction. The evaluation of the tenderers’ designs concentrated on checking their fulfilment of the Design Requirements including Definition Drawings and identifying qualifications hereto. A direct comparison of the design proposals was to some degree hampered by wide differences in their detailing, which was not specified in the Enquiry Documents. At the end of the tender evaluation, Sundlink Contractors were chosen for both the High Bridge and the Approach Bridges. This Joint Venture consists of Skanska (Sweden), Hochtief (Germany), Højgaard & Schultz (Denmark) and Monberg & Thorsen (Denmark). Their bridge consultant is CV JV consisting of Cowi (Denmark) and VBB (Sweden). 2.5
Basic and Detailed Design
The Basic Design was defined in the Enquiry Document; it should be sufficiently detailed to give all main dimensions, prestressing and main reinforcement and it should indicate the analysis procedures to be employed in the Detailed Design. Both the Basic and Detailed Design were agreed to be subdivided in more than 60 packages in order to finalise the most time critical design parts as quickly as possible. The Basic Design was first submitted to the Owner for commenting and subsequently resubmitted for approval. After this approval the Basic Design drawings (to some extent) replaced the Definition Drawings as the Owner’s expectations to the final product. Changes to the Basic Design found necessary or desirable in the Detailed Design could only be introduced with the Owner’s approval. The Detailed Design packages were also first issued to the Owner for commenting. After incorporation/clarification hereof the Detailed Design drawings were issued for construction, as the Owner did not wish to approve the Detailed Design in order to emphasise that the Contractor had the full responsibility for this. 2.6
Changes during Construction
The Contractors’ designer is retained during the construction planning, as it is important that he endorses the Method Statement for construction thus ensuring that this construction method is covered by the Detailed Design analyses. In exceptional cases the Contractor’s choice of construction method has led to a need for re-analysis, but in general the construction methods indicated in the Basic Design have been followed. The normal procedure for changing design details during construction is that the Contractor (or one of his subcontractors) propose the change in the form of a Site Question. If the proposed change is a change to the Basic Design, it shall be approved by the Owner, whereas changes to the Detailed Design may be introduced after endorsement by the Contractor’s designer and subsequently issued to the Owner for information.
3.
The Tender Design
3.1
Comparison to the Competition Design
In the Competition Design by the ASO Group all main features of the Øresund Bridge now under construction were fixed. The investigations leading to the Tender Design therefore concentrated on
3
ensuring that the main dimensions chosen in the competition were adequate and on introducing additional degrees of freedom for the tenderers. The main objective in the competition was to get a reasonable compromise between economy, aesthetics, traffic safety and environmental considerations. The first choice was a two level bridge both due to traffic safety and environment. For the traffic safety the two level bridge is the optimum solution, as the noise and headlights from rapid trains close to the road traffic would have been an extra hazard. From an environment point of view the blocking of water flow from bridge piers is a major concern, where the two level bridge leads to long spans due to a large construction depth. The second choice was a truss girder, which ensures a good view from the lower railway deck and at the same time is an economic solution. For the 6.6 km long Approach Bridges the optimum truss solution is two vertical trusses, which provide the most efficient supports for the wide road deck, when the requirements for railway clearance width and services at the lower deck have been fulfilled. All steel members in the bridge are box sections, both for aesthetical reasons and to minimise the extent of paint by use of dehumidification of the interior.
140 m Approach Span Model The third choice was to minimise the number of diagonals in the trusses, both for aesthetical reasons and to improve the views for the train passengers. This was achieved by a pure Warren truss with diagonals under 450 instead of the normally used 600. The additional cost of this solution was found to be very marginal as the local bending in the 20 m spans between nodal points was taken by a very efficient composite cross section at the upper deck.
Cross Section Approach Spans The above considerations combined with a small number of rough calculations fixed the cross section for the superstructure in the Approach Bridges. Due to the length of the Approach Bridges (6,6 km) compared to the High Bridge (1,1 km) at least 75% of the construction cost was the Approach Bridges, and therefore this was chosen as the starting point in the optimisation of the Øresund Bridge.
4
For the High Bridge the main span was not fixed in the competition rules, only that it should be more than the 330 m stated in the Treaty between the Danish and the Swedish Governments. We chose a 490 m main span, and subsequently this was found by ship simulation studies in the pretender period to be sufficient and adequate. With this span length a cable stayed High Bridge was clearly indicated, even though two entries in the competition were based on arch bridges. The chosen cross section for the High Bridge described above imposed a new problem, as the vertical trusses positioned just outside the railway area made it impossible to attach the stay cables directly to the trusses. The chosen solution to this was the unique outriggers, which transfer the cable forces to the lower nodes in the trusses. This again led to two vertical cable planes with the cables well protected from car collisions.
Elevation Cable-Stayed High Bridge In the Competition Design the stay cables were single cables with an ultimate load capacity of nearly 40 MN. In the pre-tender period it was found necessary to introduce an alternative solution with smaller stay cable dimensions in order to have a wider selection of potential manufacturers. The alternative introduced on the Definition Drawings consisted of 4 cables with their centres forming a square. Based on a question from one of the tenderers a solution with 2 closely spaced stay cables was also informed to be acceptable. This solution was chosen by the successful tenderer with the twin cables in the same vertical plane.
Cross Section Cable-Stayed Spans In the Competition Design the road deck was transversely prestressed concrete, which was also found by most tenderers to be the optimum solution. In the Tender Design it was, however, decided to include an orthotropic steel deck design and to state the maximum concrete dimensions sufficiently large to allow reinforced concrete solutions. The successful tenderer used this latter option for the in situ cast joints in the road deck above the piers, whereas the precast parts are transversely prestressed.
5
The lower railway deck underwent more substantial changes in the pre-tender period. In the Competition it was an orthotropic steel deck in the High Bridge and a thin concrete slab acting compositly with a central, trapezoidal steel stringer beam. During the pre-tender development of risk analyses and Design Requirements, the risk of a derailed train rupturing one diagonal was identified as one of the major risks for the two level bridge. It was therefore decided to contain the trains by introducing a double concrete trough with 1.8 m high walls just outside the railway clearance profile. This solution gave additional benefits by reducing the train wheel noise and by making the steel stringer redundant. Finally the outside of the concrete walls provided an excellent support for horizontal cable trays for railway, communication and traffic surveillance cables. The span lengths for the Approach Bridges were chosen to be 120 m in the competition, but during the more detailed analyses carried out in the pre-tender period it was found that the capacity of the cross section was sufficient to introduce 140 m spans as an alternative option for the tenderers. The tenderers were finally given a free choice between 100, 120 and 140 m spans, and even combinations hereof provided the shorter spans were used near the shores and either the same or larger spans towards the High Bridge. The final choice by the Contractor was three and four 120 m spans from the abutments, whereas the remaining 18 and 24 spans were 140 m.
Pylon: Competition Design and Conceptual Design In the High Bridge the most visible change during the pre-tender period related to the shape of the pylons, which became more tapered upwards and their cross section was simplified from a hexagonal to a pentagonal shape. Finally a visible cross beam above the water was moved downwards below the water level and incorporated in the foundation structure. The main feature of the pylons, the free standing legs above the bridge deck, was retained following a desk study, which demonstrated that this solution with the chosen dimensions was economic. During the pre-tender period relatively detailed Finite Element analyses of typical nodal points in the truss were carried out in order to verify that the proposed radii of curvature did not lead to unacceptable stress concentrations and/or uneconomic plate thicknesses. The outcome hereof was that the radii chosen in the competition design were found to be adequate.
6
The separation of the road and railway on the one artificial island comprises a viaduct, which leads the road to the North of the railway in a gentle continuation of the horizontal curvature on the Approach Bridge, while the railway is continued in a straight line. In the period up to the tendering a number of consultations with authorities such as fire brigades, police etc., led to definition of escape routes: • • •
emergency walkways along the railway access stairs between upper and lower deck at 600 m intervals cross-overs in the median on the motorway.
These were introduced on the Definition Drawings. 3.2
The Bridge Contract
The tender design from the successful tenderer fully complied with the Definition Drawings. He had chosen the steel deck solution for the railway deck in both the High Bridge and the Approach Bridges, but before signing the Contract he agreed to construct the concrete containment platforms in the Approach Bridges at the same cost. This solution was preferred by the Owner based on noise studies at the Swedish coast. 3.3
Changes Introduced by the Owner
The tenderers were asked to price a number of options, which could be included in the works if the Owner wanted to pay the extra cost. Two of these options were actually included, one being an extension of the width of the motorway deck from 21.5 m to 23.5 m, the other being an extension by 360 m of the western Approach Bridge. The first option was intended to be used to widen the 2.0 m service strip at the parapet to a full 3.0 m emergency lane, but it was later decided to only have 2.5 m emergency lanes and use the last 1.0 m to widen the central median from 0.5 m to 1.5 m, which would make it possible to place masts for motorway lighting in the median. The second option was introduced to improve the water flow through Øresund and thereby reduce the compensation dredging required to obtain the “zero blocking solution” stated in the Treaty between the two Governments. After signing the Contract the major change on the Bridge initiated by the Owner has been the introduction of a lower walkway at the railway deck. At the bridge ends both at Lernacken and at Pepparholm, the architect has introduced some aesthetical changes to abutments, earthworks and the viaduct. 3.4
Changes During Detailed Design
The main change introduced during the design phase was a modification to the pier tops necessitated by increased dimensions of the bridge bearings. The outer dimensions of the piers were fixed on the Definition Drawings based on analyses for the 120 m approach spans, but these dimensions had not been checked for the 140 m spans, when this option was introduced as an allowable alternative. The overall dimensions of the pier shafts were determined by large ship impact forces, which are independent of the span lengths and therefore the pier shafts were adequate for the 140 m spans. However, on the pier tops a number of aesthetical and functional requirements had limited the available space for the bearings to such an extent that the increased bearing size due to the 140 m spans could not be accommodated without visible changes to the shape of the pier tops.
7
Pier Top: Conceptual Design and as constructed The chosen solution was to omit the inclined triangle at the top of the outer face of the pier shaft, and this provided the extra horizontal surface needed for the bearings. On top of the bearings, the nodal point in the truss had an increased radius of curvature compared to the other nodal points due to the concentrated forces from the bearings. During the detailed design it was found that a further increase of this one radius was desirable due to the bearing replacement situation, where the two spans are lifted on jacks outside the permanent bearing. Following discussions with the architect, this increase of the difference between the bearing nodal point and the normal nodal points was not only found acceptable but in fact preferable from an aesthetical point of view.
4.
Conclusions
The paper has demonstrated that the design concept for the two-level bridge has been very robust in the sense that the long design process from the first sketches in the design competition to the Contractor’s detailed design has led to very few changes. The majority of the changes have been initiated by the Owner and his consultant. The reason for change has often been to make a feature more maintenance friendly but in some cases improved technical and aesthetic solutions have been found. The use of Definition Drawings as part of the Contract Documents did limit the possibilities for the bidding contractors to modify the design concept. However, when one contractor was chosen for both Bridge Contracts there was a risk that he would take the opportunity to introduce a number of major changes. That this did not happen can among others be attributed to the fact that the Definition Drawings were based on a design optimisation process and also that they represented the design the Owner wanted to see constructed. The Owner has throughout the process insisted on a strict adherence to the Definition Drawings.
8
From Eurocodes, Special Investigations and Risk Analysis To Design Requirements for the Øresund Coast to Coast Structures
Eilif SVENSSON Civil Engineer ES-Consult Ltd. Vedbæk, Denmark
Eilif Svensson, born 1945 Civil engineering degree 1970 and Ph.D. degree 1973 from The Technical University of Denmark. Director ES-Consult from 1990
Summary Establishing a physical link of the magnitude and importance such as the Øresund Coast to Coast calls for early and focused attention towards developing and implementing a coherent strategy dealing with the Design Requirements for the structural parts of the link. Design Requirements are instrumental in securing the owner and ultimately the Society, that issues such as structural safety and durability are addressed for each and every part of the Link, in a uniform manner and independent of the contract form and contract division. The owner addressed these issues at an early stage of the present project. This paper briefly gives a picture of the options available at the time, the strategic decisions taken and the organisation of the work leading to the final preparation of the Design Requirements.
1.
Early stage issues facing the owner
At the very start of the Øresund Coast to Coast project, when the most basic features of the Link had been defined, which in case of the present project given its magnitude, envisaged socioeconomic and cultural impact and bilateral character required governmental decisions in Sweden and Denmark, an owners organisation had to be established. Needless to say – at this stage the owner agenda is deluged with issues to be addressed, each and every one representing important strategic elements in the overall process of fulfilling the goals set out by the policy makers. One of these issues deals with how to define and implement the desired level of structural safety and durability. Primary questions in this context are: -
Which set of structural codes shall be/can be applied? Can the chosen set of basic structural codes properly fit the project at hand or will amendments have to be prepared? Does project specific features call for additional preparatory investigations?
A brief expose of the considerations behind these questions will be given below. 1.1
Structural and civil engineering codes
The decision on which particular set of codes to apply prompted two circumstances to be considered: -
The bilateral nature of the project. The magnitude of the project.
The first evidence has the potential of leading to a mild form of schizophrenic chaos. Given the co-operative and professional ambience of the combined Swedish-Danish owners organisation this however never has been a real concern. Any choice between Swedish or Danish codes could have been decided and accepted – however due to the nature of the problem not without an inherent arbitrariness attached to it. The shear magnitude of the project itself meant that the pre qualification would attract contractors and engineers from the international arena and ultimately that the execution of the project only could be envisaged to be undertaken by contractors with international experience. Both circumstances led the owner after more thorough contemplation referred to in a later section to adapt Eurocodes as the underlying set of Codes of Practice. 1.2
Adaptation of Codes of Practice
Regardless of the choice taken with regard to the basic set of codes the magnitude of the project dictated a thorough examination of the codes in order to reassess the suitability of all provision concerning loads, structural verification, material specifications and other related matters. Choosing Eurocodes as explained above introduced an additional concern. At the time of the decision in the early nineties a final adopted and ratified set of Eurocodes did not exist. In fact all codes and attached parts existed in premature editions – the so-called ENV’s. Consequently a consistent and complete set of amendments therefore has been prepared. These were named Project Application Documents – or in short PAD’s. 1.3
Additional preparatory investigations
In addition to preparing the PAD, which amend provisions of the codes, supplementary investigations may be called for to elucidate specific issues of importance not treated satisfactory in the codes. This may be a load of a special kind and of special influence on the structure or a special repetitive important structural feature, which one wishes to ensure focused attention in the design process. These considerations led the owner to initiate several extensive studies aiming at establishing the best possible basis for the preparation of the Design Requirements. The subsequent chapters describe more in detail the process - following the early stage clarification of the issues mentioned above - of establishing the basis for the Design Requirements for each main contract of the complete link.
2.
Preparation of Design Requirements
The key elements in the process leading from a clarified early stage strategy to contractual technical requirements for the main contracts are illustrated in figure 1 below.
Imposed requirements: Swedish-Danish treaty Authorities Environment Aesthetics
BASIC INFO. SPEC. STUDIES
RISK ANALYSIS CODES
DESIGN BASIS
PAD
DESIGN REQUIREMENTS D&R
TUNNEL
BRIDGES
OTHER CONTRACTS
DESIGN AND CONSRUCT Detailed Design
FIGURE 1. Main elements in the process leading to Design Requirements of the various contracts of the Øresund Link Coast to Coast. The Design Basis is a key document, prepared as an internal technical document containing all technical specifications and serving the purpose of being a common platform for the various contract specific Design Requirements. 2.1
Codes and PAD
The decision to apply Eurocodes in their preliminary editions as the basic Codes of Practice was taken after a more thorough investigation. Working groups consisting of Swedish and Danish experts concluded, that it was possible and feasible to apply Eurocodes as reference codes provided amendments were prepared and certain modifications introduced – in other words that a Project Application Document - a PAD – had to be prepared. The conclusions of the working groups, summarised in [1], contained specific priority issues to be addressed in the preparation of the PAD’s. The Eurocodes, more specific the ENV’s – not mentioning the associated parts – were at that time:
EC1-Structures EC2-Concrete EC3-Steel EC4-Composite EC5-Timber EC6-Masonry EC7-Geotechnics EC8-Seismic EC9-Aluminium Further systematic review of the ENV’s finally led to the preparation of the PAD’s, [3]. 2.2
Design Basis
The Design Basis [2] (also called the Technical Design Basis) is an internal document prepared at an early stage to compile all relevant design provision. It has been divided into the documents Design Basis – General Design Basis – Environmental Design Basis – Civil and Structural Design Basis – Geotechnical Design Basis – Mechanical Design Basis – Railway Works and Installations Design Basis – Safety The Design Basis obviously has a much wider scope that the Eurocode + PAD which merely are concerned with civil and structural works: It compiles the overall and general requirements as defined in the treaty and the subsequent government act, requirements as defined by authorities, requirements aiming at reducing the environmental impact and general aesthetic requirements. Other input to Design Basis has been Basic Information , Special Studies and a separate Risk Analysis, more detailed account of which are given in the following. 2.2.1
Basic Information and Special Studies
The magnitude and character of the project has motivated the owner to supplement the underlying Codes – Eurocodes+PAD – with extensive studies in order to: Determine with the greatest possible accuracy environmental forces acting on the structure from: -
Wind Waves and current Ice
The results of these studies have been reported in [5]-[8] and has served other purposes such as providing information of importance for the execution of the works. Special studies treat a wide range of subjects of importance of which just a few shall be mentioned illustrating the wide range of subjects covered: -
Calibration of partial factors and listing of relevant load cases and load combinations Wind tunnel tests leading to well defined design rules for aeroelastic forces acting on the bridge and definition of design and test requirements to be met by the contractor. Extensive geotechnical investigations improving the level of information available for the
-
contractor and enhancing the quality level of the Design Requirements. Ship-Structure impact studies Studies of the dynamic train-structure interaction
The calibration study [4] was undertaken to implement the general decision that all structural element of the Link should belong to high safety class corresponding to a safety index β = 4.7 – briefly and formally defined by an annual collapse frequency lower than 1.3∙10-6 for each structural element. Another and very important category of special studies have had a direct influence upon the predefined i.e. the mandatory features of the project. An example of this is: The span of the high bridge 490 m has been determined after several simulation studies undertaken by The Danish Maritime Institute and SSPA Maritime Consulting Sweden. The outcome of the simulation studies was a determination of the free span of the high bridge – in fact an increase compared to earlier concept studies – and a realignment of the navigation channel. A summary of these studies is given in [9]. 2.2.2
Risk analysis
Separate studies have been undertaken by a permanent group with representatives from the owner, the owners consultants and external experts in order to ensure that the general risk policy formulated by the owner: -
The total individual user risk for road or railway users shall not exceed the comparable level for the user risks on a Swedish or Danish motorway or railway having similar length and traffic intensity.
User risk comprise events and accident scenarios, which do not necessarily compromise the structural integrity of the link, but which may imply closure of the link for shorter or longer periods of time. User risks are composed of 1) 2)
Ordinary risk comparable to accidents occurring at ordinary motorways or railway Link specific risks
Some contributing factors to ordinary accidents are not present at the link (such as road intersections and branching) therefore the ordinary risks for motorway users on the link have been found to be smaller than for similar motorways. The net result from both contributions as reported in [11] show that the individual risk measured as number of fatalities per 1 billion passages of the Link is at a satisfactory level compared to the declared general policy. 21 fatalities per 1 billion passages for road users and 4 per 1 billion passages for train users. The corresponding figures for motorway and railways are 33 respectively 4 fatalities per 1 billion passages. The risk studies for the operational phase have been collected in separate reports and technical notes, an overview of which is given in [13], and annually updated in the Operational Risk Analysis reports, the last being ORA 98. Account sheets for each and every contributing scenario quantify the calculated frequency and the consequences hence giving a risk measure and contribution to the total risk from the hazards considered. These accounts are subject to review and are enclosed as part of the annual ORA. Some of the various accidental actions included in the risk analysis are listed below: -
Train derailment loads Sunken ship on tunnel roof Falling/ dragging anchor (tunnel roof)
-
Fire loads Seismic loads Rupture of cable stay Ship collision Aircraft collision
As previously mentioned, the Operational Risk Analysis considers scenarios which do not necessarily lead to structural collapse or compromise of structural integrity. However an interface directly to the part of the Design Requirements dealing with structural safety does exist for most accidental loads. An example is ship impact with the bridge structure, which turned out to be important: The risk analysis includes assessments of collision frequencies for each relevant part of the structure, piers for head on - and sideways collisions and superstructure for deckhouse collisions, for the population of ship envisaged by the prognosis. Combining the collision frequency model with a mechanical/dynamic model for the impact scenarios the ship collision design loads for each part of the structure has been defined to meet the formal high safety class target. The risk analysis of course has been taken further to include risk contributions not leading to structural collapse but being associated with other user risks, for example as reported in [14] and [15]. A summary of the various and extensive studies carried out in relation to ship collision is found in [10].
3.
Design Requirements
The Design Basis has been prepared as an internal background document being a common basis for technical requirements of the various contract documents. The technical requirements – the Design Requirements for the various contracts, confer figure 1, of course reflect the different character of the contracts but on the other hand also include identical requirements for works/ structures of a common nature. The contracts of course share the same underlying codes and PAD, also they share the same requirement to loads and load combinations as determined in the supplementary studies and described in the Design Basis.
4.
Concluding remarks
At this time – not long before the opening of the Link it is possible to take a retrospective view upon the results of the process described above. It seems to be a fair assessment, that the early preparations including the early strategic decisions focusing on defining and describing the technical requirements, followed by a consistent and thorough implementation process headed by the owner will contribute to a successful final result.
5.
References
[1]
Eurocodes as Reference Codes, Øresundskonsortiet, ES-Consult 1993-06-14
[2]
Project Technical Design Basis, Øresundskonsortiet, ØLC, May 1994
[3]
Project Application Document, Øresundskonsortiet, ØLC, 1994-03-16
[4]
Calibration of Partial factors and Load Combinations Phase 0, Øresundskonsortiet, ØLC, 1993-12-20
[5]
Basic Information. Ice Conditions, Øresundskonsortiet, DHI/LIC, 1993-08-31
[6]
Basic Information. Water Level Conditions, Øresundskonsortiet, DHI/LIC, 1993-08-31
[7]
Basic Information. Wave Conditions, Øresundskonsortiet, DHI/LIC, 1993-09-03
[8]
Basic Information. Wind and other Meteorological Conditions, Øresundskonsortiet, DHI/LIC, 1993-09-22
[9]
Summary Report of Ship Simulations in the Flinte Channel and the Drogden Channel, Øresundskonsortiet, ES-Consult 1998-03-06
[10]
Summary Report - Ship Collision, Øresundskonsortiet, ØLC, 1994-12-15
[11]
Operational Risk Analysis ORA-97, Øresundskonsortiet, ØLC, April 1998
[12]
Risk Account ORA-97, Øresundskonsortiet, ØLC, April 1998
[13]
ORA collection of Memos, Vol. I and II, Øresundskonsortiet, ØLC, April 1998
[14]
Ship-induced Derailment on a Railway Bridge, J. Jensen, E. Svensson, H.J Eiriksson and F. Ennemark, IABSE Struct. Eng.., Vol.6, no.2, 1996
[15]
Train derailment due to ship impact on bridges, E. Svensson, Proc. Int. Symp. Adv. Ship Collision, Ed. H. Gluver & D. Olsen, Copenhagen, 10-13 may 1998.
Detailed Design of the Cable Stayed Bridge for the Öresund Link Lars HAUGE Dept. Head, Major Bridges COWI Denmark
Anton PETERSEN Dir., Bridges COWI Denmark
Mr. Hauge graduated from the Technical University of Denmark in 1986. Since 1990, he has been employed by COWI, where he at present is head of the department for design of major bridges. Mr Hauge was in charge of the detailed design of the cablestayed bridge for the Øresund Link
Mr. Petersen has since his graduation from the Technical University of Denmark in 1974, been employed by COWI, where he currently is director for bridges. Mr. Petersen has been the project manager for the detailed design of the Øresund Bridges.
Summary The 7.7 km long Øresund bridge is a major part of the Öresund Link between Denmark and Sweden. The most significant element of the entire Link is the cable stayed high bridge spanning the navigation channel. The bridges were tendered on a design-built basis leaving the responsibility for the design with contractor. Sundlink was awarded the contract to built the bridges in 1995 and subcontracted the design to CV Joint Venture, comprising COWI from Denmark and VBB from Sweden. This article describes the detailed design of the High Bridge.
Fig. 1
The Öresund Bridges
The bridge will carry a four lane motorway with emergency lanes and dual tracks for a high speed railway, and will when completed be the longest cable-stayed bridge for high speed railway. The traffic is arranged in two levels with the roadway on the upper deck and the railway on the lower deck. The rails are laid in ballast over the entire length of the bridge.
1 Design Requriements Very early the Client decided the project to be based on the Eurocode system. The problems to integrate two different national standards, the Danish and the Swedish, were thus avoided. The applicable Eurocodes comprise: • EC1 Basis of Design and Actions on Structures • EC2 Design of Concrete Structures • EC3 Design of Steel Structures • EC4 Design of Composite Steel and Concrete Structures • EC7 Geotechnical Design At the time, when the Enquiry Documents were prepared (1993), the Eurocodes were only available as European Pre-standards (ENV's) or in draft versions. To obtain a fixed contractual basis for the design, it was decided to select a specific version for each of the Eurocodes as a reference document. Project Application Documents (PAD) have been prepared to supplement each of the Eurocodes. The PADs have the same function as the National Application Documents (NADs) developed by the CEN member countries, which implements the Eurocodes. Similar to projects as the Great Belt Link, general design requirements were specified by the Client in addition to the Eurocodes and the PAD's to cover special features of a major civil construction work. The general design requirements cover the areas : • Functional and aesthetical requirements as alignment, gradients, cross-sections and clearance profiles. • Civil and structural loads, load combinations, and partial safety coefficients. Methods of structural analysis and design. • Geotechnical requirements to geotechnical design and construction, including soil strength and deformation parameters. • Mechanical and electrical requirements to tunnel and bridge installations, including systems for supervision, control and data acquisition (SCADA), power distribution, traffic control, communication, etc.
In case of discrepancies between the various documents, the hierarchy between the different elements of the Design Requirements is: Design Requirements - Volume 1 (Design) Standards and codes specifically referred to herein with the exception of the Eurocodes Design Requirements - Volume 3 (PAD) Eurocodes
Fig. 2
Order of precedence of documents
The Öresund Link is the first major civil works project, which to a large extent has been designed according to the Eurocodes. Considering the complexity of the project and the state of the applicable Eurocodes, the system has proved to an operational but very comprehensive design basis.
2 High Bridge, General The high level bridge is outlined as a cable-stayed bridge with a main span of 490 m and a total length of 1090 m. The cables are arranged in a harp system with an inclination of approximately 30°. The cables are supported by 203.5 m high H-shaped pylons. A tie-down system is arranged at the piers closest to the pylons to balance live load in the main span. Expansion joints are provided at the transition to the approach bridges.
Fig. 3
High level bridge, Elevation
The overall performance of the bridge is dictated to secure a safe and comfortable operation of a railway connection. The comfort to passengers has been verified trough analysis of the vertical acceleration of passenger coaches from different train configurations. Considering the navigation clearance special attention has been paid to shrinkage and creep, of the concrete pylons and the concrete bridge deck, as the requirements to the navigation clearance have to be fulfilled both when the bridge opens and after 100 years. The vertical deflection due to shrinkage and creep from year 0 to year 100 in the centre of the main span has been calculated to 155 mm.
The backbone in the verification of the design has been a 3D finite element model of the bridge. The computer model includes all truss members as beam elements, and the roadway deck as shell elements, and allows for individual optimisation of all elements. A total of approximately 70 construction stages has been modelled to ensure that the correct force pattern in the completed bridge structure is obtained, and to ensure the correct production geometry of the elements. The model considers shrinkage and creep in accordance to Eurocode 2. Further, time-history analysis has been carried out to determine dynamic amplification factors for passage of train loads and ship collision loads.
3 Substructure 3.1 Pylons Rising 203.5 m above the sea level, the pylons of the cable-stayed bridge will be the landmark of the entire link. The pylons are designed as clean Hs without an upper cross beam and with the legs disappearing directly into the sea. The outer shape of the visible parts of the structures was determined by the ÖSK and part of the contract. The pylons are founded directly on Copenhagen limestone in level -17 m and level -18.5 for the east and west pylon, respectively. The foundation structures are cellular caissons with a footprint of 35 m x 37 m. Fig. 4 Pylon, elevation One of the key issues in the design has been to keep the dimensions and the weight of the caissons as low as possible because of the size of the available dry-dock facilities and the available draft during towout. Intensive cooperation between designers and contractors was established throughout the project to achieve these goals. The result lead to a design which to an Fig. 5 Pylon caisson outsider may look
inefficient, as for instance the ribs, supporting the bottom slab. But a total optimisation considering design, fabrication and transport lead to the present design. The structure is posttensioned in the bottom slab, in the ribs and wall and in the top slab. The dominating load for the foundation is [MN] ship impact. The caisson is designed to 100 0 withstand a ship collision force of 560 MN 0.00 -100 in the longitudinal direction and 438 MN in -200 the transverse direction of the bridge -300 excluding dynamic enhancement. Dynamic -400 -500 ship collision analyses were carried out on a -600 computer model of the entire bridge to -700 determine the dynamic enhancement and the amount of load being transferred trough the cable system to the other pylon. The Fig. 6 calculation showed peak-forces of 638 MN and 651 MN for the east and the west pylon caisson, respectively.
Shear forces in pylon leg
0.20
0.40
0.60
0.80
1.00
1.20
1.40
[s]
Shear force
Sideways ship impact force
Shear force at level -17.0 m during ship impact
Advanced soil/structure interaction calculations were carried out to demonstrate the bearing capacity and the requirements to plastic deflections after a ship collision. Prior to tender, the Client, had carried out extensive field and laboratory tests, including determination of stress strain curves for 1m x 2m plates which made it possible to determine a stress limit for the limestone. This lead to the following verification procedure for ship collision: 1. The dynamic amplification of the impact force was determined, based on a linear elastic time history analysis of the ship collision on a 3D finite element model of the entire cablestayed bridge with the foundations modelled as linear elastic springs. 2. For the verification of the soil/structure interface a non-linear material model, a DrugerPrager cap model, was calibrated, based on full-scale tests carried out by ÖSK. 3. The force-displacement curve for the foundation, subjected to the enhanced ship collision force, was determined using a nonlinear model of the caisson and the surrounding soil. Fig. 7 Plastic zone development 4. The linear elastic time history analysis was redone with the spring constant for the foundations, found in the force displacement analysis. 5. The bearing capacity of the foundation was verified. The pylon legs have an outer pentagonal shape, selected for aesthetical reasons. Having the centre of gravity dictated by the position of the cables, the cross section is balanced with thick walls towards the girder and thin walls at the opposite side to avoid long time deflections from normal forces in the pylon. Below the cross beams, the reinforcement in the legs are to a large
extent governed by ship collision. From level 17.5 (level of main deck for colliding ship) and down an intermediate wall of structural concrete has been introduced in the pylon legs to increase the shear capacity and nontensioned bars (36 mm diameter) with a yieldstress of 1030 MPa were applied in the transition between legs and caisson to be able to fulfil the requirements during ship collision. Above the cross beam at level +55 m, the pylon legs are designed to resist an accidental impact load of 8 MN in any direction. Due to aesthetical considerations the cross beams are omitted above the bridge girder which results in almost 150 m free standing legs in the transverse direction of the bridge alignment. This leads to heavy vertical reinforcement above the cross beams of the legs. The cable stays are anchored in individual steel boxes, one for each pair of stays. The horizontal component of the cable force is transferred directly through the steel between two opposite cables, and the vertical component is transferred to the concrete via Fig. 8 shear studs.
Pylon, stay cable anchorage
Extensive analyses of the interaction between concrete and steel have been carried out to verify the strength of the steel boxes and the crack widths in the concrete around the anchor boxes. The quantities for the pylons (two pylons) are 35.000 m3 of concrete, 5700 tons of reinforcement and 730 tons of post-tensioning cables and bars. 3.2 Piers The sidespan and anchor piers are designed as the approach bridge piers which in total comprise 51 piers all founded on open cellular caisson structures directly on Copenhagen limestone To limit the flow resistance, all caissons are submerged into the seabed. Depending on the water depth, the piers must be able to resist different ship impacts. The fine tuning of the bearing capacity has been carried out by filling of the piers. Eclogite (γ = 26 kN/m3, Fig. 9
Approach bridge, piers
saturated) and sand (γ = 11 kN/m3, saturated) have been applied. A goal has been to achieve as much uniformity as possible for a simplified production. In the design, a parametric 3D finite element model was established, enabling individual optimisation. COWI's in-house developed computer programme, IBDAS, was used. The programme is especially suitable for parametric modelling and has the advantage of being integrated with the CAD system. The drawings for construction were produced automatically from the 3D finite element model, thus assuring a rational production with a high degree of "automatic" quality control.
4 Superstructure 4.1 Bridge Girder The bridge girder for the high bridge is arranged as a steel truss girder with an upper transversely posttensioned concrete roadway deck and a lower deck for the railway, designed as a closed steel box. The inclination of the truss members is arranged with approximately 30° and 60°, respectively, allowing the flat diagonals to match the inclination of the cable stays. The cables are anchored to the girder on outriggers with the same Fig. 10 inclination as for the flat diagonals.
High Bridge girder, cross section
The lower steel deck has proved to be a robust structure, with a satisfactory post-accident performance when the structure is being subjected to train derailment, which results in loss of a diagonal or loss of stay-cables and fire. Diagonals, chords and the railway deck are in steel grade S420 (EN10113) except for the secondary structures inside the railway deck which are designed in S355 (EN10113). Plate thickness' vary between 9 mm in the underside of the railway deck at the centre of the main span to 50 mm in the webs of the nodes at the pylons.
Fig. 11
Dehumidification system
The interior of the steel truss is protected from corrosion by dehumidification. By keeping the interior air below 60 % relative humidity no corrosion will occur. The design ended up with 15.800 tons of structural steel, 11.000 m3 of concrete and 1900 of tons post-tensioning cables. 4.2 Cables The cables are arranged in a harp system with all cable stays in parallel. As for recently built cable-stayed bridges as the Normandy Bridge in France and the Second Severn Bridge in UK, PWS (Parallel Wire Strands) cables have proved to be competitive. The effects from buffeting, vortex shedding, forced vibrations of the supports and rain/wind induced vibrations have been investigated analytically. A final verification of the rain/wind induced vibrations has been carried out by wind tunnel testing. The cables are designed with an outer PE-sheeting with helical ribs as a countermeasure for rain/wind induced vibrations. In addition, the cables will be prepared for later erection of tie-down ropes if excessive vibration should occur. The maximum transverse amplitude of the cable vibration must be less than 1/3000 times the cable length and also less than 60 mm for a 10 minute mean wind velocity of 20 m/s at a height of 100 m. In total 2.700 tons of stay-cables are used.
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Design coordination of a design-build project Ingvar OLOFSSON Vice President Skanska Teknik AB Göteborg, Sweden
Ingvar Olofsson is head of the Division for Design of Bridges and Civil Engineering Structures within Skanska Teknik AB, a subsidiary of Skanska AB.
Summary The architectural and structural design is in a design-build project developed through all the different phases of the project. The conceptual design, where the general and functional requirements for the project are defined, is carried out by the Owner and his consultants. Pretender designs, tender design, basic design and detailed design are performed by the Contractor and his consultants, during the latter phases in close contact with the Owner. The paper discusses how the Contractor and his consultants in major design-build projects perform design coordination and design management. Examples are given from the organization of the design for the Öresund bridges. Professional design management, strictly defined design agreements, devoted and competent design organizations within each one of the design phases are, together with positive and open atmosphere in the relations with the Owner and other involved parties, essential ingredients for the successful outcome of a design-build project.
1.
Design phases
1.1
Pre-tender phase
In order to reach the primary goal (to win the contract) the Contractor and his tender project group should be prepared to start their work very early, if possible long before the inquiry documents are released. Even if the particulars of the project requirements are still unknown, getting familiar with the project and the local conditions is essential. The core of the future competitive design team is created here and introduced to the project. Hence many of the tasks mentioned below should be handled during this stage.
Collect as much information as possible of the future project. Soil investigations made for neighboring structures are often available as well as reports of previous proposals. Even reports of rejected concepts may be of interest, as they can reveal information regarding anticipated difficulties.
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1.2
Identify critical parts or areas, where special competence or experience will be needed. Complex or difficult parts of the structure should be carefully evaluated especially when new methods or inventions are being introduced. In some cases and in major projects, planning for necessary tests and simulations could be made in this stage. Allocate best possible design and engineering resources to the group. Individuals with specialist competence should be identified and engaged. As many winning concepts are connected with the choice of efficient construction methods (rather than optimizing of quantities) a close cooperation within a team of experienced designers and construction engineers is essential when developing the winning concept. Organize brainstorming meetings where alternative approaches and solutions are invented and scrutinized. A screening of available and possible construction methods, design systems and material combinations can be started up during carefully organized brainstorming sessions. Even if such a session should be unlimited and free of its nature, it has to be supervised and documented. Subjects and focuses should be chosen and varied. No options should be disqualified until disadvantages are obvious and proven. Select alternatives for detailed evaluation. In addition to the selected “obvious” alternatives also some other, promising alternatives should be chosen for detailed evaluation. New possibilities will often appear in connection with discussions around improvements to an impossible option. Estimate the need for design resources in the following phases. Be sure that your internal and external resources are well equipped not only with regard to experience and competence for a handful of specialists but also in numbers of qualified engineers and in status of computer facilities and software. Social competence is needed to achieve good relations and smooth cooperation with authorities and Owner. Prepare for a possible prequalification together with the chosen internal and external design consultants. Be aware that some consultants may be disqualified from participating in late stages of a project if they are challenged by involvement in previous phases. Prequalification phase
Prequalification is made based on the experiences gained during the pre-tender phase. Possible exclusivity for the tender phase and the future design phases should be discussed or formally agreed with the consultants, with regard to confidentiality, strategy or the specific requirements of the Owner. 1.3
Tender phase
The tender phase will to a major extent contain the same activities as the pre-tender phase. Based on the knowledge of the Owner’s requirements some alternatives can now be excluded from further investigation, while some might be added. The design resources are split up in different sub-project groups, each group working according to a time schedule. Sufficient time and resources for evaluation of new ideas and concepts popping up during the course of the work must be available. A close cooperation between the design team and the Contractor’s own engineering staff is essential for a good result. In order to maintain the intentions given by the Owner special attention should be given to the esthetical appearance of the structures as well as to environmental issues and of course to matters related to quality, durability and maintenance.
3 Risk analyses could be carried out for crucial construction phases or for comparison of risks (and the related costs) in different construction methods. While risk analyses are performed according to formal methods, the quality of the output always depends on the quality of the input. Once again, experience is essential, not only from making risk analyses but also experience gained from real construction works under corresponding conditions. Design work performed at this stage should aim at providing a winning concept for the Contractor. It should of course arrive at sufficiently low and correct quantities and costs, to be maintained in the construction phase. Likewise important is that calculations and other documentation are prepared for immediate continuation in the construction phase. At the end of this phase the conditions of the future design contracts should be negotiated with the different design consultants. 1.4
Basic and Detailed design (Construction phase)
Based on the Contract with the Owner and the time schedule, as defined in the Contract, the Basic design and the Detailed design is performed in parallel with the construction work. To save time and make an early start of the construction work possible, the Basic design phase should be an immediate continuation of the tender design. If possible the same general calculations and drawings should be used after proper, minor updating. In a design-build contract all parties must realize, that method statements and design documents must be successively approved and released for construction before the total project is known to its details. A suitable submission procedure must be worked out and agreed upon early. The procedure should define structural parts, which are technically independent of each other and thus suitable for independent handling and release. It should also be possible to define different design levels, i.e. design documents to be approved by the Owner, to be sent for information to the Owner or for internal review by the contractor only. One of the main advantages with a design-build agreement is that construction methods and design details from the very beginning can be adapted to the contractor’s available equipment and techniques. The synergy effect arising from a close and serious involvement by the contractor in the design development is important. The responsible site engineers (not only the managers) should thus contribute in the early deliberations regarding transport and lifting equipment, crane capacities, construction joints, bar lengths, bar splicing, joining of steel members etc. The above implies further that agreements with possible subcontractors should be closed soon after signing of the main contract, especially in fields where extensive or specific detailed design influencing other involved parties, has to be performed. A considerable design effort has normally to be laid down in this phase in connection with change orders from the Owner and from the Contractor’s engineering teams. Careful planning and cost control (follow-up on quantities of construction material as well as design costs) of the design activities are crucial to avoid delays as well as excessive construction and design costs.
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1.5
Endorsement
The late design phases and the successive finishing of the construction works are accompanied by endorsement of the construction material, the workmanship and the completed works. It is recommended that some of the experienced designers involved in the project take part in these activities as all design requirements and specific details of the project are well known to the designers.
2.
Design contracts
Design contracts are normally concluded separately for the different phases. Possibilities and options are given to the consultant to continue into the next phase, if successful. Local standard agreements (i.e. the Swedish ABK 96 “General Rules of Agreement for Architectural and Engineering Consulting Services”) or international standard contracts are commonly used as the basis for the design agreements. Some general comments to the different types of agreements are given below. 2.1
Fixed fee agreements
Fixed fee or lump sum agreements tend to be used when conditions and requirements are well known and design changes are not anticipated or rare. Hence, it is not recommended for a tender phase, but could be applied in other phases. The risk that the quality of the presented design might suffer from an underestimated lump sum price, should however not be disregarded. 2.2
Variable fee agreements
A variable fee agreement is commonly used in combination with agreed hourly rates for different categories of engineers. Expenses are compensated at verified costs together with an additional, agreed percentage on the prime cost. Restrictions regarding maximum, total fee or reduced rates when exceeding a certain fee target level are commonly applied to this type of agreement. 2.3
Incitement and bonus agreements
To stimulate the consultant to use his resources efficiently, and keep design costs as well as quantities low, different kind of incitement and bonus agreements are often discussed and also applied. The following types are common (combinations and variation in details are however frequent)
Reduced rates in a tender phase combined with a future “success fee” Sharing of profit if final design cost is below the target level Quantity bonus if the final built-in quantities are below the tender quantities
The two latter alternatives involve a considerable effort in follow-up and time-consuming discussions. A carefully elaborated agreement of this kind can however be rewarding to the consultant as well as to the contractor.
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Another option, so far rarely used, is to form a consortium between the consultant and the contractor, thus sharing risks as well as possible profits.
3.
Design management
The management of the design work for a major design-build project requires a number of routines and administrative tools, which should be carefully chosen and developed in an early stage of each design phase. The most important documents, the quality systems and the project quality plan, should in detail specify the applicable routines and systems to be used, of which some are mentioned below:
Organization charts for Client, Contractor, subcontractors and design organization Definition of contact persons and information paths Definition of duties and responsibilities Routines for verification, submission, approval and release of documents Routines for handling of changes, non-conformances and corrective actions Distribution lists (including numbers to telephone, telefax, e-mail, etc) Rules for exchange of information Information and planning systems, specific software to be used Design cost management systems Meeting routines and participation rules, standard agendas, periods for meetings Design time schedule, design milestones Routines for interface identification and control Diaries Document numbering systems Document standards and document lists CAD-manual Rules for safety and security Filing systems
It should be mentioned that one of the most essential early planning tasks in a design-build project is to define safe, simple and efficient communication means and paths. Information should of course be provided promptly to those needing it. On the other hand strict rules should prohibit unlimited distribution of documents just “for information”. Another important issue is to find solutions for separate handling of technical matters and issues related to design costs. Cost discussions often tend to be more time-consuming than the processing of technical questions. Simultaneous handling will have a tendency to slow down the rate of design progress.
4.
Design coordination for the Öresund Bridges
For tendering and, later on, structural design of the permanent structures for the Öresund bridges the Contractor (Sundlink) have engaged CV joint venture, consisting of highly
6 qualified engineers from the Danish consultant COWI AS and the Swedish consultant VBB Anläggning AB. Shop drawings and, to a minor extent also the detail design, have been carried out by the different subcontractor’s designers, while design of temporary facilities and auxiliary equipment has been handled by Sundlink´s internal design organizations. The organization of the work has to a large extent followed the guidelines given above, with the same key personnel engaged in the project from prequalification and tender phase into later phases. As the design work had to be carried out hand in hand with the construction works, the following proved to be essential in order to guarantee a fast and safe design work providing a cost efficient and high quality bridge design.
Close cooperation between Contractor and Consultant. A number of experienced design engineers from the Contractors own staff were on full time basis incorporated into the design teams to guarantee that the design was adapted to the planned construction methods. Frequent design meetings and close contacts also between the Owner´s and the Contractor´s design organizations. Flexibility, fast decisions and willingly accepted ad hoc meetings (often on short notice) created a friendly and cooperative atmosphere to the benefit of the project. An efficient internal review system. For advanced designs also external specialists, employed by the Consultant, were incorporated or complementary to the review groups. The agreed submittal procedure allowed for early approval of the Basic design, which formed the basis for the consecutive Detailed design. Provided that the Basic design remained unchanged no major comments were to be anticipated to the Detailed design. The Basic and Detailed design was subdivided in suitable, independent design packages. Each design package could thus be approved and released for construction more or less independently. Efficient communication systems, utilizing modern IT-technique for production and distribution of documents also over long distances. The agreement between the Contractor and the Consultant included different incitements to stimulate and challenge the Consultant, ie success fee for successful tender design and quantity bonuses in case the Contract quantities were not exceeded in the final design.
Everybody who has been involved a design-build project knows that no project develops completely as planned. Unexpected obstacles or surprises will occur, always when least wanted. Hence the successful outcome of the project will depend not only on the technical skill and experience of the staff but to a major extent also on their creativeness and devotion even in late evenings or during weekends. The latter is always efficiently promoted in a good working climate with stimulation and good leadership provided by the management.
The Öresund Bridge, Erection of the Cable-Stayed Main Span
Lars T. SØRENSEN Sundlink Contractors HB Malmö, Sweden
Niels E. THORSEN Monberg & Thorsen A/S Copenhagen, Denmark
M. Sc. in Mech. Engineering Employed by Monberg & Thorsen A/S since 1981
M. Sc. in Civil and Structural Engineering Employed by Monberg & Thorsen A/S since 1978
Summary The erection of the superstructure for the Öresund bridge is a challenging task involving development of erection techniques for girders weighing up to 6900 tonnes. The erection of the superstructure for the cable-stayed bridge was commenced by the erection of the first girder in June 1998 and completion of the erection of girders and stays is scheduled for the summer 1999.
Fig. 1 The Öresund Bridge
1. The Cable Stayed Bridge. The Öresund bridge consists of two approach bridges and a cable-stayed central bridge 1092 meters long. The main span is 490 meters which is a world record for cable-stayed bridges carrying both highway traffic and trains. The navigation clearance is 57 meters. The bridge girder is a composite structure with a steel truss and a concrete deck carrying four lanes of highway traffic on top. Inside the truss girder a steel railway deck carrying two railway tracks is installed.
2.
Prefabrication of the Girders.
The construction of the Öresund bridge is to a very high degree based on prefabrication of large elements on-shore - 8 girders with lengths 120 or 140 meters and weights up to 6200 tonnes are used for the cable-stayed bridge. The steel part of the girders for the high bridge are prefabricated in Karlskrona in Sweden and transported by barge to Malmö where they are unloaded at the girder reloading station and the concrete deck is cast.
Fig. 2 Cross section of the cable-stayed bridge The girders consist of a railway deck which is a steel box girder, two steel trusses, a concrete road deck and steel outriggers for the attachment of the cable-stays (see fig. 2). The girders are prefabricated in 20 meter sections complete with railway deck, trusses and outriggers. The girder elements are transported from the shipyard to a girder assembly yard by barge. The 20 meter long elements are painted and assembled to 120 or 140 m girders. Girder joint see fig.13
60 m 140 m girder
Fig. 3: Trial assembly of 20 meter section to 140 meter girder.
20 m section
During the assembly of the girders each 20 meter element is supported separately and the required precamber is built into the structure. When the girder assembly is complete the supports are changed to hydraulic supports with 60 meter spacing and the geometry of the girders is verified. At the girder ends a trial assembly with the first 20 meter section for the next girder is done (see fig. 3), the joint is prepared for welding and all equipment which shall be used for the girder connection at the bridge site is installed. Load out of the girders onto a barge is done by skidding and the girders are transported to Malmö.
Skidding line
Additional supports for casting
Skidding line
Fig. 4: Main bridge girder at girder reloading station in Malmö. In Malmö the girders are placed on the girder reloading station and moved by skidding to the casting positions on tracks with 100 meter spacing (see fig. 4). Additional supports are installed under the girder and used to obtain the correct precamber for casting of the road deck. Due to the heat development which occurs during curing of the concrete an additional precamber is required for compensation. The casting of the entire deck is done in one operation. Before load out of the completed girder the geometry is checked with 100 meter spacing between the supports, the girder is loaded with all the equipment to be used for the erection and with the strands for the cable-stays. The cable-stays represent a considerable weight which is used to counterbalance uneven weight distribution in the girders and thereby to obtain a balanced girder lifting with Svanen.
3.
Erection of the Girders.
The main span of the bridge is erected using an innovative method. The girders are placed by the floating crane Svanen on temporary support towers placed on the seabed.
Temporary tower 2
. Fig. 5. Installation of a 120 meter girder with Svanen
Temporary tower 1
Svanen was originally designed for the erection of the Great Belt West Bridge in Denmark afterwards the height and the lifting capacity for Svanen was increased for the erection of the Prince Edward Island Bridge in Canada. The lifting capacity for Svanen is today 8700 tonnes. For the erection of the Öresund Bridge Svanen has been equipped with a special lifting tool which is used for the erection of all the elements (see fig. 5). The lifting tool has a hinged rear part which is opened when Svanen moves in for pick up of a girder - the tool is closed and Svanen is ready to pick up a girder. Inside the lifting tool a spacing of 60 meters between the girder support points ensures that the tension in the road deck due to bending moments in the girder does not exceed the capacity. The lifting tool for Svanen is made from high strength steel and weighs 1800 tonnes. Svanen is capable of lifting girders weighing up to 6900 tonnes with the tool. Due to the high girder installation level for the cable-stayed bridge recesses are made in the concrete deck to avoid conflict with the structure of Svanen. Furthermore due to the geometry of the lifting tool and to avoid conflict with the structure of Svanen erection of some of the outriggers is done after placing of the girder.
Temporary tower 2
Temporary tower 1
Pylon girder Anchor Pier
Pier 2
Pylon
Fig. 6: Erection of the pylon girder. The first girder (the 140 meter long pylon girder - see fig. 6) is inserted between the two pylon towers from the main span and reaches 20 meters into the side span. At the pylon the girder is placed directly on the permanent bearings. The main span end of the girder is placed on a temporary tower which is placed on a grounded barge.
Temporary Guide Arrangement
Fig. 7. Guiding arrangement for the girder at the pylon.
The clearance between the concrete deck of the girder and the pylon towers is approx. 15 cm at each side during the insertion of the girder therefore a guide arrangement is used to avoid direct contact with the towers (see fig. 7). The guide arrangement is equipped with hydraulic jacks which enables the precise positioning of the girder before the placing on the permanent bearings.
Secondary leg
Primary leg
Load distributor Brackets for horizontal adjustment Hydraulic jacks Shim plates Support stack
Fig. 8. Temporary tower 1 on barge On the temporary tower the girder is placed on a stack with built in hydraulic jacks for the vertical and horizontal adjustment of the girder (see fig. 8). The stacks are furthermore equipped with POT bearings enabling node rotations, girder deflections and temperature expansion. During the load transfer from Svanen to the supports the temporary tower is transferred from a fixed tower to a pendulum tower by removal of shims at the secondary legs. Main span Girder joint Pylon girder
Fig. 9: Erection of the side span girder.
Side span girder
Anchor pier
Pier 2
The second girder (the 140 meter long side span girder - see fig. 9) is placed on the anchor pier and attached to the end of the pylon section with the girder connection arrangement. During welding of the joint with the pylon girder it is jacked up approx. 500 mm at the temporary tower to obtain the correct geometry and moment distribution in the bridge. After welding the girder is jacked down. Main span Girder joint Main span girder
Anchor pier
Pier 2
Fig. 10: Erection of the main span girder. The third girder (the 120 meter long main span girder - see fig. 10) is placed on a central temporary tower at one end and the other end is attached to the pylon section with the girder connection arrangement. During the load transfer from Svanen to the supports the central temporary tower is transferred from a fixed tower to a pendulum tower by removal of shims at the secondary legs. During welding of the joint with the pylon girder the main span girder is jacked up approx. 65 mm at the central temporary tower to obtain the correct geometry and moment distribution in the bridge. After welding the girder is jacked down.
Main span
Casting of joint in road deck
Girder joint Girder 1
Fig. 11: Erection of girder 1
Anchor pier
Pier 2
The fourth girder (the 140 meter long girder 1 - see fig. 11) is placed on pier 2 at one end and the other end is attached to the side span girder with the girder connection arrangement. During welding of the joint with the side span girder the girder 1 is jacked up approx. 600 mm at the pier 2 to obtain the correct geometry and moment distribution in the bridge. After welding the girder is jacked down.
Main span
Tower 2 is turned 180°
Anchor pier
Pier 2
Fig. 12: Half the cable-stayed bridge erected including stays. Simultaneously with the girder erection activities the stay-cables are erected and the girders are lifted off the supports on the temporary towers furthermore the joints and the recesses in the road deck is cast (see fig. 12). The temporary tower 1 is moved to a new position at the other pylon and prepared for the erection of the other bridge half. Furthermore the temporary tower 2 is turned 180° which brings the primary legs in position for the erection of the second main span girder. The main advantage of the erection of the long girders is that the expensive off-shore activities are cut down to a minimum which leads to time and cost savings compared to the normal cantilever method.
4.
Girder Connection Arrangement
The girders for the high bridge are during erection connected to the previously erected girders transferring the weight at one end directly to the previously erected girder. For this purpose a girder connection arrangement has been developed using the short permanent diagonal in the truss as a support element. Hinged upper chord connectors transfer longitudinal forces between the ends of the chords and a contact and guide arrangement, installed on the upper chords, control the local geometry in the transverse direction at the joint. Contact and guide arrangement
Upper chord connector
Joint in upper chord
Short diagonal acting as main support
Contact plates
Joint in lower chord
Fig. 13. Girder Connection Arrangement
The diagonal is temporarily hinged at both ends to enable node rotations, when the girder weight is transferred from the Svanen to the support arrangement at the joint and the temporary suppport on the top of the pier or the temporary towers. An adjustable connector controls the position of the diagonal in relation to the upper chord before load transfer is initiated. The contact and guide arrangement on the upper chords and the contact plates in the diagonal are installed during trial assembly in order to assure the correct welding gap and geometry of the joint. As the short diagonal is inclined, the resulting horizontal drift force in the upper chord is transferred by hydraulic jacks in the upper chord connector. At the completion of the load transfer the final compression force in each diagonal is 13 to 16 MN and the tensile force in the upper chord is 5.0 to 6.5 MN. During load transfer the girder is moved forward by SVANEN until contact at the guide and contact arrangement at upper chord and then gradually lowered until the upper chord connector can be activated by turning the hinged part forward and by increasing the load in each jack to 500 kN and contact is obtained at the contact plates in the diagonal Prior to the erection of the girder a load schedule has been established describing the local geometry at the joint in relation to the rate of completion of the load transfer. When the load has reached 50 % of the final anticipated load a survey is performed. An assessment of the continued load transfer is made. Load transfer is continued until the total load of the girder is transferred to its supports Adjustable push-pull connectors with a capacity of 200 kN control the vertical alignment between upper chords and lower chords before welding.
5.
Erection of the folded-down outriggers. Lifting tool for Svanen
Future position of outrigger
Hinged rear part of lifting tool
Fig. 14. Cross section of Svanen’s lifting tool and high bridge girder
Folded-down outrigger
Due to interference between the outriggers in their final position and the lifting tool or Svanen’s structure itself, as shown above, in 42 positions of a total of 80, the high bridge girders had to be erected with half of the outriggers in a down-folded position. Hinges were installed during fabrication in Karlskrona at a joint in the upper outrigger and at the joint between the lower outrigger and the lower node in order to ease the installation of the outrigger at the bridge site.
6.
Connection of the two cantilevers.
Closing the main span is an activity on the critical path of the sequence of operations. In order to limit its duration, loose members to be fitted during this operation are prefabricated and prefitted to highest extent possible. When all the girders and the stays are erected the two cantilevers are joined at the centre of the main span. While the connection operation takes place the joint is exposed to environmental loads resulting in bending moments and shear forces and normal forces at the joint. Therefore a cantilever connection arrangement has been developed to overcome these solicitations during the welding operation. Horizontal push-pull connector
Vertical push-pull connector
Vertical lattice triangle
Horizontal push-pull connector
Fig. 15. Connection Arrangement between the two cantilevers The connection arrangement consist of one horizontal and two vertical lattice triangles which enable the transfer of shear forces and torsion at the joint. Bending moments from wind load on the bridge girder is taken by strong push pull connectors installed at the chords. The system is designed to enable rapid connection of the cantilevers to obtain a quick and safe transfer from the two free cantilevers to one main bridge span. The anticipated duration of the installation of the connection arrangement is less than 48 hours at a maximum wind speed of 16 m/s. Before the closing operation is initiated, a comprehensive survey is done to establish the actual geometry of the girder corresponding to the actual load and temperature conditions in order to define the anticipated distance between girder ends at the upper and lower chords. This survey will determine the length of the infill pieces between the brackets in the longitudinal bracing.
The vertical slope of the girder ends is controlled by a combination of ballasting the road deck and stay cable adjustment to produce a relative vertical alignment between girder ends, that is in accordance with the predefined erection geometry for this particular phase. When correct geometry is achieved the longitudinal bracing is locked and it will now be capable of resisting the combined forces due to temperature loads and wind load up to 25 m/s.
7.
Erection of the Stay Cables.
The main span of the bridge will be carried by Freyssinet stay-cables. 160 stays each consisting of approx. 70 strands will be used. The 7-wire strands are individually corrosion protected and anchored by wedges at the ends. A PEHD casing keeps the bundle of strands in position and reduces the drag coefficient of the stay-cable. Galvanized strand (wires) Wax
High density polyethylene
Fig. 16. Cross section of stay cable In order to prevent rain/wind induced vibration the casing is equipped with a double helical 2 mm thick spiral. The casing with the spiral has been tested in a climatic wind tunnel and it was found that the spiral prevented the formation of a regular water rivulet and thereby provided good protection against rain/wind vibrations.
Helical spiral Twin cable connector
300 2
Fig. 17. Stay cables with the cable connector The stays are placed in pairs. Therefor the possibilty of wake galloping has been examined by wind tunnel tests. It was found that the distance 670 mm between the stays was sufficient to minimize the risk of this phenomena. The stays are however equipped with connectors at
approximately 100 meter spacing to further reduce the risk of aerodynamic interaction between the stay cable pairs. The stay-cables are erected strand by strand. The first strand to be erected in each stay is the reference strand for which the length has been measured with high precision by the manufacturer ( ±1/10000 of the stay cable length for the short stays and ±1/20000 of the stay cable length for the longest stays), this strand is stressed to the correct length. The first strand is equipped with a load cell and the following strands are all stressed until the load in the reference strand is reached. In order to obtain the correct geometry of the bridge and the correct distribution of forces in the stay cables a precise prefabrication of all the bridge elements and control of the geometry is made. This provides knowledge of all offsets of stay cable anchorages in the pylons and in the bridge deck. Furthermore the bridge geometry and force distribution will be calculated for the various erection stages taking into account actual erection loads on the bridge and the measured weight of the girders. The above mentioned measurements and calculations enable the calculation of the required length of each individual stay cable and thereby the required length of the reference strands. While the stays are erected using the “geometry method” the development of the stay force is followed closely enabling the discovery of deviations from the calculated stay cable forces. The vertical deflection of the bridge girder and the horizontal deflection of the pylons is also measured at several stages during the erection and compared to the computer calculations. The close survey makes it possible to compensate for any deviations occurring during the erection process
Cable-Stayed Bridges with Special Features Jörg SCHLAICH Prof. Dr.-Ing. Structural Engineer Stuttgart, Germany
Jörg Schlaich, born 1934, received his civil engineering degrees from the Universities of Stuttgart and Berlin, and from Case Tech., Cleveland, Ohio. He is professor and director of the Institute for Structural Design II, Univ. of Stuttgart and partner of Schlaich Bergermann und Partner, Consulting Engineers, Stuttgart, Germany
Summary Usually if we speak of cable-stayed bridge design parameters, we have their cable-arrangement, pylon-geometry, the cross-sections and the materials of their deck etc. in mind. But the overall layout is considered to be more or less invariable: a three-span arrangement with two pylons, a main-span and two holding down side-spans, and occasionally half of that with one pylon. However, the cable-stayed bridge concept offers more and can adapt to very special boundary conditions, from local availability of only certain materials or wires to unusual topographical conditions. The outcome may be e.g. one out of a large number of feasible multi-span arrangements, or a combination of cable-stayed and cable-supported. Other situations may call for cable-stayed bridges, where the deck is not straight in plan but curved, or even for convertible or folding decks.
1.
Introduction
A committed structural designer will – case by case – strive for the best possible solution, considering all individual boundary conditions, the functional, environmental, climatic, technological, human etc.. In certain cases, the cable-stayed approach may be the appropriate answer. This needs to be emphasized in times when one sometimes gets the impression that bridge designers are too hastily restricting the canon of bridge shapes to box-girders for short spans and to cablestayed for long spans. No question, after the development of cables with simple and robust anchorages, high fatigue strength and reliable corrosion protection in recent years, the cable-stayed bridge has firmly established itself in the span-range between 200 and 500 meters, and is now even approaching the 1000 m limit.
If we discuss their design parameters, we have their cable arrangements (one, two or more cableplanes in a fan-, semi-harp-, harp-shape), pylon- or mast geometries (single or double masts, pylons with H-, A-, double-A-shape etc.), deck cross-sections (slabs, grids, boxes etc.), deck materials (concrete, steel, composite "new" materials) in mind. But generally if we speak of a cable-stayed bridge, we mean a three-span-arrangement with two pylons or masts on either side of the main span and two side-spans, which are somewhat shorter than half of the main span to counterbalance the cantilevering main span or occasionally half of that with one pylon or mast [see the postscript].
Though, the author and his team are happy to have received the chance to contribute to this development -
with the first composite deck, which was even riveted to allow for an indigenous construction, by designing the 183 m/457 m/183 m Second Hooghly River Bridge in Calcutta, India [1] and following René Walther's Diepoldsau Bridge and his further research on solid concrete slabs for cable-stayed bridges [2], [3], by extending this concept to 215 m with a 45 cm solid slab, by designing, together with S. Stathopoulos, the Evripos Bridge in Greece [4],
the purpose of this paper is to make aware that the cable-stayed concept offers a much larger variety of general layouts, cable-arrangements and that even its girder must not be straight in plan. Cable-stayed bridges can in fact adapt to many different and very special boundary conditions and thus develop a large number of special features. In order to keep the length of this paper within the given limit, the author will try to exemplify this statement by describing some own cable-stayed bridge designs with such special features, but not before naming at least a few other very stimulating ones such as the multi-span Sunniberg Bridge near Klosters in Switzerland by Chr. Menn [5], the "extradosed" Odawara Blueway Bridge by A. Ogawa, A. Kasuga and H: Okamoto [6], or the Sancho El Major Bridge in Spain by C. F. Casado, I. Manterola Armisen and L. F. Troyano.
2.
Combined Cable-Stayed/Cable-Supported "Obere Argen Bridge" This valley, crossed by a 6-lane Autobahn is 730 m wide with maximum depth of only 45 m above the little river "Obere Argen". Whereas between the eastern abutment and western bank of the river the soil conditions are good over a stretch of about 440 m to allow for a continuous girder on flat foundations, the slope between the western bank of the river and the western abutment over a length of 290 m is continuously sliding downhill at a rate of some 10 – 20 cm per year permitting no foundations. Therefore, the Highway Authority through a design competition invited proposals for a bridge with a 260 m end-span followed by regular spans over the remaining 440 m, with the aim to reconcile these two completely different boundary conditions in a very sensitive rural environment in the foothills of the Alps. Finally from a number of alternatives a sequence of 86 m cable-supported spans was proposed, followed by a 3 x 86 m = 258 m combined cable-stayed and cablesupported end-span (Figs. 1 + 2).
** *
Fig. 1: "Obere Argen Bridge": Alternatives * proposed; ** built
With that, as against a one-sided pure cable-stayed layout, the height of the pylon is only half, without increasing the cable forces respectively the amount of cables needed. The cable alignment follows the topography and the bridge blends in modestly with its surroundings. – In fact, the main feature of this design, the western cable-stayed/cable-supported 258 m endspan was built whereas on the eastern side – due to cost reasons – unfortunately only a continuous girder with 56 m span without cable supports was accepted (Fig. 3).
Fig. 2: "Obere Argen Bridge": Proposal
Fig. 3: "Obere Argen Bridge", completed 1990
3.
Multi-Span Cable-Supported Bridges
3.1
Proposals for Ganga Bridges at Allahabad and Patna
Wide, alluvial rivers like the Ganga in India require caissons or well-foundations 60 or more meters in depth to resist scour (Fig. 4a). Thus for standard girder bridges, requiring piers at frequent intervals, the foundations are extremely costly. The costs of the foundations decrease almost proportional to the increase in the span, and this suggests large spans, especially with cable-stayed decks. In the sixties F. Leonhardt's innovative proposal for Allahabad basically consisted of individually balanced cantilevers. However, to counteract the cantilevering moment due to onesided traffic load, it avails only of a relatively small lever arm as given by the longitudinal distance between the tower legs (Fig. 4b). Therefore, for Patna this lever arm was dramatically increased to about 0.8 of the main span L by arranging crossing back-stays in every second span, resulting a alternating spans of length L and about 0.8 L (Fig. 4c). It is interesting to note that basically the "new" extradosed bridges of our days are nothing but a revival of the Allahabad proposal.
Fig. 4 Very long bridges with deep foundations 3.2
Proposal for the Prince Edward Island Link
The Patna type requires an expansion joint at the center of every main span of length L or better a dropped girder of say 20 m length to avoid a kink under traffic load and to account for manufacturing inaccuracies between adjacent spans. Thus such a multi-span cable-stayed bridge typically consists of self-balanced units which are [1.8 L – 20 m] long (Fig. 5). For the 12 km long Prince Edward Island Link it was proposed to choose L = 180 m and to completely prefabricate the 380 m long deck + pylon + cable-units under shop conditions ashore to overcome the adverse climatic conditions. During the ice-free period, after first installing the prefabricated foundations, the bridge units would be lifted into position by use of a floating crane (Fig. 6). This basic concept was further developed for a crossing of the Strait of Gibraltar. In this case the pylons were to be mounted on submerged caissons which would serve as pontoons anchored with cables to the seabed [7].
Fig. 5: Prince Edward Island Link, proposal 1988
Fig. 6: Prince Edward Island Link, proposed construction procedure 3.3
The Ting Kau Bridge in Hong Kong
This is one of the few multi-span cable-stayed bridges really built. Its cable-supported deck is 127+448+475+127 = 1177 m long (Fig. 7). The special features of this bridge are its two adjacent main spans with their stabilizing cables which run – as in Fig. 4c – diagonally from the top of the main tower towards the deck at the side towers. With further stabilizing cables in the transverse direction, the towers of the bridge appear like masts of a sailing boat.
Fig. 7: Ting Kau Bridge The bridge must span the 900 m wide Rambler Channel. This distance is too short for an economical suspension bridge and is rather long for a single main span cable-stayed bridge. Further, as any pier in the busy channel would require costly ship impact protection, the number of piers had to be kept to a minimum. Therefore, the conventional design of a single main span bridge of 600 to 800 m with two offshore towers was excluded. With load-carrying rock generally at –40 m, fortunately there exists an underwater hill with a peak at –30 m almost in the middle of the channel offering the chance to place one central tower at this location and two smaller towers on either side on-shore (Fig. 8) [8].
Fig. 8: Ting Kau Bridge, Hong Kong, completed 1998
4.
The Hybrid Main Span + Extradosed Side Spans of the Dresden Waldschlößchen Bridge Proposal
Dresden, the Florence of the North, needs a new bridge across the Elbe. A design competition was organized to find a solution which obstructs as little as possible the famous panoramic view of the historic city, respectively what is left of it after the air-raids during the Second World War. This resulted in the proposal of a delicate combined suspension-/cable-stayed main span – a modern paraphrase of the Blue-Wonder-Bridge at a short distance upstream –with the cable-stayed units continuing on either side for the approaches (Fig. 9). The idea of these multiple "extradosed" relatively short side-spans was to embrace the deck or to signal the car-driver with useful and decorative elements that he is travelling on a bridge (Fig. 10). However, the jury decided just on the opposite: An arch for the main span with a plain deck on either side.
Fig. 9: Waldschlößchen Bridge in Dresden, proposal, 1997
Fig. 10: Model of the Waldschlößchen Bridge in Dresden
5.
Another "Extradosed" Approach for a Railroad Bridge in Stuttgart-Bad Cannstatt
Imagine the cables of an "extradosed" bridge with several spans are milled into a plane steel sheet which is cut out where the stresses are small or imagine a haunched bridge, where the haunches are not below the deck as usual, but above and thus in tension, then you arrive at this 4-track railway bridge (Figs. 11 +12). The masts and the deck are from concrete, the sails, suspending the deck, are from 80 mm thick steel sheet. This solution resulted from a design competition and is going to be built soon.
Fig. 11: Railroad Bridge, Bad Cannstatt, view, cross-section and detail of "sails"
Fig. 12: Model of the Railroad Bridge, Bad Cannstatt (under design)
6.
Three Recent Cable-Stayed Footbridges with Special Features
We usually think of long spans if we consider the choice of cable-supported decks. But why should we not use this means as well, to give small bridges a human scale? F. Leonhardt did so already in the fifties with his fine Schillersteg in Stuttgart and many followed thereafter, however, mostly with the typical three-span-arrangement or half of that. Especially for footbridges more variety is desirable. 6.1
"Truss" Bridges for the EXPO 2000 in Hannover
For crossing several highways on the EXPO area, a number of bridges of different span and width, some permanent, some temporary were asked for in a design competition. The successful solution in a design competition uses a modular system of square 7.5/7.5 m² slabs either directly supported on poles at their four corners or indirectly cable-stayed where longer spans were needed. Stimulated by the idea of the architect Volkwin Marg, that poles at equal distance and constant height, projecting vertically beyond the deck shall signal the passage and permit the installation of lights, flags, canopies etc. a structure was developed which is a typical harp-type cable-stayed bridge, but may as well be interpreted as a cantilevering truss (Fig. 13). After all a cable-stayed bridge acts like a cantilever and this remains so if the cables are not directly fixed to the tower but diverted by struts and ties parallel to the deck at a certain level.
Fig. 13:
EXPO Hannover, footbridge
Fig. 14:
EXPO Hannover, footbridge (presently under construction)
6.2
A Folding Cable-Stayed Bridge in Kiel
This little bridge crosses the Kiel Förde, the end of a fiord of the Baltic Sea, right at the center of the town. Its middle part with a length of only 25 m has to be opened and closed 10 to 15 times per day to permit ships to pass. Again together with the architect Volkwin Marg we felt, that this bridge could become a landmark of Kiel if it reflects ships and cranes and moves in an imaginative manner. Therefore, hidden hydraulic means were ruled out as against winches and cables. Instead of going for a simple cable-stayed solution with one mast, one hinge and one back-stay, the deck was further subdivided to fold with three hinges, two masts and two back-stays in a more stimulating way (Figs. 15 + 16). For safety reasons and to avoid any restraints due to irregularities in the movement, the cable-system is statically determinate and is moved by one winch only, rotating at a constant speed.
Fig. 15: Folding Bridge, Kiel
Fig. 16: Folding Bridge, Kiel, completed 1998 6.3
An Ondulating Cable-Stayed Bridge Proposal for Kassel
A cable-stayed bridge must not be straight in plan, but may be curved without abandoning selfanchorage. Here such an unusual geometry developed from connecting two given footpaths on either side of the Fulda in a natural way (Fig. 17). A circular girder needs to be supported on one side only, because it can resist torsion by in plane bending, resulting in axial compression in the concrete deck slab and tension in the bottom chord of the supporting truss. The radial stay cables cause ring tension in the circular deck slab which partly counterbalances the axial compression from the torsional effect.
Fig. 17: Ondulating cable-stayed bridge in Kassel, proposal
Fig. 17: Ondulating cable-stayed bridge in Kassel, proposal (cont'd)
7.
Postscript: Pylons or Towers/Masts?
It has become a habit to call a pylon whatever props up the cables of a roof or a bridge. However, the word "pylon" goes back to the Egyptian temple gates which clearly consist of two vertical towers, interconnected by a horizontal beam, leaving a (small) gate beneath (a). Thus a bridge pylon has two legs connected in the transversal direction with a beam or struts and ties to form a gate. An A-support may also deserve this name (b). But any single support is just a "tower" or a "mast" (c).
Acknowledgement On these bridges the author collaborated with his partners and colleagues Rudolf Bergermann, Andreas Keil, Michael Schlaich, Jan Knippers. Thanks!
References [1]
Bergermann, R., Bhasin, P.C., Design and Construction of Second Hooghly Bridge in Calcutta. Cable-stayed Bridge Seminar, 1988, Bangalore, India
[2]
Walther, R.,. et.al, Cable stayed bridges, Telford Publ., London, 1988
[3]
Klein, J.-F., Ponts Haubanes: Comportement et Stabilité des Tabliers Minces, Ph.D-Thesis, École Polytechnique Fédérale de Lausanne, Switzerland, 1990
[4]
Bergermann, R., Stathopoulos, S., Design of the Evripos Bridge in Greece. Cable-stayed Bridge Seminar, 1988, Bangalore, India
[5]
Menn, Chr., Functional Shaping of Piers and Pylons. Structural Engineering International, 4/98, pp. 249 – 251
[6]
Ogawa, A., Kasuga, A., Okamoto, H., Prestressed Concrete Extradosed Bridge – Odawara Blueway Bridge. Prestressed Concrete in Japan, XIII FIP Congress National Report, Amsterdam, The Netherlands, 1998
[7]
Holgate, A., The Art of Structural Engineering. Edition Axel Menges, Stuttgart/ London, 1997
[8]
Bergermann, R., Schlaich, M., Monoleg Towers with Transverse Stabilising Cables. Structural Engineering International 4/98, pp. 252 – 255
Stay Cable Technology: Overview Manabu ITO Professor Takushoku University Tokyo, Japan
Manabu Ito, graduated in 1953 and given Dr. Eng. degree in 1959 from the University of Tokyo, was engaged in teaching and research of bridge engineering at his alma mater. After his retirement in 1991, he moved to Saitama and then Takushoku universities. He has been involved in many large bridge projects in Japan. He is former vice-president of IABSE.
Summary The cables of cable-stayed bridges are required to have superb mechanical properties such as high tensile strength, high elastic modulus, satisfactory fatigue resistance and sectional compactness, as well as excellent corrosion resistance, easiness of handling and installation, and naturally not to be costly. Referring to a brief chronological developments during the past half century, the paper reviews the technology of bridge stay cables. The fatigue problems and end fittings are not mentioned herein, while particular emphasis is placed on the corrosion protection and wind-induced vibrations.
1.
Introduction
The requirements for stay cables are excellent mechanical properties (such as high strength, high elastic modulus and fatigue resistance), sectional compactness, corrosion resistance, easiness of handling and installation, and naturally low cost. To find the solution to satisfy these requirements, the research and development on stay cable technology have been continuously conducted over the past half century. In the consequence, cables for cable-stayed bridges are more diverse in their types, corrosion protection methods and end fitting, in contrast to those for suspension bridges. In an international survey conducted by Hamilton and Breen [1], durability and fatigue were most highly rated keywords concerning important aspects of stay cables. Although the keyword ”vibration” was rated lower in this survey, suppression of wind-induced vibrations of stay cables has been gaining importance especially on long span cable-stayed bridges since 1980s. The present article places emphasis on the types, corrosion protection and vibration control of stay cables, while the installation and end fitting of the cables are not referred herein, mainly because of the restriction of space. Another excuse is that the content may be a little biased by the information in Japan where modern cable-stayed bridge construction started rather earlier next to Germany and fairly large amount of experiences have been accumulated. More extensive state-of-the-art of stay cables was presented by Ohashi [2] in 1991, which is a little old though. Gimsing also describes the basic types, corrosion protection and mechanical properties of structural cables in his text book [3]. As for the stay cables for prestressed concrete (PC) cable-stayed bridges, the recommendations prepared by the Post Tensioning Institute will be a good guideline [4]. The present article owes very much to these references.
2.
Mechanical Properties of Cable Materials
Cold-drawn steel wires with round section being used for bridge cables have a diameter of 4 to 7mm and very high tensile strength as compared with structural steels although ductility is lower. Their guaranteed tensile strength is 1500-1600MPa in spiral ropes and 1570-1765MPa in parallel wire strands (PWS), whereas the steel wires with deformed cross section composing locked coil ropes (LCR) and the prestressing bars have more or less lower tensile strength. A steel wire with minimum tensile strength of 1800Mpa was newly developed for the main cables of Akashi Kaikyo suspension bridge which has the world’s longest span, by increasing silicon content. Although this material for parallel wire strands has not yet applied to cable-stayed bridges, longlay seven-wire strands that initiated from prestressed concrete structures display the same level of tensile strength. The modulus of elasticity of parallel wire strand or ultra-long lay strand is only slightly less than that of the component steel material, but the Young’s modulus and tensile strength of multi-wire helical strands decrease due to the twisting of wires. A typical Young’s modulus of the helical strands is 170GPa for spiral ropes, 180GPa for LCR, and 190GPa for seven-wire strands. New composite materials have been tentatively used on stay cables of a few short span cablestayed bridges. Such fiber reinforced plastic materials as Aramid fiber cables may be more widely employed in the future.
3.
Types of Stay Cables
The types of stay cables used on earlier steel cable-stayed bridges were characterized by the specific countries: namely, LCR in Germany, spiral ropes in UK, and quick transition from LCR to PWS in Japan. On the other hand, those in PC cable-stayed bridges have been mostly associated with the development of the post-tensioning type PC bridge technology. However, with the development of cable technology and the transition from a few stay system to multi-stay system, the situation has been changed. 3.1
Helical Wire Ropes
As already mentioned, multi-wire helical strands are inferior to parallel wire strands in mechanical properties, although they are easier in handling. Therefore, spiral ropes which have been extensively used as a main cables of short span suspension bridges are not popular in cablestayed bridges except for UK. LCR is composed of two types of twisted wires: normal round wires in the core layers and the Tand Z-shaped wires in the outer layers. As compared with spiral ropes, LCR has such advantages as smooth surface, more compact cross section and less sensitivity to side pressure, stiffer to handle and a little costly though. LCR has been popular particularly in German-style steel cablestayed bridges. The largest ever used has a diameter of 174mm in the Rama IX Bridge in Bangkok. The multi-strand cables consisting of several LCRs of smaller size that were prevalent in the early German bridges are hardly used now mainly due to rather complicated anchorage details and difficulty of replacement, but similar usage is still found in Norwegian suspension bridges recently built. 3.2
Parallel Strand Cables
The seven-wire strand which has been extensively used as tendons for prestressed concrete is the simplest and most prevalent in the stay cables of PC cable-stayed bridges. As the pitch of twisted wires is relatively long, the stiffness of the strand is close to that of straight wire strand and its breaking strength is even higher. For cables, the strand is normally made from 5mm wires and its nominal diameter is 12.7mm or 15.2mm, and these strands are arranged in parallel to form a stay cable. The number of the seven-wire strands varies from 7 to 127 dependent on the required design force.
There are such a diversity of strand or cable systems using the seven-wire strands according to the corrosion protection, assembling method and end-fitting techniques, as Freyssinet, Dywidag, VSL, Stronghold, SEEE and ASP (at-site prefabricated cable system) and so on. The parallel strand cables are either shop-fabricated or site-fabricated, and sometimes their combination like SEEE. Cost saving is claimed by the site-fabrication of stay cables with individual strands pushed through a pre-installed sheath. Examples of the corrosion protection will be illustrated in the next chapter. This type of cables are also applied recently to steel or steel/PC hybrid cablestayed bridges such as Normandy Bridge in France, Kap Suimun Bridge in Hong Kong and the new Onomichi Bridge in Japan. In case of the Normandy Bridge [5] which is the world’s second longest cable-stayed bridge, the individual strand supplied by Fressynet has a 15mm diameter and protected with extruded high density polyethylene (HDPE) covering. For the new Onomichi Bridge built in 1999, each strand is also covered by extruded HDPE, and stay cables are semiprefabricated and provided with SEEE type anchorage. 3.3
Parallel Wire Cables
A parallel wire bundle of prestressing wires with a diameter of 6-7mm is incorporated as a stay cable with a polyethylene pipe filled by cement grout as corrosion protection and with HiAm anchor sockets as the end fittings. These parallel wire cables have been widely used on both PC and steel cable-stayed bridges. In Japan, the HiAm-anchor cables were adopted on such large steel cable-stayed bridges as the Meiko-West (405m span, 5mm wires, 1985), Iwaguro-jima and Hitsuishi-jima (420m, 7mm wires,1988) bridges. In the latter, polybutadiene resin was grouted instead of cement mortar. 3.4
Parallel-Wire Strand Cable
The shop-prefabricated parallel wire strands (PPWS) have been extensively used on Japanese suspension bridges since 1968, even on the world’s largest Akashi Kaikyo Bridge in which the maximum strand length reaches 4074m. The parallel wire strands to be built into suspension bridge main cables and earlier steel stay cables comprise 5.0-5.5mm wires, whereas 7mm wires are more common in recent stay cables aiming at more compact anchorage details and easier cable erection. A ”PWS” is a bundle of galvanized wires to form a hexagonal cross section, and in many cases a multiple number of PWSs are formed into one large round cable at the site. For example, the Yamatogawa Bridge in Japan has 16 squeezed stay cables each consisting of 19 strands of 217 galvanized 5mm wires and a plastic covering. The largest cable strand of this type is 337 x 7mm wires used in the Parana Bridge in Argentina. In Japan, the use of PWSs started in the late 1960’s, but it was almost switched to the New PWS described in the next section twenty years later. 3.5
Ultra-Long Lay Stay Cable
The idea of an ultra-long lay cable strand was initiated in the 1980’s as the improved variant of parallel wire strand and parallel wire cables. Twisting the wires up to 3-4o enables the wire bundle to ease reeling and make the strand self-compacting under axial tension without spoiling the mechanical properties. These cables are designated as ”New PWS” which was developed in Japan and ”HiAm-SPWC” in Europe, respectively. The New PWS is also featured by extruding HDPE cover directly onto the wire bundle so that no void will exists between the wires and the surrounding cover. New PWS is assembled by 7mm wires and the thickest one comprise 421 wires. The longest stay cable of this type is 460m long with the outer diameter of 165mm used on the Tatara Bridge, the world’s longest span cable-stayed bridge. 3.6
Bar Stay Cable
Bar stay cable consists of round steel bars with a diameter of 26-36mm, being covered by a steel pipe, the inside of which is filled with cement grout. The external steel tube is considered in the
cable cross-section when live load is applied. Since the lengths of the bars can not be long, coupling is normally needed. This type of stay member is scarcely used, particularly for large cable-stayed bridges.
4.
Corrosion Protection
Quite a few corrosion troubles were reported on the stay cables despite of rather short history of cable-stayed bridges. In the case of multiple-stay system which is prevalent in these days, the replacement of stay cables is possible but needs extra cost. Therefore, various means to protect the main tension elements from corrosion have been tried. Today the corrosion protection system usually consists of at least two barriers: the internal barrier immediately adjacent to the main tension element and the external barrier or covering which is exposed to the outside environment. The current corrosion protection methods for stay cables are well summarized by Podolny [6]. 4.1
Coating Wires
As far as the internal barrier is concerned, the wires to be used in strands for bridge cables are zinc-galvanized or non-galvanized. Mainly in the North America, epoxy coating of individual wires or seven-wire strands has been widely used instead of galvanization. As mentioned later, the combination with zinc-galvanization and cement mortar grouting is to be cautious, while disturbing observations are reported in the fatigue test with non-intersticially epoxy coated strands [7]. In addition, the manufacturing and handling of epoxy coating on stay cables should be executed very carefully [3]. 4.2
Wire Ropes
The wires for spiral ropes are zinc-galvanized and the voids are filled with a sealing compound such as ”metalcoat” which is a suspension of aluminum flakes incorporated into a hydrocarbon resin carrier suitably diluted with a solvent for ease of application. LCR in the very early cable-stayed bridges in Germany were manufactured of non-galvanized wires in fear of hydrogen brittlement, and the voids were filled with red lead during rope closing. After application of all permanent loads, the rope surface was thoroughly cleaned and two basic coats of red lead as well as two finishing coats such as iron glimmer were applied. On the other hand, LCR used on Japanese bridges were manufactured of galvanized wires, applying a minimum amount of lubricating oil during rope closing to avoid any concern about future stains of the surface. The outer surfaces were usually painted after the dead load had been fully applied. In the Onomichi Bridge, for example, the cable repainting has been executed almost every five years, and the cables seem now to be found sound after more than thirty years of use. The recent German practice of corrosion protection for LCR has been modified. In the new practice, wires are to be galvanized with zinc, the inner voids are filled by polyurethane with zinc dust or linseed oil with red lead, and outer surface of the rope is to be coated by polyurethane. Metalcoat mentioned above is also sometimes applied on LCR as the second barrier during its fabrication. 4.3
Covering or Sheathing
Covering the strand or cable as the external barrier has been common to other stay cables than helical wire ropes. One of the methods was to wrap a foamed polyethylene tape with glass fiber reinforced plastic covering over the PWS. In the early 1970’s, this was executed by hand-lay-up method on site in Japan [8]. Several years later, prefabricated-segment method was newly developed to improve the workability of hand-lay-up method. This is to fabricate FRP segments
in the shop, and just to connect them on site to form the complete covering. But an installation of catwalk was indispensable for the erection. In addition some expansion joints had to be placed on the covering with certain intervals to absorb the difference of the expansion and contraction between the cable and covering. In some cable-stayed bridges after the age of 20 years or so, such damages as small cracks on the covering and a little deterioration on the expansion joints were found. Then repairing works were needed for these plastic covering. The covering by a metal tube made of steel, stainless steel or aluminum alloy has been often applied to stay cables of PC cable-stayed bridges. Stainless steel and aluminum alloy offer the advantage of long lasting protection, while steel pipes have to be further coated: for example, the three-coat system consisting of the prime coat of self-curing inorganic zinc coating at shop and epoxy intermediate coat as well as polyurethane finish coat at site. Anyhow the installation of metal pipes should be done at the erection site and their stiffness may cause some difficulty in handling during erection when a cable is long. In case of ASP cable, two semi-circular covers of aluminum alloy are assembled into a complete tube around the bundle of parallel seven-wire strands at the bridge site. The use of a fiber reinforced plastic or polyethylene tube was initiated rather earlier in 1960’s. HDPE material which is most widely used is selected to resist weathering, high pressure, high temperature and external injury. At the same time, 2-3% carbon is mixed to protect sheath from ultra-violet rays. Now HDPE tubes are most popular for both parallel wire cables and parallel strand cables, and either shop-fabricated or site-fabricated. When heavier corrosion protection is needed, double layer PE tube is used to prevent the cracks on the outer surface from reaching to the main tension elements. In case of ”New PWS” and seven-wire strands mentioned in the previous chapter, the covering is completely shop-fabricated by a directly extruded HDPE sheath after coating wires with corrosion protection compound. In the former, any further work for corrosion protection is not required at the site. Even if the PE covering is injured, the durability of the cable can be kept for some time because wires are galvanized. The repairing of injured PE envelope can be easily done. The inspection of the cable can be also possible by tearing off a part of the PE covering and by watching the cable from the torn PE window. Although the original color of the PE covering is black due to the mixed carbon, cable coloring techniques have been developed. One is to extrude a colored thin fluoro-polymer on the black PE layer, and another method is a paint coating system that consists of an application of primer made from adhesive components for PE envelope and for the finish coat, and a baking of the primer with the far infrared ray. The finish coat is usually done by fluoro-olefin paint. The light color is preferred not only for good looking but also for reducing the temperature effect. Supplementary wrapping with colored Tedlar tapes is an alternative. 4.4
Blocking Compound
Blocking compound is the corrosion inhibiting or water repelling material used to fill the voids between the tension elements and the outer sheathing. Cement grout has been most popular blocking compound for its alkaline properties providing an active corrosion protection to the steel wires. Cement mortar grout is injected after the stay cables are erected on the bridge when the cable is under full dead load stress to suppress the formation of cracks in the grout, because the presence of cracks may be associated with the potential for fretting corrosion of steel wires. However, cracks may still occur due to shrinkage of cement mortar and stress repetition under cyclic live loading, and actually have been observed on some cable-stayed bridges. Another problem of cement grout combined with galvanized wires is a fear of hydrogen brittlement caused by reaction of zinc and cement milk. In order to avoid it, the non-galvanized wires or the galvanized wires coated with polyester to isolate zinc from cement milk have been used in this case. Further, another measure is to substitute normal Portland cement by polymer cement. The advantages of this material are that it is far more ductile, does not shrink after grouting nor bleed during placing, and does not require special technique and equipment, and that it can be used in combination with galvanized wire without a fear of chemical reaction
between zinc layer and cement. On the other hand, its disadvantages are relatively high material cost and temperature-dependent viscosity and hardening. Cement grout plasticized with polyurethane was used on some other bridges. Alternatives to cementitious grout have been sought and used for stay cables. Synthetic resin material based on polybutadiene was used on the Iwaguro-jima and Hitsuishi-jima bridges of the Honshu Shikoku linking projects in Japan about ten years ago. This two-component material, one liquid consisting of polybutadiene polyurethane polyol resin and the other of an isocyanate hardener, has very low viscosity during pouring, is very flexible after hardening, and has such low density as about half of that of cement grout. But the material and execution costs were high and it is highly temperature dependent and flammable. Epoxy resin is specified in the ASTM provisions as a filling material into the interstices of epoxy-coated seven-wire prestressing strands. Other blocking compounds are grease used on PWS or prestressing strands and wax for parallel strand cables. The petroleum is injected in a liquid state at temperature of 85-105oC and afterwards it solidifies upon cooling. However, it shrinks during cooling process and cracks may develop. A soft petroleum base wax that can be applied at ambient temperature on the monostrand system seems promising [7]. It has a melting point over 260oC and displaces any moisture on the surface of the steel. In any case, grease and wax are to be used in combination with other corrosion protection measures. It is also noted that the non-grout type PWS which is completely fabricated in shop is now available.
5.
Vibration Control
Wind-induced vibrations of stay cables have attracted concern of bridge engineers with increasing span length of cable-stayed bridges [9] and in particular since the introduction of multi-stay system with thin cables covered by polyethylene-sheath having smooth surface. The types of the wind-induced vibrations are full of variety and therefore the preventive measures that are classified into mechanical means and aerodynamic means are also manifold. 5.1
Types of Cable Vibrations under Wind
Vortex Excitation is a cross-wind vibration caused by periodically shedding vortices in the wake behind the body when their frequency coincides with the natural frequencies of the body. Since this is the resonance phenomenon in forced vibration, its amplitude is limited and inversely proportional to structural damping inherent to the body, but may occur at rather low wind velocity. Higher modes of the vibration can be also observed. Galloping is a self-excited oscillation in cross-wind direction, being caused by the negative damping effect of aerodynamic force. Although circular cables can not gallop because of crosssectional symmetry under the wind acting perpendicularly to its member axis, small deviations from a perfectly circular shape may imply galloping instability. For example, transmission line cables with iced snow attached to the lower surface have been often suffered from this galloping . Wake Galloping is the dynamic phenomenon caused by fluid-elastic interaction between neighboring cables. When two stay cables are closely placed, leeward cable may be largely excited due to the presence of windward cable. Like vortex excitation, wake galloping may occur at rather low wind speed and goes down with increasing wind speed. Rain(-Wind-Induced) Vibration was first reported on the Meiko-West Bridge built in 1985 in Japan [10]. Since then many cable-stayed bridges have suffered from this phenomenon. Its cause is the water rivulets on the upper and/or lower side of cable surface. The vibration may occur at rather low wind speed and continue in the wide wind speed range. Its direction has been mainly cross-wind but in-wind vibration can occur according to the positions of water rivulets, and the phenomenon is largely independent of the natural frequency [11].
Buffeting is a random vibration caused by turbulence in the on-coming air flow. Its amplitude is limited and suppressed by increase of structural damping. Attention should also be given to the possibility of cable vibrations that are caused by the dynamic forces acting on the girder and/or pylon. From the past experiences on stay cable behavior, however, the phenomena on which special care shall be taken are vortex excitation, wake galloping and rain vibration. Tentative or approximate stability criteria for typical vibratory phenomena have been proposed [4]. At this time, the effect of local terrain features on these wind-induced vibrations should be taken into account. In case of the Chichibu Park Bridge in Japan, for example, large-amplitude cable vibrations under moderate wind in only one span of a symmetrical two-span cable-stayed bridge have been observed because the bridge crosses a curved gorge and the terrain on both sides is strongly non-symmetrical. 5.2
Countermeasures
In general the following preventive measures are considered for wind-induced vibrations of cables when the responses are not acceptable: a) increase of structural stiffness and natural frequency b) increase of structural damping c) modification of the cable surface. a) and b) are categorized in the mechanical or structural means, while c) is the aerodynamic means to weaken the exciting mechanisms by disturbing or reducing wind-induced dynamic force acting on the cable. However, because the exciting mechanisms of different vibration types differ, the countermeasures shall fit for the phenomenon concerned. Occurrence of wake galloping depends on the spacing of neighboring cables. Very small spacing or quite wide spacing more than six times the cable diameter can remarkably moderate the response. If these conditions can not be satisfied for other design reasons or when undesirable wake galloping is observed after erection, the cable vibration can be suppressed by connecting the both cables by a few spacers or small mechanical dampers (e.g. Yokohama Bay Bridge). One of the common countermeasures that has often been adopted is to connect the stay cables with secondary cables which may terminate at a cable or at the deck (tie-down cables). Even with a few and small stabilizing ropes, stay movements can be restrained. The natural frequencies of each stay, and thus, the resistance to dynamic excitation can be raised by shortening the effective free length of the main stay cables by means of transverse connections. Such elements may be also sources of additional damping. But even if the size of stabilizing ropes is significantly smaller than that of the primary cables, they may affect the appearance of the structure to some extent. Furthermore, the rupture of these interconnecting ropes or the fatigue failure of the connection fittings have been reported in several bridges. Viscoelastic bushings can reduce fatigue and provide additional damping. In case of the Normandy Bridge, the stabilizing effect was expected to further increase by installing special clamps with damping devices in the joint of the secondary ropes and the primary stays. Structural damping of long stay cables is often so low as the logarithmic damping of the order of 10-3. The increase of the damping to some extent is effective in suppressing the amplitude of buffeting, vortex excitation and rain vibration, and in raising the critical wind speed for the onset of galloping. It is first recommended to place such damping material as neoprene ring or highdamping rubber between cable and steel exit pipe at pylon and deck anchorage. Use of damping material results in additional benefit of reduced bending moment in the cable. Further additional damping, if necessary, can be provided by mechanical damping devices. Very simple and small tuned mass dampers (TMD) represented by the classical Stockbridge damper that has been used on transmission power lines were applied to stay cables or diagonal hangers of some European cable-supported bridges. But it is not so popular for aesthetic reason. When rather high additional damping is required, the most prevalent is to install a dash-pot type viscous damper between the stay and the bridge deck. In the Brotonne Bridge, after experiencing severe oscillations of the stay cable, shock absorbers similar to those used in automobiles were attached, while in case of the Sunshine Skyway Bridge later built in the US, hydraulic (oil)
dampers were installed beforehand and it was possible to position them inside the box girder. The dampers shall not spoil the appearance of the bridge. The height of the oil dampers was designed not to exceed that of guard rails in the Aratsu Bridge in Japan (Photo 1). The mechanical dampers utilizing shear-viscous material can be more compact (Photo 2). The position of the above-mentioned dampers influences the mode shape and the damping effect of the cables attached by the damper. It is not easy to make compromise between the requirement to lower the damper position and the efficacy of the damper when the cable is long [9].
Photo 1. Hydraulic damper at the Aratsu Bridge, Fukuoka
Photo 3. Protuberance on the HDPE sheath surface at the Higashi Kobe Bridge
Photo 2 Viscous-shear type damper at the Meiko-Central Bridge, Nagoya. The elastic seal material is also inserted under the anchorage cover to reduce bent of cable.
Photo. 4. Pattern-indented surface of the Tatara Bridge stay cable. High-damping rubber between thestay and the exit pipe at the anchorage, which will be covered later, is also seen.
The aerodynamic countermeasures for the round cables are to modify the cable surface. The idea of helical fins often used on circular stacks to prevent vortex excitation was applied in the Normandy Bridge. HDPE duct is composed of two half-elements shaped by small helical filets. It is reported that these were designed to eliminate also the rain-induced vibration [5]. The first trial of this kind on stay cables, aiming at reducing the rain vibration, was the axial protuberances in the form of longitudinal ribs on the HDPE tube surface developed in the Higashi Kobe Bridge in Japan (Photo 3). Similar idea is later seen in the more simpler HDPE sheaths with fine grooves, being used on a few other Japanese cable-stayed bridges. Further on the Tatara Bridge, HDPE sheaths are provided pattern-indented surface with roughness of 1% applied disorderly in a convex or a concave pattern (Photo 4) [12]. The effect of these surface modification is linked to influence the behavior of the water rivulets. However, it should be noted that these means are not necessarily effective in suppressing vortex excitation and that the drag coefficient may be increased. In case of the cables of the Tatara Bridge, however, the drag coefficient in the super-critical Reynolds number range could be reduced to 0.6.
6.
Concluding Remarks
The overview of stay cable technology is presented in this paper. The development of cablestayed bridges in the past half century has been very remarkable in both the increase of span lengths and the number of constructions worldwide for their wide applicability and aesthetic appeal. Different from suspension bridge cables, however, the cable technology in cable-stayed bridges is much diverse not only in their types and corrosion protection system but also, although being unable to mention herein, in the methods of end fitting and anchorage details. The recent international survey [1] indicates such scattered preference on these items. The vulnerability of the stay cables to corrosion damage and wind-induced instability is still a keen concern despite of the continuing evolution of cable technology. Among them, the effectiveness of corrosion protection systems shall be determined by only time. Therefore, the appropriate methods of nondestructive inspection have to be pursued [13]. Although the choice among available technologies may depend on the features of the structure, the natural and local conditions of the site, the technology atmosphere of the area, as well as the judgement of the owners, designers and contractors, taking into account of cost estimation, the pertinent combination of the available technologies on the above-mentioned items should be determined by careful considerations for such long lasting structures as bridges. The practicability of new composite fiber materials shall be also pursued for the future development of cable-stayed bridges.
References [1] HAMILTON III, H. R.; BREEN, J. E. International Survey of Current Opinion on Bridge Stay Cable Systems. IABSE Report 73/2, Symposium on Extending the Life-span of Structures (San Francisco), August 1995, pp.843-853. [2] OHASHI, M. Cables for Cable-Stayed Bridges. ”Cable-Stayed Bridges: Recent Developments and their Future” (ed. M. Ito et al.), Elsevier, 1991, pp.125-149. [3] GIMSING, N. J. ”Cable-Supported Bridges - Concept and Design” (2nd ed.), Wiley, 1996, Chapter 2: Cables. [4] PTI Committee on Cable-Stayed Bridges; ”Recommendations for Stay Cable Design, Testing and Installation”. (Draft), Post Tensioning Institute, January 1998. [5] Virlogeux, M. et al. Design of the Normandie Bridge. Proceedings of International Conference on Cable-Stayed and Suspension Bridges (Deauville), Vol. 1, 1994, pp.605-630. [6] PODOLNY, Jr. W. Current Corrosion Protection Methods for Cable Stays. op. cit. [1], pp.855-860
[7] LAPSLEY, R. D.; GANZ, H. R. Experience, Developments and Trends for Improved Durability of Stay Cables. op. cit. [1], pp.879-884. [8] ITO, M.; TADA, K.; KITAGAWA, M. Cable-Corrosion-Protection Systems for CableSupported Bridges in Japan. Op. cit. [1], pp.873-878. [9] YAMADA, H. Control of Wind-Induced Cable Vibrations from a Viewpoint of the Wind Resistant Design of Cable-Stayed Bridges. Proceedings of the International Seminar on Cable Dynamics (Tokyo), JAWE, 1997, pp.129-138. [10] HIKAMI, Y.; SHIRAISHI, N. Rain-Wind-Induced Vibrations of Cables in Cable-Stayed Bridges. Journal of Wind Engineering and Industrial Aerodynamics, No. 29, 1988, pp.409-418. [11] VERWIEBE, C. Exciting Mechanisms of Rain-Wind-Induced Vibrations, Structural Engineering International (IABSE), Vol. 8, No. 2, May 1998, pp.112-117. [12] MIYATA, T.; YAMADA, H.; HOJO, T. Aerodynamic Responses of PE Stay Cables with Pattern-Indented Surface. op. cit. [5], Vol. 2, pp.515-522. [13] ZAHN, F. A.; BITTERLI, B. Developments in Non-destructive Stay Cable Inspection Methods. op. cit. [1], pp.861-866.
Design of Girder and Cables for Train Loads Niels BITSCH MSc Civil Engineer COWI Lyngby, Denmark Mr. Niels Bitsch, born 1958, received his civil engineering degree from the Technical University of Denmark, year 1984. Has in the past 10 years been working with the bridges of the two major links in Denmark, the Great Belt Link and the Öresund Link
1.
Lars HAUGE MSc Civil Engineer COWI Lyngby, Denmark Mr. Lars Hauge born 1962, received his civil engineering degree from the Technical University of Denmark, year 1986. Has through his work with some of the world`s largest bridges obtained considerable expertise in design of cable stayed and suspension bridges.
The Cable Stayed Bridge of the Öresund Link
The High Bridge of the Öresund Link is a Cable Stayed Bridge with a Main Span of 490 m and two side spans of 160m and141m respectively. The Pylons, with two single towers each, are constructed in reinforced concrete and the Bridge girder is a two level composite girder. The two level composite girder comprises a main carrying steel truss and an upper roadway deck slab in concrete. The Cable Stays are arranged as a harp system with 10 Cable Stays in each cable fan. The Cable Stay inclination with horizontal is 30o , and distance between the anchorages on the Girder are 20 m. For anchorage of the Cable Stays in the Pylon, a cast-in steel box has been designed. See elevation and cross section of the bridge in Figure 1-1 respectively Figure 1-2.
Figure 1-1 :
Öresund Link, Cable Stayed Bridge. Side view.
Figure 1-2 :
Öresund Link, Cable Stayed Bridge. Cross section
The structural design is based on the Eurocodes with an associated Project Application Document and a Design Requirement document. The Design Requirement document supplement and takes precedence over the other two documents, with specific loads and other requirements covering topics which are not considered in the Eurocodes. During detailed design computer models was established in order to perform the general documentation of the Bridge, but also to perform the rather complex analyses related to the Train loads : • Comfort analyses • Dynamic Actions • Fatigue analyses • Cable Stay replacement • Deflections Other complex effects with considerable design impact, but without connection to the Train loads, such as shrinkage and creep effects, shear lag and cable stay rupture, was also analysed. Focus is in this paper put on Comfort analyses, Dynamic Actions and Fatigue analyses, as these subjects in particular, are difficult analyse in detail, on complicated bridge structures. The analyses was however performed with success on the cable stayed bridge of the Öresund Link, using up to date designs knowledge, extensive computer capacity and specialist software.
2.
Comfort analyses
2.1
Requirements
A number of requirements to the accelerations and deformations of the Bridge Girder has been specified for the Bridge in order to get an adequate level of safety and comfort during crossing of the Bridge by train. With span lengths exceeding 90 m it is not possible to use conventional design rules based on Girder deflections alone in order to verify an adequate level of passenger comfort. Detailed analyses of the vertical accelerations within a passenger coach need to be performed. The analyses only comprised the accelerations induced in the trains due to the flexibility of the Bridge. The effect of irregularities of track and wheels was not taken into account. 2.2
Acceleration limitations
Figure 2-1 shows the requirements to the vertical acceleration limits within the passenger coach, in term of root-mean-square (rms) accelerations. For vertical accelerations with duration less than 0.5 seconds, the acceleration (peak acceleration) is not allowed to exceed 2 m/s2. The
accelerations of the train is frequency weighted according to ISO2631, which applies to simulate the human perception of vertical vibrations, e.g. vibrations in the longitudinal direction of the human body.
Figure 2-1 : Acceleration limits as function of duration. 2.3
Dynamic Train Models Four types of passenger trains was specified for the dynamic analyses. In the analyses the loads of the passenger trains was applied on one track, with or without rail load UIC 71 on the other track, whichever created the most unfavourable effect for the situation analysed. The passenger trains consist of a Loco and Passenger Coaches. The boogie support system of the Passenger Coaches was modelled as an equivalent single degree of freedom (SDOF) systems (Figure 2-2), used to simulate the accelerations in the passenger coach.
Figure 2-2 :
SDOF model
The SDOF system was described by a mass M, a spring Ke and a dashpot Ce. Ke and Ce are equivalent values calculated from detailed knowledge of primary and secondary spring and dashpot systems of the coach boogies. Table 2-1 summarises the parameters of the four SDOF systems and the associated natural frequencies, fe, and relative damping ratios, ζe. Passenger Coach
M (kg)
Ke (N/m)
Ce (kg/s)
fe (Hz)
ζe
T1 T2 T3 T4
17000 16800 16200 16100
390000 575000 720000 805000
52000 32000 37000 22000
0.76 0.93 1.06 1.13
0.32 0.16 0.17 0.10
Table 2-1 :
Parameters for simplified SDOF model
The general loads from the passenger trains was modelled as a set of point loads. The point loads gave a quasi-static deflection corresponding to the deflection of the entire train.
2.3
Bridge Model
The bridge structure was modelled with COWI's in-house developed finite element program, IBDAS. The finite element model, Figure 2-3, comprised all main structural elements. The concrete roadway deck was modelled using shell elements, the cable stays were modelled as cable elements, and the pylons, piers, railway deck, chords, outriggers and diagonals were modelled with beam elements.
Figure 2-3 : Øresund, Cable Stayed Bridge. Finite element model (IBDAS) 2.4
Calculations
The train induced accelerations was determined by simulation of the train response in the time domain for the four types of passenger trains crossing the bridge. The shape of the deflected bridge girder, zg , during the train crossing, comprised contributions from : • Vertical alignment of the bridge • Deflection due to crossing of the passenger trains, taking into account dynamic effects of the moving loads. • The static deflection of the bridge due to service (SLS ) loads, with a dynamic amplification factor of 1.2. (primarily UIC 71 load on other track and road traffic loads). The acceleration response in the coach travelling along the deflection shape, zg , was found by numerical integration of the equation : Mz + ce ( z − z g ) + k e ( z − z g ) = 0 where z g = z g (V / t ) and z g = z g (V / t ) with V being the speed of the train and t the time. The accelerations was derived by numerical differentiation of the displacement response, z. Finally the accelerations was frequency weighted according to ISO2631 ref. sect.2.1 and compared with the acceleration limits. The applied time step of the above integration was 0.009 seconds equivalent to spatial steps of 0.5 meters along the bridge axis (200 km/h). 2.5
Results
For each of the four passenger trains, three train load configurations was analysed : 1. Maximum main Span deflection 2. Maximum rotation of the Girder at the Expansion Joints 3. Maximum local deflections of the Railway Deck
Figure 2-4 illustrate the acceleration response along the bridge for train type T4 crossing the bridge, considering maximum mid span deflection.
Figure 2-4 :
Acceleration results for T4 with maximum mid span deflection.
Figure 2-5 compares the results with the accelerations limits specified in sect. 2.2 . For the load configuration maximum rotation of the girder at the expansion joint, the figure shows that the requirements to the acceleration is satisfied.
Figure 2-5 :
Acceleration results for T4 compared with the design requirements. All duration's.
3.
Dynamic Actions
3.1
Introduction
As part of the ULS In-service and ULS Fatigue verification of the Bridge, analysis of the dynamic train-bridge interaction were carried out. The analyses were used to determine dynamic load factors to be applied to global static rail load effects. The following global rail load effects were considered : • longitudinal load effects in the principal structural elements of the Bridge Girder • load effects in Pylons and Piers • load effects in the Cable Stays Dynamic analyses were carried out for nine different train types, for which moving point load models were provided. The influence of the dynamic behaviour of the train was not included in the analyses.
The analyses were carried out using a 3D-computer model, similar to the model used for static load effect calculations. Regarding the dynamic enhancement of local train load effects on the Railway Deck, conventional theory was used. 3.2
Train types
Nine different train types was analysed. UIC Train type 1, used for the ULS-verification of the bridge, and Passenger Train types 1-3, Freight Train types 1-3 and Heavy Rail Traffic Train types 1 and 2, used for the Fatigue verification. Figure 3-1 shows an example of the moving point load model for Passenger Train type 1.
Figure 3-1 : Passenger Train type 1, point load model The design speed of the UIC train is 120 km/h and for the "fatigue trains" 80 to 200 km/h. As the length of the UIC load is dependent on the load effect and the section considered, 28 different load models with train length between 75 m and 750 m were defined in order to create the most unfavourable effects. The length of the "fatigue trains" lies from 97.4 m to 519.2 m. 3.2
Investigated bridge parts
A representative number of sections in the Cable Stayed Bridge were examined ref. Figure 3-2 . Only dynamic effects of the Bridge Girder and the Cable Stays is described in the following. In the Bridge Girder dynamic load factors were determined for 3 different load effects, normal force, bending moment and vertical shear force, in 18 different sections along the bridge axis. Dynamic load factors determined for normal forces and bending moments, applied to normal forces and bending moments of the upper chords, lower chords, railway deck and concrete roadway deck. Dynamic load factor for vertical shear applied to normal forces and in-plane moments of the diagonals. The dynamic load factor of the Cable Stays were determined for normal forces of the cables.
Figure 3-2 : 3.3
Cross sections for which a dynamic load factor was determined.
Dynamic load factor
A dynamic analysis were carried out in order to determine the "dynamic" max/min values of the examined load effects for each of the selected cross sections described above. The result of the dynamic analysis is a combined static and dynamic value for the considered load effect. In order to get the dynamic contribution to the load effect, the static value of the load effect shall be obtained from a separate static analyses and then be subtracted from the results of the dynamic analysis. The eigen-modes and the corresponding eigen-frequencies of the bridge structure was specified as input for the dynamic analyses. The dynamic analyses were carried out using time steps of 0.1 sec. A comparison of the eigen-frequencies for the vertical modes, calculated using the simplified model used for the dynamic analyses, with the corresponding eigen-frequencies calculated with the full truss model showed very good agreement. The eigen-frequencies for the first vertical mode calculated with the simple model was equal to 0.363 Hz and the frequency calculated with the full truss model was equal to 0.351 Hz. The structural damping (Raleigh damping) used in the dynamic analyses was equal to 1%, at a frequency corresponding to the first vertical mode, f1 = 0.360 Hz, which was considered to be conservative. Based on the results of the static and dynamic analyses, the dynamic factor, Φ, was determined as: Φ = Dynamic result / Static result 3.4
Dynamic load factor results
A total of approximately 13000 dynamic load factors were determined and only a summary of the calculated dynamic load factors for the Bridge Girder and Cable Stays is presented here. In Figure 3-3 detailed information regarding the dynamic load factors for various load effects is informed.
Figure 3-3 : UIC rain type 1.Global dynamic load factors for various load effects. Table 3-2 summarises the dynamic load factors of the UIC train type 1 and the "fatigue trains", used in the design. Regarding position and name of the Cable Stays, "S" = side span position and "M" = Main span position. The cable stay numbers starts with 1 at the Pylon. UIC train type 1 Φ
Passenger train I Φ
Passenger train II Φ
Passenger train III Φ
Freight train I - III Φ
Heavy Rail train I and II Φ
Upper chords Lower chords Railway deck Concrete deck
1.02-1.05
1.10-1.40
1.10-1.15
1.06
1.04
1.02
Diagonals
1.03-1.02
1.10-1.20
1.01-1.08
1.01-1.06
1.02
1.02
Cable Stays (Tension) 1S, 1M 2S, 2M other cable stays
1.06 1.02 1.01
2.00 1.20 1.06
1.07 1.05 1.03
1.20 1.05 1.05
1.04 1.04 1.04
1.02 1.02 1.02
Bridge Girder
Table 3-2 : Summary of dynamic load factors.
4.
Fatigue analyses
4.1
Introduction
Assessment of the fatigue capacity of a steel bridge girder subjected to train loads, is a very important part of the design work. Having a cable stayed bridge makes the assessment even more complicated.
On the Øresund cable stayed bridge the fatigue capacity of all bridge elements were analysed, steel truss, cable stays and not to forget the concrete roadway deck with shear stud connection to the steel truss. The steel truss with the orthotropic steel deck for support of the two railway tracks gave many challenges. During the design of the Cable Stayed Bridge of the Øresund Link, extensive computer calculations was made in order to document the required fatigue capacity. Further "best practice" was used with respect to design against fatigue problems, without making the steel details unacceptable from a production point of view. An example of "best practice" in the design, is the "clown mouth" cut out in the transverse bulkheads, where the troughs of the orthotropic steel panel crosses, see Figure 4-1 .
Figure 4-1 : "Clown mouth" cut out in transverse bulkheads. 4.2
Fatigue loads
Eight types of "fatigue" trains was specified for assessment of the fatigue capacity. Three passenger trains, three freight trains and two heavy rail trains, each of them provided with following information's : • Train nos. per track per day • Service hours per day • Max. speed • Train configuration. Axle loads and axle positions. • Max. and mean length. • Max and mean total load. Based on the information's it was possible to find the number of train crossings during the 100 year life time of the bridge, and the numbers of train crossings with simultaneously loading of both tracks. For every girder detail investigated the dynamic effect of the train load was taken into account. For information's about the global train load effects reference is made to chapter 3. The dynamic effect of the local train loads is not regarded in this paper, but for information the dynamic load factor, Φ, was found to be in the range of 1.13 to 1.58 . The local dynamic factors was only used on local load effects on the railway deck. 4.3
Fatigue stress calculations
The stress calculations was based on results from two computer models, the global model described in sect 2.3, giving the global load effects and a detailed semilocal FEM-model giving the local load effects in the railway deck.
The stress spectres for all the details investigated was in general determined by computing an influence line for a specific effect and then traversing the load across the influence line. The Figures 4-2 and 4-3 gives the global and local stress spectre for one of the trough splices in the deck panels of the railway deck.
Figure 4-2 : Freight train 1 stress spectres for global load effects in the trough splice of the railway deck.
Figure 4-3 : Freight train 1 stress spectre for local load effects in the trough splice of the railway deck. 4.4
Fatigue assessment
Foe each of the load events (stress spectres) a stress range spectrum was calculated by means of the Rainflow counting method, using a special developed programme. The fatigue assessment was based on the calculated nominal stress ranges and a Cumulative Damage Assessment based on a fatigue strength curve with double slope constants (m=3 and m=5), and a cut-off limit at N=100 million cycles in accordance with EUROCODE 3. Construction details was classified according to Swedish codes, giving detail categories. The damage for each loading event was calculated and based on the occurrence of the loading events and the design working life of the bridge, 100 years, a total damage was calculated.
5.
Conclusion
The design for the Cable stayed bridge for the Öresund Link has proved to be both suitable and adequate for safe operation of High Speed Railway. This has been verified by extensive and advanced analyses. Finally it is important to conclude, that it has not been necessary with any special precautions in order to fulfil the comfort requirements.
An Innovative Technique for Fitting Trackwork Alignments Through the Railway Envelope of a Cable-stayed Bridge Robin SHAM Technical Director Maunsell Ltd Beckenham, UK
Robin Sham, born 1954, received his BSc in 1978 (Birmingham) and PhD (Structural Engineering) in 1989 (Imperial College). He is Technical Director responsible for Bridges & Special Structures and was Designers Project Manager for the successful Kap Shui Mun Bridge & Ma Wan Viaduct Project in Hong Kong, opened in 1997.
Summary The paper describes how an innovative technique was successfully applied to fit trackwork alignments through the railway envelope of a cable-stayed bridge against a background of difficulties.
1.
Introduction
The Kap Shui Mun Bridge and Ma Wan Viaduct, which symbolise the vision and energy of Hong Kong, were opened to traffic in May 1997. The structures form a crucial part of the Lantau Link, the rail-road infrastructure network which connects the new Hong Kong Airport at Chek Lap Kok to Kowloon and Hong Kong Island. The two-level structures carry the Expressway at the top deck and the Airport Railway in the central region of the lower deck. Emergency carriageways for use under typhoon conditions are provided on either side of the railway. The Kap Shui Mun Bridge is the worlds longest cable-stayed bridge which carries combined rail and road traffic. The design harnesses and amalgamates technologies in different disciplines, such as long-span sea Fig 1 - Kap Shui Mun crossings, tunnelling and railway works. The bridge is a product of Hong Bridge & Ma Wan Kongs first Design-and-Construct Contract for a major sea crossing. In Viaduct an extremely tight programme of 4½ years many innovative ideas were developed to integrate design with construction. The design concept targets at making possible what effectively is a tunnel in the air, to be constructed at an extraordinary rate, on time and within budget, with heavy liquidated damages imposed on a number of critical Fig 2 - Cross-section of 2-level Cable-stayed Bridge milestone dates. Table 1 lists the six critical key dates. While liquidated damages were imposed on all key dates, failure to meet Key Dates 3 and 4 would incur very substantial penalties. Key Date 3 effectively called for completion of the bridges to permit the passage of trains.
Key date no Key Date 1 Key Date 2 Key Date 3 Key Date 4
Date 10.12.1995 7.5.1996 11.8.1996 11.8.1997
Critical stage Lantau approaches - release of works area to an adjacent contractor Lantau substation for China Light and Power Release of the railway envelope to the airport railway operator Access to Lantau substation and the utilities envelope to other contractors of the employer Key Date 5 24.11.1996 Access across the bridge and viaduct to authorised contractors of the employer Key Date 6 18.5.1997 Substantial completion Table 1. Key dates for the fast track construction programme This paper describes how an innovative technique was successfully applied to fit trackwork alignments through the railway envelope, against a background of a tight construction programme and technical difficulties.
2.
The Cable-stayed Bridge
The cable-stayed structure has a main span of 430m and a total length of 750m. Structural efficiency is enhanced Fig 3 - The Railway Envelope in the by double steel-concrete composite action in the main Main Span span in that both the top and bottom flanges of the steel superstructure are formed in concrete. For aerodynamic stability however, perforations are introduced into the central region of the flanges. In the transverse direction vierendeel action is achieved by cross frames; with alternate frames being suspended from the stay cables. Stiffened steel plates form the inclined outer webs. Longitudinal bracings which coincide with the inner columns of the vierendeel frames, distribute live loads to other cross frames and reduce trafficinduced vibrations. Further efficiency is obtained by bolting the diagonals subsequent to the application of dead loads, thereby relieving them of dead load stresses from the main girder. The design of the main span enabled erection by free cantilevering from both towers. It also allowed steelwork fabrication in China and segment assembly in the Lantau casting yard prior to float-out. The simplicity of the design ensured an erection cycle of 2 weeks for each segment weighing 500 tonnes. The side spans consist of twin box girders, designed for fast erection by incremental launching. The H-shaped towers were designed and detailed for fast construction by a self-climbing formwork system; the architecture being one that combines structural simplicity with aerodynamic efficiency.
Fig 4 - Free Cantilevering from Both Towers
Fig 5 - Main Span Closure
3.
Trackwork
The trackwork for the airport railway is contained in the central region of the lower deck of these bridges. The trackform design consists of precast, post-tensioned concrete trackslabs mounted on resilient bearings which are installed on transverse beams. The trackslabs are also restrained laterally through resilient bearings fixed to concrete corbels which are positioned on either side of the trackslab and cast into the bridge superstructure. The design constitutes a non-ballasted floating trackslab system which isolates the trackform from the main bridge structure thereby minimising the generation of noise and vibration. The trackform design enabled many construction activities to be implemented concurrently. Trackslabs were precast on site while the concrete corbels were constructed in-situ on the bridge superstructures. The trackslabs were then transported to strategic locations on the ground from where they were lifted by cranes up to deck level. The slabs were craned into the railway envelope in the central region of the lower deck. A travelling gantry installed the trackslabs progressively along the railway envelope. The post-tensioning of the trackslabs trailed closely behind the construction head.
4.
Fitting Trackwork Alignments
In order to meet Key Date 3, trackwork construction had to be concurrent with bridge construction. However, trackwork construction within the partially completed bridge superstructures would only be possible if design techniques could be developed to control the setting out of the trackwork under the most unusual conditions which existed. With full co-operation from the contractor, Maunsells Wriggle technique was applied to fitting the trackwork through the railway envelope. The Wriggle technique originates from tunnel engineering and involves the determination of track alignments in three dimensions to fit through the surveyed tunnel. The technique was successfully used to fit a rail profile (vertical) and alignment (horizontal) through the as-constructed railway envelope in the lower deck. The track profile must satisfy the railway design criteria as given in Table 2. The alignment had to take account of the as-constructed shape of the railway furniture and emergency exit walkways. In all cases the minimum structure gauge must be maintained. Maximum Design Speed (km/h) Maximum Horizontal Radius (m) Maximum Applied Cant (mm) Maximum Cant Deficiency (mm) (on plain line c.w.r.) Minimum Cant Gradient in Transition Maximum Cant Gradient in Transition Rate of Change of Cant or Cant Deficiency (mm/sec @ 135km/h) Minimum Vertical Radius (m) (Crest Curve) Minimum Vertical Radius (m) (Sag Curve) Maximum Gradient Table 2 Railway Design Criteria
140 1250 150 75 1 in 1000 1 in 440 37.5 (Desirable) / 55 (Max) 5140 7260 3%
Fig 6 - Chronology of the Trackwork Construction Unlike a tunnel, a long-span crossing is subject to transient as well as long-term movement. In particular the cable-stayed main span is susceptible to considerable movement between different survey operations carried out at different times of day. Due to the very tight programme of work the survey of the approach spans had to be carried out when temporary propping and falsework were still in place and the main span closure was yet to be completed. Similarly, as construction of Ma Wan Viaduct progressed, the Wriggle exercise had to produce trackwork setting out data for the existing spans without the benefit of any survey results on spans which were yet to be built. The deflection predictions, on which the Wriggle exercise partly relied, were incrementally calibrated and adjusted, when it became possible to survey newly constructed spans. The objective of the Wriggle exercise was to produce a smooth track profile and alignment that provided the necessary clearances at pinch points and maintained minimum curvature requirements. The output from this exercise had to be supplied to the trackwork subcontractor at a staggering rate and in a form that was simple, accurate, and practical to use for setting out.
5.
Overall Methodology
The methodology for fitting a trackwork profile (vertical) through the railway envelope in the cable-stayed bridge is described as follows. Similar techniques were used for the approach viaduct. Step 1
Common reference survey station for the structures was to be established
Step 2
Level survey was to be carried out through the full length of the bridge structure
Step 3
The railway envelope was to be surveyed, determining levels at the points depicted in Fig 7
Step 4
In acquiring the survey data in Steps 2 & 3, bridge temperatures at time of survey were to be recorded
Step 5
Acquired data would be analysed by the Wriggle technique, to determine the rail profiles achievable, allowing for construction tolerances in the trackform
Step 6
The best engineering estimate of the main span deflections between time of survey and Key Day 6 would be determined, to account for the prevailing state of construction and cable stressing temporary loads, including plant and equipment on the bridge superimposed dead loads to be applied by Key Date 3 & Key Date 6 time-dependent effects
Step 7
Lower and upper bound curves corresponding to states at Key Date 3, Key Date 6 and time infinity would be determined, allowing for variability in the parameters described in Step 6, and the effects of live loads and temperature changes
Step 8
Profiles determined in Step 5 would be adjusted by values derived in Step 6, to allow for expected future structure movements between the time of survey to Key Date 6
Step 9
A new profile (the Desired Rail Profile) would be determined to maintain the depth of trackform to within specified tolerances satisfy the criteria for vertical clearance comply with the railway design criteria in terms of gradient, curvature and other considerations, at the limits of each envelope at Key Date 3, Key Date 6 and time infinity
Step 10 Data for the Desired Rail Profile would be used for setting out purposes on site. Integrated with the re-profiling, the methodology for fitting a horizontal trackwork alignment involved establishing the centreline of the bridge within the railway envelope and verifying the potential clearances. In order to ensure compliance with the clearance criteria, a design for the emergency exit walkways was specially developed. It provided much flexibility in the setting out and was well-engineered to accommodate construction tolerance of the elements in the railway envelope.
6.
Assessment of Structure Movements
The determination of the Desired Rail Profile took into consideration all expected structure movements which would occur subsequent to the time of survey.
The deflected shapes of the railway envelope were predicted for different live load, dead load and time-dependent effects. In order to tackle the inherent variability and future changes in the parameters contributing to the movements, the predicted profiles were combined to represent the expected structure movements at different times in the future. In essence, an envelope was defined by means of a lower and an upper bound curve. The calculations took into account the following phenomena: (a)
State of construction at the time of survey It was assumed that the closure segment was placed into position, the concrete stitches in the flanges were cast and the four outer cables nearest to mid-span were stressed. The design allowed for the cables anchored to the launching nose to be re-stressed after main span closure. At the time of the main span reprofiling exercise, these cables were yet to be re-stressed and the jacking forces required were not known precisely. Deflected shape A was derived in accordance with the design assumptions and a 30% variation in the predicted change in cable loads was allowed for in determining the envelope.
(b)
Temporary loads A detailed record was made of the weight and positions of the plant and equipment which were present on the bridge at the time of survey. A total of 770 tonnes was used for this construction load, which was used to determine deflected shape B. In order to allow for the variability in the magnitude or distribution of the construction loads, an envelope was calculated on the basis of the temporary loads differing by +170 tonnes.
(c)
Superimposed dead loads At the time of survey, only part of the superimposed dead load had been applied. An allowance of 15kN/m was made in the calculations involving this load. The concrete trackslabs, other elements of the trackform and bridge furniture would be installed prior to Key Date 3. Deflected shape C allowed for 31kN/m per track over the full length of bridge. The road surfacing and the remaining components of the superimposed dead load would be installed between Key Date 3 and Key Date 6. Deflected shape D allowed for 51kN/m per track over the length of the main span and 82kN/m on the side spans. The envelope allowed for a +15% variability in the superimposed dead loads.
(d)
Structural response In the development of the movement envelopes, account was taken of the variability in material properties, approximation in modelling the transverse behaviour of the bridge superstructure and other phenomena which were not explicitly tackled by the analysis. On the basis of a comparison of the results given by different analytical models, a correction of +10% was applied to each of the deflected shapes B, C and D, in addition to the adjustments which were previously explained
(e)
Creep and shrinkage The effects of creep and shrinkage were predicted analytically for different times in the future. Deflected shape E illustrates the expected creep and shrinkage movements from the time of survey to Key Date 3 (8mm in 3 months at mid-span). Deflected shape F represents the expected creep and shrinkage movements from Key Date 3 to Key Date 6 (22mm in 9 months at mid-span).
In view of the uncertainty in predicting time-dependent effects, an adjustment of +50% was applied to each of the above deflected shapes. The adjustment aimed to correct for both the magnitude of the total movement and the rate at which it takes place. The end result, supplied for use in the Wriggle analysis, was the best engineering estimate of the main span deflections between the time of survey and Key Date 6. It was given by the summation of deflected shapes A to F. A series of deflection profiles was also derived with the inclusion of transient loads, as an assessment of the lower and upper bound curves at Key Date 3, Key Date 6 and time infinity. (f)
Live loads and temperature changes Live load deflections vary from one point on the bridge to another. For an overall check, the deflected shape was the range of peak values at each point. If the gradient or curvature criteria were found to be critical at a particular location, a detailed check would be carried out Investigations showed that an overall temperature change does not induce significant vertical movements. Sizeable movements are caused by differential temperature effects between the stay cables and the superstructure A temperature difference of +15oC between the stay cables and the rest of the bridge was assumed for a load combination involving the permanent loads, live loads and temperature.
Main Span - Cross Section
Main Span - Longitudinal Section
Fig 7 - Sections through the Railway Envelope
Fig 8 - Deflected Shapes of the Cable-stayed Bridge
Fig 9 - Deflected Shapes of Main Span
Fig 10 - Deflected Shapes of Lantau Side Span
Fig 11 - Deflected Shapes of Ma Wan Side Span
7.
Conclusion
The logistics of the work associated with the railway envelope survey and track reprofiling were complicated by construction activities and the intense pressures from the construction programme. Despite these constraints, the work enabled on-site adjustments during construction to achieve compliance and was critical to the successful completion of the railway work.
8.
Acknowledgement
The author would like to thank the Government of Hong Kong Highways Department, the Kumagai-Maeda-Yokogawa-Hitachi Joint Venture, Maunsell Consultants Asia Ltd and Leonhardt Andrä und Partner for the teamwork which made the project a success.
Comfort Criteria for High Speed Trains on The Øresund Bridge Jørgen GIMSING Civil Engineer MSc Gimsing & Madsen A/S Horsens, Denmark
Anders THOMSEN Civil Engineer MSc ISC Copenhagen, Denmark
Jørgen Gimsing received his degree from the Technical University of Denmark in 1967. He is Managing Director of Gimsing & Madsen A/S and Technical Manager of the ASO Group
Anders Thomson received his degree from the Technical University of Denmark in 1994. He has worked as design engineer for the ASO Group on the Øresund Bridge design for 3 years and joined ISC in 1998.
Summary The High Bridge of the Øresund Link is the longest cable stayed bridge carrying both a motorway and a two-track railway for both passenger trains and freight trains. Due to this, considerable efforts have been made to establish a comprehensive and coherent set of design rules for the comfort of passengers in trains travelling at 200 km/h. The paper summarises the investigations carried out by the Owner’s bridge consultant to establish these rules. One of the objects of the investigations was to try to limit the number of analyses to be carried out in the detailed design. This would have been possible if it could be demonstrated that some of the requirements were always stricter than other requirements. This part of the study was, however, not very successful. Only a small number of the original requirements were deleted due to a clear demonstration that they would automatically be fulfilled.
1.
Introduction
The main features of the Øresund Bridge were developed by ASO Group (Ove Arup & Partners, SETEC TPI, Gimsing & Madsen and ISC) for a design competition in 1993. During the following 1½ year the design was refined to a tender design suitable for tendering on a “Detailed Design and Construction” basis with all visible dimensions fixed by so-called “Definition Drawings”. During this pre-tender period a number of special investigations were carried out. Some of these were related to the aesthetical design, demonstrating that the dimensions on the Definition Drawings were reasonably optimised, some were intended to provide a consistent basis for estimating cost and construction time and some were carried out to establish relevant Design and Construction Requirements. Among the latter were an investigation of comfort criteria to be fulfilled for the bridge design, especially in relation to the high speed passenger trains travelling at 200 km/h while the second railway track might be loaded by a heavy freight train. The basis for this investigation was established by the Danish and the Swedish Railway Authorities based on the six ORE (Office for Research and Experiments of the International Union of Railways) Reports: “Permissible Deflection of Bridges”.
Fig. 1 Elevation Cable-Stayed High Bridge
2.
Comfort Criteria
The requirements from the railway authorities stated limitations on: • • • • • •
vertical deformations vertical accelerations horizontal deformations horizontal accelerations torsional deformations deformations at expansion joints.
All these requirements were related to comfort criteria for passenger trains. For freight trains the only relevant criteria was related to the wheel relief factor, which should be limited to 25%. The first task in transforming the above criteria to usable Design Requirements was to define the corresponding load combinations. It was found that the Ultimate Limit State combinations were too onerous for this purpose, whereas the Serviceability Limit State combinations would be too lenient. Three new load combinations for investigations of comfort criteria were therefore set up. In all these the permanent loads including prestressing, creep, shrinkage and expected settlements were factored by 1.0. The dominant traffic load (in most cases railway load) was factored by 1.0 while the other important live loads (road traffic, wind, temperature effects) were factored by 0.5. The railway load consists of the train under investigation on one track and the UIC 71 rail load on the other track. 2.1
Vertical Deformations
For span lengths up to 90 m the deflection at mid span should be limited to 1/2000 of the span length. This requirement could for longer spans be replaced by requirements to the vertical accelerations, refer Section 2.2 below. Even for the inherent, high rigidity of the two level bridge (span to depth ratio in the Approach Bridges of approx. 13) it was found that the limitation on the deflection would be far more onerous than the limitations on accelerations, and it was decided to state the limit on deformations to be valid only for spans below 90 m. 2.2
Vertical Accelerations
The limitation on the vertical acceleration depends on the duration of the event in the following manner:
• • •
for events with a duration less than 0.5 sec., the acceleration shall never exceed 2.00 m/sec2. for events with a duration of min. 10 sec., the frequency weighted rms value of the acceleration according to ISO 2631 shall be limited to 0.35 m/sec2. for events with a duration between 0.5 and 10 sec. arms shall be limited to values between 0.5 and 0.35 m/sec2.
In principle all factors affecting the acceleration in the coaches should be taken into account, but one of the first results of the investigations was that the contribution from allowable track defects was so small that the designer was allowed to disregard this. The passenger trains, which should be included in the analysis, are 3 existing Scandinavian trains and the Euro City, refer the table below. The table also contains 4 freight trains for which only the wheel relief factor is relevant, refer Section 2.7 below. The 4 freight trains look identical in the table, the difference between them is the spring and damper system for the investigated freight wagon.
Type
Speed (km/h)
Weight (kN/m) Coaches
Loco
Mean train length (m)
Train No. 1 (T1)
X2000 (S)
200
19.2
42.3/29
140
Train No. 2 (T2)
IR4 (DK)
180
21
21
153
Train No. 3 (T3)
IC3 (DK)
180
21
21
153
Train No. 4 (T4)
Euro City
160
17.6
46.3
270
Train No. 5 (T5)
Freight train
120
28.9
44.3
520
Train No. 6 (T6)
Freight train
120
28.9
44.3
520
Train No. 7 (T7)
Freight train
120
28.9
44.3
520
Train No. 8 (T8)
Freight train
120
28.9
44.3
520
Table 1 Investigated Train Types The coaches in the modern passenger trains have a complicated system of springs and dampers at each bogie. This system is simplified to one spring and one damper arranged in parallel. The simplified effective spring and damper give the correct results assuming that interaction between the two bogies and resonance within the complete spring-damper system can be disregarded. The simplified model was stated to be acceptable in the Design Requirements. The maximum vertical acceleration occurs when passing the angular bend at an expansion joint. A number of analyses were carried out to study the effect of one sharp bend, two separate bends, each half the value at varying distances and the total bend distributed over a varying length. As an example the results for the trains T2-T5 are given in the figure below when passing 2 bends each 0.002 rad and spaced from 0 to 40 m. The figure shows that the maximum acceleration in the passenger trains is not significantly influenced by the distance between the two bends, and that the requirement for max. acceleration below 2 m/sec2 is fulfilled in all cases. For the freight wagon the influence of the distance between the two bends is marked, but it was found impossible to find a length, which would be suitable for all 4 freight wagons, both loaded and empty. The simple sharp bend at one point gives many advantages in the design of the track expansion and was therefore chosen.
Accelerations
meter Distance between bends Fig. 2 Max. Acceleration as a Function of Distance between Bends 2.3
Horizontal Deformations
The Approach Bridges of the Øresund Link are placed with a horizontal curvature with a radius of minimum 12800 metres. The minimum radius for the high speed trains is 5000 metres. The requirements from the railway authorities stated that the minimum radius shall be fulfilled for the bridge subject to wind load. It was found that this requirement was superfluous, as the inherent stiffness of the bridge was more than sufficient to fulfil it. The requirement was therefore not included in the Design Requirements. 2.4
Horizontal Accelerations
The requirement from the railway authorities was that the frequency weighted rms value of the horizontal accelerations should be less than 0.35 m/sec2. As above this requirement was not included in the Design Requirements, as it was demonstrated that it was easily fulfilled with the minimum stiffness of the bridge. 2.5
Torsional Deformations
The requirements: • •
total torsional deformation shall be limited to 1.5% torsional deformation per meter shall be limited to 0.06% for trains travelling at 200 km/h, 0.10% in all other cases
were included in the Design Requirements, even though they were found to be fulfilled for the two level bridge. The reason for keeping the requirements was that an alternative design proposed by a tenderer could have a reduced torsional stiffness, at least in theory, making the requirements relevant.
2.6
Deformations at Expansion Joints
The requirements to angular deflection are stated in the table 2 below. Angular Deflection Train Type
Horizontal
Vertical
Freight Train v ≤ 120 km/h
0.2%
0.6%
Passenger Train v ≤ 200 km/h
0.1%
0.4%
Unloaded Bridge*
0.4%
0.9%
Table 2 Permissible Total Angular Deflections at Railway Expansion Joints. *Refers to maximum permanent deformations, which can be corrected on ballasted tracks. These requirements were found to be very strict and could lead to substantial extra costs for the 2 spans adjacent to an expansion joint in order to increase the stiffness of these spans. The solution to this was to allow the Bridge Contractor to assume that the track laying would introduce a precamber at the expansion joint of up to 0.2%. This allows an angular deflection of 0.6% for the passenger train in one track, UIC 71 load in the other track plus 0.5 times road load, which was found to be just fulfilled with the steel and concrete quantities needed in the static design of the end spans. The fulfilment of the requirement to vertical angular deflection was found automatically to lead to fulfilment of the requirement for maximum vertical acceleration 2 m/sec2 in the passenger coaches. The latter requirement was, however, maintained as it is easily checked when the analysis to determine the rms value of the accelerations is carried out. The Design Requirements also include limitations on deformations at expansion joints as follows: • •
vertical displacement across a railway expansion joint max. 2.5 mm, however 5 mm during bearing replacement horizontal displacement across a railway expansion joint max. 1 mm.
The first requirement can only be fulfilled when the expansion joint is located at a pier top, which makes it possible to jack up both bridge spans during a bearing replacement. The second requirement necessitates that one of the two bearings for each span is transversely fixed, whereas the second bearing shall allow temperature movements in the transverse direction relative to the pier top. This example shows that the comfort criteria have had a considerable influence on the allowable choices of statical systems for the Øresund Bridge. 2.7
Wheel Relief Factor
The requirements from the railway authorities stated that the wheel relief for all freight wagons should be limited to 25%. It was, however, found that this requirement could not be fulfilled for an empty freight wagon in either of the four freight trains T5-T8 indicated in table 1 above. The wheel relief factor when passing an expansion joint with the allowable angular deflection was found to be up to 50%. A literature study was then carried out to determine the origin of the requirement, which was found to be Japanese rules for the “Shinkansen” high speed trains. The only requirement for wheel relief factors in freight trains found in the literature was a United States requirement of 75%. On this background it was agreed with the railway authorities to waive this requirement.
3.
Conclusions
The paper summarises some of the investigations carried out to finalise the section on comfort criteria in the Design Requirements for the Øresund Bridge. It is demonstrated that some of the original requirements from the Danish and the Swedish Railway Authorities would have been nearly impossible to fulfil and that a consistent set of requirements has been established. The main conclusion is that the comfort criteria could be fulfilled for the two level bridge design, that went out to tender in December l995. This conclusion has been confirmed by the more detailed analyses carried out by Cowi-VBB, the bridge consultant for the successful tenderer, Sundlink Contractors.
Nonlinear Dynamic Analysis of Cable-Stayed Bridges Excited by Moving Vehicles
Raid KAROUMI Researcher, Dr. Techn. Dept. of Structural Eng. Royal Inst. of Technology Stockholm, Sweden www.struct.kth.se
[email protected]
1.
Raid Karoumi, born 1964, received his M.Sc. degree in Civil Engineering in 1990 and his Dr. Techn. degree in 1999 from the Royal Institute of Technology in Stockholm. Between 1990 and 1993 he worked as a consultant and was involved in a variety of special projects.
Introduction
Due to their aesthetic appearance, efficient utilization of structural materials and other notable advantages, cable-stayed bridges have gained much popularity in recent decades. Bridges of this type are now entering a new era with main span lengths reaching 1000 m. This fact is due, on one hand to the relatively small size of the substructures required and on the other hand to the development of efficient construction techniques and to the rapid progress in the analysis and design of this type of bridges. The recent developments in design technology, material qualities, and efficient construction techniques in bridge engineering enable the construction of not only longer but also lighter and more slender bridges. Thus nowadays, very long span slender cable-stayed bridges are being built, and the ambition is to further increase the span length and use shallower and more slender girders for future bridges. To achieve this, accurate procedures need to be developed that can lead to a thorough understanding and a realistic prediction of the structural response due to not only wind and earthquake loading but also traffic loading. It is well known that large deflections and vibrations caused by dynamic tire forces of heavy vehicles can lead to bridge deterioration and eventually increasing maintenance costs and decreasing service life of the bridge structure. Although several long span cable-stayed bridges are being build or proposed for future bridges, little is known about their dynamic behavior under the action of moving vehicles. The dynamic response of bridges subjected to moving vehicles is complicated. This is because the dynamic effects induced by moving vehicles on the bridge are greatly influenced by the interaction between the vehicles and the bridge structure. To consider dynamic effects due to moving vehicles on bridges, structural engineers worldwide rely on dynamic amplification factors specified in bridge design codes. These factors are usually a function of the bridge fundamental natural frequency or span length and states how many times the static effects must be magnified in order to cover the additional dynamic loads. This is the traditional method used today for design purpose and can yield a conservative and expensive design for some bridges but might underestimate the dynamic effects for others. In addition, design codes disagree on how this factor should be evaluated and today, when comparing different national codes, a wide range of
variation is found for the dynamic amplification factor. Thus, improved analytical techniques that consider all the important parameters that influence the dynamic response are required in order to check the true capacity of existing bridges to heavier traffic and for proper design of new bridges. The recent developments in bridge engineering have also affected damping capacity of bridge structures. Major sources of damping in conventional bridgework have been largely eliminated in modern bridge designs reducing the damping to undesirably low levels. As an example, welded joints are extensively used nowadays in modern bridge designs. This has greatly reduced the hysteresis that was provided in riveted or bolted joints in earlier bridges. For cable supported bridges and in particular long span cable-stayed bridges, energy dissipation is very low and is often not enough on its own to suppress vibrations. To increase the overall damping capacity of the bridge structure, one possible option is to incorporate external dampers (i.e. discrete damping devices such as viscous dampers and tuned mass dampers) into the system. Such devices are frequently used today for cable supported bridges. However, it is not believed that this is always the most effective and the most economic solution. Therefore, a great deal of research is needed to investigate the damping capacity of modern cable-stayed bridges and to find new alternatives to increase the overall damping of the bridge structure. In this paper, the nonlinear dynamic response of a simple two-dimensional cable-stayed bridge model, subjected to a moving vehicle, is studied. Bridge damping, exact cable behavior, and nonlinear geometric effects are considered. This study focuses on investigating the influence of vehicle speed, bridge damping, and a tuned mass damper on the bridge dynamic response.
2.
Bridge and Vehicle Modeling
2.1
Bridge structure
Modern cable-stayed bridges exhibit geometrically nonlinear behavior, they are very flexible and undergo large displacements before attaining their equilibrium configuration. As an example, due to this inherently nonlinear behavior, conventional linear dead load analysis, which assumes small displacements, is often not applicable [1]. Cable-stayed bridges consist of cables, pylons and girders (bridge decks) and are usually modeled using beam and bar elements for the analysis of the global structural response. To consider the nonlinear behavior of the cables, each cable is usually replaced by one bar element with equivalent cable stiffness. This approach is referred to as the equivalent modulus approach and has been used by several investigators, see e.g. [1, 2, 3]. It has been shown in [4] that the equivalent modulus approach results in softer cable response as it accounts for the sag effect but does not account for the stiffening effect due to large displacements. Still, for some cases, e.g. for short span cable-stayed bridges, linear analysis utilizing the equivalent modulus approach is often sufficient [3], especially in the feasibility design stage. Whereas, long span cable-stayed bridges built today or proposed for future bridges are very flexible, they undergo large displacements, and should therefore be analyzed taking into account all sources of geometric nonlinearity. Although several investigators studied the nonlinear behavior of cable-stayed bridges, very few tackled the problem of using cable elements for modeling the cables. See ref. [5, 6] where different cable modeling techniques are discussed and references to literature dealing with the analysis and the behavior of cable structures are given.
In this paper, an alternative approach is presented where accurate and efficient elements are adopted for the modeling. A beam element, which includes geometrically nonlinear effects and is derived using a consistent mass formulation, is adopted for modeling the girder and the pylons. Whereas, a two-node cable element derived using exact analytical expressions for the elastic catenary, is adopted for modeling the cables. The nonlinear finite element method is utilized considering all sources of geometric nonlinearity, i.e. change of cable geometry under different tension load levels (cable sag effect), change of the bridge geometry due to large displacements, and axial force-bending moment interaction in the bridge deck and pylons (P- ä effect). The adopted beam element, able to resist bending, shear, and axial forces, is developed following the total Lagrangian approach and using a linear interpolation scheme for the displacement components. This element is chosen because it can handle large displacements and shear deformations and because it is simple to formulate the element matrices. This beam element is of minor interest and, due to space limitation, not discussed here in more detail. The interested reader is referred to the author’s doctoral thesis, reference [5], where formulation of this beam element is presented in detail. In the following subsection, the cable element matrices will be given in the element local coordinate system. Using this approach, each cable may be represented by a single 2-node finite element, which accurately consider the curved geometry of the cable. Despite the fact that this cable modeling technique has been available for many years it has, at least to the author’s knowledge, very seldom been used for analysis of cables in cable-stayed bridges. 2.1.1 Cable element Consider an elastic cable element, stretched in the vertical plane as shown in Figure 1, with an unstressed length Lu, modulus of elasticity E, cross section area A, and weight per unit length w (uniformly distributed along the unstressed length). For the elastic catenary, the exact relations between the element projections and cable force components at the ends of the element are: L 1 P4 + T j Lx = − P1 u + ln EA w Ti − P2 Ly =
(
)
T j − Ti 1 T j2 − Ti2 + 2 EAw w
u 4 , P4
(1a)
node j
u 3 , P3
y
(1b)
Ly
Lu , E , A , w u 2 , P2
where Ti and T j are the cable tension forces at the two nodes of the element. For the above expressions it is assumed that the cable is perfectly flexible and Hooke’s law is applicable to the cable material.
u 1 , P1
x
node i
Lx
Figure 1: Catenary cable element
By rewriting the above expressions for Lx and Ly in terms of the end forces P1 and P2 only using the relationships: P4 = w Lu − P2 ;
P3 = − P1 ;
Ti = P12 + P22 ;
T j = P32 + P42
(2a-d)
differentiating the new expressions for Lx and Ly and rewriting the results using matrix notation gives: ∂Lx dLx ∂P1 dL = ∂L y y ∂P1
∂Lx dP ∂P2 dP1 = F 1 ∂Ly dP dP2 2 ∂P2
(3)
where F is the flexibility matrix. The stiffness matrix is given by the inverse of F, i.e. K = F −1 . The tangent stiffness matrix K t and the corresponding internal force vector p for the cable element can now be obtained in terms of the four nodal degrees of freedom as: − k1 − k 2 k1 − k4 k2 Kt = − k1 sym.
k2 k4 ; − k2 − k4
P1 P p = 2 P3 P4
(4a,b)
where k1 = −
k4 =
1 Lu 1 P4 P2 ; + + det F EA w T j Ti
k2 = k3 = −
1 P1 1 1 − det F w T j Ti
1 Lx 1 P4 P2 + + det F P1 w T j Ti
(5a,b)
(5c)
L P L P P 1 1 P 1 P 1 det F = − u − 4 + 2 x + 4 + 2 − 1 − EA w T j Ti P1 w T j Ti w T j Ti
2
(5d)
The element tangent stiffness matrix K t relates the incremental element nodal force vector to the incremental nodal displacement vector { ∆u1 , ∆u2 , ∆u3 , ∆u4 }T . To evaluate the tangent stiffness matrix K t , the end forces P1 and P2 must be determined first. Those forces are adopted as the redundant forces and are determined, from given positions of cable end nodes, using an iterative stiffness procedure. This procedure requires starting values for the redundant forces. Based on the catenary relationships the following expressions will be used for the starting values:
{ ∆P1 , ∆P2 , ∆P3 , ∆P4 }T
P1 = −
w Lx 2λ
and
P2 =
w cosh λ + Lu − Ly 2 sinh λ
L2u − L2y − 1 where λ = 3 L2 x
(6a-c)
In cases where equation (6c) cannot be used because the unstressed cable length is less than the chord length, a conservative value of 0.2 for λ is assumed. Another difficulty arises in equation
(6c) for vertical cables. In that case an arbitrary large value of 106 for λ is used. Using equations (2a-d), new cable projections corresponding to the assumed end forces P1 and P2 are now T determined directly from equations (1a,b) and the misclosure vector { Lx , Ly} is evaluated as the positions of the end nodes are given. Corrections to the assumed end forces can now be made using the computed misclosure vector as: ∆Lx ∆P1 = K ∆L ; ∆P2 y
P1 P2
i +1
i
P ∆P = 1 + 1 P2 ∆P2
(7a,b)
where K is the stiffness matrix (the inverse of F in equation (3)) and i is the iteration number. For the present study, this iteration process continued until Lx and Ly are less than 1 ⋅ 10−5 . As will be demonstrated later, this iterative procedure converges very rapidly. To determine the unstressed cable length, Lu , for cases where the initial cable tension is known instead, a similar iteration procedure can be adopted. A starting value for the unstressed cable length is assumed, e.g. equal to the cable chord length, and cable end forces P1 and P2 are computed using the iterative procedure described above. Using equation (2c,d), cable tension can now be computed. This is then compared with the given initial tension to obtain a better approximation for Lu for the next iteration step. For the dynamic analysis, mass discretization is simply done by static lumping of the element mass at both ends giving the following lumped mass matrix (ρ is the mass density of the cable):
M=
2.2
ñAL 2
u
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
(8)
Vehicle model
The vehicle model used in this study is a so-called suspension model that includes both primary and secondary vehicle suspension systems, see Figure 2. This model is sufficient since the main concern is to investigate the dynamic response of bridges and not the dynamics of the vehicle itself and since the spans of cable-stayed bridges are considerably larger than the vehicle axle base. It is assumed that the vehicle never loses contact with the bridge and the contact between the bridge and the moving vehicle is assumed to be a point contact. The equation of motion for the vehicle is coupled to the bridge equation of motion through the interaction force existing at the contact point of the two systems. To solve these two sets of equations, an iterative procedure is adopted, as the interaction force is dependent on the motion of both the bridge structure and the vehicle. Vehicle load modeling and the developed moving load algorithm are described in detail in reference [5]. The implemented codes fully consider the bridge-vehicle dynamic interaction and have been verified in [5].
w3(t)
v (t) m3 ks
w2(t)
(b)
(a) cs
Vehicle data
m2 kp
w1(t)
cp m1
node i
node j
xc e
L
mode 1 1.5-4 Hz
mode 2 8-15 Hz
m1 = 0 kg m2 = 4840 kg m3 = 39160 kg cp = 1.76 104 Ns/m cs = 13.2 104 Ns/m kp = 15.4 106 N/m ks = 8.8 106 N/m
Figure 2: (a) vehicle model on a bridge element; (b) typical vehicle modes of vibration
3.
Nonlinear Analysis Procedure
The equation of motion for the entire bridge is obtained as: + C q + p(q ) = f (q, q , q , t ) Mq
(9)
are the bridge node displacement, velocity, and acceleration vectors, respectively, where q, q , q M the bridge mass matrix, C the bridge damping matrix, p(q) the vector of internal elastic ,t) the external force vector resulting from the dead load, the moving forces, and f( q, q , q vehicles, and the tuned mass dampers. As indicated, the external force vector is not only time dependent but is also dependent on the bridge displacements, velocities and accelerations. This vector contains the interaction forces existing at the contact points between the vehicles and the bridge and thereby couples the bridge equation of motion with those of the vehicles. For this study, an implicit procedure based on Newmark’s average acceleration method combined with a full Newton-Raphson solution procedure (i.e. the Newton-Newmark algorithm) is adopted for solving the bridge equation of motion. For the interested reader, details concerning the derivation etc. of this nonlinear dynamic procedure as well as a linear dynamic procedure based on the utilization of the dead load tangent stiffness matrix can be found in [5]. Nonlinear dynamic analysis is essential if it is believed that the bridge will not behave linearly during the application of live loads. If this is the case, the natural frequencies will vary with the amplitude of response and linear dynamic analysis will consequently be inadequate. To evaluate the nonlinear static response, an incremental-iterative procedure using full NewtonRaphson iterations is adopted. This procedure is generally expected to give quadratic convergence.
4.
Numerical Example
A 2D model of the cable-stayed bridge described in [1] was adopted for this investigation. The bridge geometry is shown in Figure 3 and the properties are given in Table 1.
5x3
v
45.7 30.5 335.3 m
146.3 m
146.3 m
Figure 3: Geometry of the cable-stayed bridge. The cables are numbered from the left to the right starting with cable 1
Girder
E (N/m2) A (m2)
I (m4)
w (t/m)
Cable no.
E (N/m2)
A (m2)
Lu (m)
w (t/m)
2.0⋅1011
0.26
19.64 †
1, 24
2.0⋅1011
0.0362
158.13
0.398
2.0⋅10
11
0.0232
134.66
0.255
2.0⋅10
11
0.0204
111.64
0.225
2.0⋅10
11
0.0176
89.43
0.194
2.0⋅10
11
0.0139
68.80
0.153
2.0⋅10
11
0.0113
51.69
0.125
2.0⋅10
11
0.0372
158.12
0.409
11
Girder central part
2.0⋅10
Pylons above deck level
2.8⋅1010
Pylons below deck level
2.8⋅1010
0.93 1.11 13.01 18.58
1.29 34.52 86.31
19.64 † 30.65 43.78
2, 11, 14, 23 3,10, 15, 22 4, 9, 16, 21 5, 8, 17, 20 6, 7, 18, 19
11
Links deck to 2.0⋅10 0.56 pylons † Including weight of cross beams.
0.10
4.38
12, 13
Table 1: Parameters for the cable-stayed bridge model defined in Figure 3 For the model, it was assumed that the girder was pinned at the ends, i.e. only rotations were allowed, and elastically connected to the pylons by vertical links. The pylons were assumed to be rigidly fixed to the piers, and all cables were assumed fixed to the pylons and to the girder at their joints of attachment. The model had 119 active degrees of freedom and was composed of 66 elements and 43 nodal points. The CPU time used by the computer (200 MHz Pentium Pro) to find the tangent stiffness matrix at the dead load deformed state and solve the system eigenvalue problem determining all 119 modes of vibration, was about 15 seconds. This indicates high efficiency of the presented elements. The first three bending natural frequencies obtained utilizing the dead load tangent stiffness matrix are: 0.332, 0.436, 0.692 Hz. Bridge damping ratios were assumed constant for all modes and equal 0.0056. This bridge model was then subjected to a 44 ton truck moving from the left to the right on a smooth road surface at the constant speed v, see Figure 3. The body-bounce and wheel-hop frequencies, for the truck model, were chosen as 1.89 and 11.35 Hz. The corresponding mode shapes and vehicle model properties are shown in Figure 2. In the following subsections, the effect of speed, bridge damping and a tuned mass damper on the bridge response is presented. 4.1
Vehicle speed and bridge damping effect
The vertical displacement of the girder at the center of the bridge, due to traffic load only, is shown in Figures 4a and 4b for different speeds and damping ratios. For the curves in Figure 4b,
Vert. displacement (mm)
the vehicle speed was v = 90 km/h. The static traffic load response is also plotted in this Figure. 1500 increments were required for the solution of the 50 km/h case, and 1000 increments for the rest.
25 5 -15 -35
v = 50 km/h v = 90 km/h v = 110 km/h
(a)
Vert. displacement (mm)
-55 As expected, damping reduces the 0 5 10 15 20 25 30 35 40 45 bridge response. For ξ = 0.0056 in Time (s) Figure 4b, the absolute maximum dynamic displacement is about 20% 25 larger than the static one (dynamic 5 amplification factor of 1.2). It can be concluded from the results in -15 Static Figure 4 that the response increases ξ=0 -35 with the increase in vehicle speed ξ = 0.0056 (b) ξ = 0.03 and that bridge damping has a -55 significant effect upon the response 0 5 10 15 20 25 and should therefore always be Time (s) considered if accurate representation Figure 4: Vertical displacement at the center of the bridge of the true dynamic response is calculated for different vehicle speeds (a) and required. bridge damping ratios (b)
The effectiveness of a tuned mass damper (TMD) in suppressing vibrations due to a single 44 ton moving truck is investigated in this study. The truck was assumed to move on a smooth road surface at the constant speed of 110 km/h. Reasonably converged reliable solutions were obtained using 1000 increments corresponding to a time step of 0.025 s. The TMD was positioned at the center of the bridge and tuned to the first bending mode of vibration. The following most often used optimum tuning parameters, derived in [7] for an undamped structure, are adopted:
ωtmd
20 5 -10 -25 -40
(10a) 3µ
8 (1 + µ ) 3
(10b)
with TMD without TMD
(a)
-55 0
90 60 30 0 -30 -60 -90 -120
10
20
30 40 Time (s)
50
60
70
10
20
30 40 Time (s)
50
60
70
(b) 0
ω = i 1+ µ
ξ tmd =
Vert. displacement (mm)
Effect of a tuned mass damper
Vert. displacement (mm)
4.2
Figure 5: (a) Vertical displacement of the girder at the center of the bridge; (b) vertical displacement of the TMD mass. The dashed vertical line indicate when the truck leaves the bridge
Axial force (MN)
Bend. moment (MNm)
Hor.displacement (mm)
where ωtmd and ωi are the circular frequencies of the TMD and the 10 dominant bridge mode to be tuned 4 to, ξtmd the damping ratio of the -2 TMD, and µ is the mass ratio which relates the TMD mass to the modal with TMD -8 mass of the dominant bridge mode without TMD (a) -14 to be tuned to, µ = mtmd / mi . The 0 10 20 30 40 50 60 70 mass ratio was here set to 0.005 Time (s) giving a TMD mass of about 15.6 ton. Some results from the nonlinear 10 dynamic analysis showing the with TMD (b) response due to traffic loads only without TMD 4 are presented in Figures 5 and 6. Figure 7 (in the abstract) shows a -2 cross section of a bridge girder with a tuned mass damper. It was found -8 from the analysis results that the 0 10 20 30 40 50 60 70 TMD not always is very effective in Time (s) reducing the maximum dynamic response during the forced vibration 0.5 (c) period (i.e. when the vehicle is on with TMD without TMD the bridge). In fact, due to the 0.2 interaction between the bridgevehicle-TMD systems, the -0.1 maximum response for certain elements and nodes can even -0.4 increase due to the TMD. However, 0 10 20 30 40 50 60 70 it is evident from Figures 5 and 6 Time (s) that the TMD is very effective in reducing the vibration level in the Figure 6: (a) horizontal displacement of the right pylon top; (b) bending moment at the right pylon fixed end; (c) free vibration period for all elements axial force in the right anchorage cable. The and nodes. This is due to the dashed vertical line indicate when the truck leaves increase of the overall damping of the bridge the bridge by the TMD.
5.
Conclusions
This paper has presented a method for modeling and analysis of cable-stayed bridges subjected to moving vehicles. Bridge damping, exact cable behavior, and nonlinear geometric effects have been considered when analyzing the nonlinear dynamic response. The study has only focused on investigating the influence of vehicle speed, bridge damping, and a tuned mass damper on the bridge dynamic response. A two-node catenary cable element was adopted for modeling the cables and it has been found that the main advantages of this cable element are the simplicity of including the effect of pretension of the cable and the exact treatment of cable sag and cable weight. Moreover, the iterative process adopted to find the internal force vector and tangent stiffness matrix for the cable element is found to converge very rapidly. According to the author’s opinion, linear
analysis utilizing the traditional equivalent modulus approach, is not satisfactory for modern cable-stayed bridges. Modern cable-stayed bridges built today or proposed for future bridges are, as they are highly flexible, subjected to large displacements. The equivalent modulus approach however accounts only for the sag effect but not for the stiffening effect due to large displacements. From the study of the traffic load response of cable-stayed bridges it is concluded that the response increases with the increase in vehicle speed and that bridge damping have a significant effect upon the response and should always be considered in such analysis. Bridge damping ratios should be carefully estimated to insure more correct and accurate representation of the true dynamic response. To obtain realistic damping ratios, such estimation should be based on results from tests on similar bridges. In addition it is concluded that a tuned mass damper is not very effective in reducing the maximum dynamic response during the forced vibration period (i.e. when the vehicle is on the bridge). In fact, such a device can even increase the maximum dynamic response of some nodes and elements. However, the reduction of the vibration level in the free vibration period is significant as the tuned mass damper increases the overall damping of the bridge by working as an additional energy dissipater In reference [5], the influence of other important parameters such as road surface roughness, bridge-vehicle interaction, and cables vibration (i.e. multi-element cable discretization) is investigated. In addition, the dynamic response of other bridge models, such as the Great Belt suspension bridge in Denmark, is also studied.
6.
References
[1]
Nazmy A.S., Abdel-Ghaffar A.M., ‘Three-Dimensional Nonlinear Static Analysis of Cable-Stayed Bridges’, Computers and Structures, 34, 1990, pp. 257-271.
[2]
Karoumi R., ‘Dynamic Response of Cable-Stayed Bridges Subjected to Moving Vehicles’, IABSE 15th Congress, Denmark, 1996, pp. 87-92.
[3]
Kanok-Nukulchai W., Yiu P.K.A., Brotton D.M., ‘Mathamatical Modelling of CableStayed Bridges’, Struct. Eng. Int., 2, 1992, pp. 108-113.
[4]
Ali H.M., Abdel-Ghaffar A.M., ‘Modeling the Nonlinear Seismic Behavior of CableStayed Bridges with Passive Control Bearings’, Computers and Structures, 54, 1995, pp. 461-492.
[5]
Karoumi R., ‘Response of Cable-Stayed and Suspension Bridges to Moving Vehicles – Analysis methods and practical modeling techniques’, Doctoral Thesis, TRITA-BKN Bulletin 44, Dept. of Struct. Eng., Royal Institute of Technology, Stockholm, 1998.
[6]
Karoumi R., ‘Some Modeling Aspects in the Nonlinear Finite Element Analysis of Cable Supported Bridges’, Computers and Structures, (in printing).
[7]
Den Hartog J.P., Mechanical Vibrations, 4th edition, McGraw-Hill, New York, 1956.
Deformability of Long-Span Cable-Stayed Bridges for Railways Domenico BRUNO University of Calabria Cosenza, Italy
Antonio GRIMALDI University of Rome Tor Vergata, Rome, Italy
Angelo LEONARDI University of Rome Tor Vergata, Rome, Italy
Summary In this paper an analysis of the statical and dynamical behaviour of long span cable-stayed bridges traversed by moving loads is developed. The structural model of the bridge is defined by referring to the fan-shaped scheme and according to a continuous distribution of stays along the girder . An analytical and a numerical analysis are developed to study the statical behaviour of the bridge by using a continuous or a discrete model of the structure; while, a numerical analysis is carried out, based upon time integration of the motion equations of the discretized structure to model the dynamical effects of the moving loads. The main structural nonlinearity arising from the elastic response of stays is accounted for together with the nonlinear effects related to the dynamical effects of the moving loads. Some numerical results show the influence of the main geometrical and load parameters on the elastic response of the bridge.
1. Introduction Cable-stayed bridges have been of great interest in recent years, particularly with respect to the fan-shaped scheme as a valid and alternative solution to suspension bridges for long spans. Troitsky (1) and Gimsing (2) have reviewed the problems and advantages of cable-stayed bridge solutions and reported on the latest and most interesting projects. For long-span bridges one of the most important problems is related to the deformability under live loads. In the case of bridges carrying both road and railway traffic, and for spans greater than 1000 m, this aspect can seriously influence the design and the feasibility of the structure. In this work an analysis of the static and dynamic behaviour of the bridge is developed, modeling the train passage as a dynamical action or an equivalent static load. Como et al. (3) analyzed the static behaviour of long span stayed-cable bridges showing the prevailing truss behaviour of the bridge. Bruno and Grimaldi (4) investigated the nonlinear static behaviour of cable-stayed bridges using both a continuous and a discrete model of the bridge, and showed the strong influence of nonlinearities for long spans. Moreover, the dynamic behaviour of cable-stayed bridges has been investigated by Bruno (5) analyzed the effects of moving loads, and by Bruno, Maceri and Leonardi (6) who analyzed aerodynamic instability problems. In above studies the fan-shaped cable-stayed bridges was studied using both a continuous and a discrete model of the bridge, and the dominant truss behaviour of the bridge was found. In particular, the influence of the dynamic properties and geometric nonlinearities of the structure are included in the analysis. In this paper the continous model proposed in the previous works is employed to develop static and dynamic analyses. In addition a discrete model is also applied to give some useful comparisons between analytical and numerical results. The aim of the paper is to give same results and conclusions related the main geometric and mechanical parameters able to influence or control the bridge deformability. In particular, the geometric aspect ratio L/H between the main span length and the tower heigth, the loads ratio p/g between live and dead loads, the relative flexural stiffness between girder and stays, are taken into account. Obtained results show the strong influence of the rail load on the midspan deflection and on the girder slopes. As well known this last quantities in many cases represent the main parameter which have to be considered in deformability control.
1
2. Bridge scheme and numerical results. The fan-shaped scheme of cable-stayed bridge of Fig.1 is considered, in which the girder is simply supported at its ends and is hung to the tops of H-shaped towers by means of two stays curtains. It is assumed that the stays spacing ∆ is a small quantity compared to the central span length Lc. The aspect ratios r1=Lc/H; r2=Ls/H of span legths to the tower height are usually obtained on the basis of economy and of the anchor cable stability condition. The longitudinal vertical plane yz is assumed to be a symmetrical one; in addition, the bridge is also symmetrical with respect to the midspan cross plane. According to the usual erection procedures, girder and towers are assumed to be free from bending under dead load g. Then, the cross sectional areas As and Ao of the couple of diffused stays and of the anchor stays, respectively, are obtained by referring to the truss scheme of the bridge: As =
g∆ ; σ g sinα
A0 =
where g ; σg = σ a p+g
1 gL s L L [1 + ( s ) 2 ] 2 [( c ) 2 − 1] 2σ g 0 2L s H
σ g0
2L p = σ a 1 + [1 − ( s ) 2 ]−1 Lc g
−1
and where σa is the allowable stress, α is the angle between a stay and its horizontal projection, p is the live load and g is the dead load. We assume that towers and girder’s axial elongations are negligible, and we apply the beam model for bending and torsion of the girder. As far as the stays behaviour is concerned, the Dischinger modulus Es*=E/(1+γ2l02 E/12σ03) is used, where Eis the Young modulus, γ is the specific weight, l0 is the horizontal projection length of the stay and σ0 is the initial tension. The tower is characterized by the flexural stiffness k and the torsional stiffness kT, while the girder is characterized by the inertia I and the torsional
stiffness factor Ct. It is convenient to introduce the following non dimensional quantities: γ 2 H 2E a= 3 ; 12σ g
ε 4 Iσ g = 3 ; 4 H g
2
τ =
Ctσ g , 2 Eb Hg
that is: -the bridge span parameter = -the girder nondimensional flexural stiffness parameter ε -the girder nondimensional torsional stiffness parameters τ For the H-shaped towers scheme, the deformation of the bridge can be described by the following displacement parameters: - the horizontal translation w of the girder; - the axial displacements ∆L, ∆R and the torsional rotations ΨL, ΨR of the tower tops; - the vertical deflection v of the girder; - the torsional rotation θ of the girder. While, if the A-shaped towers scheme is considered, the tower tops torsional rotations must be taken : ΨL=ΨR =0.
2
E A 0
k,k T 0
E A s
s
H α0
α
z
z
∆
I,C t
y
Ls
y
Lc
Ls
Fig.1. Cable stayed bridge scheme
It is possible to show (3,4) that the statical behaviour of the bridge can be studied by using a continuous structural model which gives the main bridge deformation and stress parameters. In Fig.3 some results relative to the deformation of the bridge are given, where both an analytical continuous model and a FEM discrete one of the bridge are employed. The results refers the following geometrical and material parameters of the bridge: r1=2.5; r2=5/3; 6 2 E=21x10 t/m ; k/g=50. In this figure the case of high live loads (p/g=1), like that railway bridges, is considered. It can be observed that, the transverse deflection of the bridge is practically unaffected by the tower shape, on the contrary, the torsional deformation is strongly influenced by the tower shape. The results are given in dimensionless form, where the quantity µ0 represents the nodimensional torsional couple µ0 = H σg m/Egb2. Lp c
p ct
Ls
Lc
Ls
Fig.2. Bridge scheme under moving loads A dynamical analysis of the bridge can also be developed by using both a continuous model and a discrete one to analyze free vibrations, aerodynamic instability and the dynamical effects of the moving loads. Here we use a discrete formulation via finite elements to investigate the dynamical effects of moving loads on stress and displacement characteristics. Let us consider the bridge traversed by a strip of load p moving at constant speed c (Fig.2); moreover, let λ be the moving load mass and µ the girder mass, with λ/µ=p/g. 3
The aim of the analysis is to determine the stress and displacement increments starting from the initial equilibrium configuration under dead load g. To this end a discrete model of the bridge is constructed by using a finite element model of the structure where a cubic interpolation of the vertical displacements and a linear interpolation for torsional rotations is applied. Then, the dynamical equilibrium equations of the bridge can be put in the following discrete form: .. . M s + K(s)s= F(s ,s, t ) where M is the mass matrix, K is the stiffness matrix, F is the load vector and s is the generalized displacement vector. It must be observed that in the previous equation the load vector F accounts for the dynamical effects of the moving load mass. The above nonlinear problem was solved numerically by using the Newmark integration method. Preliminary numerical experiments have been made to choose the time step-size in Newmark’s scheme. Numerical results are given in Fig.4, with the meaning: - Φv : the dynamic amplification factor of the midspan vertical deflection; - ΦM : the dynamic amplification factor of the midspan bending moment; - Φσ : the dynamic amplification factor of the midspan stay; The two cases of massless moving loads ( λ/µ=0) and moving loads with mass ( λ/µ 0) were examined. It can be observed the influence of the moving load mass on the stress and displacement amplification, particularly at high speed. References. [1]. [2]. [3]. [4]. [5]. [6].
Troitsky, M.S. (1977). Cable - Stayed Bridges . Crosby Lockwood Staples, London. Gimsing, N.J. (1983). Cable supported bridges. Wiley Interscience. Como, M., Grimaldi, A., and Maceri, F. (1985). "Statical Behaviour of Long-Span CableStayed Bridges". Int. J. Solids and Struct., 21(8), 831-850. Bruno, D., and Grimaldi, A. (1985). "Nonlinear Behaviour of Long-Span Cable-Stayed Bridges". Meccanica, Vol. 20, N. 4, 303-313. Bruno D. (1985). "On the dynamical behaviour of long-span cablestayed bridges under moving loads, Costruzioni Metalliche, N. 2. Bruno, D., Maceri, F., and Leonardi, A. (1987). "On the Nonlinear Dynamics of CableStayed Bridges". Procs. Int. Conf. on Cable-Stayed Bridges, Bangkok, Thailand, 529-544.
4
δ
M ID S P A N V E R T IC A L D E F L E C T IO N
M ID S P A N T O R S IO N A L R O T A T IO N
Θ
m
p
Θ /µ
δ 10 3 Lc
ε
= 0 .1 = 0 .2
ε ε
τ =0
5
.0
" H " -s h a p e d to w e rs
= 0 .3
τ
1
=0.
τ = 0 .0
5
" A " -s h a p e d to w e rs ( b /H = 0 .1 )
τ p g
1
a n a ly tic a l n u m e ric a l
Fig.3. Statical analysis :Flexsural and Torsional deformations
a
p g
1
= 0 .1
a n a ly tic a l n u m e ric a l
5
Φ
Φ
V
V
1.6
1.6 1.5 1.4
L 2H =2.5 l =5/3 H
6 σ E =7200/2.1x10 K g =50
1.5
a
1.4 1.3
1.3 1.2 1.1
L 2H =2.5 l H =5/3
6 σ E =7200/2.1x10 K g =50 a
1.2
p/g=1 a =0.10
λ/µ=1
λ/µ=0.5
1.1 1.0
1.0 λ/µ=0 10 20
Φ
p/g=0.5 a =0.10
30
40
λ/µ=0 50
60
70
80
10 20 30 40 50 60 70 80 90 c(m/s)
90 c(m/s)
M
1.6 1.5 1.4
L 2H =2.5 l =5/3 H
6 σ E =7200/2.1x10 K g =50 a
Φ
M
1.5
1.3
1.4
λ/µ=1
1.2
1.3
1.1
1.2
1.0 0.9
1.0
p/g=1 a =0.10
0.8
0.9
λ/µ=0
0.7
0.8 0.1
0.1
1.1
L =2.5 2H l H =5/3
p/g=0.5 a =0.10
λ µ=0
10 20 30 40 50 60 70 80 90
10 20 30 40 50 60 70 80 90 c(m/s)
Φσ
λ µ=0.5
1.1
Φσ
ο
6 σa E =7200/2.1x10
L =2.5 2H
1.1
K =50 g
l H =5/3
C (m/s)
6 σa E =7200/2.1x10
K =50 g
λ µ=1
λ µ=0.5 1.0
1.0 λ µ=0
p/g=1 a =0.10
0.9
10
20
λ µ=0
30
40
50
60
p/g=0.5 a =0.10
0.9
70
80
90
c (m/s)
10
20
30
40
50
60
70
80
90
c (m/s)
Fig. 4. Dynamical analysis of the bridge under moving loads (λ/µ=0 : massless moving loads) 6
Active Tendon Actuators for Cable-Stayed Bridge Claude DUMOULIN Civil Engineer Bouygues Travaux Publics St Quentin en Y., France
Summary Presented in this paper are the most recent numerical and experimental studies performed by the partners of a European research project, partly funded by the European Commission, which aimed at the development of Active Control Actuators for Cable-Stayed Bridge. This project is concerned with the use of active control, and more precisely active tendon control, in order to reduce induced vibrations of cable-supported structures. Such studies include development of innovative materials and techniques, numerical models of actuators and structures, manufacturing and testing of prototypes and mock-ups. At the present stage the performance requirements of the innovative actuators have been defined, the actuators and the mock-up have been constructed.
Introduction Improvements in materials have led to the construction of progressively longer, structurally more efficient and slender bridges. But consequently, structures are more and more flexible. The mitigation of deck and cable vibrations has become a major issue in cable-stayed bridge design. The increasing span length of bridges makes them more sensitive to flutter instability as well as to wind and live load induced vibrations. This project is concerned with the use of active control, and more precisely active tendon control, in order to reduce induced vibrations of cable-supported structures. The objective is not to minimise the transverse vibrations of the cables alone. Many passive damping devices have already been developed and used, especially dashpot dampers, systems of cable ties and viscous-elastic systems. These devices will be cheaper than active control systems for a long time. The main objective is to reduce the vibrations of the whole structure. In other terms, the aim is to increase the equivalent damping of cablesupported structures, which have a poor structural damping. Typically, the damping ratio, which is the ratio of the given damping to the critical value, is often lower than one percent. Furthermore, the damping (of the odd modes) of the cables will also be obtained. The proposed technology uses a control strategy developed by the Active Structures Laboratory of Université Libre de Bruxelles, a partner of the consortium. The control strategy is based on a force sensor co-located with the active tendon actuator. The basic principle of the active control is to force
the dynamic tension of the cable to produce a work by moving an anchorage according to the variation of the tension measured at the same anchorage. Stability is guaranteed, even at the parametric resonance. Numerical results have been confirmed in laboratory by experiments. An active damping ratio has been obtained, which is superior to previously published results. In spite of the strong nonlinearity of the cables, an approximate linear design method has been developed. The technique has a strong physical support; it allows prediction of the closed-loop poles with a root-locus technique. Simulations have confirmed the effectiveness of this method.
Figure 1 - Basic principle of active damping The aim of this project is to implement this laboratory development with complex civil structures. The key problem is the actuator. The ambition is to limit the number of active devices needed for the active control of a structure. Magnetostrictive actuators may provide a very innovative but unexplored solution. An alternative more classical hydraulic actuator will also be studied. The project requires activity on the following topics: • Definition of performance requirements for selected cable-supported structures and, consequently, performance needs for the innovative active control system elements. • Development of the computer simulation and the innovative active control system. • Development of improved materials, functional mechanisms, geometry, operational simplicity and life of the actuators. • Design and manufacture of actuator prototypes, including the actuator itself and the improvement of the cable needed to cope with the movement induced by the actuator stroke. • Design and manufacture of suitable mock-up structures. • Development of specific test techniques and execution of experimental analysis of the actuator prototypes. • Development of numerical models of the devices and mock-up and validation of such models based on numerical analysis of test results or available measurements of existing structures.
• Development of numerical models (integrating those previously defined and validated) and execution of detailed numerical analysis of structures to be built or retrofitted by means of the innovative active control systems, in order to improve the design of such structures. • Development of active damping and control algorithms. The partners involved in the project can cover all the relevant aspects required for a fruitful co-operation because they include R&D performers, designers of structures, manufacturers of devices, testing laboratories and end-users. They are listed in alphabetical order, with specification of their main functions relevant to the project: Bouygues Defence Evaluation and Research Agency Johs.Holt Joint Research Centre of EC – Ispra Mannesmann Rexroth Newlands Technology Technische Universität Dresden Université Libre de Bruxelles VSL
(FR) (GB) (NO) (EC) (DE) (GB) (DE) (BE) (FR)
designer of structures & end-user R&D performer designer of structures testing laboratory manufacturer of devices manufacturer of devices R&D performer R&D performer manufacturer of devices
The research is partly funded by the European Commission under the Brite-EuRam programme (Contract N°BRPR-CT97-0402, project ACE). The author as co-ordinator of the ACE project, gratefully acknowledge the contributions of the other partners of the Consortium.
Definition of performance requirements for the active control system The preliminary requirements concerning typical values for active tendons located on the main cables of a cable-stayed bridge exhibit high forces and large strokes. Hydraulic actuators could cope with these, but not magnetostrictive actuators. Three governing loads have been identified as acting on the main stay cables: a) static loads, mainly dead loads that could be considered as constant values versus time, b) quasi-static loads, variable values at low frequency, mainly thermal action or wind average value, c) and the dynamic loads, due to vibration behaviour. In order to eliminate the need of high forces induced by active tendon control on the main stay cables, an alternative solution was proposed based on the use of active tendon control on additional cable ties. This solution will drastically reduce the required static load, but would perhaps increase the actuator stroke. From a structural engineering point of view, the initial solution will both mitigate the induced cable vibrations and increase the deck structural damping while the alternative solution would only mitigate the cable vibrations. Both solutions have their field of interest in bridge design; the initial becomes very promising for long span bridges where the need of structural damping is tremendous. As explained previously, the use of active control to mitigate transverse cable vibrations is not an economic solution in civil engineering. The aim of using the alternative solution in the project is to be able to test the magnetostrictive actuators with the same mock-up as the hydraulic actuators. The ambition is
to demonstrate that the proposed magnetostrictive actuator is able to damp a substructure within industrial constraints. This also allows the use of only one mock-up, but consequently as large and sophisticated as possible, only limited by the capabilities of the test laboratory. At the end of the tests, having more information about the real behaviour of the system and better specifications, an application field has to be found. The proposed magnetostrictive devices will be the biggest units ever built in Europe. If the estimated stroke is lower than expected (and by security, the specifications have been pessimistic), applications where static loads are low could be a typical application field. Cables have to cope mainly with static forces and partly with quasi-static and dynamic loads. The active control strategy aims at the dynamic loads; the maximum of dynamic load should not exceed one tenth of the static load. Civil engineers have many difficulties to obtain specific dynamic values needed for active control requirements, the dynamic approach being very poor from this point of view regarding classical structure design. Nevertheless, part of real structures composed of cables with boundary conditions simulating parametric excitations have shown that the dynamic value is lower than one tenth of the static load. The main experience came from the laboratory experiments carried out by Université Libre de Bruxelles. The results were also extrapolated to the large-scale mock-up to be tested. Initial solutions for the bridge mock-up, i.e. active tendon on the main stay cables: • stroke : ± 5/10 cm • static force : 150 kN • frequency : ≤ 5 Hz • dynamic force : 1/10 of static force • maximum velocity : 30 cm/s Alternative solution for the bridge mock-up, i.e. active tendon on the tie cable: • stroke : ± 5 cm • static force : 5 kN • frequency : ≤ 5 Hz • maximum velocity : 30 cm/s With respect to the high share of static loads, a separate passive device should cover this in order to minimise the power consumption of the actuator system. It was decided to realise a hydraulic compensation of static load because the force level can be adapted easily to quasi-static changes. The pressure chambers of the static and the dynamic actuator part can be integrated into one unit.
Active Control Strategy and Actuator Design The Integral Force Feedback has been clearly identified as a suitable solution for the control strategy of a cable structure. In addition to a guaranteed stability and a good active damping ratio, this technique offers the big advantage to require neither a precise definition of the phenomenon inducing the vibrations nor a precise definition of the structure subjected to the vibrations. The whole information is only extracted from a good measurement of the tension. This remark is very important. Generally all the passive damping devices are tuned on theoretical simulation results, which can be partly far from the real world, and fit only with previous predefined scenarios. In some cases, a part of the filtered energy is transferred onto other vibration modes (spillover). Finally, these devices do not take into account the
ageing process of the structure components, and consequently the variation in time of the structure behaviour. More information could be find in a paper submitted to this conference by the consortium involved in the project. Mathematical models of the actuators and local control strategies have been developed with the view to be incorporated into the structural dynamics code for the complete model of the control system. Control algorithms have been developed and tested against the computer model and calibrated from experimental laboratory results.
The demonstrator The design of the demonstrator has followed several objectives: • • • • •
To have a mock-up as large as possible: the length about 30 m is only limited by the allowable space in the test laboratory, To use industrial cables and components: strand .5” and the smallest industrial anchorage, To be able to create the worst cases i.e. accordance between cables and structure frequencies (in some cases, the first torsion frequency very close to the first bending frequency very close to the first frequency of the longest cable), To obtain natural frequencies as low as possible in order to be as close as possible of the frequencies of large real structures, To obtain during the tests large amplitude vibrations as well for the cables as for the structure.
The deck, about 30 meters long (which is certainly the largest mock-up equipped with active tendons ever built), is mainly composed of two HEB500 beams whose axis are 3.00 meters spaced. These two H-beams are transversely linked each 3.50 meters by UAP150 beams, welded on the upper and lower flanges of the main beams, in order to bring to the whole structure enough transverse stiffness to avoid all buckling risks and to increase torsion stiffness. A secondary transverse bracing has been added to increase the transverse stiffness. Each H-beam is fixed on a stiff vertical wall in the laboratory, generally used as a Reaction Wall for PsD analysis. At the free end of the deck, the two main H-beams are connected transversely by a HEB400 beam (instead of two UAP 150 beams), which can be used as support for the excitation source. Four pairs of parallel stay cables support the deck. Along the longitudinal axis of the mock-up, the spacing between consecutive anchor heads is 7 meters. Transversely, two stay-cables of a same pair are 2 meters spaced. Each stay-cable is composed of one .5” strand, with a slope of 1/3 (vertical versus horizontal). This slope is very close to that of the longest stay cable of modern cable stayed bridges. The upper anchor head (dead end) is linked on the Reaction Wall. The lower anchor head is fixed on a strut composed of two UAP150 welded between the web plates of the main H-beams and allowing enough space (80 mm) for the strand. Each lower anchor head (stressing end) is equipped with a ring nut allowing a precise adjustment of the length of the stay cable. Subject to assumption that the initial stressing is carried out with a good precision, an adjustment capability of 50 mm would be more than enough. The two hydraulic actuators are located behind the lower anchor heads, on the first or the second pairs of the longest cables.
The first natural frequency of the two longest pairs of cables is higher than 4 Hz if the cables are not overloaded. In order to obtain a frequency of about 1.2 Hz for the longest cable, it is necessary to increase the distributed mass of this cable. A computation exhibits a value close to 15 kg/m. The requested mass will be obtained by fixing additional lead masses regularly spaced on the cables (7kg per mass). It turns out that, with this dead load weight, the sag of the longest cables will just be lower than the hundredth of their length. This relative sag value is close to that obtained with the longest stay cables of Pont de Normandie, before the erection of the secondary tie cables. This was not the initial objective, but only the consequence of the need to obtain a defined frequency. It can be frequently read in the literature that the most dangerous parametric excitation for cables is obtained for an excitation frequency 2f1, where f1 is the first in-plane natural frequency of the cable. In fact, a detailed analysis shows that the area of instability correspond to frequencies of parametric excitation close to 2f1/k, where k is any positive integer. Our computations show that, when the static sag is sufficient – the hundredth of the length is large enough – oscillation amplitudes at least as large with an excitation frequency f1 than 2f1 can be obtained. Moreover, the response to an excitation frequency f1 is very quick while the response to an excitation frequency 2f1 is long to take place.
Figure 2 – Demonstrator sketch Let us call H1 and H2 the shortest cables and H3 and H4 the longest ones. H1 and H2 do not need additional masses. The mass of the cable is close to 13 kg/m for H3 and close to 15 kg/m for H4. Then the first three natural frequencies of the structure are: 1.17 Hz for the first vertical bending mode, 1.27 Hz for the first torsion mode and 3.00 Hz for the first transverse mode. The structure has been stiffened versus the transverse effects.
Taking into account the discriminating tuning devices planned for the anchor heads of H3 and H4, the following situations can be obtained: 1. Regarding the test with a vertical excitation frequency of 1.17 Hz: the first in-plane natural frequency equal to 1.17 Hz (k=2) for H4 and equal to 1.75 Hz (k=3) for H3. 2. Regarding the test with a torsion excitation frequency of 1.27 Hz: a first in-plane natural frequency equal to 1.27 Hz (k=2) for H4. A good coupling between the in-plane and out-ofplane frequencies for H4 could be obtained. Each point of H4 will then describe an ellipse. Positioning an intermediate support under the deck, between H1 and H2, the first natural frequency of the whole structure can be doubled. Then a parametric excitation at the frequency 2f1 (k=1) for H4 can be obtained. Selecting the appropriate position for the intermediate support, one can finally tune the first vertical natural frequency of the structure in a manner it corresponds to any excitation frequency of the cables. Finally as it has been designed, the mock-up offers us a large scope of experiments. More than a scaled bridge, the mock-up has to be seen as a demonstrator allowing the test of the efficiency of the active control system in the worst conditions that can be faced by real structures. The tests on the demonstrator will start on spring 1999. The main objectives are to validate the active control system on a structure of a larger scale than the initial small-scaled laboratory mock-up and with industrial components. Then it could be possible to extrapolate to real structures. More information could be find in a paper submitted to this conference by the consortium involved in the project.
Numerical analysis Cable-supported structures become more and more large and flexible. The convenient assumption of a linear behaviour, as well regarding static or dynamic analysis, becomes less and less acceptable. A linear elasticity assumption remains applicable to the constitutive materials of the structures, but the displacements have to be taken into account in the equations of equilibrium, including geometric nonlinearity. Computations are then carried out using iterative methods which, although they present no theoretical difficulties, are however computation time consuming because the structure is assembled at each iteration (or at each time step in dynamic analysis). It is therefore very worthwhile to have the use of finite elements of high accuracy allowing computations with the minimum number of nodes compatible with the requested accuracy. Bouygues has developed a cable finite element model of high accuracy. For all static structural analyses, it is convenient to use only one single innovative cable finite element, whatever its length. A very specific and unusual method has been developed for dynamic analyses. The accuracy is so good that to obtain the first k th in-plane or out-of-plane natural frequencies with an accuracy better than 0.3 percent, only 2k innovative finite elements are required to model the cable, which gives a saving higher than six times that obtained via modelling using classical truss elements. Regarding a step by step integration dynamic analysis of a cable subjected to support excitation, for instance a parametric excitation, a reduction by six in the number of finite elements leads to a reduction in computation time by a factor higher than 100.
The objective is to validate this numerical tool with the experimental tests in order to have a predictive tool for the design of real structures.
Preliminary Results Numerical simulations carried out on the demonstrator with only one pair of cables equipped with actuators exhibit an equivalent viscous damping ratio between 15 to 25 percent of critical damping regarding the first vertical bending and torsion modes of the structure. The stroke of the actuators is about some ten thousandth of the cable length. If the experiment confirms this preliminary result, the number of actuators needed for a long span cable-stayed bridge in order to obtain enough damping (around 5 to 8 percent) will be low versus the total number of stay-cables.
Conclusion The research on Active Tendon Actuators for Cable-Stayed Bridge nearly reached its mid-way. Even if there is a lot of work and testing to be completed, the preliminary results are very promising. There are several interesting aspects that have put in evidence and will be deeper investigated. Particularly important is the capability to increase the structural damping which is quite mandatory for future long span bridges.
References [1].
Preumont A., Helduser S., Foersterling H., Bartlett P., 1999, “Active Tendon control of CableStayed Bridges: Control Strategy and Actuator Design”, IABSE conference on Cable-Stayed Bridges – Past, Present and Future, Malmö
[2].
Magonette G., Bournand Y., Hansvold C., Jenner A., 1999, “Experimental Analysis on a Large Scaled Cable-Stayed Mock-Up”, IABSE conference on Cable-Stayed Bridges – Past, Present and Future, Malmö
[3].
Preumont A., Achkire Y., 1996, “Active tendon control of cable-stayed bridges”, Earthquake Engineering and Structural Dynamics
[4].
Preumont A., Achkire Y., 1996, “Active damping of cable structures”, ESA Conf. on Spacecraft Structures and Materials, Noordwijk, 27-29 march 1996.
Stay Adjustment: From Design Perspective to On Site Practice
Michel MARCHETTI Managing Director Formule Informatique Paris, France
Benoit LECINQ Project Manager SETRA Paris, France
Born 1950, graduate from Ecole Polytechnique and Ecole Nationale des Ponts et Chaussées, Paris
1.
Born 1970, graduate from Ecole Polytechnique, Paris, Ingénieur des Ponts et Chaussées
Introduction
Stay adjustment is a major topic in cable-stayed bridge construction. As a matter of fact, this issue, which directly controls the stress distribution in the structure as well as the final geometry, concerns both analyses during detailed design and tensioning procedures during erection on site. More precisely, from the designer's perspective, adjusting stays consists in finding the suitable sequence of tensioning operations, so that stresses in stays and structure remain allowable during construction stages and during operations. For the site engineer, stay adjustment refers to the actions to be carried out during the construction process, in order to build a structure, which fulfills the theoretical requirements specified by the design. Experience shows that there exist a great variety of approaches to characterize and determine stay adjustment at the design level and to perform it on site. The purpose of this paper is to revisit the subject of stay adjustment, both from a theoretical and a practical perspective. We introduce a few innovative concepts, which enable to tackle this problem efficiently with specialized computer software, while taking into account technological constraints.
2.
Stay adjustment from designer's perspective
2.1. Objectives The basic design of a cable-stayed bridge deals with the general layout (height and position of the pylons, other piers, etc.) and yields a tentative cross-section of deck and pylons. Thereafter, detailed design firstly defines the arrangement and sectional areas of the cable stays, then shall find out when and how each stay must be stressed. The sequence of tensioning operations must fulfill several targets: • Practicability of stay installation and construction simplicity. From this standpoint, the ideal solution would be to stress each stay in a single step, at the time when it is installed.
1
• Structural design objectives (acceptable stresses in structure and stays during erection phases and after completion). Ideally, re-adjusting stays at different stages would make it possible to reduce bending stresses in the structure almost to zero, as erection proceeds. In many cases, the trade-off between these opposite objectives is to tension stays in two steps: firstly at installation, then just prior to finishing completion. In some projects, a global retensioning operation is required after a few years of bridge operation, in order to compensate for creep effects. 2.2. Final stage stay tensions Usually, the search for an adjustment solution starts from the final erection stage, just after bridge completion. Several solutions have been proposed in the literature, some of them involving sophisticated numerical analysis techniques, such as multicriterion optimization. These methods are beyond the scope of this article, but we simply give a hint of a possible one. As many cable-stayed bridges designed nowadays have a very slender deck, stay tensions are roughly determined by the so-called pendulum method, i.e. stay tensions balance the deck dead weight. This rule yields a tentative stay cross-sectional area. Then, the search for an optimal adjustment of the stay system can be achieved by using an iterative process that considers pylon and deck deflections, rather than stay tensions: 1. Stays being introduced without any pre-loading, the completed bridge is loaded with its permanent loads. A significant vertical deflection will happen. 2. Thereafter, stay lengths must be shortened, in order to correct vertical deflection and to recover the target profile of the deck. 2.3. Search for an adjustment solution Once the set of tensions at bridge completion has been selected, the tensioning sequence must be defined. Usually a stage by stage structural software is used to simulate bridge construction. In the framework of such a program, the installation of a stay is idealized by activating a new bar or cable finite element. For the design engineer, adjusting the stay at this stage consists in imposing an appropriate initial condition to the related element. According to his habits and to the software used, the initial condition modeling stay installation may be expressed, either by imposing the value T of the tension that must exist in the element ∆l of the distortion applied to the element or just after assembly, or by imposing the value ε = l to assembly. In the same way, retensioning of an already installed stay may be characterized, either by B B increasing the stay tension with an increment ∆T to the current tension, or T by shortening the current length with an additional strain ∆ε. o
A
In practice, the search for a solution is carried out using a trial and error b) Using imposed distorsion a) Using tension value T method: a tensioning sequence of one, after assemby prior to assembly two or more tensioning steps is Fig. 1 : stay adjustment definition proposed. Then, an analysis of all the construction stages is performed in order to verify if stresses remain allowable in the structure. The tensioning forces to be applied and the number of steps are refined, until a satisfactory solution is reached. 2
2.4. The dismantling procedure The previous task requires computing current stay tensions at any erection stage. A very popular approach often used in practice is the dismantling procedure. The basic idea is very simple: starting from a well-defined condition - e.g. the completed bridge under permanent loading - the sequence of elementary operations corresponding to the actual construction stages is performed step by step backwards. This reverse analysis enables for example to determine the value of the tension T to be applied to a newly installed stay, in order to reach the desired state at completion. However popular, stay adjustment using the dismantling method remains a tedious task, as it requires the reverse description and analysis of the complete erection sequence, from finished deck with equipment back to the dismantling of the first segment. Moreover, it is important to notice that the dismantling procedure cannot take into account time dependent effects such as creep or shrinkage, as the corresponding models implemented in structural software generally only consider construction sequences by increasing time. Hence, a simpler and more efficient procedure to determine the suitable values of the adjustment parameters shall be used. Before tackling this issue, we will firstly review a few possible means used to characterize stay adjustment.
3.
Parameters for stay adjustment characterization
3.1. Stay adjustment defined by permanent tension values In theory, the structural state of the bridge under permanent loading could be entirely defined by the set of stay T1 tensions, as it is possible to derive from this data internal forces in pylons and T i (N,V,M) R1 deck, as well as the related deflection T1 R2 profiles (Fig. 2). Unfortunately, due to Ti accuracy issues, this approach cannot be used in practice to characterize stay adjustment at permanent stage.
T
n
R
(N,V,M)
Fig. 2 : forces in deck and pylon deduced from stay An illustration is given by the analysis of re-tensioning operations to be carried tension values out on the Vasco de Gama Bridge in Lisbon. The computations have shown that the deck central span could be lifted by more than 0.60 meters without inducing a change of more than 3% in the permanent tension values. This result may be surprising, but it is clearly explained by the fact that stay tensions must balance under any circumstance the deck dead weight, due to the extreme flexibility of deck over the central span length. We shall recall that the accuracy of well calibrated jacks or tensioning cells only reaches 2 %. Hence, a practical consequence is that the actual state of a bridge cannot be experimentally evaluated by measuring the stay tensions only. Therefore, a geometrical monitoring of the bridge is required to reliably keep track of the structure evolution with time.
3
3
3.2. Stay adjustment defined by stressing force In this section, a stay is implicitly assimilated to a cable installed and stressed with a force T in a single step. From this standpoint, the installation of a stay may be split into two elementary actions: • firstly, application to the anchorages of two equal forces T with opposite B B T T directions, (EA) • then, assembly to the structure of a T T pin-jointed structural element displaying an initial tension T, and A A an axial stiffness EA. a) Forces T applied
b) Assembly of a new element
Such a description is especially suited to anchorages with initial tension T to a conventional linear stage by stage analysis, in which internal forces are determined by summing up the effects Fig. 3 : model of a stay as a finite element of each elementary action occurring from the beginning of the construction.
However, the use of the stressing force T as a parameter to represent stay adjustment suffers a severe drawback: the stressing force is not an intrinsic characterization of stay pre-loading. Indeed, stressing a stay with the same force T in presence or in absence of temporary loads, such as a mobile crane, will not yield the same tension in the stay at bridge completion. This gives rise to tedious constraints in current practice. For example, any modification in carriage weight during design requires resuming the computation of all the stressing forces, to reach the same state at the end of construction. 3.3. Stay adjustment defined by unstressed length l0 The previous two paragraphs have shown that stay adjustment must be characterized by an intrinsic parameter, i.e. a parameter that is independent on the construction sequence and on temporary loads. Moreover, a good analysis method should enable one to determine the forces in each section without having to sum up the effects of each elementary action occurring during the construction history. Stay adjustment can be achieved by assembling a cable element with a proper initial length l0 smaller than the distance l between anchorages in the reference geometry described in the model. In the literature, l0 is referred as the cable unstressed length (or cable neutral length). The unstressed length of a stay - which can be seen as the length of the cable when it is lain on a flat support, without any tension - is clearly an intrinsic parameter. 3.4. Stay adjustment defined by a pre-deformation The value of the unstressed cable length l0 has a valuable meaning only when compared to the distance l between anchorage nodes in the model theoretical geometry. Therefore, the dimensionless parameter ε, referred to as pre-deformation, which is nothing else than a strain pre-loading, is often preferred: ∆l l − l 0 ε= = l l In most cable-stayed bridges, the value of this parameter ε related to a completed bridge under permanent loading, ranges between 2.5×10-3 and 3.5×10-3.
4
The unstressed length l0 and ε are intrinsic parameters. If the mobile carriage weight changes during the design, these values, that describe the adopted stay adjustment, are not impacted. Of course, there remains to check that the new weight values still produces allowable stresses. 3.5. Stay adjustment defined by reference tension The reference tension notion was introduced in order to dispose of a common means for characterizing stay adjustment both from designer and contractor perspectives. As l0 and ε, the reference tension constitutes an intrinsic parameter, which in addition is extensive. The reference tension Tref of a stay at temperature θref is defined as the tension that would exist in the stay, if the structure deformations were frozen, i.e. if the displacements of the anchorages were prevented. We shall see later that, with this definition, the actual stay tension value T may be seen as the reference tension value modified by the effect of anchorage displacements and temperature variation. If linear behavior is assumed, the reference tension value is directly derived from the predeformation value ε by multiplying it by the axial stiffness EA: Tref = EAε
4.
Adjustment instructions for on site operations: current practice
4.1. Link between designer and site engineer: use of stressing force Most often, the adjustment instructions supplied by the designer to the site engineer are expressed in terms of stressing force to be applied to stay anchorage at given construction stages. If the complete stay is placed in one single stage before being stressed, the theoretical force value can be used straightforwardly, provided that the actual site conditions are very similar to those taken into account in the design. 4.2. Limitations due to actual site conditions However, such an ideal situation is seldom met in practice, because structure and stay temperatures, as well as site loads, always differ from those taken into account during the design. A current practice consists in determining the tensioning force value by updating the computational model with values measured on site just before stressing operations. However, this method is not very flexible, as it imposes the stringent timing constraints of the construction site on the design office that runs the computational model. 4.3. Case of a flexible deck: use of vertical deflection If the deck is very flexible, a slight error ∆T in the tensioning force T produces a significant parasitic vertical displacement ∆w of the deck. In such a situation stays are adjusted by controlling the altitude of the deck, rather than the stressing force. However, the distinguishing between a flexible deck and a rigid one is often uneasy. In most cases, the deck segments close to the pylon constitute a stiff structure, and the deck becomes more flexible when cantilever length increases.
5
4.4. Use of unstressed cable length An alternative to using stressing force or vertical deflection would be to prepare the cable stays with their exact unstressed length, and to extend them to attach their two extremities to the structure.
o
This method is often used for prefabricated stays, installed in one stage only, but also applies to stays erected by threading strands one by one, provided each strand is cut or marked at the right length. However, two accuracy issues must temper this optimistic judgment:
f re
Theoretically at least, basing stay adjustment operations on unstressed cable length has several advantages: • actual loading conditions (temperature, site loads) do not impact anymore the adjustment values, • the same procedure applies both for rigid and flexible decks.
Reference geometry Structural elements to assembly ( with initial deformation )
Fig. 4 : stay adjustment using unstressed length l0
4.4.1. Accuracy on the cable length itself If the anchorages were perfectly located at their theoretical positions on deck and pylon, the accuracy of the adjustment would only depend upon the precision attached to the unstressed cable length l0. Experience shows that the best accuracy associated with the measurement of the distance between two marks drawn on a cable is of the order of 10 mm per 100 meters. Such an uncertainty in length measurement is only a relative error of 0.01 / 100 = 10-4 which may seem fairly good. However, in cable-stayed bridges, permanent strain usually ranges between 2.5×10-3 and 3.5×10-3. Hence, the elongation of a 100 meter long stay is in the order of 0.3 meters, and the relative error on the actual pre-deformation ε, i.e. the precision of stay tension adjustment, is not better than 0.01 / 0.3 = 3.3 %. 4.4.2. Accuracy on the anchorage position The accuracy related to anchorage location has a similar effect on adjustment precision. For concrete decks cast in situ, the anchorage position is generally set by the mobile carriage. Hence, anchorages are generally located with a tolerance reaching several centimeters. In such cases, using unstressed cable length l0 as the adjustment parameter would result in poor quality (about 10 to 20%).
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Ti Ti 1
As a consequence, inaccuracy on the unstressed length of a stay (i) gives rise to significant variations about nominal values in the stay tension Ti itself, but also in the neighboring stay tensions Ti-1 and Ti+1, as well as bending stresses in the deck.
Ti
Ti 1
V
Ti
V
4.4.3. Impact on tension distribution We have said earlier that cable-stayed decks are very flexible beams when considered over the central span length. This no more the case when a short block of deck or pylon is observed locally.
Ti
1
Ti 1
Fig. 5 : stay tensions differ locally, due to deck When anchorage location cannot be bending stiffness controlled with a precision of some millimeters, unstressed cable length l0 does not constitute a suitable adjustment parameter for practical purposes. Other methods must be derived, in order to cope more efficiently with the unavoidable construction tolerances. However, the unstressed length l0 remains a valuable parameter to crosscheck the adjustment data supplied by other methods.
5.
Site procedure organization
5.1. Global scheme Stay adjustment is only one topic in the field of the survey procedures carried out during the construction of a cable-stayed bridge. Before addressing the details of a proposed stay adjustment method, we shall present the general layout of these procedures. First of all, adjustment and verification procedures must be clearly distinguished. SITE PROCEDURES
Adjustement
Stay Pre-loading
Verification
Geometry
Pylon
Deck
5.1.1. Adjustment procedures Adjustment procedures are tightly connected to the erection operations on site. Their purpose is to provide the construction team with precise instructions for site operations, in order to build a structure that complies with design specifications. These procedures split into stay installation adjustment, on the one hand, and geometrical setting of deck and pylons, which must be built with the proper shape, on the other hand.
7
5.1.2. Verification procedures Verification procedures are meant to check that the actual structural behavior of the bridge, as erection proceeds, is in accordance with the predictions of the computational model. Therefore, survey and tension measurements are performed at times corresponding to design stages and the results are compared with their theoretical counterparts. 5.2. Control of deck geometry The procedures of geometrical setting of deck and pylon are beyond the scope of this paper. We shall merely recall that: • During cantilever erection, prefabricated segments or, in the case of a cast in situ deck, the mobile carriage, are positioned relatively to the part already built, rather than at an absolute altitude given by the model. This positioning in relative terms makes it possible to obtain an accurate profile despite various parasitic effects. • Furthermore, this positioning cannot be based on the actual concrete surface, which is subjected to construction tolerances in the order of centimeters. Consequently, one must consider an ideal theoretical profile line attached to the deck. Let ηi be the vertical offset between the theoretical profile line attached to the deck and a given benchmark (i) laid on the actual surface. The value ηi is a constant that must be determineded just after segment casting, using an appropriate procedure. Knowing these offsets η, the actual deck deflection values w at all the benchmarks can be derived from simple altitude measurements, with a very good precision.
6.
Reference line Z ref Zc
Theoretical profile
Actual deck surface
w η
Fig. 6 : vertical distance η between theoretical deck profile and actual deck surface: w = Zref - Zc - η
Stay adjustment procedure using the reference tension concept
6.1. Relating current tension to reference tension The reference tension concept is useful, as it is very easy to relate the current tension in a stay to the reference tension. If we assume that the stay behaves linearly, i.e. that catenary effect can be neglected, then the behavior of the stay, considered as a sub-system of the complete structure, is clearly given by the following formula: T = Tref +
EA & & & ( u B − u A ). i − EAα∆θ l
with the notation indicated on figure 7. The first term represents the effect of stay adjustment, the second is the effect of anchorage displacements and the last is the effect of stay temperature variation from θref. This formula is a very simple way to compute the current tension T at any construction stage, knowing anchorage displacements and stay temperature. In fact, considering the stay as a subsystem replaces the computation of the complete structure by simple survey and temperature measurements.
8
EA & & & ( u B − u A ). i + EAα∆θ = Tref l
B
EA
A
i
(∆θ)
o
T−
B
o
uB
6.2. Is the reference tension really intrinsic? As already said, the reference tension is, by definition, an intrinsic parameter to characterize stay adjustment (pre-loading) and it remains constant as long as no retention of the stay is performed. Conversely, the above formula can be reverted:
uA
and it is interesting to check "experimentally" on a A computational model that the first member is actually constant throughout construction stages, provided that Fig. 7 : stay cable considered as a no re-tension operation is performed on the considered sub-system of the complete structure & stay. Knowing T at any stage, the displacements u A & and u B , and ∆θ, one can determine the value of the reference tension Tref. 6.3. Application to stay tension adjustment For sake of presentation simplicity, a linear behavior is again assumed in this section. The vertical deflection of deck benchmarks can be determined from altitude measurements, using the procedure evoked in section 5.2. In the same way, a suitable monitoring of pylon enables to keep track of its horizontal deflection. This way, anchorage displacements about their position in reference geometry can be evaluated. If stay tension as well as stay temperature are measured on site, the actual value of the reference tension Tref,temp can be easily determined by formula given in section 6.2 and cross-checking is possible. Conversely, to reach the reference tension value Tref specified by design, the elongation ∆l to be applied to the end of the cable is derived as follows: ∆l =
(
l T − Tref ,temp EA ref
)
6.4. From principle to operational procedure In practice integrated computer software is used to assist the site engineer in each stay installation and re-tensioning operation. Such programs shall be tailored on a case by case basis to each project and erection sequence, but they all rely on the simple reference tension concept presented before, and no computation of the complete structure is necessary for adjustment purposes. Second order effects (catenary) are generally not negligible during the stay installation process. Therefore, a more sophisticated model based on a non-linear behavior of each stay must be used in practice for evaluating data related to adjustment operations. But the principle of stay adjustment operations remains the same. This method can be used for adjusting prefabricated stays placed in a single stage, as well as stays installed by threading strands one by one. In the latter case, the method is particularly adapted to the use of iso-tension technique. Then, the procedure comprises 5 operations: 1. evaluate by survey the anchorage displacements and compute the tension t0 to apply to the first strand in order to impose on the stay a given fraction of the target reference tension, for example 80 % of Tref, 2. insert the first strand and stress it to the tension t0, 9
3. insert all the other strands and stress them by comparison with the first strand, using isotension technique, 4. in a further step, measure the actual tension of the complete stay, and the related values of the anchorage displacements ; then deduce the elongation ∆l to apply to the stay to reach the final target value Tref, 5. perform a check by evaluating the actual value of the reference tension through simultaneous measurements of stay tension and anchorage displacements. Using a procedure based on the reference tension concept dramatically improves the flexibility and reliability of stay adjustment operations. Indeed, discrepancies between the actual site conditions (site loads, temperature) and their design counterparts have no influence on the final result. Adjustment accuracy is outstanding, as the method is not disturbed by tolerances on anchorage location. Finally, the method preserves the flexibility of site operations timing, as the integrated software used for this procedure is parallel and independent of the complete computational model, and because survey measurement periods, during which no site loading variation can occur, is very limited.
7.
Conclusion
The reference tension concept results from continuous progresses achieved by many engineers during the last decade to improve the way of characterizing stay adjustment in design models, as well as to simplify the adjustment operations on site. The method has been successfully used on major construction projects, such as the Elorn Bridge (France), the Second Severn Crossing (UK), or the Vasco de Gama Bridge (Portugal), thus clearly demonstrating the pertinence of adjustment procedures based on the reference tension concept.
8.
Bibliography
[1] AUBLANC P., AUGUSTIN V., BERTOCCHI C., DUFRESNE J.L., ENSELME J., MARCHETTI M., PLACIDI M., REDOULEZ P., REGALLET D., VASSORD J., Le nouveau pont sur l'Elorn à Brest. Revue TRAVAUX, n° 699, June 1994. [2] COMBAULT Jacques, HERVET Jean, VESVAL Vincent, Le second franchissement de l'estuaire de la Severn, Revue TRAVAUX, n° 719, April 1996. [3] GIMSING N. J., Cable Supported Bridges, Concept and Design, 1994, John Wiley & Sons. [4] MARCHETTI Michel, Dominique REGALET, Charles BERTOCCHI, Gérard HOCHET, Elorn Bridge Stay and Geometry Adjustment, Proc. Of the Int. Conference AIPC - FIP, Deauville, October 1994. [5] VIRLOGEUX Michel, Erection of Cable-Stayed Bridges, The Control of the Desired Geometry, Proc. Of the Int. Conference AIPC - FIP, Deauville, October 1994.
10
Damping Characteristics of Carbon Fiber Composite Cables for Application in Cable-Stayed Bridges H.M.EL KADY Associate Researcher National Research Center
Egypt
M. AROCKIASAMY Professor Florida Atlantic Univesity USA
S. SAMAAN Professor Cairo University Egypt
Y. BAHIE-ELDEEN ProfessorAssociate Cairo University Egypt
M. M. BAKHOUM ProfessorAssociate Cairo University Egypt
M.A.EL GAMMAL Professor National Research Center Egypt
Summary The unique properties of fiber composites such as high strength, light weight, flexibility, corrosion resistance, etc. make carbon FRP as an attractive alternative to conventional steel for application in many structures, including Cable Stayed Bridges (CSB). The paper presents the results of experimental and analytical studies on the loss factor of CFRP and prestressing steel tendons when subjected to out of-plane loading. Analytical approach is used to verify the experimental results, and extrapolated functions are given for different cable lengths. Finally, the damping ratio is obtained for a CSB cable including the initial prestress effect, and is expressed as a function of the loss factor.
Introduction High performance fiber-reinforced polymers (FRPs) have proved as outstanding engineering materials over the past few decades. Their cost has, however, limited the applications to the areas of aeronautics/astronautics. A rapidly changing market with decrease in fiber prices makes the FRP as an viable alternative to conventional structural steel used in civil engineering applications. Several structures in Germany are experimentally equipped with glass tendons as a replacement for steel post-tensioning cables. The combination of desirable mechanical and electrical properties make aramid guy wires an excellent choice for the staying of tall antennas. Also, the high resistance to chemicals makes FRPs clearly a superior choice for structures subjected to aggressive environments. The innovative use of fiber-reinforced polymer composites can lead to significant economy in the design of massive structures, since the higher specific strength (strength/mass density) of FRPs reduces the self-weight of structures; this becomes quite significant with increasing dimensions such as cable stayed bridges. Cable stayed bridges with main spans about 2000 m are at present beyond the limit of feasibility for steel. An ideal application of FRPs is in cables for long span cable-stayed bridges ( Kim and Meier, 1991). Little information is known on the response characteristics of CFRP cables subjected to dynamic loads. Further research on the dynamic properties of CFRP is required for application in CSB, as these CSB cables are usually subjected to wind induced vibrations.The paper presents the results
1
of experimental and analytical studies on the loss factor of CFRP and prestressing steel tendons when subjected to out of-plane loading. CFRP tendons with different lengths and diameters were subjected to forced vibrations using a hydraulic shaker and white noise (up to 20Khz) on the double cantilever system. Accelerations were measured using "piezoelectric accelerometers" and the data obtained through a Fast Fourier Transform (FFT) analyzer. Analysis is performed using both the half power band width, and the resonance dwell technique to obtain the loss factor of the specimens at different frequencies, the shape function, and the relation between loss factor and the ratio between acceleration at the cantilever tip to the support movement The results are presented as graphs expressing the relationship between the loss factor, length, and the eigenvalues of different mode shapes. Similar tests are being performed also on steel strands for CSB.
Experimental method The resonant dwell technique (Gibson, et al. 1982; Gibson and Plunket 1977; Paxson 1975) is used to determine the dynamic material properties of the CFRP tendons and steel cables. The technique has proven effective in determining the material damping of a variety of composite materials. The measured material properties are determined from an energy balance approach which assumes that the amount of energy supplied due to input acceleration at the base is subsequently dissipated or damped by the cantilever beam specimen material. Double cantilever beam specimens are excited with white noise in the frequency range of 0 to 20 kHz. A schematic of the measurement process and hardware and the details of the experimental setup are shown in Figs. 1 to 3.
Accelerom eters
Noise generator
Hydraulic shaker
Power am plifiers
Specimen Power supply FFT HP analyzer
Fig.1 : Schematic of the test apparatus for measurement of response of double cantilever specimens.
2
Fig.2: Hydraulic shaker, test specimen, accelerometers, and power supply
Fig. 3. FFT analyzer, noise generator, and power amplifiers Three different materials were tested in this study: aluminum, prestressing steel and CFRP tendons. The sectional and material properties are shown in Table 1. Spectrum of resonant frequencies were obtained for specimens with different lengths. Material Aluminum (T2024) P.S (Grade 270)
Nominal Area (mm2) Diameter (mm) 12.5 126.5
Elastic Modulus (Mpa) .9e5 2.056e5
Unit Weight (N/m) 3.345
12.5
93
CFRP
12.5
49/76*
2.13e5/1.37e5*
1.496
CFRP
9.91
35.6/ 55.7*
2.13e5/1.37e5*
1.092
* Effective / nominal properties
Table 1: Sectional and material properties of specimens.
3
7
E(Mpa)
Two control aluminum specimens are tested to check the calibration and accuracy of the experimental setup, and the equipment. The diameter of both the test specimens was 12.5mm and two different lengths of 0.5m and 0.4m were considered in the tests. Different mode shapes are considered and the elastic modulus calculated for both specimens at different frequencies. Fig.4 shows that the elastic modulus of aluminum specimen is independent of the frequency of excitation. 1 .0 0 E + 0 5 9 .0 0 E + 0 4 8 .0 0 E + 0 4 7 .0 0 E + 0 4 6 .0 0 E + 0 4 5 .0 0 E + 0 4 4 .0 0 E + 0 4 3 .0 0 E + 0 4 2 .0 0 E + 0 4 1 .0 0 E + 0 4
46
398
1150
2170
3584
F r e q .(H z)
Fig.4: Elastic modulus of aluminum specimen of length 0.4metres at different resonant frequencies. CFRP tendons of two different diameters of 12.5mm ,9.9mm and prestressing steel specimens of 12.5mm diameter are tested with three different lengths of 52 cm, 41 cm, and 31 cm. Modal frequencies are detected from the spectrum at the point on the tip of the cantilever beam specimens. Transfer function for the test specimens is recorded and the flexural rigidity (EI) calculated from different mode shapes for different samples and compared with the values specified by the manufacturer. The damping factor is calculated for different specimens, at various frequencies using two different methods: the well known half power band width and resonance dwell technique Fig.5 shows the loss factor against the parameter bl for 12.5mm prestressing steel and CFRP specimens with different lengths. The parameter bl is a dimensionless quantity in which “l” is the specimen length, and
1 0 ,9 0 ,8
Loss factor
0 ,7 0 ,6 0 ,5 0 ,4 0 ,3 0 ,2 0 ,1 0 0
5
10
15
20
bl
p .s 5 2 c m p .s 4 1 c m p .s 3 1 c m c fr p 5 2 c m c fr p 4 1 c m c fr p 3 1 c m
Fig.5:Loss factor for 12.5mm diameter CFRP and prestressing steel Specimens using half power band width method.
4
b4= wn2 m/ EI where wn = angular resonant frequency of n th mode.
Loss Factor
Fig.6 shows the loss factor at different frequencies for 9.99cm diameter CFRP tendons, with lengths of 52, and 41 cm.
0,5 0,45 0,4 0,35 0,3 0,25 0,2 0,15 0,1 0,05 0
cfrp 52 cm cfrp 41 cm
0
5
10
15
bl
Fig. 6: Loss factor for .99 cm diameter CFRP Specimens. Loss factor for longer specimen lengths by extrapolation The loss factor based on the limited number of tests and specimen lengths can be extrapolated from Figs.5 and 6 for applications to longer lengths as shown below: For CFRP tendons: The following polynomial can be derived: U=1.548x-1-15.579x-2+52.588x-3-10.294x-4-30.481x-5-27.308x-6-19.479x-7 For prestressing steel tendons: The polynomial given below can be obtained; U=1.69x-1-23.21x-2+106.376x-3-58.969x-4-81.984x-5 –57.935x-6-34.302x-7
Analytical model The equation of motion for lateral vibration of the undamped beam is applicable in the present support motion problem, because the only force acting on any section of the specimen is the internal elastic shear force associated with bending of the test specimens. A solution using separation of variables for harmonic motion at a resonant frequency is given by y(x,t)= Re {A1sinbl+ A2 cosbl +A3 sinhbl +A4 coshbl} eiwrt Boundary conditions At x=0:dy/dx(0,t)=0
(a)
md2y/d2t(0,t)=Re[Feiwt]-2V(0,t) (b) and at x=l : M(l,t)=0 (c) V(l,t)=Mad2y/d2t(l,t)
(d)
5
(1)
Substitution of the boundary conditions (a) to (d) in Eqn.(1) leads to the following frequency equation: (m+m cosbl coshbl +bM coshbl sinbl-bM cosbl sinhbl)=0
(2)
where M is the accelerometer's mass, m is the beam mass/unit length. The loss factor is obtained from the following relationship: A= atip/asup=y(l,t)/y(0,t)
(3)
and can be derived as A ={(2(m Cos[b(1-Iu/4) l] +2 M b(1 - I u/4) Cosh[b(1 - I u/4) l] + mCos[2 b(1 - I u/4)l] - 2 b(1 Iu/4) M Cos[b(1-Iu/4) l]Cosh[b(1-Iu/4) l] -mSin[b(1-I u/4) l] +m Cosh[2 b(1-Iu/4) l] Sin[b(1Iu/4) l] +2bMCosh[b(1-Iu/4)l]Sin[2b(1 -I u/4) l] +2 mSinh[b(1- Iu/4) l] -mSin[2 b(1 - Iu/4) l] + mCos[b(1-I u/4) l] Sinh[2b(1–Iu/4) l]}/{(4(m +mCos[b(1-Iu/4) l] Cosh[b(1- Iu/4)l] + b(1 – Iu/4) M Cosh[b(1-Iu/4) l] Sin[b(1 - I u/4)l] -b(1-I u/4) MCos[b(1-Iu/4) l]Sinh[b(1-Iu/4) l] } (4) where: A=tip displacement/base displacement. u=loss factor. I=-1^.5 Eqn. 4 is solved numerically for different resonance frequencies to obtain the equivalent loss factors.
Estimation of damping ratio for steel and CFRP CSB cables including the effect of initial prestress Prestressed steel and CFRP cables with different lengths of 465,622,933 meters are considered having cross sectional area of 0.015 sq.m and are discretized with 100 elements in order to analyze the effect of initial prestressing forces on the damping ratio, and logarithmic decrement of one of the a typical individual CSB cable. The steel cables are prestressed with a value of 0.45 times the ultimate stress (1912 Mpa), while CFRP cables are prestressed to 0.3 times the ultimate stress (2118Mpa). Applying the energy principle, the total modal potential energy Un can be defined in terms of two parts: modal strain energy, Vn and potential energy due to initial prestress, Utn. The following formulae can be derived based on the equations given in Ref.[1] Un=Vn+Utn ζ= .5 µ Vn / (Vn+Utn) Utn = Σ .5 A σ (tan2 θ )s Where: A = the cable cross sectional area, σ = the initial prestress, θ = the element angle of rotation, s = element length. 6
ζ = damping ratio Vn = Σ0.5 E A ε2 s Where E = Young’s modulus, ε = the dynamic axial strain. = tan2 θ + 0.5 tan θ tan τ and
τ is the static angle of the element.
Material Steel
CFRP
Horizontal Cable Sag ratio Strain energy ratio Proj.(metres) length (metres) 330 465 0.0026 0.01 440 622 0.0035 0.02 660 933 0.005 0.05 330 440 660
465 622 933
0.001 0.0015 0.0022
Damping ratio
.005µ .01µ .025µ
0.002 .001µ 0.004 .002µ 0.01 .005µ
Table 2: Damping ratio for CFRP and PS cables as a function of loss factor. Table (2) shows the results obtained from the static and dynamic modal analyses of the cables with a 45 degree inclination (cross sectional area=0.015 sq.m). The damping ratio in terms of the loss factor for steel cables is five times that of the CFRP cables. Loss factors for prestress steel, and CFRP are estimated from curves (Fig.5), and is found to be almost constant for such long cables with low fundamental frequencies. The loss factor is 0.04, and 0.05 for steel and CFRP cables respectively, the value for steel is in good agreement to previously published work [1]. Also the logarithmic decrement for the steel cables under study varied from 0.1% to 0.5%, which have the same order given in previous literature [1,2].
Results and Discussions Results obtained from the experiments are in close agreement with the analytical calculations by both methods: half power bandwidth, and the frequency equation and the difference in results from the two methods was about 7%. It is worth noticing that the effect of bonding material between the individual strands is very significant, especially in the low frequency modes. That leads to obviously higher loss factor at the lowest modes especially for the CFRP strands. The loss factor tends to remain constant at higher modes for both prestressing and CFRP tendons. The difference in the loss factor for both materials decreases at higher modes. The loss factor for the cables considered in this study is almost constant, and the loss factor of CFRP is higher than prestressing steel by about 25%. Finally, the damping ratio of steel is about four times that of CFRP.
7
Potential for future applications The potentials for successful application of CFRP cables in cable-stayed bridges are great due to its higher specific strength, and equivalent modulus, excellent corrosion and fatigue resistance. The CFRP cables are more viable for use in long span CSB due to the above mentioned characteristics. Although CFRP seems to have lower damping ratio than that of prestressing steel for very long cables due to its lighter weight, the over all effect of damping for both materials in long span cable-stayed bridges is very small, thus the previously mentioned advantages still govern the superiority of CFRP for long span bridges.
Acknowledgments The authors wish to thank The Egyptian Government for providing support to the first author through the Exchange Visiting Scholar Program. They wish to express their appreciation to Dr. S.E. Dunn, Professor and Chairman, Department of Ocean Engineering and Dr. John Jurewicz, Dean, College of Engineering, Florida Atlantic University for their continued interest and encouragement.
References [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8].
1.H.Yamaguchi, and Y. Fujino,” Damping of cables in Cable-stayed bridges with and without vibration control measures”, International conference on Cable stayed and suspension bridges, Deauville, France, Oct.1994. 2.G. Hirsch, “ Cable vibration overview”, International conference Cable stayed and suspension bridges, Deauville, France, Oct.1994. R.F.Gibson, "Damping characteristics of composite materials and structures", Journal of material engineering and performance, 1992. R. Greif, B.Herbert,” Experimental techniques for dynamic characterization of composite materials”, Advances in experimental mechanics and biometics, ASME 1992. P. Kim, P. and U. Meier, “CFRP cables for large structures”, Proc. Advanced Composite Materials in Civil Engineering Structures, MT Div., ASCE, Las Vegas, Jan. 31, 1991 R.F.Gibson, A.Yau, D.A.Riegner, "An improved forced-vibration technique for measurement of material damping", Experimental Techniques, vol.6,no.2, April 1982. R.F.Gibson, R. Plunkett, “A forced vibration technique for measurment of material damping”, Experimental mechanics, 11, (8), Aug. 1977, 297-302. R.F.Gibson, R. Plunkett, “Dynamic mechanical behavior of fiber-reinforced composites: measurement and analysis”, Journal of composite materials, 10, Oct. 1976, 325-341.
8
Development of new stay cable dampers
Yves BOURNAND Mechanical Engineer VSL International France
Summary Cable vibration on cable stayed bridges is known since several years, and can be considered today as one of the most critical problems for this type of bridge. Engineers developed some damping devices that will be reviewed here, with a particular point on their installation, fatigue and maintenance. Dampers are submitted to small movements and small loads but with a high number of cycles. Fatigue and maintenance are perhaps the two important criteria to be considered. Considering the present experience, engineers analysed the design criteria of a damping system and developed a new system, the friction damper, that will be installed on the stay cables of the UDDEVALLA Bridge in Sweden.
1
Vibration phenomena
Many different phenomena can generate cable vibrations. They are mostly nonlinear, their analysis is very delicate. The precise conditions that trigger the vibrations are not fully understood, for example, conventional statics and dynamics are insufficient to precisely model the behavior of the cable under the rain vibration phenomenon. Wind/rain vibration phenomenon on cable stay bridges has only been identified within the past few years, and can be considered today as the most important cause of cable vibrations. Many bridges being designed today still don’t account for it. Of 28 such bridges in the United States, at least half have the problem.
2
Different types of damping systems
Various methods have been tried to mitigate the cable vibrations, such as : - The installation of mechanical dampers placed near the ends of the stays, at the deck or tower. In order to damp. - Cross-cables interconnecting the stay-cables of the bridge. In order to increase cable frequencies. - Shapping of the stay pipes. In order to destroy the aerodynamic excitation mechanism. 2.1. Neoprene/rubber damper It has been customary to install a small neoprene or rubber damper at the end of the steel pipe where the stay cable passes into the anchorage at the deck.
Figure 1. The design of this damper is based on expected lateral forces, and to mitigate the transmission of potentially damaging bending stresses arising from stay vibrations to the cable stay in the near field region of the anchorages. In fact, this small, compact damper has an only negligible damping effect. It is not designed for the high-amplitude, low-frequency oscillations associated with rain-induced vibrations. 2.2
External dampers
At present, the installation of dampers at the cable connection parts on the bridge deck to increase the structural damping of cables are the most common countermeasure to mitigate the vibration. The most classical solution consists in the installation of hydraulic or viscous dampers connecting the stay cable to the deck, near the lower anchorage. This installation can be as simple as for Brotonne Bridge, Elorn Bridge or Erasmus Bridge or it can be more complicated as for Normandy Bridge. This solution has the advantage to be easily accessible for the maintenance operations, but the aesthetical appearance could be criticized in some cases.
Some systems are designed so that to be installed without connection to the deck but as a ring around the cable. The damper is installed in the formwork steel pipe embedded in the deck concrete or within a steel support pipe extending the formwork pipe, as those that will be used on UDDEVALLA Bridge. Generally, the damper is located at a distance between 0,015 and 0,030 (L) from the lower theoretical hinge point of the cable. (L) is the total length of the cable. The more common types of dampers are : - The viscous dampers - The hydraulic dampers Viscous dampers consist of freely moving plates in a viscous, silicon-like material, which assures the dissipation of energy. Many bridges in Japan have been provided with viscous dampers because of the low maintenance costs. An important disadvantage is that the damper characteristic is strongly depending on temperature and frequency. According to recent experiences, its seems that hydraulic dampers have relatively high maintenance costs and complex adjustment.
Fig 2. External damper on Normandie bridge
2.3
For the designer of a damper, the objective is to produce the desired damping coefficient at the desired frequencies and temperature. On bridges it is important to place the damper on a rigid support and to have a very tight connection (no play) of the damper to the stay cable.
Cross-cables
These cables are mainly used as a temporary solution during construction or as an interim solution. Polypropylene ropes proved very effective during the eight months they were in service on Erasmus Bridge (Netherlands). Cross-cable can be used to stop or limit cable vibrations after construction of the bridge, by increasing the natural frequencies of cable above 3 Hertz to be safe.
Before to use this system as a final solution, the designer has not to forget the problems observed on some bridges, as for example on the Fred Hartman Bridge in Texas. On this bridge, the forces have broken the crosscables that were placed on the stay-cables one year after their installation in response to fatigue and fretting. $ 0,6 millions will be spent to attach new cross-cables, with better fatigue characteristics, to install shock absorbers for the stay cable anchors and to repair broken weld connections. Moreover, the vibrations have dramatically increased costs because of the need for inspections, maintenance and repairs. On some bridges, the cross-cables are replaced by stronger ones with higher tensions.
Fig 3. Cross-cables
If the bridge designer choses cross-cables it is recommended to follow the following criteria: The cables must be designed using a flexible wire rope or similar system (with high internal damping) and with good fatigue and wear characteristics.
The initial tension in these cables must be such that to be not detensioned under extreme loads so that to avoid shocks which could produce some ruptures. Thus this solution is difficult to apply on existing bridges since, the pre-tension of the cross-cables may change the stay cable geometry and particularly the angle between deck and cable at the anchorages. The main reasons cross-cables are not considered as a permanent solution by some bridge owners is that they have a major impact on the aesthetics of cable stayed bridges and they present high inspection and maintenance costs. 2.4
Shape of the stay pipes
European and Japanese engineers developed this aerodynamic solution which is used on several cable-stayed bridges, e.g. for UDDEVALLA Bridge in Sweden. Helical ribs or protuberances are added to the stay pipe ; this disrupts the flow of water, and destroy the continuous galloping-promoting rivulet. Stay pipe of 165 and 250 mm diameters have been tested with these helical ribs in the wind tunnels of the CSTB (France) and of the Danish Maritime Institute. The tests showed a strong reduction of the rain-wind induced vibration. However the designer has to be careful because some vibrations can persist as observed in some worst cases. Care must be exercised with these solutions so that to keep a small increase of the drag factor, to limit wind forces on the bridge, and to have a nice aesthetics of the stay cables.
For the designer, the shapping of the stay pipes have been developed to prevent only one, although the most important, type of vibration (rain and wind induced vibration). If the risk to have other types of vibrations is high, this solution will have to be combined with other solutions.
Fig. 4. Stay pipe with helical ribs on Normandie bridge
3
Design criteria and specifications of a damping system
- The steel elements that constitute the stay cable are generally designed for pure cyclic tension stresses. But we also have to consider the unintentional bending stresses resulting from cable vibrations which could significantly reduce their expected fatigue life and affect integrity, serviceability and durability of the stay cable system. - It can be very difficult or impossible to inspect for potentially damaging effects within the near-field region, at the cable-stay anchorages and at the damping devices. The ability and access facility to inspect the stay cables near the anchorages and the damping devices will increase the safety and durability. - In the following years, technologies and equipments will be developed to detect wire failure. These equipments will be introduced as a part of the usual maintenance equipment of the bridge. - For the designer of the damping system the most important criteria to follow could be the following : • Adjustability • Ease of access • Relative low cost • Easy mounting
• • • • • •
Installation on existing bridges Aesthetics Maintenance Reliability Not temperature dependant Damping characteristics insensitive to the frequency and the amplitude of vibrations.
- Allowable amplitude for the cable vibration is a very important issue. Bending angle of 0,5 to 0,6 degree at the cable anchorage can be a criteria of the fatigue damage. However this 0,5 to 0,6 degree bending angle means quite large amplitude of the vibration and it will not be the acceptable amplitude for visual uneasiness. Although often used, 1D or 2D amplitude criteria (D : diameter of the cable) does not seem to have any concrete reason, actual decision to use this criteria for additional reduction of the vibration seems acceptable in many cases. - In the implementation phase, special attention has to be paid to possible stay cable bending through the damper due to mobile loading of the bridge-deck.
4
A new development : the friction damper
- We observed on the existing damping systems that the cost of maintenance can be expensive. The damper can be permanently solicited to small, non-critical vibrations and very quickly it will have to support a high level of cycles and consequently a rapid deterioration and replacement. - To answer to this problem of fatigue and maintenance, D. KOVACS (Dynamik Consulting) proposed a technical solution : the friction damper. This product has been developed in collaboration with VSL for a future installation on the UDDEVALLA Bridge (Sweden).
Fig. 5. Installation of friction damper on UDDEVALLA Bridge Fig. The damper will be placed at the top of a rigid steel support pipe bolted to the steel deck structure supporting the load of the stay cable deck anchorage. The friction damper is composed of mechanical components assembled together so that to have no play (to keep a high level of efficiency). It’s composed of two parts. The movable part is tightly fixed to the strands of the stay cable by a bolted collar and will move in the three directions. The bolted collar has several friction wings. The fixed part is bolted to the steel support pipe and is composed of several spring ring blades supporting several friction screws. The ring blades are deflected so that to have a steady friction contact of the friction screws against the friction wings whatever the movements of the movable part of the damper. The main advantages of this friction damper developed for UDDEVALLA bridge are the following : • Small, non-critical vibration amplitudes remain undamped. Thus, we have reduce wearing and low maintenance costs. For UDDEVALLA Bridge, the friction forces will be adjusted so that to have an action of the damper only when the amplitude of vibration of the longest cable will be beyond 70 mm. For each cable, the friction force of the damper will be adjusted according to the allowable amplitude of vibration defined by the designer. • The friction damper is designed so that to be easily installed on existing bridges where cables are submitted to unexpected vibrations. • All components of the damper are accessible and can be easily inspected and replaced, if necessary, during the maintenance operations.
• The characteristics of the damper can be easily adjusted during the maintenance operations. This adjustment consists only to turn the four screws supporting the friction pads. • The friction forces are practically constant and independent from the speed of the point to be dampened. • The damping characteristics are insensitive to the frequency and amplitude of the vibrations. • The friction damper is designed so that to have a constant damping of the stay cable when this cable has a longitudinal movement due to load variations.
5
Conclusions
Researchers are just beginning to study vibrations on cable-stayed bridges. We observed that some progresses have been achieved but we have to recognize that today the precise conditions that trigger the vibrations are not fully understood. • The cables of bridge structures are easily excited by natural wind because of their low structural damping characteristics, therefore problems such as structural fatigue will arise. It’s important to precisely clarify the vibration mechanism in order to suppress the vibrations. • At present, the installations of dampers at the connection of the stay cable at the deck to increase the cable damping are the most common solution to reduce the vibrations. More investigations should be continued with regard to their durability and maintenance. • The definition of the damper characteristics to suppress the vibration has to be optimized, because the generation mechanism and the magnitude of aerodynamic exciting forces of this vibration is not fully clarified. And, particularly, if we have to deal with parametric excitations where the usual damping systems are not efficient. For the future : All the damping systems cited in this paper are designed to reduce the vibration of the cables. But designers are working on the complex civil structures for the future, and for these cable supported structures of the future, the objective is not only to reduce the vibrations of the cable alone, but also to reduce the vibrations of the whole structure. In order terms, the aim will be to increase the damping of the complete structure which has a poor structural damping. For these structures the existing passive damping systems have some limitations that lead designers to imagine a new kind of damping system. It’s why VSL is working inside a BRITE EURAM research program, to the development of the new generation of active control damping systems that will be used in the future.
Fatigue Reliability Evaluation of Cables in Cable-Stayed Bridges. Case Study: The Sama de Langreo Bridge. José L. GONZÁLEZ Civil Engineer ENGITEC Eng. Consultants. Andorra He received his degree in 1997 at the Thecnical University of Catalonia, UPC. At present, he is working as a consulting engineer at ENGITEC in the highway and structural department.
Juan A. SOBRINO Assistant. Prof. Technical University of Catalonia Barcelona, Spain Mr. Sobrino received his PhD in Civil Engineering at the Thecnical University of Catalonia, UPC, in 1994. Currently, Mr. Sobrino is holding a position as an assistant Professor at the UPC. His research is focused on the reliability of existing structures and both load and resistance models. Apart from his research, Mr. Sobrino is running the engineering consultant company PEDELTA, S.L. specialized in bridge design and assessment.
Summary This paper presents a procedure for the structural evaluation of fatigue damage in cable-stayed bridges due to traffic loads. The method is based on the probabilistic analysis for the calculation of the safety margin of the Cable-Stays Fatigue Limit State under traffic loads. Structural reliability techniques are introduced to obtain the statistical parameters of the resistance and load variables. A practical, real-life example, the analysis of the Sama de Langreo Bridge in Spain under real traffic loads, is presented to illustrate the general procedure. Reliability fatigue analysis of the Sama de Langreo bridge shows that current design criteria for the Fatigue State limit due to highway traffic loads (wind effects are not included in this study) leads to a very low failure probability, even for very extreme traffic load conditions. This example confirms that fatigue design specifications of Design Codes are very conservative.
1. Introduction The current methods for the verification of the Cable Fatigue Limit State in cable-stayed highway bridges are usually conservative. An accurate procedure for the evaluation of the Fatigue Limit State is presented in this paper in terms of stocastic variables based on structural reliability theory. In this document, it is presented a general probabilistic fatigue resistance model for cables made up of n parallel elements (wires, strands or bars) based on the damage variable D. This variable ranges from D=0 in the initial state to D=1 when failure is produced. Parameters of the model are estimated with bayesian techniques from real data given by one of the most important cable manufacturers [1]. This method, named “D METHOD” and its generalization “D-Bayesian METHOD” are presented in chapter two. In chapter three, some simplifications are assumed to obtain an easy semiprobabilistic method to evaluate the Fatigue State Limit.
In order to estimate the real traffic load effects in cable-stays, numerical traffic simulations can be carried out to obtain a representative stress history of cables. For the presented case study a numerical program has been used to obtain the traffic stress spectra using real traffic data coming from weigh-in-motion measurements at different highways in Spain [2].
2. Fatigue models 2.1 Load model Fatigue damage could be obtained from the load history of the element, σ(t). If fatigue damage is caused by the stress amplitude and not by the stress value, the element load history could be resumed by the load spectra (Ni,∆σi) where Ni is the number of load cycles represented by the stress amplitude ∆σi . If we assume, as in the classical Palmgren-Miner theory, that damage in an element due to ni cycles of ∆σi stress amplitude is given by: n Di = i N ui eq. 1 with: Nui= C∙∆ ∆σi-n ∆σi>r0
eq. 2
Where C and n represent material properties and r0 is the fatigue limit which will become the most important parameter in the resistance fatigue models. We can describe the element damage as: m
D = ∑ Di
eq. 3
i=1
where m is the number of pairs (Ni, ∆σi). It would be helpful to resume the spectra in a single pair of values Neq, ∆σeq. Equation 4 may be used: m
N eq ⋅ ∆σ
n eq
= ∑ n i ⋅ ∆σ ni
eq. 4
i= 1
m
Where:
N eq = N t = ∑ n i
eq. 5
i=1
According to the equivalent stress amplitude there are basically two families of load models. Those that consider the fatigue limit as a constant r0 and those that consider the fatigue limit as a function of the damage variable D, r(D). Some usual possibilities are:
s= ∞
∆σ
n eq
∫s
=
n
s = r0
⋅ f ∆σ ( s ) ⋅ ds
eq.6
D= 1
∆σ
−n eq
=
∫ ∆σ
eq
( D ) − n ⋅ dD
eq.7
D= 0
s= ∞ n
∆σ eq ( D) =
∫s
n
⋅ f ∆σ ( s) ⋅ ds
s= r ( D )
eq.8
1 n− 2
r( D ) = r0 ⋅ (1 − D ) ; n>2 eq.9 There is an additional family of models that considers the ultimate number of cycles of amplitude ∆σi as: Ni= C∙(∆ ∆σi-r)-n ∆σi>r ; r : fatigue limit
eq. 10
The same algebraic operations leads to the models: s= ∞
∆σ
n eq
∫ (s − r )
=
n
0
s = r0
⋅ f ∆σ ( s) ⋅ ds
eq.11
D= 1
∆σ
−n eq
∫ ∆σ
=
eq
( D) − n ⋅ dD
eq.12
D= 0
s= ∞ n
∆σ eq ( D) =
∫ ( s − r( D))
s= r ( D )
r( D ) = r0 ⋅ (1 − D )
1 n− 2
n
⋅ f ∆σ ( s ) ⋅ ds ; n>2
eq.13 eq.14
Using these models it is possible to obtain a simple expression for the element damage variable when we have a variable amplitude stress process by obtaining a constant amplitude stress process from the former variable amplitude stress process D=
N eq ⋅ ∆σ neq C eq.15
=
S C
This is the main expression to describe the resistance model of the element. It becomes obvious that the load is represented by the product: m
S = N eq ⋅ ∆σ neq = ∑ n i ⋅ ∆σ ni
eq.16
i= 1
And the fatigue resistance by the Paris-Erdogan parameter C R=C
eq.17
Of course, failure is produced when S=C or D=1 and the failure probability can be expressed as:
Pf=P(S≥ ≥C)=P(D≥ ≥1)=1-P(D<1)=1-FD(1)
eq.18
Pf=P(D
eq.19
Or alternatively
Where Dmax,assumed is the maximum assumed damage. In the next section, a distribution function of the element damage variable is introduced. 2.2 Single element resistance fatigue model: It is usual to accept a Weibull distribution function for the probabilistic fatigue resistance model: L c − λ α0 Fc ( clL ) = 1 − exp − ⋅ L δ 0 0
c≥λ eq.20
where L is the legth of the element, L0 is the laboratory reference length and α0 ,δ0 and λ are parameters to be estimated in the laboratory [3,4]. This distribution function leads to the S-N-Pf curves: (Nt-N0)∙∆ ∆σeqn = C
eq.21 1
where:
L α0 C = λ + δ 0 ⋅ − ⋅ Ln(1 − Pf ) L0
eq.22
or alternativaly to the failure probability : L (N − N 0 ) ⋅ ∆σ eq Pf = 1 − exp − ⋅ δ0 L 0
n
Some examples of S-N-Pf curves are shown in figure 1.
− λ
α0
eq.23
1600
Stress amplitude (MPa)
1400 1200 1000
800
Pfe=0.95 600
Pfe=0.5
400
Pfe=0
r0=247 200 0 0.00E+0
4.00E+5
8.00E+5
N0=42351
1.20E+6
1.60E+6
2.00E+6
number of cycles
Figure 1. S-N-Pf. Curves.( Pfe=0,Pfe=0.5 and Pfe=0.95) It is shown that in the case of large number of cycles, probability curves are too close to each other in order to try to design in the non zero probability zone, so we need to design in the zero probability zone. As this zone is controlled by the fatigue limit, this parameter becomes the most important in resistance fatigue models. 2.3 Cable fatigue model. D Method. Using the probabilistic fatigue resistance model for a single element it is possible to obtain an upper and lower limit for the distribution function of the global damage variable: ne
Dt =
∑D i=1
e( i )
ne This variable tries to describe the global fatigue damage in a cable made up of n parallel elements.
eq.24
Of course each of these elements is controlled by the Weibull distribution function introduced in 2.2. The main problem is to avoid the statistical dependency of the De(i) variables caused by the stress redistribution process when failure occurs in one of the elements. Let us introduce the new variables:
δ e ( i , j ) = D e ( N t , ∆σ eq ( j ) ) =
n ( N t − N 0 ) ⋅ ∆σ eq ( j)
eq.25
C δe(i,j) is the i-element damage as all stress cycles had the constant amplitude associated to a j broken elements situation: ∆σ ( j ) = ∆σ ( 0 ) ⋅
ne ne − j eq.26
∆σeq(j)= ∆σ(j) - r0 so, if De(i,j) is the i-element damage when j elements are broken, we have:
eq.27
De(i,j) ≤ δe(i,j) j=1,i
eq.28
Otherwise, there will not be a stress redistribution process until the first failure is produced, so: De(i,0) = δe(i,0) i=1,ne.
eq.29
We can obtain the following expressions from previous ones : De(i,j)≤De(i,k) j≤ ≤k
eq.30
De(i,0) = δe(i,0) ≤ De(i,j) ≤ δe(i,j)
eq.31
If Dt(i) is the cable damage when i elements are broken, we can write: m−1 m m P( D t ≤ ) = ∑ P( D t ( i ) ≤ ) ⋅ P( nº failure = i ) = ne ne i=0
=
m−1
ne
i=0
j= i + 1
∑ P( ∑ D
e( j ,i )
≤ m − i ) ⋅ P( nº failure = i )
eq.32
Let’s try to aproximate these expressions: On one hand we have: so:
De(j,i) ≤ δe(j,i) j=i+1,ne
eq.33
ne
ne
j= i + 1
j= i + 1
P( ∑ D e ( j , i ) ≤ m − i ) ≥ P ( ∑ δ e ( j , i ) ≤ m − i ) eq.34 and: so:
De(j,i) ≥ δe(j,0)
eq.35
ne
ne
j= i + 1
j= i + 1
P( ∑ D e ( j , i ) ≤ m − i ) ≤ P( ∑ δ e ( j , 0 ) ≤ m − i )
eq.36
On the other hand we have: P(nºfailure=i ∆σeq(0)) ≤ P(nºfailure=i) ≤ P(nºfailure=i ∆σeq(i))
eq.37
It is possible to identify the nº failure variable distribution with a binomial with a Pfe(i) parameter as follows: P( nº failure = il∆σ eq( i ) ) = ( ni e ) ⋅ Pfei ( i ) ⋅ (1 − Pfe ( i ) ) ( n e − i ) eq.38
L (N − N 0 ) ⋅ ∆σ eq( j ) Pfe ( j ) = 1 − exp − ⋅ δ0 L 0 ne ∆σ eq( j ) = ( ∆σ eq( 0 ) + r0 ) ⋅ −r ne − j 0
n
− λ
α0
eq.39 eq.40
These expressions let us obtain an upper and a lower limit for the Dt distribution function: P( D t ≤
ne m−1 m ) ≤ ∑ P( ∑ δ e ( j, 0 ) ≤ m − i ) ⋅ P( nº failure = il∆σ eq( i ) ) = Pf ,sup ne i= 0 j= i + 1
eq.41 ne m− 1 m P(D t ≤ ) ≥ ∑ P( ∑ δ e( j,i) ≤ m − i) ⋅ P(nº failure = il∆σ eq( 0) ) = Pf ,inf ne i= 0 j=i +1
eq.42 These limits become closer when m is lower than ne. An example is shown in figure 2. It is posible to include probabilistic distribution of the model parameters getting into a bayesian context: P( D t ≥
m m ) = ∫ P( D t ≥ lp ) ⋅ dP(p ) ≤ ∫ Pf (sup) ( mlp ) ⋅ f p (p ) ⋅ dp ne ne Ωp Ωp
eq.43
where p is the parameters vector.
Pf(inf), Pf(sup)
1.0
Pf(sup) Pf(inf)
0.5
0.0 0.0
10.0
20.0
Dt %
30.0
Figure 2 Upper and lower limit of Dt distribution function: ne =100, N=2∙106 cycles, ∆σ=264.5 MPa, L=L0=2m, N0=42351 cycles, r0=247 MPa,n=2.06, λ=6.974∙108, δ0=1∙1010, α0=1.45 When N is very high (design zone) the upper limit is more useful:
P( D t >
m )= ne
r0 = ∆σ − ∆r0 ( λ )
∫
P( D t >
r0 = 0
m lr ) ⋅ dP( r0 ) < ne 0
r0 = ∆σ −
r0 = ∆σ
∫ dP( r ) = ∫ f 0
r0 = 0
r0 = 0
r0
( r0 ) dr0 = P( r0 ≤ ∆σ )
eq.44
so the fatigue limit becomes the most important parameter in fatigue resistance models that can be used for the stay-cables or anchorages.
3. Safety criteria To evaluate de fatigue safety margin, the following expression may be used: ∆σ eq,d ≤ ∆σ adm,t
eq.45
with: s= ∞ n
∆σ eq,d =
∫s
s= 0
n
⋅ f ∆σ ( s) ⋅ ds
eq.46
If no data is available, a conservative value of n=3 may be used: µ ∆σ adm,t = r 0 eq.47 γ fat where µr0 is the mean of fatigue limit and γfat is the proposed safety factor that depends on [5]: • • •
Coefficient of variation of the equivalent stress amplitude V∆σ Coefficient of variation of the Fatigue Limit Vr0 ∆σeq,d) Reliability Index β = − Φ −1 (Pf ) with Pf=P(ro<∆
when normal distribution is supposed for fatigue limit and equivalent amplitude stress, the safety factor verifies the following implicit equation. 2 r0
γ fat = 1 + β ⋅ V ⋅ γ
2 fat
2 ∆σ
+V
≈ 1 + β ⋅ ( Vr0 ⋅ γ fat
2 V∆σ ) + 2 ⋅ Vr0 ⋅ γ fat
eq.48
The above mentioned formulation could be applied to any mechanic system with a fatigue limit resistance parameter as anchorages, etc.
4.
Case study. Sama de Langreo Bridge.
To illustrate the possibilities of the above proposed methods, in this chapter a case study is presented. The Sama de Langreo bridge is an asymmetric cable stayed bridge with a single tower over the Nalon river placed in the north of Spain designed by Fernandez Casado, S.L. built in 1989. The main span over the river has a length of 130 m. The total length of the bridge is about 300 m, including side spans. The bridge has two traffic lanes with a total width, including shoulders, of 14.17 m. The tower is an A-shaped concrete construction, located on the right riverside and has a height of 57 m. The girder of the superstructure consists of a reinforced concrete voided slab girder. The cross section height is only 1.3 m. The main span and side span are supported by two vertical cable fans consisting of 16 steel cables anchored in the girder each 15 m. Figure 3.
The aim of this investigation is to find the fatigue damage (or the fatigue level of safety) in the stay cables due to traffic loads on the bridge. Wind effects or other variable loads are neglected in this study.
Figure 3. Sama de Langreo Bridge elevation.
4.1
Fatigue analysis
The fatigue analysis has been made taking into account the following considerations: •
A simplified structural model consisting of a grillage model of the superstructure (bridge girder) with nodal springs to simulate the stay cables.
•
Traffic simulations have been developed using a numerical simulation program developed in [2,6]. The program is based on Monte Carlo simulations, taking into account free or congested traffic on the bridge. Two different free and congested traffic situations have been studied with different truck intensities (see Table 1). Traffic situation nº 1
Traffic situation nº 2
Car intensity
70 %
50 %
Truck intensity
30 %
50 %
% of vehicles in lane 1
47 %
57 %
% of vehicles in lane 2
53 %
43 %
Table 1. Sama de Langreo Bridge elevation.
•
Stress spectra has been obtained for different stay-cables. Stress amplitudes vary between 5 and 140 MPa, with equivalent amplitudes around 40 to 80 MPa (Figure 4). These values are very conservative if compared with those used in the fatigue design. The obtained values of equivalent amplitudes are about 40-50 % of fatigue design admissible stresses for traffic loads. 0.80
frecuency
0.60
0.40
0.20
0.00
stress amplitude (MPa)
Figure 4. Stress spectra obtained using numerical simulations in the cable-stay nº 8. •
Using the stress spectra due to traffic loads, safety margin for fatigue may be obtained for different resistance models. Figure 5 shows the reliability index (inverse of the Gaussian probability of failure), for two different fatigue limits (ro) and for two different variations of these limits in order to take into account the uncertainties in the cable-stay resistance (or anchorages). The obtained reliability index β is always higher than the minimun accepted in structural codes β >3,5 to 5, even for the very conservative traffic conditions assumed in this study. 20.0
Vr=0.05
18.0
Average r0
16.0
200 MPa
14.0
x e d n i β
250 MPa
12.0
Vr=0.1
10.0 8.0 6.0 4.0 2.0 0.0 0
40
80
120
160
200
equivalent stress amplitude(Mpa)
Figure 5. Reliability Index versus equivalent stress amplitude for two different fatigue resistance limits (ro) and for two different coeficient of variation of this parameter Vro.
5.
Conclusions
As the main conclusion, in this example it is clear that safety criteria for fatigue design seems to be very conservative. On the other hand, technical specifications for fatigue of stays and anchorages should be more realistic, and fatigue tests should be carried out on the range of real behaviour of these elements under traffic loads or other variable loads (winds, etc). More data and further investigations are needed to obtain simplified and realistic fatigue design specifications for stay-cables.
6.
References
[1] [2]
TYCSA, Data of fatigue strands. Internal report of TYCSA 1997. Sobrino, J.A.; Evaluation of structural safety and serviceability of existing prestressed and reinforced concrete bridges (in Spanish). Ph. D. Thesis, Civil Engineering School, Barcelona. 1993.
[3]
Castillo, E. & Fernández Canteli, A.;Statistical models for fatigue analysis of long elements, IABSE periodica. 1992
[4]
Arnold, B.C., Castillo E. & Sarabia, J.M.; Classical and bayesian analyses of fatigue strength data, IABSE periodica, Madrid 1992
[5]
Thoft-Christensen, P.& Baker, M.; Structural reliability theory and its applications. Springer-Verlag, 1982.
[6]
Sobrino J.A.; Structural evaluation of an old prestressed concrete bridge. IABSE Symposium. Extending the lifespan of structures, pp. 817-822. San Francisco, 1995.
7. Acknowledgements The authors thanks Prof. Javier Manterola of Fernández Casado, S.L. (author of the Sama de Langreo Bridge) for the information provided for the case study. The authors also wish to thank Mr. Jesús París of TYCSA for the fatigue data used in this paper.
The Super High Damping Rubber Damper on the Stay-Cables of Meiko East Bridge Minoru MIZOE Mgr, Head Office Japan Highway Public Co. Tokyo, Japan
Sinji MUROI Mgr, Civil Eng. Division Nippon Steel Co. Tokyo, Japan
Takashi HORII Civil Eng. Bridgestone Co. Yokohama, Japan
Toshiyuki ISOBE Mgr, Civil Eng. Bridgestone Co. Tokyo, Japan
Renji KIYOTA Mgr, Civil Eng. Yokogawa Bridge Co. Funabashi, Japan
Yasuo IMADA Civil Eng. Yokogawa Bridge Co. Funabashi, Japan
Summary The stay-cables of the Meiko East Bridge have a parallel wire strand coated with polyethlene tubes. In Japan, a rain vibration has been often observed at the cable coated with the smooth surfaces, such as a polyethylene. Both damping countermeasure and consideration foraesthetics point of view, was requiredin Meiko East Bridge. As the countermeasure, a damping device using SDR(Super Damping Rubber) that can be installed inside of a waterproof cover, was adopted. As a result of experiments, the required damping of the cable were obtained. This paper gives an outline of the damping device and experimental results of thestay cable in Meiko East Bridge.
1. Introduction Meiko East Bridge is one of the three cable-stayed bridgesto across the Ise Bay in Japan. The bridge has 700m in total length and a center span length of 410m. The stay cables are arranged in two planes of a multi-fan shape. Each stay cables is made of galvanized wires and coated with polyethylene tubes. The longest stay cable is 209m in length, and the maximum diameter is 165mm. In the cables mentioned above using in a cable-stayed bridge,a vortex induced vibration and rain vibration are easily caused by the wind because of the smooth surfaces on the cables and low structural damping. The rain vibrations induced by both wind and rain have often been reported forthe cables having a smooth surface, such as a polyethylene and 120-200mm in diameter. In Japan, rain vibration was recognized on the stay-cables inMeiko West Bridge-l for the first time, which is located at 3km west from Meiko East Bridge and opened in March 1985. For the design of Meiko East Bridge it was decided tocontrol rain vibration because of the reasons mentioned above.Some techniques have been used to control rain vibration; (1) to install the damping devices on the cable nearbythe anchor point, (2) to connect neighbor cables with wires, (3) to improve theaerodynamical characteristics of cables by increasing roughness on their surfaces. At Meiko East Bridge, both damping countermeasure and consideration foraesthetics point of view,
were required. The cable damping device using SDR(Super Damping Rubber) that can be installed inside of a waterproof cover at the top of anchor pipes was adopted as the countermeasure. 700 m 410 m
145 m
145 m
TP+130.2m
TP+130.0m
N.H.H.W.L=TP+1.4m
P1
P2
C30N C26N
40 m
CL
P3
P4
Fig. 1 General View of Meiko East Bridge
2. Damping required for stay cable Since 1984, the field measurementsand wind tunnel tests have been done for many cable-stayed bridge designs. As a result, when the Scruton’s number Sc is less than 50 and a natural frequency of the cable is less than 3.0Hz, the vibrations occur. Sc is given as follows. m⋅ Sc = (1) ⋅ D2 where, m; cable mass. ;δ logarithmic damping decrement of a cable. ρ; air density. D; cable diameter. Therefore, if Sc could be designed greater than 60, which has natural frequency less than 3.5Hz, we can prevent rain vibration. In order to prevent vortex induced vibrations of the cable, not as much damping is required. Regarding cable damping countermeasure, the aesthetics of the bridge was an important consideration in Meiko East Bridge. For this purpose, we decided to adopt a cable damping device using SDR(Super Damping Rubber) that can be installed inside of a waterproof cover at the anchor pipe.
3. Outline of the device SDR is installed between the cable and the anchor pipe. One side of the SDR(rectangular section) is connected to an anchor pipe and the other side to a cable. When the cable is excited, a relative displacement occurs between an anchor pipe and the cable, and the SDR undergoes a shear distortion. SDR can absorb the vibration energy of a cable due to this shear distortion. This device is useful for all radial vibrations of a cable. Figure 2 shows the structure of the device, and photograph1 shows the views before and after installing the waterproof cover.Generally, in a
cable-stayed bridge, the steel pipe is used for the anchor. The device is installed at the top of an anchor pipe, then covered by waterproof cover. The device needs no additional attachment points on the bridge deck, andthe devices are simple to maintain.
Cable SDR Steel pipe Waterproof cover
Fig. 2 Cable Damping Device using SDR
a) Without Waterproof Cover
b) With Waterproof Cable
Photo 1 Cable Damping Device
4. Material properties of SDR
Load P (KN)
We have developed SDR by blendingon SBR(styrene butadiene rubber) polymer, high damping carbon and some plastics toachieve the high damping properties. The hysteresis loss at shear distortion for SDR is shown in figure 3. SDR has greater damping characteristics than the HDR(High Damping Rubber) used for seismic bridge 3 bearings. However, the shear modulus and damping coefficient of SDR are dependent on 2 shear distortion, shear velocity and ambient 1 temperature. Figure 4 shows variation of the shear modulus with and temperature. 0 Damping coefficientdepends almost on entirely temperature. These material were -1 developed experimentally andcan be -2 expressed by some influential functions. Shear modulus; -3 -3 -2 -1 0 1 2 3 G(γ, f, T) = CGf (f) ⋅ CGT (T) ⋅ G( γ) (2) Shear Distortion ƒÁ where, Fig.3 Hysteresis Loops of SDR CGf (f); velocity revision coefficient.
CGT(T); temperature revision coefficient. G(γ); shear modulus at shear distortion γ. Damping coefficient; (γ, f, T) = C (f) ⋅ C (T) ⋅ ( γ) (3) where, Chf(f); velocity revision coefficient. ChT(T); temperature revision coefficient. h(γ); damping coefficient at shear distortionγ. 5
Shear Modulus G(KN/mm2)
Shear Modulus G(KN/mm2)
5 4 3 2 1 0 0.0
0.2
0.4
0.6
0.8
1.0
4 3 2 1 0 -10
0
Shear Distortion ƒÁ
(a) Variation of Shear Modulus (G) with Shear Distortion (γ ) (f=1.0Hz,T=20? )
10
20
30
40
Temperature T(•Ž)
(b) Variation of Shear Modulus (G) with Temperature (T) (γ =0.2,f=1.0Hz)
Fig.4 Shear Modulus of SDR
5. Calculation method of additional damping decrement A dynamic modelof a damping device with SDR can beshown in figure 5. The hysteresis loss of SDR is due to viscous damping. The additional damping decrement of a cable damping device can be expressed as follows. 2 ⋅ { ( c )} = ⋅C ( 3) a M ⋅ where, δa; additional logarithmicdamping decrement by the device. φ(χc); mode amplitude of a cable at damping device installed position. C; viscous damping coefficient of a damping device. M; equivalent mass of a cable. = m∫ 2 ( )d (m; mass per unit length)
Cable K
C
ƒÔC L
Fig.5 Model of Cable Damping System
ω; circular frequency. Mode amplitude φ(χc) can be obtained by mode analysis. The equivalent value C of viscous damping coefficientis shown (5).
C=
2⋅h
⋅K
(5)
where, h; damping coefficient of SDR. K; stiffness of SDR. A ⋅ G (γ ) = (6) H A, H; section area of SDR, thickness. G (γ); shear modulus of SDR. γ; shear distortion of SDR.
6. Confirmation of the cable damping 6.1 Experiment method Through experimentation we have confirmed an additional damping decrement. The cable damping devices were installedon two cables(C26N, C30N) at the upper row of a bridge. We excited a cable to make free vibration and got damping decrements of the cable using the free vibration wave shape(see photograph 2). The vibration mode was set up within 3.0Hz of the known range for rain vibration. We experimented from 1st to 5th mode concerningthe cable Cable-Number Cable Construction Corrosion Protection Cable Diameter Cable Length Cable Unit Weight Frequency
Photo.2 Experiment Situation
C26N C30N 283 galvanized wire( 7mm) 265 galvanized wire( 7mm) Polyethylene coating Polyethylene coating 0.150 m 0.145 m 198.5 m 143.7 m 91.6 kg/m 85.7 kg/m 0.56 Hz 0.78 Hz
Table 1. Dimensions of Cables 6.2 Calculation of additional damping decrement Figure 6 shows the relationship betweenstiffness and additional damping decrement of SDR with depended ontemperature and shear distortion. The value of additional damping decrements are shown at ? symbols. Table 2 shows additional damping decrements that can be obtained for each vibration mode of a cable. In case of the range of 0.05-0.30 of shear distortion and 0-40? of temperature, a logarithmic
0.05 0.04 ƒÁ=0.05
0.03
ƒÁ=0.10
0.02 ƒÁ=0.30
0.01 0.00
0
1000
2000
3000
4000
5000
Additional Damping Decrement ƒÂa
Additional Damping Decrement ƒÂa
damping decrement is 0.020-0.035 for C26N cable and is 0.026-0.041 for C30N cable. As assuming a structure damping decrement of a cable is 0.005 before damping device installing, a damping decrement after installing is estimated as 0.025-0.041 for C26N cable and is estimated as 0.031-0.046 for C30N cable. On the other hand, when Scruton’s number is 60,required damping decrement is0.018 for each cable. The estimated damping decrement ofthe cable should exceed the required value. 0.05 0.04 0.03
0 •Ž
40 •Ž
0.01 0.00
0
1000
Stiffness K(KN/m)
(a) δ a – K (T=20? )
20 •Ž
0.02
2000
3000
4000
5000
Stiffness K(KN/m)
(b) δ =0.20) a – K (γ
Fig.6 Variation of Additional Damping Decrement (δ a) with Stiffness (K) (C26N-Cable,1st mode)
Cable- Mod Frequenc Require Temp Additional Damping (ƒÂ‚•) Numbe Dampin (•) ƒÁ=0.3 ƒÁ=0.1 ƒÁ=0.0 ‚†(Hz•j C26 1 0.56 0.01 0 0.02 0.02 0.02 20 0.03 0.03 0.03 40 0.02 0.03 0.03 2 1.12 0.01 0 0.02 0.02 0.02 20 0.03 0.03 0.03 40 0.02 0.03 0.03 3 1.68 0.01 0 0.02 0.02 0.02 20 0.03 0.03 0.03 40 0.03 0.03 0.03 4 2.24 0.01 0 0.02 0.02 0.02 20 0.03 0.03 0.03 40 0.03 0.03 0.03 5 2.80 0.01 0 0.02 0.02 0.02 20 0.03 0.03 0.03 40 0.03 0.03 0.03 C30 1 0.78 0.01 0 0.03 0.03 0.02 20 0.03 0.03 0.03 40 0.03 0.03 0.04 2 1.56 0.01 0 0.03 0.02 0.02 20 0.03 0.03 0.03 40 0.03 0.03 0.04 3 2.34 0.01 0 0.03 0.02 0.02 20 0.03 0.03 0.03 40 0.03 0.03 0.04
Damping (ƒÂa•\ƒÂ s) 0.02 0.03 0.03 0.02 0.03 0.03 0.02 0.03 0.03 0.02 0.03 0.03 0.02 0.03 0.03 0.03 0.04 0.03 0.03 0.04 0.03 0.03 0.04 0.03
•` 0.03 •` 0.03 •` 0.04 •` 0.03 •` 0.03 •` 0.04 •` 0.03 •` 0.03 •` 0.04 •` 0.03 •` 0.03 •` 0.04 •` 0.03 •` 0.03 •` 0.04 •` 0.03 •` 0.04 •` 0.04 •` 0.03 •` 0.04 •` 0.04 •` 0.03 •` 0.04 •` 0.04
Logarithimic Damping Decrement of Cable before setting Damping Device (0.005) ƒÂs•F
Table 2 Calculations of Additional Damping Decrement
200 150 100 50 0 -50 -100 -150 -200 0
10
20
30
40
50
60
Time (sec)
(a) Time Histories without Damping Device Amplitude (gal)
Figure 7 shows a typical example of the experimental results for the C26N cable. The damping decrement does not depend on amplitude. The vibrations of damping decrement is caused by coupled vibration of the cable having a similar natural frequency. The dispersion at small amplitude range is caused by wind.
Amplitude (gal)
6.3 Results of experiment
200 150 100 50 0 -50 -100 -150 -200 0
Logarithmic Damping Decrement ( ƒÂ a +ƒÂ s )
Table 3 shows the complete result of experiment. The structural damping decrement ofthe cable without damping deviceis 0.0050.010. The structural damping 10 20 30 40 50 60 decrement of a cable is greater than Time (sec) estimated values because of (b) Time Histories with Damping Device absorbers installed on the tower. 0.10 An averaged of logarithmic •{: without Damping Device 0.08 •›: with Damping Device damping decrement is 0.033-0.045 0.06 at C26N cable and 0.042-0.046 at 0.04 C30N cable in the range of amplitude 5-310gal. The damping 0.02 decrements of 1st mode of C26N 0.00 0 20 40 60 80 100 120 140 160 180 200 cable and 2nd mode are smaller Amplitude (gal) compared with the other mode due (c) Logarithimic Damping Decrement to the influence of coupled vibration. Experimental damping Fig. 7 Typical Time Histories and Logarithmic decrement is in excess the estimated Damping Decrement of C26N-Cable (3rd Mode) value by calculation. The damping decrement has not dependence on vibration mode. Cable- Mode Number Temp. ( ) C26N 1 4.1 4.3 2 4.2 4.1 3 4.4 4.8 4 5.2 4.9 5 5.3 5.4 C30N 1 5.4 5.6 4.8 2 4.7 5.0 5.0 3 5.1 5.1 5.0
Damping Decrement Additional Damping Decrement ( a) a s) Amplitude Measured Average Calculated Measured / (gal) Temp.( ) =0.13 Temp.( ) =0.13 5 20 0.020 0.045 0.036 5.0 0.026 4.1 0.030 1.17 5 15 0.020 0.043 0.033 4.3 0.028 1.09 15 75 0.033 0.052 0.040 5.0 0.024 4.2 0.030 1.23 15 75 0.039 0.050 0.042 4.1 0.030 1.23 25 125 0.039 0.050 0.045 5.0 0.024 4.4 0.034 1.43 25 125 0.039 0.050 0.045 4.8 0.034 1.43 40 270 0.026 0.052 0.042 5.0 0.023 5.2 0.037 1.58 40 230 0.030 0.051 0.042 4.9 0.037 1.58 50 200 0.035 0.049 0.042 5.0 0.023 5.3 0.035 1.50 50 310 0.039 0.050 0.045 5.4 0.035 1.50 5 30 0.039 0.050 0.046 5.0 0.029 5.4 0.042 1.46 5 30 0.041 0.051 0.046 5.6 0.040 1.39 5 25 0.038 0.051 0.045 4.8 0.040 1.39 15 70 0.038 0.052 0.045 5.0 0.028 4.7 0.039 1.42 15 75 0.038 0.051 0.046 5.0 0.040 1.45 15 75 0.035 0.050 0.043 5.0 0.036 1.31 30 130 0.022 0.058 0.042 5.0 0.027 5.1 0.036 1.34 30 180 0.038 0.052 0.045 5.1 0.035 1.30 30 180 0.021 0.060 0.044 5.0 0.038 1.41
Table 3 Test Results of Cables
7. Conclusion In this paper, we described the abstract of a cable damping device using SDR(Super Damping Rubber) that was adopted to Meiko East Bridge. The damping effects was estimated by the calculation, and confirmed throughthe field experiments. Experimental results exceed calculated value. As a result of these experiments, damping devices were installed at all cables except some lowerrow cables. Since completion in April, 1998, wind induced vibrationhas not been observed. The original aesthetics of the bridge were maintained by installing the cable damping devices within a waterproof cover of the cable anchor pipe.
References [1]. [2]. [3].
[4].
Public Work Research Center, Report on Study of Wind Resistance of Cables in Cable-Stayed Bridges, 1993. S.Kuranishi and T.Takahashi, Vibration Analysis of Beams with Damping at Discrete Location, Proceedings of JSCE, No.187, 1971. Y.Imada, R.Kiyota, Y.Suizu and Y.Kasahara, Development of Damping Device Using Shear Resistance of High Damping Material, Proceedings 48th annual conference of JSCE, 1, 1993. Y.Imada, T.Sasaki, R.Kiyota, and K.Goda, Experiment for Control Means On Cable Vibration Using High Damping Rubber Damper on Cable-Stayed Bridge, Proceedings 50th annual conference of JSCE, 1-(B), 1995.
Corrosion Protection of Locked Coil Ropes at Road Bridges Arnold HEMMERT HALSWICK Civil Engineer Arnold HemmertHalswick, born 1954, received his diplom degree in 1981 and his doctor degree at the RWTH Aachen in 1986. Since 1987 he works in steel structures at the BASt.
Siegfried SCZYSLO Civil Engineer Fed. Highway Res.. Inst Siegfried Sczyslo, born 1937, received his graduate degree in 1959 and worked at consultants and steel structure companies to build steel bridges. Since 1971 he works in steel structures at the BASt and since 1986 he is head of the group steel structures, corrosion protection at the BASt.
Summary The subject are corrosion protection measurements at ropes resp. cables of bridges in Germany. According to the experiences over the years resp. decades standards were drafted and improved according the experiences which were won in working.
1.
Introduction – Rope Bridges in Germany
In the course of federal motorways, major roads and some city roads in Germany there are about 40 big road bridges which have high strength cables. All but one bridges have locked coil ropes, one bridge has parallel wire strands. In Germany there are no bridges with bundles of strands how they were used elsewhere last time e.g. in France at the Normandie Bridge near Le Havre. Most bridges are cable stayed bridges, some bridges are suspension bridges, at two bridges there are under-guyings. Closely packed bundled single ropes are called as cables, see Fig. 1.
Left: Reconstruction of the suspension bridge over the river Rhine near Cologne-Rodenkirchen with a cable still without hangers on the left Fig. 1: Cable
Right: Side view of a hexagonal cable
2
2.
Locked Coil Ropes
2.1
General
Locked coil ropes inside consist of round wires and outside of several layers of Z-wires which tighten the inner structure by their shape and order, see Fig. 2. They have the advantage that a wire takes load after two lay lengths if it is broken. The lay length is the distance within a single wire turns around the longitudinal axis of the rope one time with a spiral. This behaviour is got by pressing this wire into the structure of the rope through contraction of the rope caused by the spiral structure. At parallel wire strands a broken wire is lost for the strength over the whole length of the cable. Furthermore locked coil ropes have the advantage that they can be designed in a more slender way than parallel wire strands and that by the locked type the inner structure of the rope is mechanically tightened and therefore much better protected against corrosion attack. But it seems that they have the disadvantage that they are more expensive than parallel wire strands having the same strength. Regarding the rope mechanics it has to be considered that they have a lower modulus of elasticity than parallel wire strands by reasons of the spiral structure which is about 170 000 N/mm².
Fig. 2: Cross section of a locked coil rope, see [1] 2.2
Galvanizing of Wires
In the beginning (about 1959 – 1965) the single wires were not galvanized. Later on only the outer wires were galvanized, and since the end of the seventies all wires are galvanized. The zinc layer amounts to 280 – 300 g/m² corresponding about 40 µm. At some bridges wires were used which were electrogalvanized with a coating of about 500 g/m² corresponding to about 47 µm, but in the meantime only galvanized wires prevailed on the market. The center wires are round, the outer layers of the wires have a Z-profile. In the beginning trapezoidal wires were used also between the round and Z-profiled wires, but they were let away by reasons of fatigue since the middle of the seventies. They had the advantage that they formed as at a stone arch bridge an arch which additionally defended the entrance of water in the inner of the rope.
3 The galvanizing alone is not a sufficient corrosion protection. Especially at the corners of the form wires the zinc layer is thinner as at the plane areas. Therefore an outer corrosion protection is necessary in the form of a coating, consisting of several coats, see Fig. 3.
Fig. 3: Sequence of coats 2.3
Blocking Agent
Beside some exceptions red lead was and is used as blocking agent which is filled in the inner of the rope during the fabrication of the single layers. The aim is that by the blocking agent an easy gliding is possible between the single wires (lubricating) and that the single wires are protected against corrosion. As these characteristics must be available over the whole life time the blocking agent has to fulfil high requirements of the lubricating, the corrosion protection and the durability. Until now in Germany the normal blocking agent was red lead known from the sector corrosion protection. But there were some attempts to use mixtures of polyoil and zinc dust because of the galvanized wires, but the experiences so far at bridges show that because of the higher viscosity the risk exists that the blocking agent comes out of the rope due to the contraction. Also artificial waxes were used, but in one case the last layer of wires was fabricated without a blocking agent because of the uncompatibility with the outer corrosion protection coating what seems doubtfully facing the thoughts to the sense of a blocking agent. The standard blocking red lead agent can come out of the rope, if during the fabricating mistakes were made. 2.4
Rope anchoring
The anchoring of a rope is normally done by the embedding of the wires in cast corpus consisting of a zinc alloy and by wedging the wires against each other in the socket. Beside the stressing of axial loads according the strength of the cable a radial tension strength develops in the socket consisting of cast steel or rolled steel by the wedging. Therefore a high level of exemption from cracks is required which is verified by ultrasonic tests. If no clear result are got a radiographic inspection is necessary. For the outer condition a magnetic particle test must be carried out. If damages are found it is allowed that they are touched up, but every socket must fulfil the requirements for its own.
4
3.
Rules
3.1
General
Standards were drafted and introduced in the responsibility of the German Ministry of Transport to avoid mistakes at this member sensitive and important for safety and to have a basis for the invitation to bid for rope works. By this a high level of quality at the fabrication of the rope and the capability for inspection under traffic is to be ensured. The maintenance is also dealt with in detail. These additional technical contract conditions mention the special things of locked coil ropes if they are used at bridges. Additional to the regulations in the standards requirements to the rope or cable (rope bundle) and to the corrosion protection are formulated to fulfil the expectations to the life time: It is counted on that the existing bridges reach 80 to 100 years supposed that the heaviness of the traffic does not grow strongly and that no other life time diminishing influences occur which are not determined by the structure itself. For the structure itself a regular test of the stability is necessary in any case. The rope is not understood as a working part, but modern structures allow the changing of single ropes in an accidental case. 3.2
TL Seile
Technical Delivery Conditions are carried out for Locked Coil Ropes, short TL Seile (Ropes) [1], where requirements for the rope itself are laid down. The requirements are widespread from the single components over the fabrication to the delivery on site. The bridge rope consists of the locked coil rope with the in-locating blocking agent and the sockets at both ends of the rope, which are fixed at the ends by casting. For the blocking agent a number of characteristic values has to be guaranteed. For the rope cast the rope is put through the openings of the sockets. The ends of the rope are opened to a broom of wires and cast in the socket with molten metal. An alloy of zinc is used as cast metal. In the course of the fabrication of the ropes a number of tests has to be carried out, ending with a tensile test at the rope for the verification of the ultimate strength with the destruction of the specimen. The TL Seile contains a technical delivery condition for the standard blocking agent red lead at its own within characteristic values are fixed. The aim is that these values deviate as little as possible as this stuff can be seen as well-tried. The TL Seile contains also an instruction for the carrying out of the standard test for fatigue of the rope. It is important that the specimen comes out of the delivery for the structure. 3.3
ZTV-KOR-Seile
The Technical Delivery Conditions for the Corrosion Protection of Bridge Ropes, short ZTVKOR-Seile [2] (in preparation) will replace in a short time the still existing Guidelines for the Corrosion Protection of Bridge Ropes, short RKS [3]. Die ZTV-KOR-Seile concern all measurements for the corrosion protection at bridge ropes and cables. They are subdivided as follows: General
5 -
Design considering corrosion protection Planning of the corrosion protection measurements Surface preparation Protective paint materials, sealing material, injection material and protective systems Execution of the corrosion protection work Health/safety/environment protection requirements and disposal of blast-cleaning rubble Acceptance Guarantee Inspection and testing of the ropes and cables Reference standards
There are three supplements; Requirements to the qualification of the execution personal Protocol for the corrosion protection Example for working instructions in drawings and texts for the different member areas at ropes and cables Basis among other things is the EN ISO 12944 Parts 1 to 8 [5]. The sense of these detailed instructions is to be not obliged to invent everything new at any structure. It cannot be expected that every time the same personal comes to site and bring along experiences. Therefore recommendations for the execution of repair works are given for the special conditions at rope and cable bridges, especially in the drawings of supplement 3. Many times it is referred to the new DIN EN ISO 12944 [5]. The surface preparation according Part 4 of DIN EN ISO 12944 has great importance as on the one side blocking agent is still on the surface of the rope from the fabrication and can have effects as a separation layer, on the the other side the new coating should be resistant and durable. Very often it is worked with rotating brush at galvanized ropes, see Fig. 4.
Fig. 4: Surface preparation with rotating brush The corrosions protection works itself can be done from a cabin where a protection against weather influences must be given, see Fig. 5, which protects at the same time the environment against damaging effects e.g. by dust and paint. If a further surface preparation than with rotating brushs is necessary a housing in on the complete length of the rope or cable from the bridge deck up to the pylon is necessary.
Fig. 5: Cabin for the corrosion protection The use of sealings is required, e.g. by bellows of synthetic material, see Fig. 6, so that no moisture enters the rope anchoring.
Fig. 6: Bellows for the sealing of a rope
4.
Maintenance of the ropes
4.1
Provided tests
At the construction works in the responsibility of the road administration in Germany the German standard DIN 1076 [4] is used. A main inspection has to be done every 6 years and between after 3 years a simple inspection. Beside this a currant observation takes place normally every 3 months and a yearly inspection where no bigger auxiliary measures are used as e.g. bridge inspection trolley. If a test seems to be necessary after an inspection or if exceptional events could have damaged the bridge a test for a special reason is executed. The former usual test loading is not carried out in Germany for decades as the benefit is to less opposite the damage which eventually occurs by the normally big loading of a loading test. 4.2
Bridge rope inspection machine
For the main inspection at bridges with ropes and cables in Germany a Bridge rope inspection machine was developed. It is a kind of cable railway with whom a driving of the ropes and cables is possible without loading the tensile elements themselves. A carrying rope bearing the
7 cabin is passed over the pylon/pylons. For the operating a number of machine components are necessary, see Fig. 7.
Fig. 7: Bridge rope inspection machine 1
hasp
5
2 3
poller station deflection unit for the carrying rope deflection unit for the traction rope
6 7
deflection unit at the pylon shaft for carrying and traction rope deflection spreader traction rope
8
traction rope winch
4
4.3
9
working platform with lift winch
10 11
carrying rope Chassis with hangings
Magnetic inductive test
For the inspection of ropes to detect wire fractures the magnetic inductive test is used. To do this a magnetic sensor is pulled along the single rope and the sensor reacts to changes of mass. By the different intensity of the signals of the magnets located around the rope a localisation of new wire fractures is possible by comparison with the test 6 years before. By comparison of the summed up wire fractures with the condition just after completion of the structure during the first test an estimation of the bearing behaviour is possible. It is only necessary to sum up these wire fractures which lay within four lay lengths because every broken wire bears the full load after two lay lengths. As the magnetic sensor has a big load and stresses the rope surface by wheels directly caution is necessary at the corrosion protection coatings. Investigations are desirable to develop less sensor loads.
5.
Investigations of Ropes
By the bast investigation were carried out with the aim to get information about the mechanical situation for bridges ropes in the structure. Beside that investigations were done about the climatic effects by exposure tests. At a chemical laboratory the chemistry of the blocking agent itself was investigated. In particular the water absorption was important. Also the outer corrosion protection was investigated especially in covered areas later not accessible as clamps, saddles, anchorages e.g., and long time experiences were evaluated.
8
At long time measures at a cable stayed bridge the load changes at ropes were registered [6]. It was shown that the big rope elongations did not result from rope vibrations but from superstructure vibrations. However the sums of the elongations are nearly the same for both reasons due to the more frequent occurence of the rope vibrations e.g. as a result of wind. Temperature measures were also carried out at ropes where the temperatures were measured on and under the corrosion protection coating and the sensors, see Fig. 8, located in one cross section up and down, upstream, downstream each 90° progressively. There were big differences on and under the coating, where in Fig. 9 the given curves are the mean values of the four temperatures. For the conditions in the rope this means that also at intensive sun shine the temperatures in the inner rope are not as high as on the surface of the rope.
Fig. 8: Temperature sensors
9
Fig. 9: Temperatures at the rope on and under the corrosion protection coating
6.
Conclusion
The locked coil rope in bridge structures presents itself as a robust, durable and easy-care member if the requirements of the above mentioned regulations are fulfilled which can be inspected easily, too. Single wire breaks of the outer layer possibly appearing are not critical and can be seen at the surface.
7.
Literature
[1]
TL Seile– Technische Lieferbedingungen für vollverschlossene Brückenseile. Bundesministerium für Verkehr, Abteilung Straßenbau. Verkehrsblatt Verlag Dortmund 1994
[2]
ZTV-KOR-Seile – Zusätzliche Technische Vertragsbedingungen und Richtlinien für den Korrosionsschutz von Seilen und Kabeln im Brückenbau. Bundesanstalt für Straßenwesen Entwurf 1998
[3]
Richtlinien für den Korrosionsschutz von Seilen und Kabeln im Brückenbau – RKSSeile. Der Bundesminister für Verkehr, Abteilung Straßenbau, Deutsche Bundesbahn Ausgabe 1983
10 [4]
DIN 1076: Ingenieurbauwerke im Zuge von Straßen und Wegen, Überwachung und Prüfung. Normenausschuß Bauwesen (NABau) im DIN Deutsches Institut für Normung e.V. März 1983
[5]
DIN EN ISO 12944 – Parts 1 - 8: Paints and varnishes – Corrosion protection of steel structures by protective paint systems 1998
[6]
Eilers, M., Hemmert-Halswick, A.: Seilverfüllmittel – Mechanische Randbedingungen für Brückenseile. Bericht der Bundesanstalt für Straßenwesen, Brücken- und Ingenieurbau Heft B 16. Wirtschaftsverlag NW Bremerhaven 1997
[7]
Vermerk BSG des LVR Köln 1988
Experimental Analysis of the Active Tendon Control of a Large-Scale Cable-Stayed Bridge Mock-up.
Georges MAGONETTE
ELSA Laboratory, Ispra (VA), Italy.
Carl HANSVOLD JOHS.HOLT A.S., Oslo, Norway.
Vito RENDA
Yves. BOURNAND
Alan G. JENNER
Heino FÖSTERLING
ELSA Laboratory, Ispra (VA), Italy.
VSL France, Massy, France.
Newlands Technology Ltd, , Mannesmann Rexroth AG, VT Hull, GB. Lohr, Germany.
Summary A large-scale cable-stayed bridge mock-up has been constructed and installed at the ELSA Laboratory of the JRC-Ispra. This mock-up has been equipped with active tendon actuators to increase the structural damping in order to mitigate vibrations. The testing campaign in preparation at ELSA aims to validate the control strategy for active damping developed at the Université Libre de Bruxelles and to analyse the behaviour of the most critical element of the active damping system: the actuators. This paper is part of a trilogy [1, 2] submitted to this conference by the consortium involved in the Brite-Euram project ACE [3]. It is focused on the mock-up description and on the preparation of the experimental verification of the active system installed on the bridge mock-up. The testing activity is currently in course and the experimental results will be presented at the conference.
1.
Introduction
Improvements in materials and computational technology have led to progressively longer and more slender cable-stayed bridges (Fig. 1 and 2). Long inclined cables are characterised by low structural damping and low natural frequencies. They are flexible and light and prone to vibrate under dynamic disturbances from wind and traffic. Stay cables are designed to be tension elements that can support loading up to about 50% of the ultimate strength of the steel elements used for the stay. From about 1977 several events of cable vibrations have been observed in various types of cable-stayed bridges. During stay vibrations some stays can reach peak amplitudes of oscillation of more than five times the stay diameter. During these vibrations, the resulting stresses in the stay are unknown. The state of stresses in the steel element is critical in the anchorage region due to bending stresses with effect of fatigue and fretting in this area. Damage of anchor details and cable ducts has been reported. Much progress has been made in bridge dynamics during the last 10 to 20 years. In several cases the exciting mechanisms have been identified, and engineers and scientists have progressively got a better understanding of the problems. A frequent reason for cable vibrations appears to wind in combination with rain: the so-called rain-wind induced vibrations. But also wind and traffic loads may give parametric excitation of the cables resulting in unacceptable oscillations. To prevent such vibrations, passive measures like cross-ties interconnecting the stay cables or dampers installation at the bridge deck have been widely used. But some problems have occurred with these systems. The initial tension of the cross-ties must be selected with care in order to avoid detensioning and shock effects in the cable system. Viscous dampers located
near the cable anchorage at bridge deck have a limited damping effect, in particular in the case of parametric excitation. For long cables, the active damping strategy may be applied. The aim of the active control system is to upgrade the damping of the structure and consequently to mitigate the induced vibration of the stay cables. The methodology considered here is based on an active tendon consisting of an actuator collocated with a force sensor. The active damping is based on the control of the displacement of the cable anchor point. This technique developed at the Université Libre de Bruxelles [4, 5] has a strong physical support and its effectiveness has been confirmed experimentally by tests performed on small-scale mock-ups.
Figure 1: The Skarnsundet cable-stayed bridge in Norway (Trondheim).
Figure 2: The Normandie cable-stayed bridge in France (Le Havre).
The computer simulation software developed in the ACE project takes into account the cable dynamics, its interaction with the structure and the possibility of active control of some of the cables. The main objectives of the experimental analysis of the cable-stayed mock-up are to provide benchmarks for checking the validity of the dynamic computer model and to study the effect of active control applied to a representative model of a bridge structure. The potential interaction between cables and structure will be analyzed by the tests achieved on the mock-up. The validation of the active control system prototype on a large-scale mock-up will give us a better knowledge of the non-linear dynamic behavior of the cables and of the real loads in the cables and the anchorage. The proposed design and testing of the large-scale bridge mock-up are outlined here. After the description of the mock-up and of the control actuators, details are given on the measurement system and on the testing campaign in preparation to assess the performances of the active tendon system. The experimental results not yet available at the moment will be presented at the conference.
2.
Mock-up description
The bridge mock-up has been designed by Bouygues. It is a cable stayed cantilever beam that will basically represent a cable-stayed bridge under construction. The deck, about 30-m long (which is the maximum dimension allowed in the ELSA laboratory), is mainly composed of two H-beams whose axis are spaced 3.0-m apart (Fig. 3). They are appropriately linked each 3.5-m with transversal H-beams to provide to the whole structure sufficient transverse and torsion stiffness. Each H-beam is fixed to the Reaction Wall. The vibration excitation source is anchored at the free end of the deck. Four pairs of parallel stay cables support the deck. Each2 stay-cable is composed of one T13 strand (7 non-circular wires, total section of 112mm ) with a slope of 1/3. This slope is very closed to that of the longest stay cable of modern
bridges. A couple of secondary tie-cables will be inserted in order to study the control of transverse vibrations of the stay-cables. The static tension being about 70 kN, the first free frequency of the longest stay cables (29.5 m long) is around 5.7 Hz, which can be rarely met on modern cable stayed bridges. To give the stay cables enough sag and consequently reduce their free vibration frequencies, they are heavily overloaded with split lead cylinders. This increases their average mass to an amount of about 15 kg/m. In this way, the sag of the longest stay cables is about 0.8 % of their length and their first free frequency in the vertical plane is closed to 1.2 Hz.
By positioning the intermediate support under the deck, the vibration frequencies of the whole structure can be varied.
Figure 3: large scale cable-stayed bridge mock-up in construction at the ELSA Laboratory of the JRC-Ispra. It is possible to adjust the stay cables length in order to obtain a very critical situation for the structure: the first vertical free frequency of the complete structure (flexion) can be very close to that of the longest stay cable. By positioning an intermediate support under the deck, the vibration frequencies of the whole structure can be varied and eventually adjusted to be very near to the double value of the first vertical free frequency of the longest stay cable. Similarly by modifying very slightly the length of the stay cables or by reducing the amount of additional masses gripped on the stay cables, it is possible to merge or to separate modal frequencies and to create critical situations for the structural behaviour. As designed, the mock-up will allow the complete analysis of numerous particular situations. Without the intermediate support under the deck, the first modal frequencies of the structure are estimated to 1.10 Hz for the first flexional vertical mode, 1.17 Hz for the first torsional mode and 3 Hz for the first flexional horizontal mode.
3.
Actuator description and tests
3.1
Hydraulic actuator
The main function of the hydraulic actuator is to track the displacement command required by the damping law. As the actuator is mounted between the bridge deck and a stay cable it has to carry both the static and the quasi-static loads (bridge deck and live loads). Energy-saving concerns led to the design of an actuator integrating two functions within one device: an asymmetric large cylinder (pressurised by an accumulator) compensates the static load while a smaller double rod cylinder provides the displacement necessary to satisfy the damping law (Fig. 4).
Figure 4: Hydraulic Actuator (Principle) The manufacturer carried out the preliminary tests. A special set-up was designed to analyse the dynamic performances of the hydraulic actuator and to fit its numerical model. Nevertheless the response of the actuator depends of the external loads and disturbances. Therefore it is necessary to incorporate the actuator into the structure (bridge mock-up) in order to: • assess the functioning of the actuator under real load conditions including the spring-mass behaviour of the cable and the lateral forces acting on the actuator head. • optimise the setting of the control loops. • test the auxiliary functions (soft start/stop, monitoring functions, ...) and the fail-safe situations. • measure the energy consumption and establish an energy balance. • achieve the measurements necessary for the validation of the actuator/ bridge numerical model. • investigate alternative electro-hydraulic designs. During the experimental tests all important state values describing the dynamic behaviour of the electro-hydraulic system will be measured and recorded for documentation. This includes the command signal, the cylinder load cell signal, the servo-valve spool position, the cylinder displacement, the oil pressure in the cylinder chambers and in the accumulator, the oil supply pressure and the oil flow. The electro-hydraulic control sensors provide most of these measurements. The frequency filter designed to separate the static and dynamic components of the force acting on the cylinder will be fine-tuned to an optimum transfer function.
Moreover, as we assume that the performances of the prototype actuators in terms of dynamic requirements are overestimated, the experimental analysis should lead to optimised final specifications and alternative hydraulic concepts should be established to reduce the energy consumption to a minimum.
Figure 5: Mannesmann Rexroth double-function electro-hydraulic actuator for stay cable actuation. 3.2
Magnetostrictive Actuator
In engineering applications, the term magnetostriction is used to describe the magnetic-field induced strain exhibited by magnetic materials. For actuator and transducer applications, e.g. sonar and active vibration control, the material Terfenol-D, (typically Tb0.3Dy0.7Fe1.95) is of significant technological importance. This material is characterised by large magnetostrains, typically 1000-1600 ppm, with a high intrinsic force capability and is available commercially. A variety of devices, resonant and non-resonant, have been designed and constructed to harness the properties of Terfenol-D [6, 7]. Previous work on a non-resonant actuator with the highest possible bandwidth resulted in Europes largest actuator to date. This was capable of generating a net ac force of ~ 9 kN up to 400 Hz with a 20 mm diameter active element for 6 kW of input electrical power [8]. Each application usually has a set of unique specifications. These may include large displacements, minimum power consumption, etc. Compliance of the load has an effect on actuator forces and displacements. The design has to be chosen according to the actuators ultimate use. Within the remit of the ACE project two magnetostrictive transducer systems have been designed and are in the process of being fabricated for incorporation into a mock-up bridge test facility. These are intended for active damping trials of unwanted vibrations in the mockup. This aspect of the project was deemed to be highly innovative, both in terms of the technology to be employed and the scale of the actuators to be produced. These represent the largest such actuators to be constructed in Europe, to date. Each transducer consists of two Terfenol-D rods (30-mm diameter, 254 mm long) and a surrounding ac drive coil (with a limited dc biasing capability). Surrounding each drive coil is a ring-magnet stack supplying a static biasing field, which enables each transducer to operate within a linear region of the magnetic field strain loop. Without lever system amplification, the transducers would be expected to achieve ~ + 0.1mm of strain with an associated force ~13kN for an associated drive current of + 4 A. By using a lever system this is to be altered to achieve a maximum strain of ~ + 2 mm with an associated force of ~ + 0.64kN (for a gain of 20:1). Prestress biasing, necessary for optimum magnetomechanical performance, is through
the use of externally located disc springs which can be easily interchanged to alter compliance and maximum pressure loading (up to ~40MPa) (Fig. 6). After fabrication, each device will be characterised to enable actuator integration into a local control-structure prior to inclusion in the bridge mock-up (Fig. 7). A Instron tensile/compressive test rig has been modified to allow such a characterisation (Fig. 8). An example of the tests envisaged are as follows; conduct impedance and strain analyses under various internal prestresses and drive frequencies with and without external mechanical to determine optimal prestress. Characterise the performance of device for transient response.
0.5 m
Figure 6: Schematic of magnetostrictive actuator
Figure 7: System configuration and attachment
Instron crossbeam
Load cell
Laser probe positions Variable ‘k’ lever arm adapter ~80% extant
Ability to change transducer’s location required
Instron base
Transducer support base
Figure 8: Transducer characterisation set-up
4.
Exciter
The mock-up will be excited by a shaking devices located at the free end of the deck. The forced vibrations will be obtained by means of electro-hydraulic device operating in a frequency sweep excitation manner. This kind of excitation, where the input force can be perfectly monitored and measured, is the most suitable to perform experimental modal analysis. The exciter will produce a unidirectional force with a continuously adjustable amplitude and frequency in the range of 1 to 50 Hz. The total mass of the structure being about 10,000 kg, the maximal exciting force value has been estimated in the range of 1.5 to 2.5 kN. The objective is to get, in all critical situations listed in chapters 2 and 5, a vertical vibration of the deck with an amplitude close to 25 cm peak to peak without any active tendon control system; this could not bring any part of the mock-up in a dangerous situation. The electro-hydraulic exciter, especially designed for this application, is equipped with modular inertial masses. Loaded with a 450-kg mass it is able to generate a sinusoidal inertial force of 2.5 kN at a frequency of 1 Hz. For a given frequency, changing the displacement amplitude or the inertial masses can vary the exciting force. Three positions have been selected for the installation of the exciter on the transversal beam located at the free end of the deck: • a central vertical position to excite the vertical flexional modes, • a decentralised vertical position to excite both the flexional and torsional modes,
•
5.
a central horizontal position to excite the torsional modes. In this last case there will be also a quasi-static excitation on the flexional transversal modes with a low amplitude response.
Testing campaign
The specific objectives of the testing campaign are: • to improve the understanding of induced vibrations (the mock-up will be subjected to forcing functions), • to validate the numerical tools for prediction of dynamic behavior of cables, • to verify the capability of the active system to mitigate the effects of induced vibrations, • to evaluate in detail the performances and the reliability of the whole implementation. The testing campaign will begin with modal analysis of the structure equipped with the cables without additional masses. Performing frequency sweep excitation and free vibration tests the first vertical mode (≈ 1.1 Hz), the first torsional mode (≈ 1.17Hz) and the modal damping coefficients will be determined accurately. These values will be used to adjust the numerical model and to compute the masses of the lead cylinders to fix on the longest cables. Afterwards, following the same procedure, the structure equipped with the overloaded cables will be characterised. In addition, the tension of each of the four longest stay cables will be accurately adjusted to obtain the same vibration frequency for the two cables of each pair. The vibration frequency and the damping coefficient of each cable will be determined by applying an excitation at half-length with the help of a small electro-dynamic exciter. The measurements will be carried out with accelerometers or laser scanning systems. Successively, by adjusting the structural parameters of the mock-up, modifying some coefficients of the control law or changing the force loading conditions, a large spectrum of critical configurations will be investigated. In a very close frequency interval, with the adopted adjustments, the following cases can be found (assuming that stay cables #4 are the longest ones): The first vertical free frequency of the complete structure (flexion behaviour) can be made very close to that of the longest stay cable. By modifying very slightly the length of the stay cables, it is possible to clearly separate the frequencies of the first vertical mode of stay cables #4 and the first vertical mode of the structure. Similarly, it is possible to nearly merge the frequencies of the first vertical modes of both stay cables #3 and #4 and the complete structure. Positioning the intermediate support under the deck, between the lower anchor heads of stay cables #2 and #3, the first free frequency of the whole structure can be very near from the double value of the first vertical free frequency of stay cable #4; this is an other situation considered as critical for the structure behaviour. By reducing the amount of additional masses gripped on the stay cables, the first free frequency of the stay cables #4 can be very near from two times the first vertical free frequency of the structure, which is an other critical situation (sub-parametric excitation). Finally, the efficiency of secondary tie cables with or without active tendon control systems will also be tested. As designed, the mock-up will allow the complete analysis of numerous critical situations. This mock-up is unique to improve our knowledge in stay cable dynamics. While substantial progress has been made in the study of components of active damping systems, little attention has been paid to the overall performance of the system applied to a realistic structure. The structural control system consists of a number of important components such as sensors, controllers, actuators, and power generators that must be part of an integrated system. Moreover, a number of implementation-aspects must be addressed such as intermittent and fail-safe operations, integrated safety, reliability and maintenance. These issues require experimental verification under realistic conditions.
6.
Instrumentation
Special care has been assigned to the selection of the most appropriate dynamic testing techniques and to the selection of the transducers, including their conditioning electronics. Measurement equipment will include conventional instrumentation consisting of temposonic and inductive displacement transducers, accelerometers, and strain gauges. Load cells will be installed in series with the stay cables and the secondary cables. Laser displacement sensors will be used to monitor the lateral displacements of the deck. To measure the tendon vibrations other techniques will be considered such as line-scan camera and a laser scanning systems currently in development at the JRC. Depending of its frequency spectrum, each signal will be acquired with a constant sample frequency included between 50 and 1000 Hz. Each test has duration from 6 to 10 minutes. All the measured values will be recorded continuously on hard disc and will be processed subsequently. To help the users to interact with the experiment, some measures such as the cables tension will be displayed in real-time.
7.
Conclusion
A large-scale cable-stayed bridge mock-up has been constructed and installed at the ELSA Laboratory of the JRC-Ispra. This mock-up has been equipped with active tendon actuators to increase the structural damping in order to mitigate vibrations. The bridge mock-up and the exciter system have been designed to allow an independent adjustment of all the parameters of the controlled system: • the excitation force in amplitude, frequency or direction (flexion and/or compression), • the vibration modes of the structure (by moving an auxiliary support or changing the cables tension), • the number of active devices (1 or 2), • the gain of the control law, • the delay between the activation of the control and the start of the exciter. The experimental tests will be repeated with different loading conditions to provide the reliable data necessary for the validation of a numerical model that includes the structural dynamics, the control system and the actuator dynamics. The deliverables will help the various industrial involved in cable-supported structures to better understand the behaviour of the structures when exposed to vibrations induced by wind, live load, or seismic phenomena.
Acknowledgements Funding under the EC Brite-EuRam programme (Contract No. BRPR-CT97-0402) is gratefully acknowledged. The authors acknowledge the contributions of their colleagues at DERA, Farnborough, UK; BOUYGUES BTP, St Quentin en Yvelines, France; Technische Universität Dresden, Germany; and Université Libre de Bruxelles, Belgium.
Reference [1]
A. Preumont, S. Helduser, H. Foersterling, N. Galloway, "Active Tendon Control of Cable-Stayed Bridges: Control Strategy and Actuator Design", IABSE Conference on: Cable-Stayed Bridges - Past, Present and Future. Malmö, June 2-4, 1999.
[2]
C. Dumoulin, "Active Tendon Actuators for Cable-Stayed Bridge", IABSE Conference on: Cable-Stayed Bridges - Past, Present and Future. Malmö, June 2-4, 1999.
[3]
ACE Project funded by the European Community under the Industrial & Materials Technologies, Programme Brite Euram 3, Proposal N.BE96-3334, Contract N.BRPRCT97-0402, ACE: Active Control in Civil Engineering (1998).
[4]
F. Bossens & A. Preumont, "Experiments of active control of cable structures", MOVIC-4, Zurich, August 1998.
[5]
Y. Achkire, "Active Tendon Control of Cable-Stayed Bridges", Université Libre de Bruxelles, Faculty of Applied Sciences, Department of Mechanical Engineering and Robotics, Thesis for the degree of Doctor in Applied Sciences (1997).
[6]
R.D. Greenough, I.M. Reed and M.P. Schulze, Magnetostrictive Actuators in Advances in Actuators (Institute of Physics, London) Ed. A.P. Dorey and J.H. Moore, chapter 8, pp179-211 (1995).
[7]
F. Claeyssen, D. Colombari, A. Tessereau and B. Ducros, Magnetostrictive Actuators , IEEE Trans. Mag 27(6), p5343 (1991).
[8]
M.G. Aston, R.D. Greenough, A. G. Jenner, W.J. Metheringham and K. Prajapati, Controlled High Power Actuation Utilising Terfenol-D , Proc. the 3rd International Conference on Giant-Magnetostrictive Materials, Honolulu, Hawaii, USA, November, 1996. J. Alloys and Compounds 258 (1-2), pp.97-100 (1997).
Vibration Control of Stay Cables J. STUBLER Technical Director Freyssinet International Vélizy (France)
P. LADRET Principal Engineer Freyssinet International Vélizy (France)
J.B. DOMAGE Principal Engineer Freysssinet International Vélizy (France)
Summary During the recent past years several analyses have been conducted dealing with the vibration characteristics of stay cables. The fundamental theories as well as the fundamental behaviour of various types of cables have been developed. At the same time, various remedies and vibration control devices were proposed by contractors and suppliers. This paper reviews the previously used systems and presents the up-to-date technology which is available today. It covers the streamline sheath coping with the rain and wind vibration phenomena, the internal or external hydraulic dampers, the visco-elastic dampers and the damping cross ropes. Calculations of the damping system characteristics, prediction and measurement of the damping ratio are presented.
1. Introduction Cable vibrations can be excited by dynamic wind forces acting directly on the cable itself or by the movements of the cable attachments on the pylon or on the deck due to the action of traffic loads or of the wind itself. Four different sources of vibrations are considered in the analysis : - parametric excitation by the movements of the pylons and the deck ; - rain and wind vibration ; - low wind dry vortex ; - galloping.
2. Damping definition a The logarithmic decrement is defined as δ = ln n where a n+1 and a n are two an +1 consecutives amplitudes of the vibration of a system left free to vibrate.
Figure 1 Usually the stay cables have a high fatigue resistance but, consequently, low natural damping characteristics.
3. Damping analysis 3.1 Excitation due to movement of pylon and deck Calculations of the amplitude of vibrations have to be done for each wind speed and each mode of the structure. The root mean square amplitude is then calculated. Two criteria should be considered : 1. Appearance and comfort requirements (at 15 m/s wind speed). a Amplitude « a » should be limited to L = cable length < 0,0006 . L 2. Admissible deviation angle at the anchorage : depending on the cable system, α is the admissible deviation angle at the anchorage. a α Amplitude « a » should be limited to < . L π 3.2 Rain and wind vibrations The presence of a double helical rib will reduce the amplitude of stays. This has been demonstrated by the two wind tunnel tests carried out at the CSTB laboratory (Nantes) in 1992 for the Normandie bridge and at the Danish Maritime Institute in 1997 for the Øresund bridge.
Figure 2 In case of no helical ribs, a stability criteria could be deducted from SAITO [1]
Sc =
mδ > 10 2πρD 2
m = cable mass per unit length
δ = logarithmic decrement ρ = air density D = cable diameter
Sc is the SCRUTON number or the mass damping parameter. For typical stay cable (mass and diameter) the requested logarithmic decrement should be higher than 3 to 6 %. 3.3 Low wind dry vortex This kind of vibration, induced by vortices around the cable profile, appears at a certain wind speed V such that ND V= 0,22 is the STROUHAL number 0,22 N = frequency of cable vibration. This phenomenon excites only the high frequencies in low wind conditions (small amplitudes of vibrations). This is not a major concern in most cases and a logarithmic decrement δ > 3 % should be recommended.
3.4 Galloping This phenomenon has been observed apparently in Japan for high wind condition [1]. If it has never been clearly identified on a bridge, one reason could be the fact that at high wind speed, the value of the aerodynamic damping is high. It is interesting to look at some recent experiences : a) Second Severn bridge There could be two interpretations of the phenomenon which occurs on January 1995. One of them is that it was galloping , the other is that it was excitation of the deck from the wind which was exciting the stay cable (the Second Severn stay cables have a low frequency as the stay cables have a low permanent stress). The vibration amplitudes of the stay were huge. This level of vibration is a first indication that it could be a deck induced excitation. In addition to that, the mode of the deck was a frequency similar to the stay cable one. After the erection of the cross ties on that bridge, a second vibration event occurs ; at that time the cables were stable but the deck has some higher vibration. So it really seems to be that it was an excitation of the deck. When the cross ties were installed the energy of the deck was no more shared with the stay cable. b) Normandy bridge mξ is coming from an extrapolation of an article by ρD 2 SAITO [1] published at the Normandy Symposium (October 1994) with C = 35 to 40. If this criteria is applied on the existing bridge we should have experienced huge galloping. A proposed criteria Vcrit = CND
ξ =
δ damping ratio - to - critical 2π
During construction – longest stay : Vcrit = 40 × 0,3 × 0,2
70 × 1,6 × 10 −3 = 3,62 m/s. 1,23 × 0,2 2
c) Elorn bridge . before placing dampers : Vcrit = 40× 0,63 × 0,2
92 × 1,27 × 10 −3 = 7,76 m / s 1,23 × 0,2 2
. after placing dampers : Vcrit = 19,42 m/s. No galloping has been observed. These observations tend to prove that the SAITO results are questionable. No doubt that more research is needed on that subject of galloping.
4. Damping technologies 4.1 Damping ropes The natural frequency of the stays can be modified by means of transversal cables connected to them. This solution which is effective although expensive and delicate to install has been used for some large bridges. It is recommended when the vibration frequencies of the deck or pylon are close to the frequencies of the stay cables. For the Normandie Bridge, the main vibration period for vertical bending would have been of the same magnitude as the vibration period of the longer cables i.e. 4.5 seconds. The cross ropes reduce the periods of the cables to 1.25 second and less (ref. [2]). Four ropes connect all cables in each plane of stays. Their tension was selected to avoid slackening effects. They consist of a bundle of stainless steel wire ropes fully embedded in HDPE and other dampening plastic material. They went through a testing programme for fatigue and damping capacity. A steel collar provides the fixation of the ropes on each stay and facilities for any orientation. 4.2 External hydraulic damper This damper is specifically designed to each project. The damping capacity can be tuned to obtain the required logarithmic decrement. However it requires a regular maintenance and it is not always meeting the aesthetics objective of the designer. 4.3 Internal visco-elastic damper (IED) and Internal hydraulic damper (IHD) This damper is completely invisible from the deck since it is located inside the steel guide pipe of the stay cable.
Figure 3
5. Vibration control Calculation models have been developed to evaluate the logarithmic decrement δ provided by the various types of damping systems. A universal damping surface has been established allowing an accurate tuning of the damper. On the other hand damping measurement can be
carried out on the cables after installation. Examples of Tagus bridge in Lisbon (Portugal) and Charles River bridge in Boston (USA) are shown here below :
Charles River bridge (Boston)
Tagus bridge Lisbon (Portugal)
REFERENCES [1] Saito T., Matsumoto M. and Kitazawa M. (1994) : Rain-wind excitation of cables on cable-stayed Higashi-Kobe bridge and cable vibration control, Proceedings of Conference on Cable-stayed and Suspension bridges / Deauville (France), 12-15 October 1994, pp. 507-514. [2] Virlogeux M. (1995) : Design of cables for cable-stayed bridges : the example of the Normandie bridge, Proceedings of the International Symposium on Cable Dynamics / Liège (Belgium), October 19-21. [3] Virlogeux M. (1998) : Cable vibrations in cable-stayed bridges, Proceedings of Bridge Aerodynamics Symposium / Copenhagen (Denmark), 10-13 May 1998. [4] Matsumoto M. (1998) : Observed behavior of prototype cable vibration and its generation mechanism, Proceedings of Bridge Aerodynamics Symposium / Copenhagen (Denmark), 10-13 May 1998.
Active Tendon Control of Cable-Stayed Bridges: Control strategy and Actuator Design A. PREUMONT Université Libre de Bruxelles Bruxelles, Belgium
S. HELDUSER Technische Universität Dresden, Germany
F. BOSSENS Université Libre de Bruxelles Bruxelles, Belgium
R. BONNEFELD Technische Universität Dresden, Germany
H. FÖRSTERLING Mannesmann Rexroth Germany
Summary This paper is part of a trilogy describing the Brite-Euram project “ACE”. The first part of the paper describes the control strategy for active damping of cable structures with an active tendon collocated with a force sensor. The main analytical results for predicting the closed-loop poles are summarized and the procedure for selecting the number and the location of the active tendons is outlined. The second part of the paper describes a laboratory experiment with a small size mock-up representative of a cable-stayed bridge during its construction phase. The control of the parametric vibration of passive cables due to deck vibration is demonstrated. Finally, the third part of the paper outlines the conceptual design of an hydraulic actuator for industrial applications.
1. Introduction In recent years, cable structures have had spectacular applications in large cable-stayed bridges. However, cable and deck vibrations have become a major design issue, because the ever increasing span of the bridges makes them more sensitive to flutter instability as well as to wind and traffic induced vibrations. An overview of the stay cable vibration and control is available in [1]. The difficulty of damping the stay cable vibration justifies the development of active devices for future large bridges. This paper is part of a trilogy describing the current status of the Brite-Euram project ACE [2,3,4]; it is a follow-up to several papers where the theory was gradually developed [5,6,7,8,9,10]. Its goals are to confirm and extend previous results obtained with a laboratory size mock-up, and to outline the design of an hydraulic actuator as required for a large scale application. It is organized as follows: section 2 summarizes the control strategy for active damping of cable structures, section 3 states without proof approximate analytical results for the closed loop poles. The experimental results obtained with the laboratory mock-up are described in section 4 and the conceptual design of the hydraulic actuator is outlined in section 5. Section 6 gives some concluding remarks.
2. Control of Cable Structures 2.1. Tendon control of strings and cables The mechanism by which an active tendon can extract energy from a string or a cable is explained in Fig.1 with a simplified model assuming only one mode (Rayleigh-Ritz), for situations of increasing complexity. The simplest case is that of a linear string with constant tension To (Fig.1.a); the equation becomes nonlinear when the effect of stretching is added (cubic nonlinearity). In Fig.1.b, a moving support is added; the input u of this active tendon produces a parametric excitation, which is the only way one can control a string with this type of actuator. The difference between a string and a cable is the effect of gravity which produces sag (Fig.1.c).
Fig.1: Mechanism of active tendon control of strings and cables In this case, the equations of motion in the gravity plane and in the plane orthogonal to it are no longer the same, and they are coupled. In the gravity plane, the active tendon control u still appears explicitely as a parametric excitation, but also as an inertia term − α c u whose coefficient
αc depends on the sag of the cable; even for cables with moderate sag (say sag to length ratio of 1% or more), this contribution becomes significant and constitutes the dominant control term of the equation. On the contrary, in the out-of-plane equation (y coordinate), the tendon control u appears explicitely only through the parametric excitation, as for the string. The use of the parametric excitation to damp the transverse vibration of a string was explored by J.C. Chen [11]; the same strategy was used to control the out-of-plane vibration of cables by Y. Fujino [12] who also investigated the use of the inertia term for active damping of cables in the gravity plane [13]. These attempts used non-collocated feedback of the transverse amplitude; they worked well when the interaction of the cable with the supporting structure was weak, but they became unstable when the interaction was strong. On the contrary, the approach followed in the present study, which is based on collocated actuator/sensor pairs, is guaranteed to stabilize all the states which are controllable and observable.
2.2. Control strategy It is widely accepted that the active damping of linear structures is much simplified if one uses collocated actuator-sensor pairs [7]; for nonlinear systems, this configuration is still quite attractive, because there exists control laws that are guaranteed to remove energy from the structure. The direct velocity feedback is an example of such "energy absorbing" control. When using a displacement actuator (active tendon) and a force sensor, the (positive) Integral Force Feedback (1) u = g ∫ T dt
Fig.2: Active damping of cable structures (refer to Fig.2.a for notations) also belongs to this class, because the power flow from the control system is W = −T u = − gT 2 . This control law applies to nonlinear structures; all the states that are controllable and observable are asymptotically stable for any value of g (infinite gain margin). 2.3. Experiment The foregoing theoretical results have been confirmed experimentally with a laboratory scale cable structure similar to that represented schematically in Fig.2.a, where the active tendon consisted of a piezoelectric actuator [6]. Figure 2.b shows the experimental frequency response between a force applied to the structure and its acceleration; also shown in the figure is the free response of the structure with and without control. We see that the control system brings a substantial amount of damping in the system, without destabilizing the cable (theoretically, the control system does indeed bring a small amount of damping to the cable, which depends on the sag, as we have seen in the previous section); this behaviour is maintained at the parametric resonance, when the natural frequency of the structure is twice that of the cable.
2.4. Decentralized control The foregoing approach can readily be extended to the decentralized control of a structure with several active cables, each tendon working for itself with a local feedback following Equ.(1). This statement was verified experimentally on a T structure controlled with two cables [8]. It is important to point out that the concept of active tendon control of cable structures does not require that all the cables be active; on the contrary, the control system would normally involve only a small set of cables judiciously selected. Next section summarizes the main results of an approximate linear theory to predict the performance of the control system and provides design guidelines to select the active cables.
3. Closed-loop Poles If we assume that the dynamics of the active cables can be neglected and that their interaction with the structure is restricted to the tension in the cables, it is possible to develop an approximate linear theory of the closed-loop system.
Fig. 3: Root locus of the closed-loop poles For a decentralized feedback control law g δ = K c−1T (2) s where T is the local force measurement, δ is the active tendon displacement, Kc is the stiffness of the active cable (Kc-1T represents the elastic extension of the active cable) and g is the control gain (the same for all control elements), the following results have been established in earlier studies [6]: 1. If we assume no structural damping, the open-loop zeros are ± jωi where ωi are the natural frequencies of the structure where the active cables have been removed. 2. The open-loop poles are ± jΩi where Ωi are the natural frequencies of the structure including the active cables.
3. As g goes from 0 to ∞, the closed-loop poles follow the root locus corresponding to the openloop transfer function (Fig.3) s 2 + ω i2 G (s) = g (3) s s 2 + Ω i2 Thus, the closed-loop poles go from the open-loop poles at ± jΩi for g=0 to the open-loop zeros at ± jωi for g → ∞. 4. The depth of the loop in the left half plane depends on the frequency difference Ωi−ωi and the maximum damping, obtained for g = Ω i Ω i / ω i , is
( (
) )
Ωi − ωi (4) 2ω i 5. For small gains, the modal damping ratio resulting from the active tendon control is given by gν i ξi ≈ (5) 2Ω i where νi=(Ω2i-ω2i )/Ω2i is the modal fraction of strain energy in the active cables.
ξ imax =
Equations (4) and (5) can be used very conveniently in the design of actively controlled cable structures.
4. Experiment The test structure is a laboratory model of a cable-stayed bridge during its construction phase, which is amongst the most critical from the point of view of the wind response. The structure consists of two half decks mounted symmetrically with respect to a central column of about 2 m high (Fig.4); each side is supported by 4 cables, two of which are equipped with active piezoelectric tendons (Fig.5). The maximum stroke of the active tendon is about 100µm.
Fig.4: Experimental set-up for the cable-stayed bridge (the small picture shows the Skarnsund bridge –Norway– in its construction phase)
Fig.5: Design of the active tendon 4.1. Closed-loop poles Figure 6 shows the evolution of the first bending and torsion closed-loop poles of the deck when the control gain increases (these poles have been obtained with the MATLAB Frequency Domain Identification Toolbox from frequency response functions). Also shown on the figure are the predictions of Equ.(3); the agreement is good for moderate values of the gain. For larger gains, when the modal damping exceeds 20%, the discrepancy between experimental and analytical results increases, but this seems to be essentially related to the identification algorithm which cannot distinguish oscillating poles from highly damped frequency responses (Fig.7). Note that damping ratios significantly larger than 20% can be obtained. Figure 7 shows typical frequency responses between the voltage applied to one of the active tendons and its collocated force sensor, for several values of the gains (respectively g1, 3g1, 10g1). We note that for large gains the resonant peaks of the structure have totally disappeared and that the one of the cable is also considerably reduced.
Fig.6: Evolution of the first bending and torsion poles of the deck with the control gain
Fig.7: Frequency response between an active tendon and the collocated force sensor 4.2. Control of parametric resonance In this experiment, the bridge deck is excited with an electrodynamic shaker and the tension in the two passive cables on one side is chosen in such a way that the 1st in plane mode of one of them is tuned on the global bending mode of the deck (f), while its neighbour is tuned on f/2, to experience the parametric resonance when the deck vibrates. This tuning is achieved by monitoring the cable vibration with a specially developed optical measurement system described in [14].
Fig.8: Vibration amplitude of the bridge deck and the two passive cables at f and f/2
Fig.9: Detail of Fig.8 between t=10 and t=14 sec showing the transition from the forced response at f to the parametric resonance at f/2 Figure 8 shows the vibration amplitude of the deck and the transverse amplitude of the in-plane mode of the two passive cables when the deck is excited at resonance; the excitation starts at t=5sec and the control is turned on after t=30 sec. We note that : 1. The amplitude of the cable vibration are hundred times larger than the deck vibration. 2. The parametric resonance is established after some transient period in which the cable vibration changes from frequency f to f/2. The detail of the transition to parametric resonance is shown in Fig. 9. 3. The control brings a rapid reduction of the deck amplitude (due to active damping) and a slower reduction of the amplitude of the cable at resonance f (due to the reduced excitation from the deck). 4. The control suppresses entirely the parametric resonance at f/2. This confirms that a minimum deck amplitude is necessary to trigger the parametric resonance.
5. Hydraulic actuator design Although appropriate to demonstrate control concepts in labs, the piezoelectric actuators are inadequate for large scale applications. For cable stayed bridges, the active tendon control must simultaneously sustain the high static loads (up to 400 t) and produce the dynamic loads which are one order of magnitude lower than the static ones (<± 10 %). This has led to an active tendon consisting of two cylinders working together: one cylinder pressurized by an accumulator compensates the static load, and a smaller double rod cylinder drives the cable dynamically to achieve the control law. The two functions are integrated in a single cylinder, as illustrated in Fig.10; the double rod part of the cylinder is achieved by a rod in rod design.
Fig.10: Conceptual design of the hydraulic actuator This solution saves hydraulic energy and reduces the size of the hydraulic components. The double rod part of the cylinder is position controlled. The long term changes of the static loads as well as the temperature differences require adaptation of the hydraulic conditions of the accumulator. A medium size actuator based on the foregoing concept will shortly be tested in the large mockup described in a companion paper [3].
6. Concluding remarks The use of tension cables for active damping of cable structures has been investigated theoretically and experimentally. The decentralized control approach proposed is simple, robust and easy to implement ; in case of a sensor or actuator failure in an active tendon, the corresponding control loop simply returns to its passive state. Simple formulae have been developed for predicting the closed-loop poles; these formulae have been confirmed experimentally and they can be used very conveniently in the design, for selecting the number and location of the active tendons. The active control of a cable parametrically excited by the deck has been demonstrated experimentally. The conceptual design of an hydraulic actuator for large scale applications has been outlined; it will be used in the large scale experiment described in [4].
7. Acknowledgments This study was partly supported by the Brite-Euram project n° BE96-3334: ACE (Active Control in Civil Engineering) and the national program IUAP IV-24 on Intelligent Mechatronic Systems.
References [1] Yamaguchi, H. and Fujino, Y., “Stayed cable dynamics and its vibration control”, International Symposium on Advances in Bridge Aerodynamics, Copenhagen, May 98. [2] ACE, “Active Control in Civil Engineering”, Brite Euram project n° BE96-3334. [3] Dumoulin, C., “Active Tendon Actuators for Cable-Stayed Bridge”, IABSE conference on Cable-Stayed Bridges – Past, Present and Future, Malmö, June 1999. [4] Magonette, G., Bournand, Y., Hansvold, C., Jenner, A., “Experimental Analysis on a Large Scale Cable-Stayed Mock-up”, IABSE conference on Cable-Stayed Bridges – Past, Present and Future, Malmö, June 1999. [5] Ackire, Y. and Preumont, A., “Active tendon control of cable-stayed bridges”, Earthquake Engineering and Structural Dynamics, Vol. 25, N°6, June 1996, pp. 585-597. [6] Preumont, A. and Achkire, Y., “Active Damping of Structures with Guy Cables ”, AIAA, J. of Guidance, Control, and Dynamics, Vol. 20, N°2, March-April 1997, pp. 320-326. [7] Preumont, A., Vibration Control of Active Structures: An Introduction, Kluwer Academic Publishers, 1997. [8] Achkire, Y., Active tendon Control of Cable-Stayed Bridges, Ph.D. dissertation, Active Structures Laboratory, Université Libre de Bruxelles, Belgium, May 1997. [9] Preumont, A., Achkire, Y., and Bossens, F., “Active tendon control of large trusses”, 39th SDM Conference, Long Beach, April 1998. [10] Bossens, F. & Preumont, A., “Experiments of active control of cable structures, MOVIC-4, Zurich, August 1998. [11] Chen, J., “Response of Large Space Structures with Stiffness Control”, AIAA, J. Spacecraft, Vol. 21, N°5, September-October 1984, pp. 463-467. [12] Fujino, Y., Warnitchai, P., and Pacheco, B., “Active Stiffness Control of Cable Vibration”, ASME, J. of Applied Mechanics, Vol. 60, December 1993, pp.948-953. [13] Fujino, Y. and Susumpow, T., ”An experimental study on active control of planar cable vibration by axial support motion”, Earthquake Engineering and Structural Dynamics, Vol. 23, 1994, pp. 1283-1297. [14] Achkire, Y. & Preumont, A., “Optical measurement of cable and string vibration”, Shock and Vibration, Vol. 5, 1998, pp. 171-179.
CFRP-Tendons - Development and Testing Dipl.-Ing. Frank ROOS Lehrstuhl für Massivbau Technische Universität München Munich. Germany
Dr. J.F. NOISTERNIG Dywidag Systems International GmbH (DSI) Munich. Germany
Frank Roos, born 1969, received his civil engineering degree in 1997. He is now a research assistant at the Lehrstuhl für Massivbau at the Technische Universität München conducted by Univ.-Prof. Dr.Ing. Konrad Zilch.
Johannes F. Noisternig, born 1966, received his doctoral degree in mechanical engineering in 1995. 1991 1995 he was a research assistant at the Institute for Composite Materials (IVW) at the University of Kaiserslautern. Since 1996 he is the head of the polymer group in the technical department of DSI.
Summary Carbon fibre reinforced plastic (CFRP) in form of wires is a material with very interesting properties for stay cables or tendons like high tensile strength, high fatigue resistance as well as low weight and excellent chemical resistance. The anisotropic composition is the main disadvantage which makes it difficult to anchor the wires. This paper gives a short overview of the properties of CFRP-wires, the requirements for stay cables or tendons and the development of such a system by DSI as well as testing of stay cables at the Lehrstuhl für Massivbau of the Technische Universität München.
1
Introduction
The use of carbon fibre reinforced plastics in the past was restricted to the aerospace and defence industry. Besides the advantages of the strength / weight ratio and a high degree of chemical inertness in most civil engineering environments this new building material has very high material and manufacturing costs. Due to this fact the replacement of conventional civil engineering materials like steel and concrete succeeded very slowly in the past. This has changed since the high priced defence industry reduced its demand of these materials, advanced methods of manufacturing were introduced and the prospect for large volume applications in the construction industry appeared. First considerations on CFRP-tendons were made in the early eighties, when the possibility of a stay cable bridge over the Strait of Gibraltar, which is not possible if constructed in steel, was discussed. On closer examination the anchorage of CFRP-tendons was found to be the most important problem of this new building material was found [1]. The first applications have been realized in Japan and the USA [2]. In the last years also in Europe intensive developments have been started and lead to a first application of two CFRP-stay cables in the Stork Bridge in Winthertur, Switzerland in 1996 [3]. In Germany the DSI in co-operation with the Lehrstuhl für Massivbau of the Technische Universität München started a research project on CFRP-stay cables or tendons with a suitable anchorage in 1996. Today the developed CFRP-system
DYWICARB is ready for applications as stay cables in bridges or as tendons in other civil engineering constructions.
2
Carbon Fibre Reinforced Plastics
These materials consist of carbon fibres and a matrix. As carbon itself is very brittle the composition combine the excellent mechanical properties of carbon fibres with the ductile behaviour of the matrix, which is in most cases an epoxy resin. The reason for this change of brittleness of carbon fibres is on one hand due to structural and on the other hand due to static reasons. If a homogenous component consisting of carbon has a small notch in the surface or a defect of micro millimetre dimension in the inside it may fail suddenly. If an individual fibre of many fractures, the bundle will not break. When the fibres additionally are embedded in a matrix, the fibre takes up loading again at both sides of the fracture point. So the composition of two materials which on the first glance seems to be very complicated shows its advantages. These are mainly a very low density, a high strength and stiffness, a strong resistance against aggressive media and very good fatigue properties. Carbon fibres which have a diameter between 7 and 9 µm are mainly produced from Polyacrylnitril (PAN) pre-fibres in a multiple process of heating and stressing. By using several methods of manufacturing it is possible to achieve different properties of carbon fibres. The tensile strength ranges from 2000 N/mm2 up to 4500 N/mm2 and the modulus of elasticity from 200 000 N/mm2 to 650 000 N/mm2. To produce CFRP-wires the fibres are embedded in a matrix by pultrusion. Table 1 lists the properties of the CFRP-wire Carbon-Stress® used for the DYWICARB system and of conventional tensioning steel. Diameter Fibre volume content Tensile strength Modulus of elasticity Elongation at rupture Density Thermal coefficient of expansion
Carbon-Stress® CFRP-wire 5 mm 65 Vol.-% 2700 N/mm² 160 000 N/mm2 1.6 % 1600 kg/m³ 0.2 x 10-6 K-1
tensioning steel 5 mm ->1670 N/mm2 205 000 N/mm2 6.0 % 7850 kg/m3 1.2 x 10-5 K-1
Table 1: Properties of CFRP-wires and tensioning steel
3
Requirements to CFRP-Tendons
CFRP-systems have in no way been standardised nationally or internationally up to now. Therefore, it is very difficult to work out a valid table of requirements for CFRP-stay cables or tendons. However, working groups in Japan (JSCE), USA (ACI 440) and Canada (CSA S806) as well as Europe (fib task group 9.3) are striving to standardise materials, applications and calculation methods. The fib task group 9.3 is preparing progress reports for 1999 for a public discussion of such requirements. Standardisation and characterisation of the material of CFRP-elements can roughly be based on recommendations known from steel. However, it has to be clear that in contrast to steel, CFRP is no homogenous material and thus different CFRP-elements also show different properties. For a general characterisation of the material, not only the mechanical properties under static and
dynamic loading, but also durability as well as the behaviour under influences of different media are of importance. As the behaviour of a CFRP-stay cable can not be described exactly by calculation, tests have to be performed for each project. The testing can be done according to the PTI recommendations for Stay Cable Design, Testing and Installation [4]. With regard to the application of CFRP-tendons generally a high static and dynamic capacity of the anchorage must be achieved to exploit the material as far as possible. For the dynamic test the upper load range is 0.45 of the theoretical ultimate load with an amplitude of 160 MPa. Normally the ultimate strength of a single CFRPwire can not be reached in stay cables with a large number of wires due to the anchorage problem. The typical failure of CFRP-elements is a wire fracture in the first third of the anchorage length. So the acceptance criteria of the PTI should be changed. For the ultimate strength test of the stay cable after two million load cycles not the ultimate strength of one wire but of the whole stay cable should be the reference for the acceptance. The failure load of a stay cable after the dynamic test has to be 0.9 (this value has to be discussed in the task groups) of the static ultimate load of a similar stay cable specimen. There should be no wire fracture during the fatigue test. For the evaluation of the durability of CFRP-systems, especially of anchorages, the lifetime under permanent load as well as the behaviour under chemical influence have to be determined. In pilot projects CFRP-systems have to be controlled by optic sensors or similar devices. The installation should only be done by well educated stuff and companies with quality assurance as well as supervision.
4
Development of the CFRP-Tendon
The key problem in the application of CFRP-tendons or stay cables is to anchor them. The best way to do this is to anchor the CFRP-wires in conical steel hulls, filled with potting material (see figure 1). The secret of a high load capacity is the composition of the potting material, and the geometric form of the steel hull as well as the CFRP-wires themselves. The first step to a CFRPstay cable was the development of an anchorage for a single CFRP-wire [5].
Figure 1: Sketch of the anchorage After the first successful tests the number of wires was increased up to seven. For this anchorage numerical simulations were carried out [6]. With a FE-program a model was developed and calibrated as well as verified through comparison with static load tests carried out at the Technische Universität München. The model was used to conduct parametric investigations with the aim of reducing the critical transverse stresses in the anchorage. The efficiency factor for a tendon with 7 wires rose from 69 % in the beginning up to 99 % in the end. Subsequently the
number of CFRP-wires of the tendons was increased to 13 and 19 wires and finally stay cables with 91 and 103 CFRP-wires were manufactured. As potting material DYWIPOX CBV which is a two-component epoxy resin system was used. Dynamic tests followed by static tests were done on tendons with 7 and 19 wires and stay cables with 91 (as described in chapter 5.2) and 103 wires. The type of failure of these tendons is always the same. Several secondary failures in the free cable length caused by shear fracture of the CFRP-wires in the first third of the potting hull leading to the total collapse. While the tendons with 7 and 19 wires showed a sudden fracture of the whole specimen the stay cable with 91 wires broke wire by wire. After the problem of anchoring the wires had been solved the main task was to improve the manufacturing process and the installation of the tendons and stay cables. Up to this time all anchorages were potted in a vertical position which is very difficult to do on a building site. With the new technique developed by DSI it is now possible to inject the potting material into the hulls in a horizontal position. After successful testing on tendons with 7 and 19 wires a test on a stay cable with 103 wires has been finished in January 1999. The stay cables developed by DSI are parallel arranged wires over the whole length. To protect them against ultraviolet radiation and wind erosion they are guided in a polyethylene or polypropylene sheathing in their free length.
5
Testing of the CFRP-Tendon
Most of the testing on the CFRP-tendons and all tests on the CFRP-stay cables were done at the Technische Universität München. This chapter deals with the testing of a stay cable with 91 CFRP-wires. 5.1
Testing Equipment
For the testing of stay cables the Lehrstuhl für Massivbau of the Technische Universität München, is equipped with a testing arrangement for dynamic and static loading up to an ultimate load of 19 000 kN(see figure 2).
Figure 2: Sketch of the stay cable testing equipment
The testing machine consists of two reinforced concrete abutments with a centre hole through which the cable is guided. The tensile force applied on the specimen is measured by three load cells at the fixed abutment. Two sets of jacks each consisting of three equal jacks have to be installed between the two abutments. One set of jacks is used for static loading of the specimen, the other for the fatigue loading. Depending on the size of the cable specimen different sets of dynamic jacks can be used for the fatigue loading. So all together there are three sets of jacks available for the testing machine. Shocks caused by wire fractures during the test are recorded by shock meters. The piston strokes of the dynamic jacks are controlled by sine impulses. Due to the feasibility of individual controlling of each dynamic jack, a rotation of the adjustable abutment is possible. This rotation induces an eccentric loading of the cable specimen. An additional dynamic jack can be installed to apply a transverse deviation at mid span position of the cable specimen. The technical data of the testing machine are as follows: • static load capacity at a maximum piston stroke of • dynamic load capacity - big dynamic jacks at a maximum piston stroke of maximum frequency (depending on the elongation of the specimen) - small dynamic jacks at a maximum piston stroke of maximum frequency (depending on the elongation of the specimen) • length of the cable specimen • inclining angle for grouting • rotation angle of the adjustable abutment • usual measurements during a stay cable test - force applied on the cable specimen - oil pressure of the jacks - stroke of the pistons - elongation of the cable specimen - displacement of selected wedges and wires, deflection of the wedge plates • additional measurements if requested - strains in the wedge plates, trumpets - displacement of clamps, tubes.
19 000 kN 240 mm 10 500 kN 9 mm 0.5 - 0.8 Hz 3 200 kN 20 mm 1.0 - 1.8 Hz 5.1 - 5.5 m 0 - 65 degrees 0 or 1 degree ± 0.5 ± 0.1 ± 0.01 ± 0.01
% % mm mm
± 0.01 mm ± 0.01 mm/m ± 0.01 mm
5.2
Testing
The cable specimen was manufactured by DSI in the laboratory i.m.b. in Utting, Germany, as follows: First the 91 wires were inserted into four spacers in a horizontal position and the ends were cleaned properly. After that the cable specimen wires were put up in a vertical position and the potting material was injected into the steel hulls where the wires run in parallel. First the northern anchorage was filled. Then the cable was turned around and the southern anchorage was also filled. To protect the cable against bending and damage throughout the whole process of fabrication, transport and installation into the testing machine, the two steel hulls were connected and fixed with two steel L-sections. The cable specimen was mounted in the testing machine at the Technische Universität München.
Figure 3: Steel hull
Figure 4: Potting material
Figure 5: Manufacturing
A shock meter was installed in both anchorages which should record possible shocks caused by wire fractures during the fatigue test. Besides these measurements, the load, the oil pressure of the three jacks, the stroke of the pistons and the displacement of the adjustable abutment were recorded during the whole test. After installation the fatigue test was started and proceeded continuously until 2 million load cycles were reached. The maximum load was 45 % of theoretical failure load. The aimed stress range was ∆σ = 160 N/mm2. The average frequency of the test was about 1.2 Hz. During the fatigue test no wire fracture occurred in the free length or in the anchorage of the cable specimen. The displacement of the adjustable abutment (anchor block) at maximum load increased due to the application of two million load cycles by 1.10 mm. This elongation was mainly caused by the pull-out of the potting material from both steel hulls. The stay cable showed very good fatigue properties as expected from CFRP. After the fatigue test was completed the static load test was performed. The cable was loaded up to a load of 3 600 kN. The ultimate load of a single CFRP-wire was 50 kN. Corresponding to this value the ultimate load of 3 600 kN of the cable with 91 wires is equivalent to 78% of the
theoretical ultimate load. The specific elongation of the whole cable specimen corresponding to this load was about 1,9 %. The test was stopped after six wire fractures where the first occurred at a load of 3 500 kN. Due to the type of material the wires showed linear elastic behaviour up to the failure. The cable specimen broke wire by wire not as suspected with a sudden fracture of the whole cable specimen. Figure 6 shows the specimen at the anchorage before the ultimate strength test. The wire fractures are shown in figure 7 and 8.
Figure 6: Anchorage before the ultimate strength test
Figure 7: Wire fracture at the anchorage
Figure 8: part of the free length of the specimen
After the cable was fully unloaded and dismounted the condition of the cable specimen was investigated by a visual inspection. The components of the cable specimen showed no extraordinary deformation besides the wire fractures at the entrance of the potting material and the spacers.
6
Conclusion and Outlook
CFRP is a very interesting building material. Using this composition the advantages of the carbon like low weight, high stiffness and resistance against aggressive media can be activated without having the disadvantage of brittleness. The key problem how to anchor the wires which prevented the use in the past is solved. Working groups in Europe, USA, Canada and Japan are working on the standardisation of CFRP-systems. Testing is even more important for CFRP- stay cables than it is for steel. With the available equipment and the experience made in the last two years at the Technische Universität München testing can be performed without any problem. The developed CFRP-stay cables as well as CFRP-tendon system DYWICARB are now available and can be used for first applications. It can be hoped that the use will rise as fast as the knowledge resulting from latest research work.
7
References
[1]
Meier, U.: Proposal for a carbon fibre reinforced composite bridge across the Strait of Gibraltar at its narrowest site. Proc. Inst. Mech. Eng., Vol.201, No. B2 : 1987 (pp.73-78) Saadatmanesh, H. ; Ehsani, M.R.: Fibre Composites in Infrastructure. 2nd International Conference ICCI Tucson, Arizona : 1998 Schurter, U. ; Meier, B.: Storchenbrücke Winthertur. In: Schweizer Ingenieur und Architekt. Nr. 44 : 1996 (pp. 976-979) Recommendations for Stay Cable Design, Testing and Installation. Post-Tensioning Institute. Phoenix, Arizona, August 1993. Noisternig, J.F.: Zum Tragverhalten von Verankerungssystemen für CFK-Litzen im Spannbetonbau. Fortschritt-Berichte VDI-Reihe 4 Nr. 133. Düsseldorf : VDI-Verlag, 1996. Noisternig, J.F. ; Dotzler, F. ; Roos, F. ; Jungwirth, D. ; Zilch, K.: Entwicklung eines Zug-/Spanngliedes aus CFK für das Bauwesen. 2. Symposium Neue Werkstoffe in Bayern“. Bayreuth : 1998
[2] [3] [4] [5] [6]
Bridge Consolidation by Using Cable - Stayed Method
Victor POPA
Michael M. STANCIU
Dr. Eng. IPTANA-SEARCH Co. Bucharest, ROMANIA
Bridge Engineer IPTANA-SEARCH Co. Bucharest, ROMANIA
Victor Popa, born 1942, received his civil engineering degree from Technical Construction University of Bucharest in 1966. He is currently Head of the Bridge Design Department at IPTANASEARCH Co. and associate professor at TCUB.
Michael M. Stanciu, born 1957, received his civil engineering degree from the University of Oklahoma in 1983 and his Master of Science in 1987. He is president of IPTANA-SEARCH, an American-Romanian civil engineering company, located in Bucharest, Romania.
1.
Generalities
The increase of the road traffic and vehicle load during the last decades imposed the necessity to consolidate some of the existing older bridges. Many of these bridges require both the carriage-way widening and structure consolidation. The consolidation of these bridges generally require the consolidation both of the superstructure and of the infrastructure. Sometimes the consolidation of the infrastructure and mainly of the foundations is very difficult and expensive, mostly because of the reduced space under the bridge and the existence of the crossed obstacle. Under these circumstances, is very difficult or impossible to use suitable equipment. These inconvenient may be eliminated using cable-stayed method for the consolidation of the existing bridges. The method consists in supporting the existent superstructure deck from the pylons or towers by straight inclined cables. The pylons or towers are built in different solutions, according to the structure of the bridge requiring the consolidation. By this method the consolidation of the existent infrastructures can be avoided and replaced with the construction of new pylons which can be built in better construction conditions. The method can be successfully used also when is required only the consolidation of superstructure. Some possible bridge consolidation solutions and two examples of bridge consolidation presently under construction in Romania using this method are presented in the following.
2
2
Method description
The bridge consolidation by using cable-stayed method consists in building towers or pylons that will support the existing superstructure deck by straight cables.The number of superstructure deck supports will be increased, thus diminishing the stresses in the strengthening structure. The pylons or towers usually are built in the existent bridge pier axes but, depending on the designer creativity, they can be placed in any other favorably locations. This method can be used mainly for bridges with simple supported or continuous beams but also for other structure types such as frames, vaults and arches. The method can be used for reinforced or prestressed concrete structures as well as for metal or composite structures. The bridge consolidation by cable-stayed method is frequently accompanied by additional structure prestresses made with external prestressing tendons. Also, to accomplish the new structures it is necessary to build transverse prestressed beams with cantilevers which will be anchored from the pylons by cable stayes. For bridges with simple supported beams, the continuity of the beams on the piers will be ensured by additional prestressing tendons. Depending on the construction of the cable-stayes supports, bridge consolidation by cable-stayed method can be divided in two categories as follows: 1st - Bridge consolidation when the existing foundation consolidation is not required or is easy to be carried out; 2nd - Bridge consolidation when the existing foundation consolidation is an impossible or very difficult and expensive work. 2.1
Presentation of the first category of bridge consolidation
If foundations of the existing piers are in good condition and don’t require consolidation (e.g.: piers based on rock or very hard soils) or can be easily consolidated, then the method consists just in construction of towers for anchorage of the cable-stayes. Fig. 1 shows the example of a bridge having the superstructure consisting of three spans continuous prestressed concrete girders requiring only the consolidation of the superstructure.
Figure. 1 Elevation of a bridge with three-span continuous girders a) existing bridge, b) proposed solution
3
The superstructure having a box cross section (fig. 2a ) can be consolidated by cable-stayed method by building two towers. The cable anchorage towers may be supported either by the existing superstructure (fig.2b) or by the existing piers (fig.2c).
Figure 2 Bridge cross section a) existing bridge, b) bridge consolidated with towers supported by the superstructure, c) bridge consolidated with towers supported by the piers The towers will be fastened on the superstructure or on the piers with transverse prestressing tendons. The towers may have steel structure (to decrease the load on piers and the construction time period) or composite structure. If the foundations bear higher loads, the towers may be built of reinforced concrete with special steel elements only in the connection areas of the towers with the supporting elements. To fix the cables on the superstructure, special cross beams with cantilevers will be built of reinforced concrete with prestressing tendons. The cantilevers may be built entirely or partially of steel or composite elements. For steel bridges, the cantilevers and the towers may be entirely of steel. Fig.3 shows the elevation of a reinforced concrete bridge requiring consolidation. The piers are based on rock and allow an important increase of the loads. However, the superstructure is calculated for an inferior class and requires consolidation in order to bear the new loads. In the mean time should be analyzed the solution for the carriage-way widening from two to four lanes. To bear increased loads, the existing superstructure (fig. 4a ) can be consolidated using the cablestayed method, building towers supported by the superstructure over the existing pier (fig.4b). If the carriage-way should be doubled, the towers supporting the cable-stayes may be built on the carriage-way axis (fig. 4c ).
4
Figure 3 Elevation of a bridge with two span continuous girders a) existing bridge, b) proposed solution for consolidation
Figure 4 Bridge cross section a) existing bridge, b)proposed solution for consolidation
5
2.2.
Presentation of the second category of bridge consolidation
Considering the bridges for which the consolidation of the existing foundation is impossible or very difficult and expensive for various reasons, the following consolidation solution can be used. We consider the case of the bridge in fig. 5 for which the consolidation of the existing foundations is impossible due to the small space existing under the bridge.
Figure 5 Elevation of a bridge with three-span continuous girders a) existing bridge, b) proposed solution The superstructure of the bridge consists in a box prestressed concrete girder as shown in fig. 6a. In this case, pylons, having their own foundations, may be built to take over the additional load transferred through the cable-stayes (fig. 6b).
6
Figure 6 Bridge cross section a) existing bridge, b) proposed solution for consolidation with two new pylons
3.
Examples of Romanian bridge consolidation projects using the cablestayed method
In the following are presented two projects elaborated in Romania for old bridge consolidation by the cable-stayed method. 3.1.
Bridge over Jijia River at Carniceni
The bridge was built during 1915-1920. The bridge superstructure was destroyed during the Second World War and was reconstructed in 1954 in accordance with the original project.
7
Figure 7 Bridge over Jijia river at Carniceni. Elevation a) existing bridge, b) proposed solution The bridge superstructure consists of Gerber reinforced concrete beams. The existing bridge has seven spans with an average length of 15.00m each (fig.7a). The bridge has a narrow carriageway of only 5.00 m wide (fig. 8a). Both the infrastructure, mainly the foundation, and the superstructure suffered important damages in time. The increase of the road traffic on the road upon which this bridge is located imposes the widening of the carriage-way and the appropriate consolidation of the strengthening structure. The bridge crosses Jijia river at its confluence with a big river, namely Siret. This big river has an important impact on the water level under the bridge in case of floods. The technical-economical study has determined that the foundation consolidation has a high investment cost. Under these circumstances, the solution of the consolidation by the cable-stayed method proved to be more profitable, thus avoiding the consolidation of four infrastructures foundations (fig. 7b). The pylons of the cable-stayed structure can be built, without any special problems, near the existing bridge. For the bridge carriage-way widening is necessary to build two new side beams that complete the existing superstructure (fig. 8b). The superstructure becomes a three span continuous structure supported by cable-stayes as shown in fig.7b. The elevations of the P1, P3, P4 and P6 piers are demolished down to the soil level, in this manner also increasing the water drainage under the bridge by eliminating some obstacles. The P2 and P5 piers of the old bridge are incorporated in the new P1 and P2 pylons of the consolidated bridge.
8
Figure 8 Bridge over Jijia river at Carniceni. Cross section a) existing bridge, b) proposed solution 3.2. Bridge over Dambovita River at Gemenea The bridge was built in 1951 and has six spans of 20.45 m each. The total length of the bridge superstructure is 123.00 m (fig. 9a).
Figure 9 Bridge over Dambovita river at Gemenea. Elevation a) existing bridge, b) proposed solution
9
The bridge superstructure is made of simple supported pre-cast beams. There are six main beams in the cross section. The bridge carriage-way is 7.00 m wide (fig.10a). The bridge infrastructure is based directly on an superficial alluvial bed. After the floods of 1970 and 1975, the bridge suffered important damages, when P4 pier was unequally plunged down with about 1.00 m. Thus the pier was also rotated, and the superstructure of the adjacent spans were displaced together with the pier.
Figure 10 Bridge over Dambovita river at Gemenea. Cross section a) existing bridge, b) proposed rehabilitation solution To restore the traffic, P4 pier was consolidated with drilling piles and the displaced superstructure was lifted. The bridge rehabilitation project was elaborated for the consolidation of all piers, but the high costs for the consolidation stopped the works on the other piers. Presently the traffic is restricted on this bridge. The unsuitable condition of the foundations of this bridge and also the deterioration of the superstructure determined this bridge to be included again into the consolidation programme. From the technical-economical analysis of the consolidation solution, the cable-stayed method resulted to be the best. For this bridge, four piers can be eliminated if a pylon will be built at the middle of the bridge, near the existing pier P3 (fig.9b). The foundations and the towers of the pylon will be built separately of the existing bridge (fig. 10b). After the pylon construction, the existing superstructure will be consolidated and widened
10
building an extra slab of reinforced concrete over the existing one. The bridge superstructure will become a continuous structure by building cross beams with pre-stressed cantilevers placed in the superstructure joints. The cantilevers will be used for the cable-stayes anchorage. The superstructure consolidation and its continuity will be achieved by longitudinal prestress with external prestressing tendons. The damaged concrete structure will be also repaired at the same time with the new pylon execution.
4.
Calculation particularities for bridge structures consolidated by the cable-stayed method
Using the cable-stayed method for bridge consolidation, the original static scheme of these structures will be radically modified. Thus, the original statically determined structure ( simple supported beams or Gerber beams) become a statically undetermined cable-stayed structure. The calculation should consider the effective stresses in the original existing structure, which remain included in the new structure, and the stresses appearing in different phases of the loads applied on the new statical structure modified accordingly. Should also be considered the physicalgeometrical characteristics of the structure corresponding to each load phase and construction element of the structure. Finally it is concluded that the calculus is similar to the calculation of the composite structures.
5.
Conclusion
Bridge consolidation by cable -stayed method can be an efficient alternative solution to solve the problems of the old bridges. Use of this consolidation method may ensure some important technical - economical advantages as follows : - lower investment cost; - better drainage of water under the bridge; - improvement of the bridge aesthetics. Ingenuity and creativity of designers may ensure the achievement of very interesting and special new bridge structure. The calculus has to consider the effective stresses both in the original and the new statical structure.
Application of Simultaneous Identification of Tension and Flexural Rigidity at once to the Bridge Cables Ichiro YAMAGIWA Researcher Kobe Steel, Ltd Kobe, Japan
Hideo UTSUNO Senior Researcher Kobe Steel, Ltd Kobe, Japan
Koji ENDO Researcher Kobelco Res. Inst. Inc. Kobe, Japan
Kenichi SUGII General Manager Kobe Steel, Ltd Kobe, Japan
Summary A new vibration method to estimate the flexural rigidity and the tension of cable is examined. Periodicity of natural frequencies are derived analytically from the frequency equation of the cable’s bending vibration with the tension. Utilizing the coefficient of the polynomial equation which derived this periodicity, the flexural rigidity EI and the tension T are simultaneously identified. Experiments using spiral rope for a cable-stayed bridge were carried out to verify the present method. There was good agreement between measured and calculated data.
1. Introduction When cable-stayed bridges are erected the tension of the cables are adjusted to the designed specification. The tension of the cable is directly measured by a load cell or hydraulic jack, but recently practical formulas derived by the vibration method are often used1). In these practical formulas the first or second natural frequency of the cable vibration is used and it is assumed that the flexural rigidity is known. The flexural rigidity is frequently investigated in the preliminary test using a test piece of cable. However it is difficult to investigate the flexural rigidity for all boundary conditions and all tensions during the erection because the flexural rigidity varies according to the boundary condition and the tension2). Actually, the flexural rigidity is measured for only the typical condition. For this problem we proposed a new vibration method in which the tension and the flexural rigidity was identified by using plural natural frequencies3),4). In this method the tension and the flexural rigidity are identified by using the analytical equation derived from the frequency equation of the cable vibration. Additionally, the precision of tension is studied by a numerical simulation and an experiment using steel rod. As a result it was established that this method is practically useful. In this paper we apply the proposed method to the actual cables of a cable-stayed bridge and study the precision of tension. The convenience of this method is confirmed in the actual erection.
2. New vibration method 2.1 Theoretical equation The cable vibration is considered to be a one-dimensional beam’s bending vibration with the tension. The equation of motion for one-dimensional beam’s bending vibration with the tension is given by: EI
∂4w ∂2w ∂2w −T + ρA =0 4 2 ∂x ∂x ∂t 2
(1)
where w is bending displacement, EI is flexural rigidity, T is tension, ρ is mass density, A is cross-sectional area. Bending displacement w is shown by the product of the function of the shape of the natural mode and the time function: (2) w ( x , t ) = W ( x ) e x p ( jω t ) Substitution of Eq. (2) in Eq. (1) leads to the next principal function. (3) W ( x ) = C 1 co s( α x ) + C 2 sin ( α x ) + C 3 co sh ( β x ) + C 4 sin h ( β x ) where α, β are defined as 2
α =
ρA ω 2 T + 2 EI EI
T 2 EI
(4)
β =
ρA ω 2 T T + + 2 EI EI 2EI
(5)
−
2
where ω is the natural angular frequency. In the first place solving Eq. (3) on the simply suppo rted boundary condition of both ends, the following frequency equation is obtained: (6) sin(αL) = 0 where L is the length of the beam. The solution of Eq. (6) has periodicity and is given by: (7) αL = iπ, i = 0,1,2 ,¥¥¥ Substituting Eq. (4) in Eq. (7), we can derive the next equation connected between the mode number i and the natural frequency fi.: T π 2 EI 4 (8) i + i2 f 2 = i
4 ρ A L4
4 ρ A L2
Secondary solving Eq. (3) on the fixed boundary condition of both ends, the following frequency equation is obtained: (9) 2 α β {1 − c o s ( α L ) c o s h ( β L ) } + {β 2 − α 2 } s in ( α L ) s in h ( β L ) = 0 Rearranging the expression using approximation, Eq.(9) is simplified: (α 2 + β 2 ) sin(αL + φ) = 0 tan φ = −
2 αβ 2ω =− 2 T β −α 2
(10) (11)
ρ AEI
The solution of Eq. (10) has periodicity and is given by: (12) Substituting Eq. (4) in Eq. (10), we can derive the next equation connected between the mode number i and the natural frequency fi. αL + φ = iπ , i = 0,1,2,¥¥¥
4
fi 2 =
π 2 EI φ T φ i − i − + 4ρAL4 π 4ρAL2 π
2
(13)
Eq. (8) is considered to be Eq.(13) with the term Φ/Π omitted. Eq. (8) and (13) express the relation between the square of the mode number and the square of the natural frequency. Using that equation we can calculate the tension and the flexural rigidity from the coefficient of the term of the second power or the fourth power of the mode i.
2.2 Simultaneous identification method of tension and flexural rigidity In this section the simultaneous identification method of tension and flexural rigidity is shown in two cases of boundary condition. 2.2.1 Simply supported boundary condition The squares of the measured natural frequencies are plotted against the squares of the mode number in Fig.1 (Filled circle). Least-squares fitting using Eq. (8) is applied to these data (Solid line in Fig.1). As a result of curve fitting we can calculate the tension and the flexural rigidity from the coefficient of the second power term or the forth power term of the mode i. 2.2.2 Fixed boundary condition In the case of fixed boundary condition Eq. (13) is applied. In Eq. (13) the term of Φ/Π is the function of EI and T. Therefore Eq. (13) is a non-linear equation and needs iterative calculation. Fig.2 shows the flow chart of this calculation. First initial T and EI is calculated using leastsquares fitting of Eq. (8). Secondary substituting that value in Eq. (11) and (13) and using leastsquares fitting, new T and EI is calculated. This calculation using Eq. (11) and (13) repeats until convergence of T and EI.
Initial T,EI Eq.8 least-squares fitting Calculate Ф Eq. 11 Calculate T,EI Eq.13 least-squares fitting T,EI Converge?
No
Yes
T,EI identified
Fig 1
Least squares fitting for natural frequencies
Fig 2
Flow chart in fixed boundary condition
2.3 Precision of tension and flexural rigidity 2.3.1 Clear boundary condition If the boundary conditions of both ends are known like simply support or fix, T and EI can be calculated accurately using Eq. (8) or (13). We made an experiment using a test piece of cable for the case of fixed boundary condition. The experimental condition is shown in Table 1 and the result of the experiment is shown in Fig.3. In Fig.3 the vertical axis is the ratio of the estimated tension by this method to the measured tension by the load cell. That ratio expresses the precision of the identification in this method. The horizontal axis is parameter ξ and will be explained later. In this result this method can identify the precision of the tension to less than 1%.
Material Spiral Rope Linear Density 1.113 kg/m Theoretical EI 295 Nm2 Length (m) Given tension (kN) 2 48.8 99.6 148.4 5 49.6 99.3 144.9 Table 1: Experimental condition
Figure 3: Precision of estimated T
However in the actual cable the boundary condition is known in only a few cases. Therefore we simulated the precision of the tension and the flexural rigidity by assuming the boundary condition was not known and investigated the precision limit in 2.3.2. 2.3.2 Order number of using eigenvalue data In Eq. (8) and (13) it is considered that the first term is the contribution of the flexural rigidity EI and the second term is the contribution of the tension T for the natural frequencies. The ratio of the first term and the second term of Eq. (13) is written as: 2 φ i − 4ρAL2 π ξ2 K= = 4 π2 i − φ / π 2 φ π 2 EI ( ) i − 4 π 4ρAL T
(14)
where ξ=
T ⋅L EI
(15)
ξ is the non dimensional parameter1). When ξ is large the behavior of the cable is close to the vibration of a string, when ξ is small the behavior of the cable is close to the vibration of a beam. According to Eq. (14), using a higher mode number i is better for calculating EI and using a lower mode number i is better for calculating T. Therefore, in this method we use from the first to the fifth mode of natural frequencies for calculating T and use the five largest measured natural frequencies for calculating EI
2.3.3 Numerical simulation for unknown boundary condition The method of simulation is as follows. First natural frequencies were calculated by Eq. (9) (B.C. simply supported) using given T and EI. Next T and EI were calculated by Eq. (8) (B.C. fixed) using calculated natural frequencies. Finally calculated T and EI were compared with given T and EI. Additionally the opposite pattern was simulated. That is, T and EI were calculated by Eq. (13) using natural frequencies calculated by Eq. (6). Table 2 shows calculation parameters. Density ρ: 7.8 x 103 kg/m3 Young’s Modulus Ε: 2.06 x 1011 N/m2 Length Diameter Linear Density L(m) D (mm) ρ A (kg/m) 1, 3.95, 11 6 0.22054 1, 3.95, 11 8 0.39207 Table 2: Calculation Parameters
EI(Nm2) 13.10515 41.41876
Given Tension (kgf) 75, 125, 250, 375, 500 125, 250, 500, 750, 1000
The mode number used for calculation was from the first to the fifth for T and the largest five for EI. Fig.4 and Fig.5 show the result of the precision of T, Fig.6 shows the result of the precision of EI, and Table 3 shows the lower limit of the precision of T and EI. In Fig.4 - Fig.6 the vertical axes are the ratio of the estimated value to the given value. That is, the precision of the identification of T and EI. The horizontal axes is parameterξ. In Fig.4 and Fig.5 the explanatory notes show the equations used for calculation. In Fig.4 the tension is calculated for natural frequencies with the fixed boundary condition. In the case of Eq.(13), T is estimated accurately. This is because the assumed boundary condition of Eq. (13) and the data boundary condition are the same. In the case of Eq. (8) as ξ is smaller, the precision of T is lower. On the other hand, as ξ is larger, the precision of T is higher. In the case of larger ξ the influence of boundary condition for natural frequencies is small, so that the difference of the precision of T according to the two equations is small. Fig.5 shows the same result for Fig.4. The shift value of the precision from 1 against ξ is same in Fig.4 and Fig.5. In short, the precision of T depends on parameter ξ. This shift value is the precision of T in the largest difference of boundary condition between equation and data. The precision of T in Fig.4 and Fig.5 is the lower
Figure 4: Precision of estimated T (B.C.Fixed) limit of the precision using this method.
Figure 5: Precision of estimated T (B.C. Simply supported)
Fig.6 shows the result of the estimation of EI using Eq. (8) (B.C. simply supported) for natural frequencies with the fixed boundary condition. In Fig.6 the parameter is the mode number used for calculation of EI, and it shows that the measured highest mode number changes. According to Fig.6, as the mode number used for calculation is higher, the precision of EI is higher. As ξ is larger, the precision of EI is higher and the difference of the precision of EI according to the used mode number is smaller. Table 3 shows the precision of T and EI from Fig.4 - Fig.6. The precision of EI is classified by the mode number used. The precision of T and EI is decided by parameter ξ and their precision is higher when ξ is larger. In the following examination of an actual bridge cable ξ is more than 50. ξ
10
30
50
100
6-10
11.5%
9.6%
7.5 %
4%
16-20
5.5%
5.2%
4.8 %
3.5 %
26-30
3.55%
3.5%
3.3%
2.8 %
70 %
15 %
8%
4%
EI
Figure 6: Precision estimated EI (B.C.Fixed)
of
T (1-5)
Table 3: Precision of T and EI
3. Experiment Using Actual Cable We carried out an experiment for the actual cable during the erection of a bridge to confirm the simulated precision by this method. The situation of the experiment is shown in Picture 1. The specification of the cable and the experimental condition are shown in Table 4 and the outline of the cable is shown in Fig.7.
Specification of cable Material Coating spiral rope Diameter 22 mm Linear density
2.9263 kg/m
Experimental condition Cable number
BRI-GI-SI
BRI-GI-S2
Given T kg f 902
Length m
1768
21.04
3189
21.05
5535
21.06
1169
24.33
1831
24.33
3297
24.33
5535
24.33
21.05
Table 4: Experimental condition
Figure 7: Cable of the cable-stayed bridge The following is the control method of the cable tension in this experiment. In Fig.7 one end of cable was installed on the main tower through pin. The other end was set in the stand fixed to the girder by a sleeve screw and double nuts. We carried out the experiment with cable floating from the stand using a hydraulic jack. The tension was monitored by the load cell in the hydraulic jack. The cable length was measured as the length from the upper set point to the contact point of nut and the hydraulic jack cylinder. The vibration of cable was raised by a hammer striking at a point 1.5m from the contact point of the hydraulic jack and measured by an accelerometer at points 1m and 2m from the contact point of the hydraulic jack. Natural frequencies were analyzed from measured data by FFT. Vibration was measured at 2 points in order to avoid overlooking natural frequencies by agreement between the node position of the vibration mode and the sensor position. One of the results of FFT analysis of the cable vibration is shown in Fig.8. The vertical axis shows relative vibration velocity and its value is not important. The numbers in this graph are the mode number of natural frequencies. This graph shows that natural frequencies from low to high are raised regularly. The result of the estimation of T and EI are shown respectively in Fig.9 and Fig.10. We applied Eq. (13) to natural frequencies from the first to the fifth mode for calculating T and to the five largest natural frequencies for calculating EI. In Fig.9 the vertical axis is the ratio of the estimated T to the given T (load •Figure8 cell). Assuming the given T is correct, the precision of T is less than 8% and its result agree with the result of section 2. This Figures 8: Frequency analysis of cable precision is sufficient in practical use for the vibration measurement of the cable tension. In Fig.10 the vertical axis is the ratio of EI (estimated cable EI divided by EI of the steel bar with the same diameter as cable). The horizontal axis is the given T (load cell). The ratio of EI is nearly constant in spite of the tension. In the spiral rope the flexural rigidity EI increases as the tension increases, but the EI of this cable is constant. We consider that this is because cable is covered with polymer and the restrained condition among the wires composing the cable is not changed.
Additionally, in order to confirm the propriety of the identified T and EI we compared the natural frequencies calculated by Eq. (9) using the identified T and EI with the measured natural frequencies. One of the results of the comparison is shown in Fig.11. The result show that there is good agreement between calculated and measured frequencies. We expressed this difference between calculated and measured value as a percentage and calculated the average for all measured modes. This average error in the case of Fig.11 is about 1.8%. Fig.12 shows the
average error in various experimental conditions. It was found that the average error is sufficiently low and the identified T and EI is correct. Moreover, this method can measure the tension for one cable in about 5-10 minutes including the installation of the sensor and is very simple and speedy. For reasons of simple measurement we paid attention to the plural higher mode frequencies which are usually ignored. The advantages of this method compared with the usual method are as follows. (1) In the usual method, a preliminary test using a test piece of cable is necessary because the value of flexural rigidity EI is necessary for calculation of tension T. However, in this new method, a preliminary test is not necessary because the tension T and the flexural rigidity EI are calculated simultaneously during the erection. (2) If special order natural frequency(e.g. first order, second order) is not raised, the tension can be estimated due to the use of plural natural frequencies. Moreover, the effect of sag in the first natural frequency is avoided. (3) Discrimination between the cable's natural frequency and noise peak frequency is easy because of the regulation of plural natural frequencies.
4. Conclusions Our conclusions are as follows. 1) We proposed new method for simultaneously identification of the tension and the flexural rigidity using plural natural frequencies of the cable vibration. 2) In a clear boundary condition the tension and the flexural rigidity can be identified accurately. In an unknown boundary condition, like an actual bridge cable, the lower limit of the precision is obtained quantitatively by numerical simulation. 3) Applying this method to the actual bridge cable, the precision of the identified tension agrees with the simulated precision. 4)By applying this method to the erection of a cable-stayed bridge, it is proved that this method is simple and speedy. 5) This method can be applied to a very extensive field using the bar expressed one-dimensional beam apart from cable, because the use of an equation of motion for the one-dimensional beam’s bending vibration with tension T.
References [1]. [2]. [3]. [4].
T.Shinke, K.Hironaka, H.Zui and H.Nishimura : Practical formulas for estimation of cable tension by vibration method, Jour.of JSCE, No.287,pp.26-32,1979 (in Japanese) T.Shimada and A.Nishimura : Effect of flexural rigidity on cable tension estimated by vibration method, Jour of JSCE, No.398/I-10,pp.409-412,1988 (in Japanese) I.Yamagiwa, H.Utsuno, N.Sugano and K.Sugii : Vibration method to estimate flexural rigidity of cable and cable tension at one time, Jour.of Structural Engineering, JSCE, Vol.42A,pp.547-554,1996 (in Japanese) I.Yamagiwa, H.Utsuno, K.Endo, K.Sugii : Identification of flexural rigidity and tension of the one-dimensional structure by measuring eigenvalues in higher order, D&D Conf., JSME, No.97-10,pp.411-414,1997 (in Japanese)
Dynamic characteristics of two newly constructed curved cable-stayed bridges Carmelo GENTILE
Assistant Professor Dept. Struct. Eng. Politecnico of Milan
Born in 1958, Carmelo Gentile received his civil engineering degree in 1984 and his Ph.D. in 1990, both from Politecnico of Milan. He has published widely in the fields of earthquake engineering, system identification and fullscale testing of bridges.
Francesco MARTINEZ y CABRERA Professor Dept. Struct. Eng. Politecnico of Milan
Born in 1929, Francesco Martinez y Cabrera received his civil engineering degree in 1956 from University of Naples. He has published widely in a variety of research fields including r.c. and p.c. structures, bridge engineering and cable-stayed bridges.
Summary This paper describes the experimental program of field tests conducted on a couple of curved cable-stayed bridges and the successive identification of theoretical (finite element) models of the structures. The main objectives of the research program were: (a) to identify vibration modes of the structures using ambient and free vibration tests; (b) to correlate computer models with experimental results; (c) to compare the modal and structural behaviour of the bridges.
1.
Introduction
Theoretical and experimental investigation of two cable-stayed bridges is described in the paper. The analysed bridges (Fig. 1) were recently erected in the neighbourhood of the new air terminal of the Malpensa 2000 airport (Milan, Italy). Specifically, the bridges are placed in the north- and south-side of the air terminal, respectively. The structures are in principle perfectly equal and are characterised by a curved deck with longitudinal and transverse slope. This geometric layout is very unusual for roadway cable-stayed bridges and only one dynamic investigation of a curved cable-stayed bridge was performed before (Deger et al. 1996). The experimental program of dynamic tests was conducted in three days (for each bridge) and included extensive measurements of ambient vibrations induced by traffic to determine the dynamic characteristics of the bridges. The most significant mode shapes and associated natural frequencies were evaluated at 30 different locations of the deck and tower. A total of 11 vibration modes were identified in the frequency range of 0−10 Hz for both bridges. Due to the curvature of the bridge deck, special attention was devoted to the evaluation of the degree of coupling between vertical and transverse vibration of the deck. Furthermore, the mode shapes of the two bridges were compared by using standard techniques such as MAC (Allemang & Brown, 1983), NMD (Waters, 1995) and COMAC (Lieven & Ewins, 1988). Basing on these global indices, the bridges show very similar behaviour, being the natural frequencies of the north-side bridge slightly lower than the corresponding ones of the south-bridge. The reason of the above discrepancy in the modal behaviour was investigated by using threedimensional finite element models. Once the models were established, the structural parameters were refined in order to enhance the match between theoretical and experimental modal parameters. The basic difference between the two bridges was found to be related to the deck Young modulus. The optimal value of this parameter turned out to be about 30000
N/mm2 for the north-side bridge and 34000 N/mm2 for the south-side bridge.
2.
Description of the bridges
The tested bridges carries two lanes of traffic from the A26 highway to the Terminal 1 of Malpensa 2000 airport. The two bridges curve with a radius of 100 m and 6% longitudinal slope so that the air terminal seems to be embraced from the bridges which, at the same time, provide a limit to the airport area. Thus, the layout of the bridges gives an unique appearance to the airport and architectural concerns played a determining role in the design. Bridge construction began in 1994 and was completed in 1997. Fig. 1a shows a view of the north-side bridge. The curved bridge girders have a centreline length of 140 m with two equal side spans and 4 cables supporting each side span. The ultimate capacity of the individual stays ranges from 8745 to 20405 kN. The deck is a five-cell box concrete girder (Fig. 1b), 11.75 m wide and 1.35 m high, which was cast in place and post-tensioned. The curved decks have an average transverse slope of 4%. The cast-in-place concrete tower (Fig. 1c) is about 37 m high and consists of two legs connected by a lower concrete cross-beam supporting the deck and an upper steel strut providing the anchorage for the stay cables.
3.
Full-scale testing
The dynamic tests included extensive measurements of ambient vibrations induced by traffic. A microcomputer-based measurement system was used on-site to measure and record the dynamic response of the bridge. Ambient vibration response was acquired in about 50 minute records per channel and data were sampled at 200 points per second per channel. The response of the bridges a)
c)
b)
Figure 1. a) View of the north-side bridge; b) Cross-section; c) View of the tower
Figure 2. Location and numbering of sensors for the test of bridges at selected points was measured using PCB (model 393C) accelerometers, each with a battery power unit. Two-conductor cables connected the accelerometers to a computer workstation with a data acquisition board for A/D and D/A conversion of the transducer signals and storage of digital data. A schematic of the sensor layout is shown in Fig. 2. In addition to the ambient vibration survey, free vibration tests were conducted to verify natural frequencies and mode shapes determined from the ambient vibration tests. Free vibration was induced by the passage of one axle of a truck over a standardised RILEM plank (which was located at selected locations) and sudden braking. Space limitations in this paper preclude a complete analysis of all results; however, it can be said that ambient and free vibration methods were found to give virtually the same results in term of natural frequencies and mode shapes for both bridges and a greater number of normal modes was identified during ambient vibration tests (Gentile et al. 1998).
4.
Data processing and analysis
As it is usual for bridge structures (see e.g. Abdel-Ghaffar & Housner 1978, Murià-Vila et al. 1991, Gentile & Martinez y Cabrera 1997) the analysis of ambient vibration data was based on the classical spectral techniques described by Bendat & Piersol (1993). Modal frequencies were identified by the locations of peaks in the auto-spectra (ASD) and in the amplitude of cross-spectra (CSD) with a resolution of 0.025 Hz. Furthermore, the coherence functions were computed to assess the quality of data and to investigate non-linear response at each mode. The experimental mode shapes are obtained from the amplitude of square-root ASD curves and cross-spectral phases were used to determine directions of relative motion. To investigate the correlation between the corresponding mode shapes of the two bridges, the Modal Assurance Criterion (MAC, Allemang & Brown 1983), the Normalised Modal Difference (NMD, Waters 1995) and the Coordinate Modal Assurance Criterion (COMAC, Lieven & Ewins 1988) were calculated. The MAC indicates the degree of correlation between the two mode shape vectors φA,k, φB,j and is defined as: (φ AT,k φ B , j ) 2 (1) MAC(φ A ,k , φ B , j ) = T (φ A, k φ A, k )(φ BT, j φ B , j ) MAC values vary from 0 to 1; a value of 1 implies perfect correlation of the two mode shape vector (one vector is a multiple of the other) while a value close to 0 indicates uncorrelated (orthogonal) vectors. The NMD is related to the MAC as follows:
1 − MAC(φ A ,k , φ B , j )
NMD(φ A ,k , φ B , j ) =
(2) MAC(φ A ,k , φ B , j ) Practically, NMD is representative of the fraction, on average, by which each component differs between the two vectors φA,k, φB,j. The NMD is more sensitive to mode shape differences than the MAC (Maia & Silva 1997) but it is not bounded by unity; thus the comparison is more difficult for weakly correlated modes but is more discriminating when two modes are highly correlated. In the COMAC, correlated modes from the two sets A and B are paired at a definite measurement station r. The COMAC at point r is defined as: COMAC (r ) =
N
N ∑ φ A,rk φ B ,rk k =1
∑ (φ k =1
A, rk
)
2
2
N
∑ (φ
B , rk
(3) )
2
k =1
where φA,rk and φB,rk denote the r-th components of vectors φA,k and φB,k, respectively. The value of COMAC(r) (ranging from 0 to 1) is a measure of the correlation of corresponding modes at the location r. This index is particularly feasible to indicate the location where the two sets mainly differ. Thus, a value of COMAC(r) close to 1 implies that no significant changes of all modal deflections occurred at r while COMAC(r) should be minimum where the main differences take place.
5.
Dynamic behaviour of the bridges and comparison of modal parameters
For both bridges, 11 vibration modes were identified by spectral analysis in the frequency range of 0−10 Hz. A selected number of normal modes of the north-side bridge is shown in Fig. 3. The identified modal behaviour was strongly dominated by the vertical components, either pure bending or torsion. In fact, the ratio of the maximum vertical and transverse modal amplitude of the deck was found to be always greater than 5.0. Generally, the maximum amplitudes of the vertical and transverse components occur at different stations a) Mode DV1+
f = 0.781 Hz
b) Mode DV2+
f = 1.221 Hz
c) Mode DV3+
f = 2.344 Hz
d) Mode DV4+
f = 2.808 Hz
e) Mode DV1−
f = 3.687 Hz
f) Mode DV2−
f = 3.809 Hz
Figure. 3. Examples of vertical and torsional modes of the north-side bridge deck
along the deck. Thus, the observed modes can be basically arranged as follows: 1. vertical bending modes of the deck (DV+) with anti-symmetric deck modes generally involving a greater longitudinal participation of the tower than the symmetric ones; 2. torsional modes of the deck (DV−) which are usually coupled with longitudinal motion of the pylon and slight transverse displacement of the deck. An illustrative example of the spectral analysis in Fig. 4 shows the acceleration spectra (square root ASD) of the deck at locations 15 and 20 (see Fig. 2) for the two bridges. In the spectral plots of Fig. 4, the thicker line refers to the north-side bridge while the thinner one refers to the southside bridge. The inspection of the acceleration spectra in Fig. 4 first reveals a remarkable consistency of occurrence of spectral peaks for each bridge. This information and the coherence values (which were always very close to 1 in the frequency range where spectral peaks occur) suggest both a good quality of data and the linearity of the dynamic response. Furthermore, Fig. 4 clearly shows that spectral plots from the two bridges exhibit peaks of similar shape which are slightly shifted along the frequency axis. Specifically, all spectral peaks of the south-side bridge responses are located at greater frequencies than the corresponding ones of the north-side bridge. As it had to be expected, the two bridges exhibit very similar mode shapes. The correlation of the corresponding mode shapes of the two structures is illustrated by: a) Fig. 5, which directly compares the corresponding mode shapes of the two bridges for a selected number of vibration modes at the deck measurement stations; b) Table 1, which compares the corresponding mode shapes and scaled modal vectors of the two bridges through frequency discrepancy ∆, the MAC and the NMD. It should be noticed that the values of MAC and NMD in Table 1 were computed from vertical and longitudinal modal displacements; furthermore, the frequency discrepancy between the corresponding natural frequencies of the north- and south-side bridge is defined as:
∆=
a)
f NORTH − f SOUTH f NORTH
Amplitude (cm/s2)
1.2 Ch. 15 - North-side bridge 0.9
Ch. 15 - South-side bridge
0.6 0.3 0.0 0
2
4
6
8
10
frequency (Hz)
b) Amplitude (cm/s2)
2.0 Ch. 20 - North-side bridge 1.5
Ch. 20 - South-side bridge
1.0 0.5 0.0 0
2
4
6
8
10
frequency (Hz)
Figure 4. Comparison of acceleration spectra from the two bridges at different locations
Mode Identifier
f NORTH
f SOUTH
(Hz)
(1)
(2)
MAC
(Hz)
∆ (%)
NMD (%)
(3)
(4)
(5)
(6)
DV1+ 0.781 0.825 5.63 0.9995 2.18 DV2+ 1.221 1.270 4.01 0.9992 2.89 DV3+ 2.344 2.441 4.14 0.9886 10.74 DV4+ 2.808 2.905 3.45 0.9931 8.35 DV1− 3.687 3.882 5.29 0.9935 8.07 DV2− 3.809 4.004 5.12 0.9904 9.85 DV5+ 4.541 4.810 5.92 0.9877 11.17 DV6+ 5.371 5.664 5.46 0.9926 8.62 DV3− 7.300 7.666 5.01 0.9843 12.61 DV4− 7.471 7.886 5.55 0.9732 16.61 DV7+ 8.789 9.058 3.06 0.9889 10.61 Table 1. Comparison of natural frequencies and mode shapes of the two bridges North-side bridge South-side bridge
b) Mode DV2+
0.5
dd
0.0 -0.5 -1.0 1
2
3
4
5
6
7
8
1.0 0.5 0.0
dd
1.0
Normalised mode shape
Normalised mode shape
a) Mode DV1+
-0.5 -1.0
9 10 11 12 13 14 15 16 17 18 19 20
1
2
3
4
5
6
Measurement points
-0.5 -1.0 4
5
6
7
8
1.0 0.5 0.0
dd
dd
0.0
Normalised mode shape
Normalised mode shape
0.5
3
-0.5 -1.0
9 10 11 12 13 14 15 16 17 18 19 20
1
2
3
4
5
6
Measurement points
-0.5 -1.0 4
5
6
7
9 10 11 12 13 14 15 16 17 18 19 20
8
9 10 11 12 13 14 15 16 17 18 19 20
1.0 0.5 0.0
dd
dd
0.0
Normalised mode shape
Normalised mode shape
0.5
3
8
f) Mode DV2−
1.0
2
7
Measurement points
e) Mode DV1−
1
9 10 11 12 13 14 15 16 17 18 19 20
d) Mode DV4+
1.0
2
8
Measurement points
c) Mode DV3+
1
7
-0.5 -1.0 1
2
3
4
5
6
Measurement points
Figure 5. Comparison of selected mode shapes of the two bridges
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Measurement points
By comparing the natural frequencies and mode shapes of the two bridges, the following comments can be made: 1. there is a one-to-one correspondence between the observed vibration modes of the bridges, being the natural frequencies of the south-side bridge slightly higher than the corresponding ones of the north-side bridge. The frequency discrepancy (see Table 1) ranges from 3.06% to 5.92%, with a medium value of 4.79%. Since the environmental conditions during the test of the bridges were controlled and nearly equal (ranging the temperature from about 11°C to 15°C), the above difference in natural frequencies is possibly related to structural behaviour; 2. the first two mode shapes are practically equal (being the NMD less than 3%) while the other modes generally exhibit an average difference of about 10%; 3. by examining the local correlation of mode shapes through the COMAC (Lieven & Ewins, 1988) in order to highlight the locations where the two sets of mode shapes mainly differ, a nearly uniform distribution of values was found, ranging the COMAC between 0.980 (location 6 in Fig. 2) and 0.996 (location 16 in Fig. 2). The nearly uniform distribution of discrepancies in both natural frequencies and mode shapes suggests that the differences of modal behaviour could be related to different elastic properties of the concrete in deck and tower of the two bridges. The reliability of this hypothesis was investigated and verified by using three-dimensional finite element models.
6.
Structural modelling, theoretical behaviour and model optimization
The theoretical analysis was divided in two parts. First, a simplified model (described by Gentile et al. 1998) was formulated using a reduced number of 3D beam finite elements (107 elements, 102 nodes). The results from a dynamic analysis of this model were used to determine the location of the sensors in the field tests and to evaluate the importance of geometrical nonlinearity. Specifically, the model development began by accounting for the overall non-linear behaviour due to geometry change by using in the linear dynamic analysis the stiffness as obtained from a non-linear static analysis corresponding to the dead load deformed state of the bridge. Once this analysis was performed, it was found to produce practically the same results of a linear elastic analysis without special consideration being given to the load state or deformed geometry of the structure, as it happened in other theoretical and experimental studies in the literature (see e.g. Wilson & Liu 1991, Casas & Aparicio 1993). After the tests, a much more detailed finite element mesh was carried out with the arrangement of nodal points and elements shown in Fig. 6. The model involved 4366 degrees of freedom and used a large number of finite elements for the deck structure, so that a regular distribution of masses can be obtained. The models was developed using the following assumptions: a) the box girder deck was modelled by using 904 four-noded shell elements with 6 degrees of freedom per node;
Figure 6. Three-dimensional finite element model: general arrangement
b) the tower was modelled using 30 3D beam elements while linear elastic truss elements were used to represent the cable-stays; c) the tower footing was fixed; d) a Poisson ratio of 0.15 was assumed for both tower and deck; e) the possibility of free sliding in the direction of the curved centreline at the abutments was simulated by means of radial pinned-pinned rod elements. A preliminary dynamic analysis was performed assuming for the concrete Young modulus of both deck and tower a base value of 35000 N/mm2 (which was established from design data) in order to check the similarity between experimental and theoretical modal parameters. The results from the base model analysis confirm that: 1. a great portion of the bridge dynamic response is associated with vertical motions of the deck, either in pure bending (DV+) or torsion (DV−) with or without significant participation of the tower. Specifically, within the 18 vibration modes involved in the frequency range up to 10 Hz, 12 are vertical modes of the deck, 1 is a transverse mode of the deck, 4 are transverse or longitudinal modes of the tower while strong coupling in the three orthogonal directions occurs in only one vibration mode; 2. slight coupling exists between transverse and vertical motions of the deck. The columns (3)-(6) of Tables 2-3 compare the experimental natural frequencies and mode shapes of the north- (Table 2) and south-side (Table 3) bridge and the corresponding modal parameters of the base model through frequency discrepancy, the MAC and the NMD. Experimental modal data were then used to adjust some parameters of the base model. Basing on the results of the previous section, the updating of models involved the Young moduli of deck (ED) and tower (ET). Since the corresponding theoretical and experimental mode shapes were quite similar in the investigated variation range of the parameters, the model updating for both bridges was carried out to correlate the analytical frequencies as closely as possible to the identified ones. Thus, the optimal estimates of ED and ET are defined to be the values which minimize the following: Nm fi M − fiC = (4) J ∑ fM i =1 i being Nm the number of identified modes and fiM , fiC the i-th measured and computed natural frequency, respectively. A plot of error function (4) in the neighbourhood of its minimum is shown in Fig. 7 for the north-side bridge. Fig. 7 clearly highlights a different rate of change
8 7
J
6 5 4 3 2 34000
36000
38000
40000
42000
ET (N/m 2 m)
44000
46000
Figure 7. Error function plot for north-side bridge
36000 34000 32000 30000 2 m) 28000 N/m ( 26000 E D
of J with respect to ED and ET , being greater the sensitivity to ED; a similar behaviour holds for south-side bridge as well and it has to be expected since all identified modes involved significant vertical motion of the deck. However, although with different sensitivities, the error function J gives a clear indication about the optimal values of both ED and ET. At the end of the optimization procedure, the optimal estimates of ED and ET were approximately: 1. ED = 30000 N/mm2 , ET = 40000 N/mm2 for the north-side bridge; 2. ED = 34000 N/mm2 , ET = 40000 N/mm2 for the south-side bridge. Thus, the basic difference between the two bridges seems to be related to the values of ED while the elastic modulus of the pylon is practically the same for both bridges. The modal parameters of the updated models are compared to experimental data through frequency discrepancy ∆, the MAC and the NMD in columns (8)-(10) of Tables 2-3. Tables 2 and 3 refer to the north- and south-side bridge, respectively. In general, the updated models shows excellent agreement in both frequencies and mode shapes (at the measurement locations) for all identified modes; specifically, it is noted that the models exhibit slightly lower frequencies than the measured ones with the maximum discrepancy being lower than 5%. Exp. f NORTH Mode Identifier (Hz)
(1)
(2)
Base Model (ED =ET =35000 N/mm2)
Refined Model
f (Hz)
∆ (%)
MAC
NMD (%)
f (Hz)
∆ (%)
MAC
NMD (%)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
DV1+ DV2+ DV3+ DV4+ DV1− DV2− DV5+ DV6+ DV3− DV4− DV7+
0.781 0.761 2.56 0.9976 4.86 0.766 1.04 0.9980 4.47 1.221 1.306 6.96 0.9985 3.92 1.270 4.01 0.9982 4.27 2.344 2.369 1.07 0.9847 12.45 2.243 4.31 0.9839 7.85 2.808 2.972 5.84 0.9700 17.57 2.778 1.07 0.9914 9.34 3.687 4.053 9.93 0.9613 20.06 3.829 3.85 0.9765 15.52 3.809 4.107 7.82 0.9615 20.01 3.872 1.65 0.9717 17.07 4.541 4.969 9.43 0.9886 10.76 4.616 1.65 0.9899 10.10 5.371 5.627 4.77 0.9962 6.16 5.234 2.55 0.9961 6.28 7.300 7.857 7.63 0.9412 24.99 7.322 0.30 0.9506 22.81 7.471 7.995 6.48 0.9224 29.00 7.390 1.08 0.9280 27.86 8.789 8.829 0.46 0.9703 17.49 8.814 0.28 0.9528 22.26 Table 2. Comparison of theoretical and experimental modal parameters for the north-side bridge Exp. f SOUTH Mode Identifier (Hz)
(1)
DV1+ DV2+ DV3+ DV4+ DV1− DV2− DV5+ DV6+ DV3− DV4− DV7+
(2)
Base Model (ED =ET =35000 N/mm2)
Refined Model
f (Hz)
∆ (%)
MAC
NMD (%)
f (Hz)
∆ (%)
MAC
NMD (%)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
0.825 0.761 7.76 0.99776 4.79 0.785 4.85 0.9979 4.58 1.270 1.306 2.83 0.9989 3.39 1.303 2.60 0.9987 3.63 2.441 2.369 2.95 0.9766 15.46 2.353 3.61 0.9837 12.88 2.905 2.972 2.31 0.9849 12.38 2.928 0.79 0.9741 16.30 3.882 4.053 4.40 0.9720 16.98 4.029 3.79 0.9806 14.07 4.004 4.107 2.57 0.9486 23.27 4.070 1.65 0.9812 13.83 4.810 4.969 3.31 0.9828 13.24 4.904 1.95 0.9835 12.95 5.664 5.627 0.65 0.9905 9.81 5.556 1.91 0.9916 9.21 7.666 7.857 2.49 0.9624 19.75 7.767 1.31 0.9786 14.79 7.886 7.995 0.87 0.9620 19.89 7.834 0.66 0.9703 17.49 9.058 8.829 2.53 0.9562 21.39 8.956 1.13 0.9484 23.34 Table 3. Comparison of theoretical and experimental modal parameters for the south-side bridge
7.
Conclusions
Ambient vibration testing and identification of finite element model of two curved cable-stayed bridges was presented and discussed. The following conclusions can be drawn: 1. no experimental evidence was found that would suggest either the existence of non-linear behaviour of the bridges during the tests or a strong coupling of vertical and transverse vibration of the deck of bridges; 2. 11 vertical modes were identified for both bridges in the frequency range 0−10 Hz, being a one-to-one correspondence between the identified modes of the two bridges; 3. the mode shapes of the bridges were compared by using standard techniques such as MAC, NMD and COMAC. This correlation analysis clearly indicates that the bridges show very similar mode shapes, being the natural frequencies of the south-side bridge slightly higher than the corresponding ones of the south-side bridge; 4. the discrepancies of modal parameters was found to be nearly uniform; this suggests that the differences of modal behaviour could be related to different elastic properties of the concrete in deck and tower of the two bridges. 5. The above hypothesis was confirmed by using experimental data to evaluate the optimal value of Young moduli of three-dimensional finite element models. Once the models were established, the structural parameters were refined in order to enhance the match between theoretical and experimental natural frequencies. The optimised finite element models showed very good agreement with the experimental results and the main difference between the two bridges was estimated to be a difference of about 13% in the value of the Young modulus of the deck.
Acknowledgements The cooperation of V. Imparato, G. Paracchini and their staff from the S.E.A. society is gratefully acknowledged. The authors would like to thank A. Gennari Santori for the assistance in during the field tests and A. Saisi for the valuable help in the investigation of the north-side bridge.
References [1].
Abdel-Ghaffar, A.M. & G.W. Housner 1978. Ambient vibration tests of suspension bridge, J. Engg. Mech.Div. ASCE 104: 983-999. [2]. Allemang, R.J. & D.L. Brown 1983. Correlation coefficient for modal vector analysis, Proc. 1st Int. Conf. Modal Anal.: 110-116. [3]. Bendat, J.S. & A.G. Piersol 1993. Engineering applications of correlation and spectral analysis. 2nd Ed., Wiley Interscience. [4]. Casas, J.R. & A.C. Aparicio 1993. Theoretical and experimental dynamic behaviour of the Alamillo cable-stayed bridge in Sevilla, Spain, Proc. Eurodyn '93: 995-1002. [5]. Deger, Y., R. Cantieni, C.A.M. deSmet & A.J. Felber 1996. Finite element model optimization of the new Rhine Bridge based on ambient vibration testing. Proc. Eurodyn '96: 817-822. [6]. Gentile, C. & F. Martinez y Cabrera, 1997. Dynamic investigation of a repaired cablestayed bridge. Earthq. Engg. Struct. Dynam., 26: 41-59. [7]. Gentile, C., F. Martinez y Cabrera. & A. Saisi 1998. Dynamic testing and seismic response of a cable-stayed bridge. Proc. XI European Conf. Earthq. Engg., CD-ROM, Rotterdam: Balkema. [8]. Lieven, N.A.J & D.J. Ewins 1988. Spatial correlation of mode shapes, the coordinate modal assurance criterion (COMAC), Proc. 6st Int. Conf. Modal Anal.: 690-695. [9]. Maya, N.M.M. & J.M.M. Silva (Eds.) 1997. Theoretical and experimental modal analysis. Research Studies Press Ltd. [10]. Murià-Vila, D., R. Gomez, & C. King 1991. Dynamic structural properties of cablestayed Tampico bridge. J. Struct. Engg. ASCE 117: 3396-3416.
[11]. Waters, T.P. 1995. Finite element model updating using measured frequency response functions, Ph.D. Thesis, Department of Aerospace Engg., University of Bristol. [12]. Wilson, J.C. & T. Liu 1991. Ambient vibration measurements on a cable-stayed bridge, Earthq. Engg. Struct. Dynam., 20: 723-747.
Field Observation of Aerodynamic Response of Meiko West Bridge Yuji SUZUKI Kazuyuki MIZUGUCHI Japan Highway Public Corp. Japan Highway Public Corp. Nagoya, Japan Nagoya, Japan
Toshio UEDA Hitachi Zosen Corp. Osaka, Japan
Satoru SAKUMA Toshiaki MAEKAWA Yoshikazu KOBAYASHI Japan Highway Public Corp. Japan Highway Public Corp. Hitachi Zosen Corp. Nagoya, Japan Nagoya, Japan Osaka, Japan
Summary The Meiko West Bridge is composed of two adjacent cable-stayed bridges whose interval is 50m, after the construction of the phase II line bridge in 1998. This paper describes the aerodynamic behavior of those parallel bridges measured in the site wind in order to verify the phenomena derived from the 3-dimensional wind tunnel test in a boundary layer turbulent flow. And also the characteristics of the rain-wind-induced oscillation measured on the staycables of both bridges is referred simultaniously.
1. Introduction The Meiko West Bridge is composed of two cable-stayed bridges with flat box girders as shown in Fig.1. The interval between parallel cable-stayed bridges is 50m. The phase I line bridge was completed in 1985, and this existing bridge has been put in service. The phase II line bridge was finished in 1998, and that is the new bridge. Now both bridges become a part of the Ise-Bay Highway that will link the New Tomei and Meishin Expressways. The aerodynamic stability of these bridges in tandem arrangement was investigated by the the wind tunnel tests using the 3-dimensional aeroelastic models with the scale of 1/100 in Hitachi Zosen’s wind tunnel facility as shown in Fig.2. From the results, it is concluded that the vortex-induced oscillation occurs in a smooth flow, but it vanishes in a turbulent flow. The field observation was performed in order to certify those phenomena. It is well known that the rain-wind-induced vibration was discovered for the first time under erection of the phase I line bridge of the Meiko West Bridge in Japan. By this time all staycables of this bridge have been connected mutually by the wire ropes. Therefore it will be necessary for any controlling device to be installed if the same phenomenon occurs in the stay-cables of the phase II line bridge. In order to obtain the materials for design judgement, the field observation of the stay-cable’s motion was also carried out simultaneously.
2. Field observation of girder’s motion The characteristics of the wind on the site were measured by the ultlasonic anemometer set on the deck of the phase I line bridge. The flat box girder’s motion was picked up by the servotype accelerometers. Those data were recorded on the opto-magnetic type disk using the automatic measuring system through the variable triger level of the wind velocity and the girder’s motion. Each data unit among 10 minutes was delivered with 0.05 sec sampling time. Many precious data including the monsoon and three times typhoons which are the 7th to 9th one in 1997 were obtained. The wind direction was predominantly northwest on the land side and southeast on the seaside as shown in Fig.3. There is no difference between this time data and the data measured 10 years ago with the same ultrasonic anemometer. Accordingly each wind
Fig.1 Outline of Meiko West Bridge
Fig.2 3-dimensional wind tunnel test in boundary layer turbulent flow
Fig.3 Histogram of wind direction
Fig.4 Relationship between turbulent intensity and wind velocity
Fig.5 Histogram of turbulent intensity
direction corresponds diagonaly to the axis of the bridge girder respectively. Figure 4 shows the relationship between the turbulent intensity and the mean wind velocity on the landside and seaside wind. And the histograms of turbulent intensity on both landside and seaside wind are shown in Fig.5. From Fig.4 the turbulent intensity is nearly over 10% at about 10 m/s where the vortex-induced oscillation may occur in a smooth flow. Such wind situation certificates that the 10% turbulent intensity selected in a boundary layer turbulent flow of wind tunnel test investigating the effect on the vortex-induced vibration was appropriate. From Fig.5, the mean turbulent intensity is about 15% on both side winds, and the estimation of the gust response occurred in a boundary layer turbulent flow with 15% intensity will be suitable. From the characteristics of some wind data obtained, the longitudinal turbulent scale is estimated 30m to 340m. The spectrum of wind velocity is good agreement with the Karmantype spectrum as shown in Fig.6.
Fig.6 Spectrum of wind velocity The vertical bending motions of the girder measured before and after the center connecting stage are shown in Fig.7 and Fig.8, respectively, comparing with the wind tunnel test results in a smooth or a turbulent flow. Every data show the standard deviation of dynamic responses at the center of each main span. Each relationship between the vertical bending motion and the wind velocity resembles the tendency of the gusty response generated in the boundary layer turbulent flow of the wind tunnel. The vortex-induced vibration didn’t occur in the natural wind with turbulence. The amplitude of gusty response is less than one derived from the wind tunnel test in a boundary layer turbulent flow with 10% or 15% turbulent intensity. Therefore it is concluded that there is no problem in the fatigue strength, referring to the design assessment based on the wind tunnel test results.
3. Field observation of stay-cable’s motion The measured stay-cables are C9 and C10 cable at the side span and C21 and C22 cable at the main span, whose are selected according to the experience during observation of the phase I line bridge as shown in Fig.9. During erection of the phase II line bridge, C11, C12 and C13, C14, C15 and C16 cable are measured by turns instead of above mentioned cables. The rainfall level was picked up by the rainfall strength meter, and the in-plane motions of staycables were measured by the servo-type accelerometers.
Fig.7 Vertical bending motion before center connecting stage stage
Fig.8 Vertical bending motion after center connecting
Fig.9 Objected stay-cable Ten times rain-wind-induced vibration’s data were obtained. Those rain-wind-induced vibrations were apt to occur in the main span side cables against the northwest direction wind and in the side span side ones against the southeast direction wind. Both cables coincide with the called positive posture side ones against the wind direction respectively.
Fig.10 Occurrence frequencies
Fig.11 Spectrum of cable motion in rain-wind-induced vibration
Fig.12 Amplitude of cable motion
The distinguished frequencies contained in the rain-wind-induced vibrations are shown in Fig.10. The aspect of the rain-wind-induced oscillations of two bridges are apparently different each other. Each example of cable motion spectra are shown respectively in Fig.11. The oscillation in the phase I line bridge’s cable is composed of many vibration modes, i.e. from 1st to 20th mode, and on the other hand the oscillation of the phase II line bridge’s cable includes only a few modes like 3rd to 7th mode. This different appearance was caused by the reason why the hard rubbers for suppression of bending at the end of cables and the rubber covers for sealing the cable-anchorage pipes were set on the phase I line bridge’s cables, but there were no attachments on the cables of the phase II line bridge under construction. Such behavior in the phase II line bridge is apparently similar to the one measured in the phase I line bridge under construction about 10 years ago. The maximum total value derived from the addition of each mode’s displacement whose are separated by FFT analysis are about 30cm on the phase I line bridge as shown in Fig.12 . Fig.11(a) shows the rain-wind-induced vibration of the center-span cable C21 occurred in the northwest wind with a weak rain, and Fig.11(b) shows the one of the side-span cable C9 occurred in the northeast wind with a comparatively strong rain. The inspection on the fatigue strength of stay-cables was performed, and it is concluded that there is no problem on the fatigue strength. The vortex-induced vibration often occurred in the stay-cables as shown in Fig.13. In this figure the data denoted as the symbol + indicates the relationship between the vortexshedding frequency and the mean wind velocity. From this relationship the Strouhal number St=fd/V is estimated about 0.15, whose value is a little lower than St=0.18, one of the circular cylinder in a turbulent flow. In Fig.13 the data denoted as the symbol ρ or ◊ are derived from the rain-wind-induced vibration, and those frequencies are nearly constant. The vortexinduced vibration denoted as the symbol, and the rain-wind-induced vibration denoted as the symbol measured in the phase I line bridge 10 years ago are similar to the data obtained this time in the phase II line bridges. Anyway the observated amplitude of the vortex-induced vibration was very small. According to the above-mentioned results, the controlling devices with high viscous damping rubbers have been installed on both bridges from the view point of serviciability, taking the aesthetic design into consideration as shown in Fig.14. The capacity of the installed dampers was decided based on the Scruton Number Sc=m symbol 100 \f "Symbol" \s 12δ/symbol 114 \f "Symbol" \s 12ρ d2 = 60 (m : mass of cable per unit length, symbol 114 \f "Symbol" \s 12ρ : air density, d : diameter of cable, symbol 100 \f "Symbol" \s 12δ: structural damping of cable in logarithmic decrement). symbol 100 \f "Symbol" \s 12δ equals 0.025 to 0.029 in the phase I line bridge’s cables, and about 0.02 in the phase II line bridge’s ones. Of course, the wire ropes connecting mutually are removed in all cables of the phase I line bridge.
Fig. 13 Relationship between occured frequencies and wind velocity
Fig.14 High viscous damping rubber installed at the end of stay-cable
4. Conclusion The wind tunnel test results using the aeroelastic model in a boundary layer turbulent flow on the Meiko West Bridge composed of 2 cable-stayed bridges with the flat box girders in tandem arrangement were certificated by the field observation. It is confirmed that the assessment on the safety and the serviciability based on the wind tunnel test results is adequate. From the results of the field observation on both rain-wind-induced vibration and vortexinduced oscillation of the stay-cables, it is cleared that there is no problem in the fatigue strength. But, from the view point of the serviciability, the controlling devices with the highviscous damping rubbers are installed.
Acknowledgement This study was done under the technical guidance by the committee on the design and construction of the Meiko West Bridge, whose chairman is Prof. Emeritus of Tokyo University Manabu ITO. The authors express their sincere appreciations to the members of the committee for their valuable advice. And also the authors wish to thank Prof. Masaru MATSUMOTO of Kyoto University for his helpful advice on the field observation of the stay-cables.
References [1] Tadashi NAGAI, Satoru SAKUMA, Toshiaki MAEKAWA and Toshio UEDA : Aerodynamic response on cable-stayed bridges with flat box girders in tandem arrangement, The 14th wind engineering symposium, Dec. 1996, in Japanese. [2] Yuichi HIGAMI : Rain-wind-induced vibration on cable-stayed bridge, Japanese Association of Wind Engineering, Vol.27 Mar. 1986, in Japanese. [3] Civil Engineering Research Center Corp : The report of aerodynamic study on cables in cable-stayed bridges, 1993, in Japanese.
Rehabilitation of the Luangwa Bridge Peter REINHOLDT Department Head COWI AS Lyngby, Denmark Peter Reinholdt, born 1953, received his civil engineering degree from the Engineering Academy of Aalborg Denmark in 1976. He is head of Department of Design and Supervision of Bridges.
Ejgil VEJE Department Head COWI AS Lyngby, Denmark
Jimmy KALVSLUND Project Lead Engineer COWI AS Lyngby, Denmark
Ejgil Veje, born 1954, received his civil engineering degree from the Technical Univ. of Denmark in 1981. He is head of Department of Maintenance and Rehabilitation of Major Bridges.
Jimmy Kalvslund, born 1963, received his civil engineering degree from the Technical Univ. of Denmark in 1989. He is Project Lead Engineer in the Department of Operation Management and Systems.
Summary The Luangwa Bridge is a cable stayed bridge situated in Zambia. The bridge was built between 1966 and 1968. Since its early days the traffic on the bridge has been restricted to the crossing of one vehicle at a time with a maximum gross weight of 50 tonnes travelling with a maximum speed of 15 km/h. A rehabilitation of the bridge was carried out in 1997 to strengthen the bridge and enhance its load bearing capacity. The rehabilitation included replacement of all cables and strengthening of the bridge girder and the pylons. Construction work had to be completed within a time slot between two rainy seasons, which represented a serious constraint on the project.
1.
Introduction
1.1
Location of the bridge
The Luangwa Bridge is situated on the Lusaka-Chipata Road (the Great East Road) connecting Zambia and Malawi. The bridge is located approximately 232 km east of Lusaka.
1.2
Technical description
The Luangwa Bridge is a cable stayed bridge build in 1966 - 1968 with a total length of 303.5 metres with a main span of 222.5 metres. The height of the pylons are 33.4 metres measured from the bridge deck. At the main piers the bridge superstructure including the pylons is supported by steel columns with a height of 13.9 metres. The steel columns are supported on pier foundations made of reinforced concrete.
Fig. 1 Elevation of the Luangwa Bridge The superstructure consists of two main girders made as rectangular steel box girders (height/width = 2.0/0.6 metres). The steel box girders are bolted together in 10 metres sections with friction grip bolts in splice connections. The bridge deck is made as a reinforced concrete slab with a thickness of 0.15 metres. It is supported by steel cross girders (I-beams) with a spacing of 2.6 metres. The main girders, the cross girders and the concrete deck behave as a composite structure. The superstructure is supported by a double cable system. The original Design Criteria were according to British Standard BS 153 with HA-loading. 1.3
Experienced problems
Shortly after the opening of the bridge it became evident that it was not behaving as intended. Two factors were especially of concern. The vertical profile of the bridge girder differed greatly from the theoretical profile of the bridge. One reason for this problem was that the stay cables were too long. They were designed with a fixed length and there was no possibility of adjusting the length.
Fig. 2 Profile of the bridge deck
Another factor was the failing of the high friction grip bolts in the splice connections of the steel box girders. During the years after the opening of the bridge, a number of these bolts started failing, with severe traffic restrictions as a consequence. Only one vehicle at a time was allowed to cross the bridge with a maximum speed of 15 km/h and a maximum gross weight of 50 tonnes. 1.4
Remedial works
In 1972-73 remedial works were carried out: •
•
•
•
The cable stays were shortened by applying clamps, reducing their length by approx. 135 mm in order to improve the vertical alignment of the bridge Inside the main steel girders horizontal compression steel tubes were mounted near the towers and horizontal tension cables were installed near the middle of the bridge Failed friction grip bolts were replaced The steel towers were filled with concrete below deck level.
2.
Fig. 3 Cable Clamps
Inspection and Rehabilitation Study
The department of international development assistance of the Danish Ministry of Foreign Affairs, Danida, offered in 1993 to finance a condition assessment and rehabilitation study for the Luangwa Bridge. 2.1
Inspection
The inspection of the bridge was carried out in 1993 covering both visual inspection, nondestructive and destructive testing. The visual inspection revealed large cracks in the concrete in the top of one of the main piers and in one of the abutments. The cracks in the top of the main pier were clearly caused by splitting forces from the steel towers on top of the main pier. The cracks in the abutment were located behind the main anchorages for the bridge girders indicating insufficient reinforcement. In spite of the remedial works carried out in 1972-73 with the intention of rectifying the longitudinal profile there was still a considerable sag in the main span. The clamps applied to the cables had reduced the sag but not eliminated it. Furthermore, a more local sag in the alignment was measured in the middle of the main span probably due to overloading of the friction joints of the main steel girders. The reason for the failure of high friction grip bolts in the splice connections of the main steel boxes was examined and found to be caused primarily by intergranular cracking in the bolt shaft caused by hydrogen. These cracks had developed after the tightening. Ultrasonic tests on the bolts still in position showed that the elongation of the bolts varied several millimetres indicating a tensioning procedure out of control. Severe pitting corrosion was found on the cable stays. The painting of the cable stays was cracked and there was virtually no adhesion to the cable surface any more.
Fig. 4 Severe pitting of cables
2.2
Rehabilitation Study
The inspection of the bridge was followed by a comprehensive rehabilitation study. Structural calculations were based on a 3D FEM-model of the bridge established in the in-house developed programme IBDAS (Integrated Bridge Design and Analysis System). The model included information about the original length of cables, remedial works etc. The behaviour of the model was cross checked by comparison of deflections with measured deflections from a loading test performed on site with a 30 tonnes truck. This showed a good correlation as the deviation was within the accuracy of the measurements. Structural calculations showed that many of the elements of the bridge were heavily overloaded. The rehabilitation study concluded that the bridge had to be thoroughly strengthened in order to provide a satisfactory safety level for the traffic passing the bridge.
3.
Rehabilitation Design and Rehabilitation Works
Based on the recommendations of the rehabilitation study Danida decided in 1996 to offer financing of a rehabilitation of the Luangwa Bridge. 3.1
Modelling for the Rehabilitation Design and Rehabilitation Works
For the analysis and design of strengthening measures the IBDAS FEM-model was further refined to take into account the full history of construction of the bridge. This included back tracking the construction phases for the main girders, the casting of the concrete deck in sequences, shortening of the stay cables and other remedial measures carried out in 1972-73. As the rehabilitation included installation of new bottom plates, splice plates and bolts in the main steel girders of the bridge deck, all bolted connections had to be opened. To do so the connections had to be either in a virtually “stress free” state or had to be temporarily fixed by clamps or equivalent. The chosen method of rehabilitation involved bringing the deck into a “stress free” state. An achievement of a "stress free" condition is influenced by many factors and several scenarios had to be envisaged. Therefore an envelope of occurrences were considered and these were considered to be described by the following two assumptions: 1. Model the construction sequence from when the bridge was built, reinforcement measures applied in 1972-73 and assume joints to be opened with zero moment. 2. Ignore all constructions phases and assume all loads to be applied simultaneously on the rehabilitated structure. 3.2
Rehabilitation Works and Method
The rehabilitation design prescribed the following measures: •
Removal of clamps and tension cables from previous attempts to strengthen the bridge
•
Replacement of existing cable stays with new and stronger stays
•
Strengthening of the anchorage plates for the cable stays
•
Replacement of all friction grip bolts in the joints between the steel sections of the main bridge girders
•
Replacement and installation of splice plates
•
Installation of additional bottom plates to the main bridge girders
•
Installation of additional crossbeams under the concrete deck
•
Filling of the steel towers above deck level with concrete
•
Replacement of the main anchorages of the bridge at the abutments
•
Increase of the weight of one of the abutments
•
Strengthening of the steel columns below deck level
•
Application of a compression ring at the top of the main pier to prevent splitting
To replace the existing cable stays, the bridge deck had to be supported by temporary towers at each cable anchorage point. This was only possible during a period with low water level in the river due to the risk of the temporary towers being washed away. The water depth of the Luangwa river varies from approx. 2 metres during the dry season from April to November up to approx. 910 metres during the rainy season from December to March. The constraints to the duration of the rehabilitation were severe as a time extension beyond the given time slot would have meant closing down the site and securing the bridge during the rainy season at an intermediate stage of the rehabilitation works. The de-stressing of the existing cables had to be performed in two steps. First the cable clamps installed during the remedial works in 1972 in order to shorten the stays had to be removed. No records of the forces used to tighten the clamps had been traceable. The forces applied by the clamps had to be determined by measuring the geometry of the compressed clamps. After removal of all cable clamps, the stays still had a considerable force left. As the cables were fabricated with no possibility of shortening or extension, the de-stressing of the remaining force was difficult. A new clamp system was made which could span a short distance of a set of cables. By pushing the clamps together the section of cable in between was de-stressed. It was then cut by a cutting torch and the clamp system was de-stressed. Now the bridge was in fact with its temporary towers a traditional girder bridge. The chosen method of rehabilitation by bringing the bridge girder into a “stress free” condition was achieved by use of a travelling girder. The travelling girder was designed to span neighbouring support points lifting the deck section undergoing rehabilitation. The travelling girder was in practice a bridge in itself and in position it still allowed for traffic passing the bridge. Spanning a maximum of 56 m and weighing 90 tonnes, it was designed to carry both the weight of 55 m bridge girder and the traffic loads. The travelling girder was successively moved on top of the bridge deck on temporary rails into positions between two temporary towers. Once in position the weight Fig. 5 Travelling Girder of the bridge girder underneath was transferred to the travelling girder. This was done by use of macalloy bars connecting from the travelling girder through drilled holes in the bridge deck to temporary crossbeams underneath the girder. The macalloy bars were stressed and controlled using jacks and load cells. The virtual “stress free” condition was achieved in this way and the required opening of bolted joints could be performed to allow fitting of the new splice plates and new bolts. When opening the first joints it was in some places observed that the bottom flanges of the two neighbouring sections were in close contact, and because of composite effect with the concrete deck at the upper top flange the joint still possessed moment capacity. In other cases a small slip occurred and bottom flanges were seen to move towards each other before a near stress free state was achieved. This information was used to further adjust the FEM-model and by applying the
right combination of forces in the macalloy bars it was possible to achieve near stress free states in the joints before opening them in the remaining sections of the bridge. The new cables were locked coil cables with adjustable length. The anchorage system was made to fit the existing anchorage plates in the girder and the towers. Thanks to a very intense and close contact during construction between the contractor on site, the supervision team and the design team in Denmark the contractor succeeded in finishing all critical operations and removing the temporary towers from the river bed before the heavy rains made the water level in the Luangwa River rise dramatically by mid December 1997.
4.
Operation and Maintenance
With the chosen level of rehabilitation the bridge is now able to carry HA loading and HB loading up to 25 units. The HA loading is a formula loading representing normal traffic. The HB loading is an abnormal vehicle unit loading. For the Zambian authorities to be able to control the daily traffic on the bridge and administrate permits for heavy transports a set of restrictions was defined for a range of realistic heavy vehicles. A Maintenance Manual for the rehabilitated bridge has been prepared. The manual included a suggestion for a setup of inspections to be performed as part of the maintenance.
Design of Structural Monitoring Systems
J. LAIGAARD JENSEN Ph.D COWI Lyngby, Denmark
Lars PEDERSEN M.Sc. COWI Lyngby, Denmark
Jakob Laigaard, born 1961, received his civil engineering degree from the Aalborg University, Denmark in 1986. He has specialised in structural monitoring and structural dynamics.
Lars Pedersen, born 1966, received his civil engineering degree from Aalborg University, in 1991. He has specialised in structural monitoring and instrumentation of large structures.
Summary This paper reviews and discusses approaches and processes involved in the design of structural monitoring systems. Within the civil and offshore engineering industry, monitoring systems are used either as permanent or as ad hoc systems (testing) providing information with objectives of obtaining information maximising revenue with respect to design, construction, operation and maintenance, and repair of structures. The design of such systems may simply be carried out based on a pragmatic basis resting on compromises within what may be called good engineering judgement, or the design decisions may be made on a more rigor basis applying rational cost-benefit analyses. Through a discussion of principles and examples, this paper discusses these aspects of the design of structural monitoring systems. It is argued that there are very good reasons for forcing the design process into a more rigor framework based on rational decision approaches, well known from experimental design in general.
1.
Introduction
In the civil and offshore engineering industry, since the mid seventies, there has been extensive use of structural monitoring systems and structural testing based on ad hoc monitoring systems applied on large structures. Within civil engineering industry, new large span suspension bridges such as the Great Belt Bridge, [1,2], and the Tsing Ma Bridge, [3], both have been designed with extensive monitoring systems. Similarly, new cable-stayed bridges, ranging from the Øresund Link Bridge (being build) to bridges such as those of the Lantau Fixed crossing, [3] and the Farø Bridge, [4] comprise also quite extensive installations of instrumentation. Also, tall buildings subjected to wind or earthquake loads are quite normally extensively instrumented, [5].
-1-
Within the offshore industry, uncertainty in severity of wave climate as well as difficult inspection conditions have made structural monitoring a standard tool for enhancing safety of offshore structures. The standard objectives have been monitoring of wave and wind climate together with platform displacement response, and fatigue life in terms of stress cycles, [6]. The layouts of such systems have varied a great deal and this suggest that the design approach on structural monitoring system may have been based on different approaches and criteria. In the offshore industry, some platforms have hardly a wave height sensor whereas others have an extensive number of accelerometers and strain gauges. With respect to the civil engineering industry, table 1 shows an example of difference scales of structural monitoring. The table compares the number of sensors between the permanent structural monitoring systems of the Great Belt and the Tsing Ma Suspension Bridges. The table shows a significant difference in the amount of instrumentation. One reason is of course different conditions with respect to site, environment and operation, another reason may be differences in the priorities in the design of the structural monitoring system. A detailed assessment of the actual causes for the different scale of instrumentation is not possible in this context but the table indicate together with other similar cases, that it may be worthwhile considering how structural monitoring systems are designed. Sensor Type Temperature Sensors Settlement Sensors Displacement Sensors Strain Gauges Wind Sensors Accelerometers Corrosion Sensors Table 1
2.
Tsing Ma Suspension Bridge 115 9 2 110 6 17 0
Great Belt Suspension Bridge 50 50 20 0 2 0 42
Comparison of structural monitoring systems for Tsing Ma and Great Belt Suspension Bridges (estimated number of sensors on primary structure).
Structural Monitoring Objectives
In reviewing the design of structural monitoring systems, it is important to focus on the fact that the product being sold is information. Sometimes information obtained through monitoring proves needed, at other times information may be obtained by other means, e.g. by experience or theoretical ways, and finally quite frequently there is no need for further information at all. When use of structural monitoring systems are considered, it is important to be aware that such system can and should be tailored to the information needed. That is, for some information it may be more plausible to obtain the information through small ad hoc monitoring systems being used for a short period of testing. In other cases, the need for information is extensive and of long term nature, meaning that it may be worthwhile installing a permanent system. In short, the objectives of a structural monitoring system must be clarified at an early project stage of the design or modification of a structure. This is important as the potential information from structural monitoring systems interacts with decisions to be made with respect to design, construction, operation and maintenance of the structure. Also, it is important because the implementation of the structural monitoring system interacts significantly with construction work -2-
and hence probably also the critical path of the project. Hence in the design of structural monitoring systems, the objectives and the monitoring concepts must be discussed and determined as a holistic exercise before irreversible decisions are taken. Consequently, such design exercise should ideally take place as a cost-benefit study where the pay off of each structural monitoring item is considered. Here, the pay off is defined by the benefits (additional revenue or saved costs) compared to the costs of the implementation and operation of the structural monitoring system. In total for a given structure, the cost-benefit study must consider how the structural monitoring systems may interact with structural aspects such as: • • • • • • •
2.1
design construction operation commissioning maintenance requalification verification for R&D Design
In the design process, the consultant should consider how a structural monitoring system may be used as a tool to obtain a sufficient high level of safety with respect to: • • •
new structural concepts deviation from existing codes and standard deviation from the imposed design basis
To use structural monitoring as a tool, the approach will typical be to carry out ad hoc testing on another structure (full-scale or model), or to implement a structural monitoring system allowing for later design or operational modifications, if the acquired information supports such a decision. 2.2
Construction
In the construction phase, the contractor should together with the owner consider how a structural monitoring system may be used to increase the efficiency of the applied construction methods. This could be related to: • • • •
enhancement of personal safety enhancement of structural safety allowance for working methods deviating from tender conditions decrease sensitivity of working method with respect to weather and other ambient conditions.
In such cases, structural monitoring is used as a control tool for on-line quality assurances which allows for increased efficiency in construction methods. 2.3
Commissioning
At the hand over of a structure, the owner, operator or contractor may apply structural monitoring as a tool for documentation of the fulfilment of design requirements. In this case, the acquired information may be used to ensure quality as well as to provide an important element in handling any dispute effectively. -3-
2.4
Operation
In the operational phase, the consultant or operator should consider how a structural monitoring system may be used by the operator to control: • • •
2.5
operational risks efficiency in operation structural integrity Maintenance
With respect to maintenance which actually is a part of the structural routine operation, the consultant and operator should consider how structural monitoring may be used by the operator as an efficient inspection tool for planning of maintenance and repair tasks. This may comprise control of: • • •
2.6
durability of the structural integrity of the structure efficiency of repairs and maintenance Requalification
In connection with changes in operation or lifetime extension, the consultant may use structural monitoring as a tool for requalifying the structure by increasing information about the structural performance. Also changes in codes may call for requalification of a structure and thus require further information about the actual structural performance. 2.7
Verification for R&D
Sometimes structural monitoring systems are justified by the need for verification. In such cases verification is quite frequently used as an objective where the actual information acquired cannot be used for changes in decisions for the given structure but rather serves a more broad banded purpose within research and development. Thus such structural monitoring systems will typical be more to the benefit of the joint industry rather than the contractor, owner or operator of the given structure. This point should be realised and in cases where structural monitoring systems are setup for research orientated purposes, the most logical project set-up would in general be joint industrial projects. This approach is reasonable well-known within the offshore industry (e.g. Ocean Test Structure in U.S.A, and the Tern Platform in the British North Sea ) whereas it is less well-known within the civil engineering industry.
3.
Design and Implementation of Structural Monitoring Systems
Structural monitoring systems provide a central tool for obtaining information assisting in making the right decision regarding the objectives outlined in Section 2. The right decision will be a decision which is right at the time of decision with the information available at the time. Hence, the need for a structural monitoring system should be seen in the light that it is expected that the system will provide information which will have an impact on decisions to be made. This implies answering the question: •
Should structural monitoring be carried out at all? -4-
In next phase, the following questions must be considered: • •
What would the allowable monitoring costs be? Of a number of alternative structural monitoring alternatives which should be chosen for implementation?
Answering these questions may be carried out on a quite pragmatic basis or it may be attempted to go through a more rigor and rational decision process. 3.1
Design in a Pragmatic Framework
In practice, design of structural monitoring systems is quite frequently carried out on a fairly pragmatic basis leading to decisions based on compromises between interests involved. The interests involved are represented by a number of players who are engaged in the design decisions, cf. Fig.1. The players will represent economical interests as well as safety interests related to users and authorities.
Consultant
Operator Contractor Users (Customers)
Owner (Investors) Authorities
Fig. 1
Players in the decision making on structural monitoring systems
However all players points of views may not only rest on strict rational arguments with respect to economy and safety issues but also on less rational arguments which may be related to personal, political or secondary commercial interests. Hence, a complicated mixture of interest may rule the discussions on the design of a structural monitoring system. This is further complicated by the multidisciplinary character of the design of structural monitoring systems comprising conventional structural engineering, construction engineering, instrumentation, operational risk analyses, probabilistic studies and experimental design. In total, this complexity means that a pragmatic decision process may very well depend somewhat randomly on the power balance of interest involved and thus lead to less efficient structural monitoring systems where benefits are not balanced by the costs. 3.2
Design in a Rational Framework
To avoid ineffective structural monitoring systems, the best approach is to seek to put the decision process into a rational framework with the objective of identifying the expected benefits and costs of the structural monitoring items. In the rational approach, a cost-benefit study is carried out based on a probabilistic assessment of the expected value of gathering information by a structural -5-
monitoring system compared to the expected costs of obtaining this information. An initial exercise to be carried out in the early conceptual design of structural monitoring systems is therefore to consider the value of an ideal structural monitoring system providing complete information. This value of complete information defines the maximum acceptable costs of structural monitoring systems to be considered. A subsequent detailed cost-benefit analysis should of course consider costs and revenue together with the uncertainties associated with consequences of the decisions as well as uncertainties of the information obtainable. Hence, a decision on carrying out a structural monitoring task should therefore consider: 1. 2. 3. 4. 5. 6.
The alternative decisions to be made on the basis of the acquired information The consequences (economical and other) of a given choice of decision The degree of perceived uncertainty with respect to consequences of each choice The further information which appears necessary to chose an alternative. The uncertainty associated with the information obtainable by structural monitoring The costs of structural monitoring
1 to 5 relate to the benefits of information obtainable from the structural monitoring system whereas 6 represent the costs. In the case of ranking different structural monitoring alternatives, the benefit-cost ratio must be considered, and the most favourable alternative chosen. A rational decision analysis may be carried out on by a decision tree analysis with the objective of identifying the most optimal structural monitoring design. Figure 2 shows a simple example for illustration only, involving a number of sub exercises: • • • •
A number of decision strategies are chosen: For instance structural monitoring versus no structural monitoring. Discrete outcomes of information, Ii obtained by the structural monitoring are identified: For instance positive result versus negative result. A number of project decisions Di are identified: For instance new design vs. conventional design. The probability, P(θiIi) of the real outcome θi given the obtained information, Ii, is obtained through the well known theorem of Bayes based on a´priory probabilities, the information acquired from the monitoring system, and the uncertainty of the acquired information.
Based on the decision tree set-up: • • • •
The economical consequences, Vi of each outcome, θi are identified The expected revenue, Ri of each branch is derived Non-optimal branches are cut off The expected revenue by implementation of the structural monitoring system is calculated and compared by the decision of no implementation of a structural monitoring system.
The decision tree analysis is in itself quite simple, and the largest difficulty arise from discretizising the decision process into a finite number of alternatives. The problem of associating costs and probability may seem difficult but it is a problem which exists and has to be solved independently on how the decision process is organised. Hence, the advantage is that the decision tree analysis forces the decision maker to face and discuss the consequences and uncertainties associated with the decision process. This will assist in promoting the real and important costs and -6-
benefits and thus result in better and more efficient structural monitoring systems. It is therefore emphasised that this type of rational decision approach are going to become a more important and frequently used tool in the design of structural monitoring systems.
Outcome θ1
Decision No Monitoring
Decision D1
Consequence V1
P(θ1) Outcome
Consequence V2
θ2 Decision D2
P(θ2) Outcome Stop
Consequence 0 Outcome θ1
Decision Monitoring
Information I1
Decision D1
P(θ1|I1) Outcome θ2
Decision D2 Information I2
Outcome Stop
θ1 P(θ1|I2) Outcome θ2 Decision D2
Fig. 2
4.
Consequence V2
P(θ2|I1)
Outcome Decision D1
Consequence V1
Consequence 0
Consequence V1
Consequence V2
P(θ2|I2) Outcome Stop
Consequence 0
Example of Decision Tree for analysis of cost benefits.
Examples: Structural Monitoring in Practice
Currently the design practice may not in general be claimed to be carried out in strict agreement with a rational decision approach. However, a number of examples from Danish bridges suggest that rational aspects in structural monitoring can be identified, and there is a sound basis for maturing the design practice into a rational framework for design of structural monitoring systems. 4.1
Handling of Girder Vibrations in Design
In the late construction phase of the Great Belt Suspension Bridge, excessive vibration response was observed for the girder of the suspension bridge, [7]. On this basis, an ad hoc monitoring system was installed and response measurements carried out. The objective was to assess whether installation of pre-designed guide vanes would lead to acceptable vibrations. This implied quantification of wind response mechanisms and determination of structural damping for updating design response predictions and wind tunnel tests (with and without guide vanes mounted). The measurements showed that vortex shedding frequently occurred in connection with the 5th vertical girder mode for wind directions approximately orthogonal to the bridge axis. The structural damping was identified to be very low (0.25%) which was the cause for the unacceptable level of vibrations. On this basis, it was decided to mount guide vanes on the bridge. -7-
After the guide vanes have been installed, there has been no excessive vibrations.
Fig. 3 4.2
Example of measured build-up of wind induced girder vibration before installation of guide vanes on Great Belt Suspension Bridge. Construction, Monitoring of Critical Phases
The Farø Bridge in Denmark, inaugurated in 1985, have been subject to a number of full-scale measurements during construction, [5]. The central span of the cable-stayed bridge was cantilevered out from the bridge pylons and one of the critical phases was just before the main span was made continuous at the center. In this phase the wind speeds at the site and the vibration response of the cantilevered section were closely monitored to assess the risk of severe windinduced vibrations and thus to control the safety of the structure. 4.3
Commissioning of Railway Track
By structural testing, the track quality of the Great Belt, West Bridge (railway bridge) was tested in terms of ballast stiffness, and a number of deformation and load measurements were carried out at the bridge expansion joints. The testing was carried out in connection with hand over from the railway track contractor to Great Belt Ldt., and the subsequent hand over of the railway track to the railway operator. For a number of runs with IC3 trains several sections of the railway track and the track at all expansion joints were tested.
Fig. 4 Tests with IC3 trains running 140 km/h.
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The test results suggested that sleeper displacements were larger at the bridge expansion joints than of the track in general. Test with a breaking freight train showed that the loads in hydraulic buffers of the expansion joints and girder displacements were acceptable. The results were used as hand over documentation of the quality and state of the railway track and structural elements interfacing with the railway track.
4.4
Operational Safety Monitoring System
As the Great Belt Bridges span waters with high intensity of heavy vessel traffic, a monitoring system has been installed to control the operational risks associated with ship traffic. Due to the risk of large economical consequences and possible loss lives, the objective of the system is primarily to avoid ship impact and secondly to detect an impact. A dedicated surveillance system monitors ship traffic in the entire Great Belt region. In case of risk of imminent collision with one of the bridges, alarms will be issued to the authorities responsible for follow-up actions possibly in the form of requests for immediate closure of the bridges to traffic. As back-up monitoring system, the bridges are equipped with tilt-meters and displacements sensors with the purpose of instant detection of a ship impact. Due to the need for immediate action these structural monitoring systems are continuously monitored by fail-safe SCADA systems with pre-set alarm thresholds, and the status of the alarms can be surveyed by all parties involved in emergency tasks. 4.5
Maintenance through Durability Monitoring
For the concrete structures of the Great Belt Bridges and the Øresund Bridge durability monitoring systems have been installed. The objective has been to optimise the planning of future maintenance of concrete structures. Throughout operation, the concrete structures will be exposed to chlorides contained in air and sea water and the chlorides will eventually penetrate the concrete cover to the reinforcement and result in corrosion with the risk of excessive maintenance and repair costs. For the Great Belt and Øresund Bridges, the permanent monitoring systems cover about 300 stateof-the art corrosion sensors. Fundamentally, the embedment sensor consists of six dummy reinforcement bars, and through periodic surveillance of the corrosion state of these bars, the sensor assembly will monitor the arrival times of chlorides at different depths below the concrete surface. The sensors monitor the: •
• •
penetration rate of chlorides and thus time to corrosion of the actual reinforcement hidden accumulation of maintenance needs efficiency of existing or modified maintenance.
The essential system features are that the measurements detect on-coming durability problems at early stages of degradation, and Fig. 5 Corrosion sensor. that they provide the operator with information on the present and future condition of different structural elements. Hence, maintenance programmes can be reviewed on a regular basis and maintenance efforts can be allocated to the structures and elements hereof as and when needed. The investment in the monitoring system is expected to result in considerable cost savings during operation of the structures which are designed to last for 100years. -9-
The durability monitoring system described in this section is believed to be the monitoring system for the next generation of concrete structures. Since the instrumentation of the Great Belt West Bridge in 1992-93, similar type of systems, though of minor scale, have today been installed in about 15 countries world wide.
5.
Conclusion
The paper has reviewed and discussed the design of structural monitoring systems. The paper suggests that the use of decision tree analyses may be used to ensure efficient structural monitoring systems through systematic cost-benefit analyses. Large differences in the layouts of structural monitoring systems, suggest that existing design practice does not always result in optimum system design due to a pragmatic approach in the design. However, a number of examples of structural monitoring systems shows that the rational aspect of system in general is quite obvious. There appears therefore to exist a sound basis for introducing more rational design methods. Consequently, it is foreseen that in the future, design practice will mature and to much larger extent comprise the use of rational methods for the design of structural monitoring system.
6.
References
[1]
Andersen, E.Y. and L. Pedersen, Structural Monitoring of the Great Belt Bridge, Proceedings of the 3rd Symposium of Strait Crossings, Ålesund 1994.
[2]
Andersen, E.Y., Monitoring for Structural Health, International Workshop, "Infrastructure Development", Hong Kong, dec. 1991.
[3]
Lau, C.K., Wong, K.Y. and K.S. Ho, The Wind and Structural Health Monitoring System (WASHMS) for the three long-span cable-supported bridges in Hong Kong, IABSE, International Association for Bridge and Structural Engineering, 15th Congress, June 16 20 1996, Copenhagen.
[5]
Ostenfeld, K.H. and H.E. Langsø, Full Scale Measurements and Monitoring of Major Cable-Stayed Bridge, International Conference on Cable-Stayed Bridges, Bangkok, 1987.
[6]
Jensen, J. Laigaard, System Identification of Offshore Platforms, Ph.D. Thesis, Aalborg University, Department of Building Technology and Structural Engineering, April 1990.
[7]
Jensen, J. Laigaard et al, Estimation of Structural Damping of the Great Belt Suspension Bridge, to be presented at EuroDyn Conference, Prague, 1999
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The Faroe Cable-Stayed Bridge - Maintenance Experience with Major Components Matthew L. BLOOMSTINE Project Manager COWI AS Lyngby, Denmark Matthew L. Bloomstine, born 1955, received his engineering degree from the Technical Univ. of Denmark in 1987. He has specialised in inspection, maintenance and rehabilitation of major bridges.
Erik STOLTZNER Civil Engineer, Danish Road Directorate, Copenhagen, Denmark Erik Stoltzner, born 1944, received his civil engineering degree from the Technical Univ. of Denmark in 1969. He is Area Manager for Operation and Maintenance in the Bridge Department.
Summary A cable-stayed bridge such as the Faroe Bridge is a unique and complicated structure, which requires a systematic and technically correct maintenance. This paper presents experience from operation, inspections and maintenance works over the first 14 years of service, with focus on certain major components. Overall costs for operation and maintenance are also presented, as well as costs for some particular operation and maintenance activities. Based on experience from the first 14 years, the estimated annual total cost of operation and maintenance over the next ten years corresponds to approximately 0.6% of the present value of the cost of construction. This is quite a low level, which indicates the success of maintenance considerations in the design and an effective operation and maintenance program.
1.
Introduction
The Faroe Bridges are two bridges with a total length of approximately 3.3 km, which connect the Danish islands of Zealand and Falster and carry the southern motorway, which connects Copenhagen with Germany and the rest of Europe. The 1,596 m long northern bridge crosses the sea between Zealand and the small Faroe Island. The southern bridge, which is the subject of this paper, is a cablestayed bridge between Faroe and Falster with a length of 1,726 m. Construction of the bridges commenced in 1980 and they were opened for traffic in 1985.
Figure 1 An overview of the Faroe Cable-Stayed Bridge 1
The superstructure of both bridges is a steel box girder, which is continuous over the entire length with expansion joints located at each end. The cable-stayed section of the southern bridge has a navigation span of 290 m with a vertical clearance of 26 m and two side spans, each with a length of 120 m. The cables are arranged as a fan system of single cables, which are placed in a central plane symmetrically around the pylons. The cables are of the parallel wire type and protection is provided by PE ducts, which are grouted with cement mortar. The general arrangement of the bridge is shown in figure 2. The superstructure was designed and construction supervision carried out by COWI. The superstructure was built by the contractor Monberg & Thorsen. The Ministry of Traffic under the Danish State is the owner. The Danish Road Directorate is responsible for operation and maintenance with assistance from COWI.
Figure 2 General Arrangement of the Faroe Cable-Stayed Bridge During the design work special attention was given to: • •
Aesthetics - concerning the bridge itself and the alignment with respect to the existing landscape. Economy - concerning construction and maintenance costs.
This paper presents operation experience, inspection routines and experience, maintenance works and costs from the first 14 years of operation concerning the following topics: • • • • • • •
2.
General routines for inspections. Corrosion protection of cables. Wind induced cable oscillations and the system introduced to minimise these. Corrosion protection of the steel box girder by means of dehumidification. Water intrusion - problems and remedies. Expansion joints which each have a total movement capacity in the range of 1 m. An unexpectedly early replacement. Access equipment.
General routines for inspections
Inspections of the bridge are generally carried out according the Danish Road Directorate's manual "Inspection of Structures, November 1994". For general use concerning structures the manual specifies the following three types of inspections: • • •
Running/Continuous Inspection, a quick visual inspection with focus on obvious damages that can impede the structure in fulfilling its purpose with regards to traffic safety. General Inspection, a thorough and systematic inspection of all components of a structure, performed at regular intervals between one and six years. Special Inspection, normally prescribed when a potentially serious damage is observed during a General Inspection. The inspection is composed of two main activities: a technical inspection to determine the cause and extent of damages and an economic inspection, which investigates different repair strategies in order to determine the most economical solution. 2
The above mentioned inspections are implemented for the Faroe Cable-Stayed Bridge in the following manner. Running/Continuous Inspection Running inspection is carried out on a daily basis by the Road Directorate's own bridge personnel. The bridge master, who originally worked for the contractor during the construction phase, makes at least one round trip by car over the bridge each weekday. During this trip special attention is paid to major components such as stay cables. Any obvious damages will be detected and reported at an early stage. Approximately once a month the bridge master performs a walking inspection through the entire bridge girder and along the carriageway (on the emergency walkway) with stops at major components. General Inspection Due to the size and complexity of the bridge structure as well as access and budget limitations it is not feasible to conduct a general inspection of all components in the course of one year. Therefore, individual components or groups of components are inspected each year, in such a manner that all components are subjected to a general inspection about every fifth year. Special Inspection Special inspections are carried out as deemed necessary in the general inspection reports.
3.
Corrosion protection of cables
The stay-cables are parallel wire cables, manufactured by Stahlton AG. Each cable is composed of between 145 and 277 individual 7 mm diameter wires. The cables are protected by heavy walled watertight polyethylene ducts (thickness 9.1 to 11.4 mm) and cement mortar, see figure 3. The PE ducts have the purpose of keeping water and contaminants away from the cables. The cement grout is thought to protect the cable wires by providing a passive atmosphere in the same manner as concrete does for steel reinforcement. The PE ducts are continuous from the anchorage at the top of the pylon to the anchorage in the bridge girder. Both anchorages are located in areas which are protected by dehumidification (cf. section 5), which prevents intrusion of moisture in the ends of the PE ducts. Hence the only possible entrance of water and contaminants to the cables is through possible defects in the PE ducts. The latest inspection of the cables was carried out in 1996, eleven years after the bridge opening. The inspection was performed from 72 m boom, which was parked on the carriageway. With this boom it was possible to access the entire length of all 36 stay cables and approximately 50% of the total cable length was visually inspected at close hand. The general condition of the PE ductswas evaluated as good. There were no signs of cracking, discolouring or other signs of ageing. The only damages which were found were identified as originating from the construction period. These were primarily superficial scrape marks. There were also three patch repairs which had begun to deteriorate. These will be further inspected and re-evaluated during the next inspection, which is planned to be carried out in Figure 3 Cross section of cable 2001.
4.
Wind induced cable oscillations and minimisation
As the result of the use of different analysis methods including a special computer program considerable wind induced cable oscillations were expected. Therefore, on-site investigations and measurements 3
were carried out during construction and after completion of the bridge. The investigations generally confirmed the calculated values and a system to reduce the oscillations was devised. The individual cables were interconnected by an upper and lower pre-stressed wire system, as shown in figure 4. The original wire system was composed of steel brackets with neoprene lining on the cables and stainless steel wire connecting these. The wires were wrapped around a thick washer in the bracket and secured by two wire locks. This system effectively reduced the oscillations to a minimal level for all cables with the exception of the first cable on each side of each pylon. These cables have special wind conditions, as they are nearly vertical and are placed so close to the pylons. Under certain conditions wind and rain induced oscillations with an amplitude in the range of approximately ±0.5 m occurred. Figure 4 Interconnection of stays After about four years of service the first wire in the interconnecting system ruptured. Upon closer examination it was discovered that all the wires showed signs of wear from abrasion between the wire the washer. A more robust design for connection of the wires was devised, with 10 mm marine grade stainless steel wire, a fork and stud terminal allowing easy adjustment of the pre-stressing force on one end (cf. figure 5) and a fork terminal on the other end. This system has proven to be much more robust. After seven years of service the first wire ruptured and a close inspection of all the wires was carried out. One more wire was found to be seriously damaged and two others had signs that damages might soon occur. All damages occurred in the vicinity of the terminals and all four wires were replaced. The total number of damages was only a fraction of the number of damages in the original system and these first occurred after a much longer period. A solution for the oscillations of the first cables by the pylons was applied at the same time that the wire system was improved. The cables were spirally wrapped with a gradient of one rotation per meter with a 16 mm polyethylene duct. Inside the duct is a 4 mm steel wire which is pre-stressed to approximately 50 N and fastened at the bottom end to a spring. This system has effectively reduced the oscillations to an acceptable level.
Figure 5 Detail of improved interconnecting wire system and original pre-stressing method
4
During the last inspection in 1998 a tensiometer, as shown in figure 6, was purchased to measure the pre-stressing force in the individual wires. This device measures the force required to deform the wire a certain amount in a perpendicular direction over a fixed length. This force is automatically transformed to the axial force. The instrument was calibrated by the manufacturer to the dimension of the wires. The original method required unloading of each wire by straps and a winch and measuring with a dynameter as illustrated in figure 5. This method was cumbersome and time consuming and therefore only a spot check of the pre-stressing forces were measured. Use of the tensiometer is quick and easy with a digital display of the prestressing force and allows an accurate measurement. A complete check of all the pre-stressing forces was quickly performed during the inspection and maintenance work. Figure 6 Measuring of pre-stressing force by means of tensiometer
5.
Corrosion protection of the steel box girder
The internal surfaces of the steel bridge box girder are protected from corrosion by means of dehumidification. This was the first bridge to be protected internally by dehumidification alone. The bridge box girder, with a total length of 1,726 m, is divided into 3 dehumidification sections, each with approximately a third of the total length. A dehumidification plant is installed in each section. Each plant is composed of a sorption dehumidification unit with fresh air intake and moisture laden air discharge and a fan unit for circulation. The fan unit is connected to two trapezoidal stiffeners for forward air flow. The return air circulates through the box girder and through the manholes in the bulkheads. The system is illustrated in figure 7.
Figure 7 Principle layout of dehumidification system. 5
The dehumidification system is set to generally maintain a relative humidity of approximately 40%, which is well below the 60% level where corrosion can start. This difference allows for a margin of safety and sudden falls in the temperature, which correspondingly give sudden rises in the relative humidity. The dehumidification system has proven to be completely effective, as no signs of condensation or corrosion have been observed during the regular inspections. Sensors which constantly measure the relative humidity are connected to the bridge monitoring system. The control system for the dehumidification system has been adjusted during the operation period in order ensure a cost effective operation. To take advantage of the low night time price for electricity, the control intervals have been modified to the following values: • •
Night: Day:
Start at RH 40%. Start at RH 50%.
Stop at RH 35%. Stop at RH 48%.
With these control levels the dehumidification plants run almost exclusively at night and takes full advantage of the low rate. The bridge monitoring system has an alarm which is activated when the relative humidity reaches a level of 50%. This occurs about 10 times a year and the level is automatically brought down within a couple of hours. The average electrical consumption per year is approximately 60,000 kWh, which with Danish prices cost about US$ 7,000 per year. The individual dehumidification plants are serviced once a year for an average total cost of approximately US$ 1,500. The total average cost for operation and maintenance of the dehumidification system for corrosion protection of the 160,000 m2 steel surface area is about US$ 8,500 per year. This corresponds to approximately US$ 0.04 per m2 steel surface per year.
6.
Water intrusion - problems and remedies
Wind conditions on a major cable-stayed bridge are much more extreme than at the local ground level because of the height of the structure and turbulence caused around pylons and other components. This can result in water being pressed in through joints and connections which are believed to be watertight. Water intrusion has occurred at the following locations: • • •
The steel anchorage boxes at the top of the pylons The neoprene cuffs at the upper cable anchorages The neoprene cuffs at the lower cable anchorages
During routine inspections it was found that water accumulated in the anchorage boxes during stormy weather. The tightness of the anchorage boxes was tested by applying a slight overpressure on the inside and brushing soap water on the outer surfaces. Leaks were identified by the bubbling action of air seeping out. The joint filler in the joints between the 3 box sections were leaky and the bolt connections were leaky around the bolt heads, even though these were painted after erection. The joint filler in the section joints was replaced with a new elastic joint filler and the joints were covered by stainless steel sheets to protect them from the environment. Elastic joint filler was also applied around the bolt heads. No further water intrusion has been observed since these improvements were made, however, future maintenance of the joint filler is foreseen. Neoprene cuffs overlap the cables and the anchorage pipes where the cables enter the upper anchorage. These cuffs were originally fastened with two steel clamps on each end and this was thought to be a watertight connection. Inspections revealed the opposite, as water accumulations were found in the cuffs. A twofold solution was devised. A strip of silicone filler was applied under the cuff before tightening the clamps. In order to be able to easily check for water intrusion in the future, plastic hoses were placed with one end in the bottom of the cuff and one end on the inside of the anchorage box, which is easily accessible. It is now possible to easily inspect for water and remove it if necessary. A pulled back cuff and an inspection hose are shown in figure 8. Follow up inspections have proven that the connections are generally tight now. 6
Figure 8 Opened cuff at upper anchorage and inspection hose and inside the anchorage box Similar neoprene cuffs overlap the connection where the cables enter the bridge girder. The upper edge of the cuffs have been sealed with elastic joint filler. However, the cuffs have a tendency to slide down here, do to cable vibrations, and leave the joint filler behind. Water can then intrude through the connection. The solution is regular inspection and maintenance of these connections, which are easily accessible. As noted in section 3, the stay cables are covered by PE ducts. These ducts cover the cables in the areas under the cuffs and all the way to the anchorage, such that the water intrusion in these areas has not been in contact with the cables. The lessons from this experience are: • • •
7.
Special attention should be paid to making connections watertight, although permanent watertightness is not possible for some connections. The areas near the connections should be easily accessible for inspection and means to prevent water accumulation should provided. Regular inspections of potential areas for water accumulation should be performed to prevent damages.
Expansion joints
The 1,726 m long bridge girder was at the time of opening, to the best of our knowledge, the longest continuos bridge girder in the world and it still ranks among the world's longest. The main reason for designing such a long girder was to reduce the number of expansion joints to a minimum and thereby reduce the amount of maintenance associated with these, improve driving comfort and reduce construction costs. As the bridge girder is so long the requirements to the design movement capacity of the expansion joints was very high. These requirements led to a total movement capacity for the southern joint of 1,040 mm and 880 mm for the northern joint. The joints are of the lamella type with lamellas perpendicular to the bridge axis with sealing strips in between and supporting joists underneath, which slide in and out of joist boxes. After only 4 years of service life fatigue damages began to appear. There were two typical types of damages, cracks running up through the lamella in the vicinity of the support and cracks in the welded support connection. Damages were regularly registered and repaired. The damages first appeared in the most sensitive areas, but continued to spread and increase in number. It was concluded that it was not worthwhile to repair the joints, as there was an inherent problem in the manufacturer's design. After only 9 years of service and many repairs, it was decided to replace the expansion joints. In order to minimise replacement costs certain main design features were incorporated in the technical specifications for the new joints. The necessary movement capacity was re-evaluated on the basis of recorded data for movement of the end bearings from the bridge monitoring system. It was possible to reduce the original requirement to movement capacity and still maintain an appropriate margin of safety. The other means of reducing costs was to reuse the existing joist boxes and thereby save manufacturing 7
costs and even more importantly minimise site work. The expansion joints were replaced in 1996 at an average cost of approximately US$ 160,000 each. Aside from some minor adjustments carried out under the guarantee during the first year, the new expansion joints have been performing satisfactorily.
Figure 9 Replacement of expansion joints
8.
Access equipment
In order to perform inspections and maintenance works a variety of access equipment is necessary. Equipment which can be effectively used on the Faroe Bridges and other bridges is owned by the Danish Road Directorate. Other equipment, which has a limited use and a high cost of procurement, is rented for certain inspections and maintenance works. The following access equipment is owned by the Danish Road Directorate: Skyclimber wire supported platform A special Skyclimber platform system was designed for use on the Faroe Bridges. It can be assembled and used for inspection and maintenance of the pylon legs above the roadway, the cable anchorage boxes at the top of the pylons and the piers. For use on the pylon legs there are permanent fixtures on top of the pylons for attaching the wires. The platform can be assembled with either 3 sides to cover the upper regions of the pylons or with 4 sides, encompassing all 4 surfaces of the pylon leg, as shown in figure 10. For use on the cable anchorage box a smaller platform for two persons can be assembled. For use on the piers there are movable fixtures which are fastened to the top of the pier. The platform is assembled with 3 sections corresponding to half of the hexagonal cross section of the piers. Bucket snooper boom The bucket snooper boom is truck borne, as shown in figure 10. It has a bucket for two persons and reaches out over the edge of the bridge girder and can reach about 10 meters in under the bridge girder, corresponding to half the width of the girder. This boom has mainly been used for spot check inspections and minor repairs of painting on the bottom of the bridge girder. It requires a great deal of maneuvering and has limited room and load capacities and is therefore not suitable for thorough inspections and major repairs. It is used on many different bridges throughout Denmark. Wire supported platform A similar system to the Skyclimber, though somewhat simpler, has been used for inspection of the areas of the pylons below the bridge girder. The platform has one straight section with an adjustable length and it has been used on a number of major bridges in Denmark. Support girders are erected along both edges of the bridge girder and wires for suspension of the platform are fastened on these girders. Fixed local platform A small fixed platform has been retained from the construction period. It is lifted into position by a truck borne crane and fastened to the guard rails along the edge of the bridge girder. It is useful for local repairs on the outer edge of the bridge girder and especially for maintenance of the horizontal bearings at the northern pylon, for which it has been specially modified.
8
Figure 10 Access equipment, Bucket snooper boom and Skyclimber platform The following equipment has been rented for inspections: Fürg 72 m truck borne boom The Fürg 72 m truck borne boom has been used for inspection and maintenance of the upper cable anchorages and the stay cables. With the boom parked on the roadway it is possible to reach up slightly higher than the top of the pylons. Truck borne underdeck platform A truck borne underdeck platform has been used for inspection of the surface treatment of the entire bottom side of the bridge girder. The platform is long enough to cover the entire width of the bridge girder, making possible an entire inspection travelling in one direction.
9.
Overall maintenance economy
After 14 years of operation it is possible to give some figures for the costs of operation and maintenance of such a structure. Operation activities are here defined as the annual recurrent activities as well as minor repairs. Operation costs include the owner's administration, running and general inspections, minor repairs, such as local repairs of pavement and painting, and service, such as cleaning, service of electrical and mechanical installations and service of the monitoring system. Annual operation costs are shown below in table 1. Administration Running inspections Substructure Superstructure Pavement Electric and computer installations Mechanical installations Electricity consumption and the like Vehicles Cleaning Miscellaneous Total
20 33 15 13 13 12 40 39 13 25 10 233
Table 1: Annual operational costs in 1,000 US$ (excl. VAT)
9
At current prices it would cost approximately US$ 115 million excl. VAT to build the Faroe cablestayed bridge. The annual cost of operation is hence approximately 0.2% of the present value of the cost of construction. Since the bridge opened it has been necessary to carry out major repairs amounting to approximately US$ 1,000,000. This amount covers the following works: • • • • • •
Replacement of interconnecting wires on stay cables Replacement of expansion joints Replacement of 3. km bitumen joint filler at edges and surface treatment of steel edge plates Sealing of anchor boxes at pylon tops Modernization of monitoring and control system Repair of horizontal bearings at pylon
On the basis of general inspections, necessary repairs over the next ten years are estimated to cost about US$ 5,000,000. This corresponds to an average annual expenditure of US$ 500,000.Hence, the estimated average annual repair costs correspond to approximately 0.4% of the present value of the cost of construction. Estimated repair costs are shown below in table 2. Items Substructure Pylons Pier Cable-stays Erosion protection Superstructure Surface treatment Pavement Safety barrier Mechanical equipment Total repair costs
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 15
80 30
80 30 50
80
300 2100 800
800 200
30 45
160 460
910
50
800
0 2470
0
110
200
Table 2: Estimated repair costs in 1,000 US$ (excl. VAT) The total estimated cost of operation and maintenance per year for the next ten years is approximately 0.6% of the present value of the cost of construction. This is quite a bit below the normal figure for operation and maintenance of bridges in Europe, which is generally accepted to be in the range of 1% to 1.5% of the cost of construction. This indicates that the maintenance considerations in the design work have succeeded and that the maintenance works are carried out in an effective manner.
10. Conclusion Despite a high level of consideration to maintenance aspects in the design of the Faroe cable-stayed bridge and other cable-stayed bridges, there are still a number of challenging problems to be solved during the service life. There is still room for improvement concerning accessibility and maintainability. The lessons learned from maintenance should be incorporated into future design work in order to obtain even better bridges with lower maintenance costs and a long service lives.
10
Emergency Rehabilitation of the Zárate-Brazo Largo Bridges, Argentina Henrik ANDERSEN Civ. Eng. COWI Lyngby, Denmark
Dietrich L. HOMMEL Diplom-Ingenieur COWI Lyngby, Denmark
Ejgil M. VEJE Civ. Eng. COWI Lyngby, Denmark
Henrik Andersen, born 1964, received his civil engineering degree from the Technical University of Denmark in 1989. He has specialised in design and rehabilitation of cable supported bridges.
Dietrich L. Hommel, born 1940, received his civil engineering degree from the Technical University of Braunschweig, Germany, in 1966. He has specialised in Project Management of large bridge projects.
Ejgil M. Veje, born 1954, received his civil engineering degree from the Technical University of Denmark in 1981. He is Head of Department for Rehabilitation of Major Bridges.
Summary In November 1996 a cable stay ruptured on the Guazú Bridge. The bridge is one of the two almost identical Zárate-Brazo Largo Bridges across the Paraná river between Zárate and Brazo Largo in Argentina. The two cable stayed bridges carry combined highway and railway traffic and are 550 m long with a main span of 330 m. The bridges carry a 4 lane highway and a single railway track placed eccentrically and the bridges were opened to roadway traffic in 1977 and railway traffic in 1978. During the service life of the bridge there had been no prior indication of the critical situation of the cables. The cables consist of high-strength, non-galvanised, parallel wires protected by cement grout and a PE-pipe. The cable anchorage's are of the HiAm type. COWI was immediately after the failure retained as consultant by the bridge owner Direccíon Nacional de Vialidad in order to ensure and document the safety of the bridges and to investigate the causes of the cable failure. Emergency rehabilitation has been carried out with as limited as possible restrictions to traffic. The required traffic restrictions has been evaluated on the basis of reliability methods, which have been applied to establish a Rehabilitation Design Basis. Possible causes for the severe deterioration of the less than 20 years old cables have been evaluated. A combination of corrosion and fatigue has been found to be the cause. Whether or not one of the two by itself would have been sufficient to cause the rupture of the cable has not been verified. The corrosion has taken place due to insufficient corrosion protection of the non-galvanised wires. The likely cause is that the cement grout, which was supposed to be the main corrosion protection, was insufficient in the anchorage zone due to the presence of a non-protecting epoxy tar. The fatigue has taken place due to larger traffic loads than accounted for in the original design, but not least due to large amplitude cable vibrations. These vibrations have theoretically caused stress ranges well above the endurance limit of the wires. The corrosion has increased the fatigue stresses locally due to stress concentration.
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1.
Introduction
A large number of cable stayed bridges have been constructed around the world as this bridge type often is the most economical structure for medium to large spans. The stay cables are critical structural elements of these bridges. Unfortunately, the cables are perhaps also the less robust of the various structural elements. Larger partial safety factors are for a number of reasons applied for the design of stay cables than for structural steel. Cables are designed to the ultimate breaking load instead of the load causing first yield and account of the wire bundle effect and the length effect is taken. Sufficient fatigue resistance, including a certain allowance for the deterioration of the cables, is furthermore accounted for.
Fig. 1 Guazú Bridge
Despite this, experience has shown that deterioration and subsequent ruptures of the cables actually do occur. It has been necessary to replace the cables on even fairly new bridges, such as Chaco-Corrientes in Argentina and Köhlbrand in Germany. The recent rupture of a cable on a cable stayed bridge in Argentina has confirmed the importance of a careful design of details, including corrosion protection and of continuous inspection and maintenance of cables and other critical structural elements. In November 1996, a cable ruptured on the Guazú Bridge in Argentina without any prior indication of a possible critical state of the cables. The cable failed close to the bottom socket which plunged into the river. The socket was recovered by divers later on. The visual inspection revealed that the failure had taken place about 200 mm from the bottom socket and severe corrosion and fatigue like rupture of the wires were observed. COWI Consulting Engineers and Planners was entrusted with the emergency rehabilitation of the bridges by Direccíon Nacional de Vialidad (DNV). The safety of the bridges and their users should be ensured and documented in both the short and the medium term. Furthermore, COWI was asked to investigate the possible causes for the cable failure. The continued operation of the bridge during rehabilitation is often a critical issue for both the users and the bridge owner/operator, and at the same time the safety of the bridge users is essential. The bridge might provide the only connection between two destinations or in case of closure a large detour maybe the only alternative. This is the case for the Zárate - Brazo Largo Bridges, where a detour of several hundred of kilometres, apart from ferry services, is the only alternative. Today a cable stayed bridge is typically designed such that cables can be replaced with more or less unrestricted traffic allowed on the bridge. Previously, this situation was not always allowed for in the design. In case of major deterioration of the cables, such as for the present bridges, traffic restrictions are even more necessary. A rational planning is required in order to minimise the necessary traffic restrictions. For the present project, reliability methods have been used for the establishment of a Rehabilitation Design Basis (RDB). The RDB has utilised the available information, such that the operation of the bridges could continue with the largest possible traffic amount on the bridges. The present paper describes the emergency rehabilitation of the bridges and the evaluation of the possible causes for the deterioration.
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2.
Zárate - Brazo Largo Bridges
The Zárate - Brazo Largo Bridges are important parts of the infrastructure in Argentina providing a crossing of the national road No 12 over the two main branches of the Paraná River - Las Palmas and Guazú approximately 100 km north west of Buenos Aires.
Fig. 2 Elevation of cable stayed bridges (all units in m) The two bridges constitute two identical cable stayed steel girder bridges with main spans of 330 m and side spans of 110 m and a total of 16 km concrete approach spans. The bridges carry 4 lanes of roadway traffic and a single railway track. The present paper only deals with the main cable stayed bridges. In Fig. 2 and Fig. 3, respectively, an elevation of the main bridges and a cross section of the girder are shown.
Fig. 3 Cross section of girder (all units in mm)
The bridges were constructed during the years 1972-77 and opened to roadway traffic in 1977 and railway traffic in 1978. The cables consist of high-strength, non-galvanised, parallel 7 mm diameter wires protected by cement grout and a PE-pipe. The cable anchorage’s are of the HiAm type. The number of wires in the cables varies between 103 and 337. These bridges were the first highway bridges constructed using these cables with this corrosion protection. Previously, only pedestrian bridges had been -3-
built with this system applied.
3.
Emergency rehabilitation
The emergency rehabilitation of the bridges has included: • Evaluation of the present condition of the bridges through inspection, non-destructive and destructive testing • Evaluation of the present load conditions by measuring the permanent cable forces by a vibration method and establish the characteristic traffic load (rail and road) on the basis of information on the present traffic • Evaluation of the effect of large amplitude vibrations of the cables • Evaluation of partial safety factors by means of reliability based methods • Evaluation of the required temporary strengthening and of the most urgently required cable replacements • Evaluation of required traffic restrictions in order to ensure adequate safety at all times The various investigations and analyses are described in more detail in the following chapters.
4.
Fig. 4 UT-inspection of original cable. Temporary strengthening also shown.
Initial Investigations
Immediately after the rupture of the cable on the Guazú Bridge, both bridges were closed to all traffic. The contractor Albano - DyCASA -Freyssinet was working on another bridge rehabilitation project in Argentina for the same bridge owner and was immediately asked to replace the failed cable. In order to establish detailed information on the actual state of the cable stays, it was decided to carry out various non-destructive testing of the cables. Initially, a visual inspection was carried out of all cables, including cutting of “windows” into the PE-pipes and removal of cement grout as close as possible to the anchorages in order to observe the degree of corrosion of the wires. The cable had failed just in front of the anchorage at the lower end. Ultrasonic inspection was hence an appropriate method for identification of similar problems and this was initiated. Furthermore, it was decided to carry out a measurements of the permanent load in the cable by means of the vibration method both in order to receive a confirmation of the permanent load and to reveal any major changes in stiffness caused by significant wire breaks. The investigations revealed that a number of cables had corroded wires and that a large number of wires were broken on some cables. The cable with the largest damage had 62% damaged wires. On top of this, its neighbouring cables had damages between 41% and 20%. This was indeed extremely critical and could have caused a collapse of the entire bridge possibly within a reasonable short period of time. The ultrasonic inspections were carried out at top and bottom sockets and both cables in the roadway side and in the railway side were investigated. Only cables in the roadway side turned out -4-
to be damaged, and the damages were significantly larger at the bottom socket than at the top socket. The cable force measurements revealed that the permanent forces in the cables had changed with up to 20% since similar measurements were carried out just before the inauguration of the bridges. The largest reduction in permanent force was found for the cable which also had the largest damage according to the ultrasonic inspection. In order to ensure the safety of the bridges, it was decided to introduce a temporary strengthening by means of Freyssinet strands, typically 8 Nos. T15 strands each with a breaking strength of 265 kN. This was applied both to the damaged cables and to the neighbouring cables. This temporary strengthening served two purposes. Firstly, the strands took over a part of the permanent load in the original cables, and secondly they would carry part of the variable load. An example of the strengthening is shown in Fig. 4. Initial tensile and fatigue tests were carried out on test specimens from the failed cable. The tensile test revealed a reduction in tensile strength for test specimens taken from the corroded part of the wires, whereas test specimens from a non-corroded part of the wires still were complying with the original specification.
5.
Rehabilitation Design Basis
Framework The design of new structures are typically carried out according to existing Codes. With respect to reassessment of existing structures and especially unique structures such as cable stayed bridges, the existing codes are not always fully covering or they are too conservative. A specific design basis is hence established in such cases. For the Zárate-Brazo Largo Bridges, it was decided to establish a Rehabilitation Design Basis (RDB) using reliability methods in order to have a basis for rational planning. All available information on materials, the structure and traffic has been used as input for the RDB. The Load and Resistance Factor Design (LFRD) approach has been utilised. Therefore, it has been necessary to establish the following parameters on the basis of the available information: • Characteristic loads and resistance variables • Partial safety factors for load and resistance • Load combination factors For a detailed description of the Rehabilitation Design Basis reference is made to [1] and [2]. By means of the RDB, it has been possible to evaluate the allowable traffic on the bridge in a number of situations during the emergency rehabilitation. Material properties Initially tensile and fatigue tests were carried out on test specimens from the failed cable. Later on, as more cables were replaced, a larger number of tests were carried out on specimens from 2 additional cables. The tested wires were categorised as corroded or non-corroded and both tensile strength and fatigue characteristics were established for the two groups of wires. In both cases a reduction of the characteristic tensile strength was found. It shall be noted that only cables with large damages at the sockets have been replaced and hence tested so far. The test specimens described as non-corroded were, however, obtained some metres from the failure or corrosion zone, and the degree of conservatism is expected to be limited. The tests revealed that the characteristic breaking strength was 1,525 MPa for non-corroded wires and -5-
1,460 MPa for corroded wires. This could be compared to the value of 1,670 MPa in the specification. Fatigue test were carried out in order to establish both SN-curves and a Smith-diagram for the wires. Traffic load The bridges carry both highway and railway traffic, and on the basis of the available information characteristic loads for both highway and railway traffic have been established. The characteristic loads have been developed for the most critical stay cable. This value has then conservatively been used for all cables as only limited savings could be obtained by utilising individual characteristic loads for the various cables. The complete information required for the establishment of the characteristic load has not been available and some parameters have hence been estimated on the basis of data from Denmark and Europe in general. The highway traffic load for unrestricted traffic is shown in Table 1. This traffic load shall be compared to the original design load which was 7 kN/m in each of the four lanes. The highway traffic load has hence increased significantly. Besides, the characteristic traffic load has been established for a number of traffic restrictions too. The characteristic railway load was determined to 70.2 kN/m compared to the original design value of 62.8 kN/m in general with an increase to 96.4 kN/m over 35 m length to cover the larger intensity of the locomotive. The traffic load which has been allowed on the bridge during the emergency rehabilitation has varied. During the various emergency phases and dependent on the level of knowledge of the existing structure, the traffic has been restricted to such an extent that sufficient safety of both the bridges and for their users were ensured. Location
UDL (kN/m)
Axle loads (kN)
Lane 1
28.9
2 x 300
Lane 2
9.4
2 x 200
Lane 3
9.4
2 x 100
Lane 4
9.4
-
Table 1
Characteristic highway traffic load
Immediately after the rupture of the cable the bridges were closed to all traffic as the state of the remaining cables were unknown. As more information was established and strengthening of the bridges initiated, it was possible to open the bridges to restricted traffic. The general allowable traffic (both roadway and railway, including the possibility for simultaneous roadway and railway traffic) was evaluated a number of times as the rehabilitation progressed. During each of the cable replacements the necessary additional restrictions to the allowable traffic were evaluated in addition. Partial safety factors and load combination factors The general derivation of partial safety factors for the cables is described in [1] and [2]. Only a brief description is included in the following. The partial safety factors for the cables depend, among others, on the deterioration of the cable due to fatigue. On the basis of the fatigue tests of wires from 3 cables and the expected fatigue loading derived on the basis of the traffic information and the vibrations of the cables, the partial -6-
safety factor has been determined for the cables. By this method, it has been possible to evaluate the partial safety factors for various periods of time. Ultrasonic inspections has been utilised in order to carry out a monitoring of any possible development of the wires breaks and to allow for an update of the safety. Partial safety factors for highway and railway loads and load combination factors was established on the basis of recommendations in JCSS [3].
6.
Cable vibrations
Large amplitude vibrations of a number of the cables have taken place. Visual observations of amplitudes of approximately 1 m have been made. Furthermore, pressure marks in the PE-pipes at locations, where these pass out of the anchorage boxes at the girder level indicate vibrations of a similar magnitude. In the present scope of work no detailed investigations of the causes for the cable vibrations have been carried out. It shall, however, be noted that the vibrations do not only occur during rainy conditions. The vibrations are hence not believed to be rain-wind induced vibrations. Preliminary investigations have pointed out that the vibrations might be caused by vibrations of the deck as there are common eigenfrequencies of some cables and the deck. The wind tunnel testing, carried out in connection with the original design, found that the deck could vibrate heavily in case of winds with a large vertical component (attack angles 2.5o - 5o) at wind speeds between 10 and 20 m/s [4]. The theoretical peak stresses caused by these vibrations are even larger than the permanent tensile stresses in the wires. This was determined under the conservative assumption that the wires are fully restrained at the entrance to the socket. No guide deviators were included in the original design of the bridges in order to limit the bending stresses. There is no doubt that vibrations of this magnitude shall be prevented on cable stayed bridges as it only is a matter of time before deterioration due to fatigue will be initiated. For the cables replaced during the emergency rehabilitation, it has been recommended to install "wind ropes" connecting the cables in order to limit the amplitude of the vibrations. Furthermore, it has been recommended to install guide deviators in order to decrease the bending stresses at the socket.
7.
Cable replacements
A total of 13 cables have been replaced during the emergency rehabilitation corresponding to all cables with more than 6% damage. The damaged cables have been concentrated on the Guazú Bridge where in total 10 cables have been replaced, including the one that ruptured in November 1996. The existing cables have been removed by an untraditional method. The state of the cables were uncertain and a brittle failure could not be ruled out. It was therefore decided not to use a hydraulic jack for the Fig. 5 Removal of existing cable by de-stressing and removal of the cables and an alternative cutting of individual wires method was developed by the contractor. The PE-pipe and the cement grout was removed along almost the -7-
entire length of the cable manually by personnel in a lift. The cable was then secured by a steel rope connected to the tower head and the girder in order to control it during the following operations, where each individual wire of the cable was cut as shown in Fig. 5. Initially, all wires of the original cable were cut before the temporary strengthening (Freyssinet strands) was removed and the remaining top and bottom part of the cable could be removed. Later on the temporary strengthening was removed before the wires were cut. Before, during and after the removal of a cable, levelling of the bridge deck and measurement of permanent forces in the cables were carried out in order to ensure that the bridge behaved as foreseen. In all cases a good agreement between the predicted and the measured movements and forces was found. The new cables installed consist of a number of Freyssinet strands. They are designed to a higher service load than the original cables as noted in a previous chapter. A complete rehabilitation of the bridges is expected to be carried out during 1999/2000.
8.
Cable failure causes
Possible causes for the severe deterioration of the less than 20 years old cables have been evaluated. The evaluation has revealed that a number of factors have contributed to the deterioration of the cables. A combination of corrosion and fatigue damage have caused the failure of one cable and large damages to a number of other cables. The cross section of the cable that failed in November 1996 is shown in Fig. 6. The corrosion system applied for the cables were stateof-the-art at the time of the design and construction of the bridges. In this particular case the system has, however, not provided sufficient corrosion protection of Fig. 6 Ruptured cable the non-galvanised wires. The cement grout, which was supposed to be the main active corrosion protection, was insufficient in the anchorage zone due to the presence of a non-protecting epoxy tar. Following intrusion of water through defects in the PEpipe or due to condensation of water inside the PE-pipe, corrosion has been initiated. The fatigue damage has taken place due to larger traffic loads than accounted for in the original design, but not least due to large amplitude cable vibrations. These vibrations have theoretically caused stress ranges well above the endurance limit of the wires. The corrosion has furthermore increased the fatigue stresses locally due to stress concentration.
7.
Conclusion
A combination of corrosion and fatigue have caused severe deterioration of a number of cables on the Zárate - Brazo Largo Bridges. The corrosion protection of the high strength wires have proven insufficient as the grouting of the non-galvanised wires have been inadequate close to the bottom cable socket. The traffic load has been larger than accounted for in the original design and this has increased the fatigue loading. A significant contribution to the fatigue load is, however, stemming from large amplitude vibrations of the cables. The bending stresses in the parallel wires have not been limited -8-
by deviator guides, which could have reduced the stresses significantly. All available information on the structure, the materials and the traffic has been used to establish a Rehabilitation Design Basis and by use of reliability methods, it has been possible to minimise the required traffic restrictions during the various phases of the emergency rehabilitation. The most severe deteriorated cables have been replaced. Final rehabilitation of the bridges is expected to be carried out during 1999/2000.
8.
References
[1]
Hommel, D., Faber, M.H., Maglie, R., Aspects of safety and operation of bridges during rehabilitation. Proceedings of the international symposium on advances in operation and maintenance of large infrastructure projects. Copenhagen, Denmark, 1998.
[2]
Hommel, D., Veje, E., Engelund, S., Zárate-Brazo Largo Bridges, Rehabilitation Design Basis. IABSE Conference Rio de Janeiro, 1999.
[3]
Joint Committee on Structural Safety (JCSS), Background Documentation, Eurocode 1 (ENV 1991, Part 1: Basis of Design, March 1996.
[4]
Atkins, An aerodynamic investigation of the Zárate-Brazo Largo Bridge, Argentina, 1971. Prepared for Techint-Albano SA
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Field Observation and Vibration Test of the Tatara Bridge Kazunori YAMAGUCHI Civil Engineer Honshu-Shikoku Bridge Auth. Onomichi, Japan
Yasuhiro MANABE Civil Engineer Honshu-Shikoku Bridge Auth. Onomichi, Japan
Nobuyuki SASAKI Civil Engineer Mitsubishi Heavy Ind., Ltd Hiroshima, Japan
Kunihiro MORISHITA Civil Engineer Mitsubishi Heavy Ind., Ltd Hiroshima, Japan
1. Introduction The Tatara Bridge ,the longest span cable-stayed bridge in the world, has a total length of 1,480 meters and a center span length of 890 meters and is located at the Onomichi-Imabari Route. The bridge consists of the girder (height is 2.7 meters), the reverse Y-shaped tower (overall height is 220 meters) and 168 cables (21 rows×8 planes), and has a steel-concrete composite structural system. Pre-stressed concrete girders are placed at the ends of each side spans. As for the dynamic structural properties, this bridge is tend to appear the sway easily because of a long-span and the behavior of numbers of long cables(maximum length is 460 meters). The dynamic stability against wind and earthquakes required to be evaluated and in advance the further investigations such as a wind tunnel tests and natural vibration analyses with a model of this bridge had been carried out. Moreover, several field observations and vibration tests have been performed since the beginning of the construction. This paper introduces the outlines of following two terms out of these field vibration investigations by comparing with the results of previous analyses . (1)Field vibration test The field vibration test had been performed from November to December 1998 when the construction of pavement almost completed. The exciters were used and vibrated the girder in the vertical directions to investigate three vertical bending and two torsinal vibration modes, and in the horizontal directions to investigate three bending vibration modes in the normal direction of the bridge axis. The horizontal vibration in large amplitude is the first trial on such a longspan bridge. The aims of field vibration tests are to confirm the dynamic properties of important vibration modes by comparing with the results of analyses, especially structural damping, and to verify the vibration design of this bridge, furthermore, to make these observed data useful for the future design of the long-span cable-stayed bridge by investigating the phenomena of a coupled vibration consisting of girder and cables and the causes of structural damping. (2)Response observation in the strong wind The field observations in the strong wind have been performed for about two years, from the beginning to the completion of the construction in order to keep safety under construction, to evaluate the efficiency of the countermeasure to prevent cable vibration and to investigate the response properties against strong natural wind. The construction and above field investigations has been completed and now these data are being analyzed in detail. In this paper, the basic data analyzed already until now are reported.
2. Field Vibration Test 2.1 Testing procedure The exciters used in the field test were newly developed especially for the excitation in such a long period of this bridge. The specifications are shown in Table-1. These are a pair of large exciters and enable to work in both vertical and horizontal directions. The exciting direction is changed by using each steel frames supporting motors and weights, respectively corresponding to the tests for the vertical and horizontal vibrations. In the vertical vibration test, two exciters were placed at both ends of the cross section of the bridge and they were operated in the same phase and the opposite phase to excite vertical bending and torsional vibration modes respectively. In the horizontal test, two exciters were operated in the same phase. The exciters were installed at the point in distance of three eighth of the mid-span from the end of girder in the longitudinal direction. The location of transducers are shown in Fig.-1. The servo-type accelerometers were used in order to measure vibrations of girder, tower and cables. Two sensors were installed on the principal cables shown in Fig.-1, and accelerations in both vertical (in-plane of cable) and horizontal (out-of-plane cable) were respectively measured. These sensors were properly replaced to cables that swayed greatly during field test. As regards all bearings, the strain gauge type displacement meters were installed and slip of bearings in the horizontal direction were measured. Furthermore, the wind direction and wind speed were measured with Ace Vane type anemometer, and outside temperature was measured for reference. The situation of field vibration test is shown in Photo.-1.
Photo.-1 Situation of field vibration test
Fig.-1 Subject bridge and measuring points
Table-1 Specification of the exciter
2.2 Theoretical analysis Previously theoretical analysis were carried out to compare with field test results. The natural vibration analysis was performed using three dimensional frame model of a whole structure system shown in Fig.-2. The cable models had 50 nodal points with mass that were linked by spring elements each other, and cable sag was taken into account. As the above cable models, coupled system consisting of girder and cable, have too many nodal points and analysis must be performed using large dimensional matrix, it is difficult to analyze directly using a whole structure system model. Therefore, the mass condensation method 1) and the partial structural combined method 2) were used as the efficient and accuracy analysis method.
Fig.-2 Analytical model
2.3 Test results and discussion (1)Natural frequency and vibration mode Examples of amplitude response curves are shown in Fig.-3. These indicate the amplitude-excitation frequency relations and phase-excitation frequency corresponding to the vertical and horizontal excitations. In the lower frequency range, there are single peaks, respectively corresponding to the 1st symm. vertical bending and 1st symm. horizontal bending mode, however, the shapes of curves in the higher frequency range are complicated. There are several peaks in the amplitude response curve of each modes and similarly on the phase response curves. The cause would be considered as coupled vibration between girder and cable. As the minimum frequency of cables is 0.25 Hz on the top cable and another cables have higher frequency, the coupled vibration is tend to be excited in higher frequency range than 0.25 Hz. Such phenomena of coupled vibration appeared in the sine excitation test.
Fig.-3 Amplitude and phase response curve
In this paper, the peak frequency and amplitude distribution, on which the maximum response of girder was obtained, were selected respectively as the natural frequency and the mode shape of each modes out of many data. The comparisons of natural frequency and mode shapes between test results and analysis results are shown in Table-2 and Fig.-4. As the results, there is a less difference than 10% on the natural frequency and only a few differences on the mode shapes. (2)Structural damping Structural damping in logarithmic decrement was calculated with free vibration data corresponding to each modes obtained by suddenly stopping excitation in the resonant condition. Examples of free vibration data are shown in Fig.-5 and it indicates that the damping changes according to the change of amplitude of the girder and damping tends to increase proportional to the amplitude of girder. The structural damping at each modes was calculated as the average damping in the range from the maximum amplitude to the amplitude reduced to 70% of the maximum one. The results are shown in Table-2. It is important that the structural damping change greatly according to each vibration directions.
*)
*) : reference data, under investigation
Table-2 Test results
Fig.-4 Comparison of mode shapes Regarding to the vertical bending and torsional vibration modes in the vertical excitation, the damping is δ =0.01 0.05, and on the horizontal bending vibration mode in the horizontal excitation δ =0.10 0.20, that are much larger than ones of vertical vibration. As the reason, it is considered that the attachments such as fairings installed at the ends of the cross section of girder have influence of these phenomena. There are several attachments such as fairings for wind resistance and handrails at the ends of the cross section. These are separated at regular interval 10 meters in the longitudinal of the girder not to propagate stress, and linked to each members with loose-tightened bolts. On the horizontal vibration, it is predicted that as the amplitude become larger, the more bolts Fig.-5 Free vibration and structural damping would slip and the friction force would have more influences of the damping. In order to verify this prediction, the slip of bolts were measured with displacement meters installed on the joint of fairings at the mid-point of the mid-span. As the results, it was confirmed that the above prediction might be right.
Sudden stop of exciter
(3)Cable vibration This chapter reports about the phenomena of coupled vibration between girder and cables obtained in the field vibration test.
Girder(3/8L)
a)Linear coupled vibration There happened several coupled vibrations between girder and cable on numbers of vibration modes mentioned in 2.3. General coupled vibrations were excited when the excitation frequency of the girder became near one of cable. In this case, this phenomenon is considered as the linear coupled vibration. The mode in this phenomenon is almost same as one of the result of natural vibration analysis mentioned in 2.2.
Cable(C53)
Fig.-6 Non-linear coupled vibration
b)Non-linear coupled vibration (parametric excitation) On the other hand, non-linear coupled vibration was excited, when the frequency of the cable was nearly equal to half of the excitation frequency of the girder. This is considered as the nonlinear coupled vibration excited due to fluctuation of cable tension. This phenomenon had been confirmed in another field vibration test 3) . The non-linear coupled vibration was excited at resonance of 1st asymm. tosional vibration mode in this test. C53 cable suddenly began to oscillate in half frequency of exciting frequency during the girder was being excited. The comparison of the amplitude between girder and cable is shown in Fig.-6. After non-linear coupled vibration was excited, exciters were stopped due to a sudden increase of the cable amplitude. The 1st asymm. torsional vibration mode would be excited only in case that an asymm. wind blow in the normal direction of the bridge axis in a stormy condition, therefore it is considered that non-linear coupled vibration would be rarely excited. However, the confirmation of the possibility that such a vibration will be excited including reinvestigation of data in wind tunnel test will be carried out quantitatively.
3.
Response Observation in the Strong Wind
3.1 Observation procedure The response observations of dynamic properties against strong wind have been performed for about two years from the beginning of the construction until the completion. The observation points are represented in Table-3. The meteorological data are measured with anemometers and rain gauge, and the response observations are performed on the girder and cables. The number and points of observations were changing properly according to the construction progress. These observations were performed automatically using the developed automatic system.
Table-3 Observation points
3.2 Summary of observation data A vast amount of observation data has been stored up since the beginning of the observation, and these are now in progress. Here, next two kinds of data are shown as the typical observation data. (1)Response of the girder against typhoon During the observation, several typhoon had hit the bridge. The typhoon which carried the strongest wind was the 98-10th typhoon which passed on 17th and 18th October. At this time, the construction was almost completed including the pavement construction. The properties of wind and response of the girder at this time are shown in Fig.-7. The maximum instantaneous wind speed was recorded up to 30.2m/sec and the average wind speed of ten minutes was 22.3m/sec. The wind direction was in the normal direction of the bridge axis (270 degrees from the bridge axis) at this time. The girder vibrated the most greatly in both vertical and horizontal directions at the same time when the maximum wind speed was observed, and the maximum amplitude was 6.9cm and 8.5cm respectively on the horizontal and vertical directions. The girder vibration and results of its Fourier analysis are shown in Fig.-8. It is confirmed that the amplitude in 0.1Hz prevailed on the horizontal vibration and ones in 0.23Hz and 0.27Hz on the vertical, and these results are almost same as the field vibration test results mentioned in the section 2.
Fig.-7 Time histories of wind and responses
(2)Cable vibration The dimple processed type polyethylene pipes were used on the cables as the aerodynamic countermeasure for cable vibration. These were developed in order to prevent rainvibration. In the field observation under construction, Fig.-8 Responses of girder the amplitude of the cable was measured in order to confirm the efficiency of this countermeasure. A vast amount of observation data on the cable vibration in the strong-windy and rainy conditions such as a seasonal wind and a typhoon has been stored up since the beginning of the observation, however there have happened no injurious rainvibration until now and the effect of the countermeasure has been confirmed. On the other hand, there often happened the high frequency vibrations assumed to be a vortex-induced vibration on the cable under construction. The properties of observed vortex-induced vibration are explained below.
The relations between wind speed and prevailing cable amplitude, and between wind speed and frequency of cable are respectively shown in Fig.-9(a) and (b). In Fig.-9(a), it is confirmed that the cable amplitude increases from the lower wind speed and the maximum amplitude happens at about 5.0m/sec and in the higher wind speed range the amplitude gradually decreases. In Fig.-9(b), the prevailing frequency of the cable increases proportional to wind speed. As the Strouhal number calculated using these observation data distributes in the range from 0.15 to 0.18 on the all cables, above mentioned prevailing frequency is considered as one of a vortexinduced vibration.
(a) (b) Fig.-9 Relation between wind speed and cable response
On the past happened accidents of a vortex-induced vibration, several Fig.-10 Effect of filling rubber seal examples have been reported that a vortex-induced vibration was prevented by filling rubber seals (additional damping δ to a cable is about 0.005) into the entrance of cable in the girder. On the Tatara Bridge, rubber seals were filled into several the entrance of cable and the effect was confirmed on basis of field observation data. The comparison of cable vibration between unfilled cable and filled in almost same wind conditions is shown in Fig.-10. It is confirmed that the amplitude is reduced because of filled rubber seal and this countermeasure for a vortex-induced vibration is efficient to such long cables.
4. Summary Firstly, the results of field vibration test are summarized as follows; (1)The frequencies in filed tests and ones in analyses are almost same on the important 8 modes taken into account, furthermore, each modes are very similar. (2)The structural damping on the vertical bending and torsional modes are relatively small by comparing with the test results of another long-span cable-stayed bridges, however these satisfy the design value δ =0.02. This cause is considered that this bridge is very long-span bridge and easy to be influenced by cable vibration. On the other hand, the structural damping on the horizontal bending mode is large and this cause is presumed that bolts installed on the fairings and so on would slip according to the horizontal girder vibration. (3)Linear coupled vibration between girder and cable was excited in the condition that the frequency of the cable vibration was equal to exciting frequency of the girder. On the other hand, non-linear coupled vibration (parametric excitation) was excited at resonance of 1st asymm. torsional vibration mode and at that time the frequency of the cable has become the one second of exciting frequency of the girder. It is considered that non-linear coupled vibration would be rarely excited, however, the confirmation of this phenomenon will be performed.
Next, the results in the response observation of strong wind are summarized as follows; (1)The maximum gust response of the girder was 7 8 cm on both vertical and horizontal vibration against a typhoon blowing at about 30m/sec (the maximum instantaneous wind speed) and these are small relatively. (2)It was confirmed that there was no injurious rain-vibration and the aerodynamic countermeasure (using dimple processed type polyethylene pipes) was efficient. In addition, it was confirmed that the countermeasure by filling rubber seal into the entrance of the cable in the girder enabled to prevent a vortex-induced vibration often happened. These data are under analysis still now and the new results would be presented in the near future. Acknowledgements: The authors would like to thank Professor YAMAGUCHI Hiroki, Department of Construction Engineering, Saitama University in carrying out the experiment. Refference [1] K. Morishita et al. : Non-linear Seismic Response Analysis of Long Span Bridge, Proc. of 2nd World Conference of Structural Control, June-July 1998. [2] K. Washizu et al. : Handbook of Finite Element Method II, Application Part, Baifukan, pp.57,1983(in Japanese). [3] I. Okauchi et al. : Field Vibration Test of a Long-Span Cable-Stayed Bridge Using Large Exciters, Journal of Struct. Engrg., JSCE, Vol.14, No.1, pp.83s-93s, April 1997.
Second Monitoring and Surveillance of the Response of a Cable-stayed Bridge Roberto GOMEZ Dr. Eng. Institute of Engineering, UNAM Mexico, Mexico
David MURIA-VILA Dr. Eng. Institute of Engineering, UNAM Mexico, Mexico
Roberto SANCHEZ-RAMIREZ M. Eng. Institute of Engineering, UNAM Mexico, Mexico
J. Alberto ESCOBAR Dr. Eng. Institute of Engineering, UNAM Mexico, Mexico
Summary Experimental data obtained during a second non destructive testing program carried out on the Tampico bridge is presented. A comparison of ambient vibrations of the deck is performed with the results of a similar set of tests carried out in 1988; some dynamic parameters and modal assurance factors are calculated and compared. From the new testing program, parameters of pylons and cable forces are derived from ambient vibrations of the piers and stays, respectively. Results from static and dynamic loading are presented as well. Information from the experimental testing program is used to calibrate a numerical model that will be used to evaluate the structural safety of the bridge.
1. Introduction The Tampico bridge was the second cable-stayed bridge built in Mexico. It is located in the northeast state of Tamaulipas on a highway along the Gulf of Mexico. The bridge crosses the Panuco River and carries four lanes of traffic with sidewalks and a central barrier. Its total length is 1543 m distributed in three sections: a main cable-stayed span of 878 m length and two bridge viaducts. The viaduct on the left shore is 476 m long and the one on the right shore is 189 m. A hybrid type of deck was constructed. Steel box girders were used on most of the central span (360 m) and pre-fabricated prestressed concrete box girders for the remaining part of the deck. The cable-stayed system comprises 44 cables arranged in a semi-fan layout. Regarding the importance of this bridge, just before its opening in 1988, the Bridge Department of the Ministry of Communication and Transportation decided to carry out an experimental program in order to determine the dynamic properties of the superstructure. Natural frequencies and mode shapes were calculated from acceleration time histories recorded during ambient vibration testing. From the results of a pullback test, damping characteristics were obtained as well (Muria-Vila et al, 1991; AEIC, 1988). Currently, new live loads, wind conditions, temperature and mass changes, corrosion effects, relaxation of cable forces and prestress losses may have modified the structural properties of the bridge. A surveillance of its structural integrity can be accomplished by evaluating its current dynamic response. In this paper the results of a new and extended experimental program are presented. The same locations of the recording points, used in the 1988 field-testing program, are used in this study. Ambient vibrations are used to calculate natural frequencies of the superstructure and to derive frequency functions (transfer, coherence and phase angle functions). From the analysis of these functions modal shapes are derived. Based on modal assurance criteria such as MAC and COMAC factors, the mode shapes obtained during the 1988 monitoring program are compared to the ones derived in 1998. Time histories of accelerations produced by dynamic loads were also recorded. The response of the bridge under different arrays of trucks, of known weight, running at different velocities was studied. Comparison of the ambient and dynamic responses is presented and evaluated in terms of changes in natural frequencies of the deck.
In addition to the measurement of accelerations on the deck, acceleration records were registered on the whole set of stays. Based on the theory of cable vibrations, this information was used to derive their natural frequencies and to calculate the magnitude of their tension forces. These values are compared to those obtained by means of hydraulic jacks, devices regularly used for this type of measurements. The results of this study will contribute to a safer operation and optimal maintenance programs of the bridge.
2. Instrumentation During the 1988 field testing program only acceleration records were obtained. For this new evaluation of the bridge, in addition to accelerometers, strain gauges, LVDT´s and anemometers were used. These sensors were located along the length of the main central steel deck (360 m length) and on some locations along the height of pier 13. Figure 1 shows the location and numbering of the acceleration recording points, two sections (C and R) where 10 strain gauges were placed and the location of two photo electric cells. All of them located between pylons 13 and 14. Figure 2 is used to display the position of the strain gauges inside the box section of the deck.
Figure 1. Recording points along the deck.
Figure 2. Location of strain gauges, sections C-C and R-R.
With respect to the LVDT´s, two of these were placed on the top surface of the foundation cylinder (caisson) of pier 13 (Figure 3): one on each side of the column of this pier. The purpose of these sensors was to register the vertical movements induced during the loading of the bridge, and consequently calculate the rotation of the pier with respect to a vertical axis perpendicular to the road surface. As mentioned, in addition of the recording points of accelerations located on the deck, four points were selected along the height of piers 13 and 14: one at the top, one at the bottom, one at the bifurcation of the pylon (to form an inverted “Y” shape) and one on the deck. Wind velocities and directions were monitored using two anemometers, one located at the top of pier 13 and the other one located on the deck (see Figure 3). During the dynamic tests velocity of the trucks was calculated with the information provided by the photo electric cells (Figure 1). All sensors were connected through amplifiers, filters and signal conditioners to the personal computer where the measurements under static load and time histories were recorded. A more complete description of the registration scheme can be found in the correspondent technical report (Gómez et al. 1998).
Figure 3. Location of sensors along pylon 13.
3. Field Testing Static loading was produced by five trucks, six axles each, positioned on different arrays along the length of the main central deck, between pylons 13 and 14. The average weight of the trucks was 65 t and the maximum static load applied to the bridge was 326 t. A simultaneous recording of vertical displacements and longitudinal strains was carried out. During this part of the experimental work traffic was not allowed on the bridge. Ambient vibration of the bridge was produced by the regular traffic and two trucks passing in opposite lanes and in opposite directions. Wind velocity was measured; the maximum value never exceeded 9 m/s. Dynamic excitation of the superstructure was produced by the same trucks used for the static loading program, but running along the bridges. Vibrations produced during the ambient and dynamic tests were registered using several arrays of accelerometers oriented in different directions. Time history data was recorded for each event of the instrumentation program (Gomez et al, 1998). However for the dynamic testing, time histories of strains and displacements were also recorded. A well known random signals analysis (Bendat and Piersol, 1986) was used to process ambient vibration records. An average of different number of readings and a suitable “windowing process" was taken to calculate frequency responses: power spectrum, transfer, coherence and
phase angle functions. Emphasis was placed on the determination of natural frequencies of the superstructure and pylons and mode shapes of the superstructure. On the other hand, ambient vibrations (traffic and wind) and vibrations produced by pulling a rope tied to the cable, were registered for each cable. These vibrations were processed to derive natural frequencies, which were then used to calculate tension forces of the stays.
4. Results 4.1 Results of Field Tests Using Static Loads For different load cases, Table 1 shows some values of longitudinal strains registered with the strain gauges. The location of points C1 to C5 and R1 to R5 can be seen in Figure 2. For the first test (PE1), only one truck, on the inner lane, was used. Its third axle was placed coincident with the middle line of the central span. For the second test (PE2), a second truck was placed on the outer lane and parallel to the first one. The fourth test (PE4) included two more trucks but on the opposite side of the road with similar positions to the ones used for test PE2. Table 1 shows the different kind of strains produced (tension and compression) and their variation along the deck. It is also observed that when the number of trucks increases, the values of strains increase as well, and that values of strains at stations C are greater than the ones registered at section R. Because the high torsional stiffness of the box section, the effect of loading only one side of the bridge is slightly observed in sensors C5 and R5. When using five trucks in convoy on the inner lane, the results obtained are shown on the row denoted as PE5. This pattern of strains shows significantly better the deformed configuration of the deck, this is, zones of positive and negative flexure. The maximum values of strains registered were produced during test PE4. On the other hand, values of vertical displacements obtained with the LVDT´s were used to calculate the rotation of the pier. Results found were of very low magnitude, which confirmed the high stiffness of the pylon. TEST C1 C2 PE1 -39 -68 PE2 -74 -100 PE4 -181 -198 PE5 -127 -129 TEST R1 R2 PE1 -2 10 PE2 25 29 PE4 19 11 PE5 14 9 + tension; - compresion
C3 95 176 361 257 R3 -40 -70 -146 -169
C4 86 174 351 256 R4 -43 -69 -134 -163
C5 108 202 382 270 R5 -46 -67 -129 -176
Table 1. Microstrains registered. 4.2 Results of Ambient Vibration Tests Vertical, transverse and longitudinal movements were recorded simultaneously at different points along the deck. Typical results of power spectrum and transfer functions obtained at different pairs of points along the deck are shown in Figure 4. Because of the location of these points, this recording scheme allows the observation of different levels of vibration along the deck, the analysis of the degree of symmetry of the response and the identification of frequency values associated to high contents of energy. In spite of the difference in magnitudes, this figure shows how the peaks of the transfer functions oscillate around the same frequencies. Figure 5 shows another kind of frequency functions for another set of pairs of points located on opposite sides of the roadway. Besides the transfer function, coherence and phase angle functions are also used to identify possible natural frequencies of the superstructure. The
analysis of vibrations recorded on opposite sides of the deck allows the identification of torsional natural frequencies, which are associated to high coherence values and opposite phase angles. For example, frequency functions of points 11 and 12 in Figure 5, show that the value of 0.98 Hz has an associated value of 180 degrees, and for the same value, the phase angle of points 15 and 16 is of the same magnitude but opposite sign. On the other hand, the coherence is close to 1.0 for points 11 and 12 and close to 0.8 for points 15 and 16. The above facts demonstrate the similarity of vertical vibrations on both sides of the deck and the torsional movements around an imaginary longitudinal axis of the superstructure. The same evidence was found comparing the frequency functions at pairs of points on different sections along the deck (Gómez et al. 1998). Transverse vibrations were recorded as well. Some results are presented in Figure 6 where power spectrum functions reveal that the functions a more similar and that is easier to perceive the coincidence of “peaks”. When comparing these functions with those presented above, a slight coincidence of “peaks” can be observed in the range of high frequencies. This fact shows that the vertical and transverse responses of the superstructure might be slightly coupled. Simultaneous recording of different type of vibrations at the same transverse sections were also considered. Figure 7 is shows a complete set of frequency functions obtained from the signals recorded, simultaneously, in the vertical (V) and transversal (T) directions, on location number 27.
Figure 4. Power spectrum and transfer function of vertical movements. Based on the whole set of results obtained, the 3D vibratory response of the superstructure was studied. Thus, some significant natural frequencies calculated for some modes of vibration of the central span are shown in Table 2. In the same table the values obtained during the 1988 testing are reported as well. It is worth to mention that although the same recording scheme was used during the two experimental programs (1988 and 1998), the goals of the first one were less ambitious and consequently a minor number of frequencies and modes were identified,
particularly for asymmetric and transverse modes. The values reported in Table 2 show that the differences are very small for the first three vertical and the first transverse and torsion natural frequencies. Differences are higher when comparing the rotational modes. However, a trend to lower values of frequencies can be observed.
Figure 5. Power spectrum, phase angle and coherence functions of vertical movements.
Figure 6. Power spectrum and transfer functions of transverse movements.
Figure 7. Frequency functions for vertical and of transverse movements recorded simultaneously. Mode V TORSION (year) 1988 1998 1988 1998 1S 0.40-0.42 0.39 1.06-1.11 0.98 1A 0.54 -0.59 1.95-2.05* 2S 0.90-0.94 0.88 3.10-3.16* 2.49-2.98* 2A 1.17 3.37 3S 1.44-1.49 1.42 4.48-4.52 4.80-4.90* 3A 1.76 5.32-5.38* 4S 2.73-2.80 2.20 4A 2.25 5S 3.75-3.85 3.52-3.61 5A 4.15-4.40 * coupled with T direction; A: asymmetric; S: symmetric
T 1988 0.45 -
1998 0.44 0.73 1.71 1.86-1.90 4.20 4.80-4.90 5.33 5.77-5.86 6.25 6.64-6.60
Table 2. Natural frequencies of the deck (in Hz). From the spectral analysis of signals recorded along the deck vertical and transverse modal configurations for the superstructure were identified; some of them are presented in Figure 8 in plan or elevation views; the longitudinal axis is used to define the length along the instrumented section of the deck. Furthermore, the modal shapes for the two testing programs carried out (1988 and 1998) can be used to evaluate qualitatively their dynamic correlation base on the Modal Assurance Criterion (MAC) and the Coordinate Modal Assurance Criterion (COMAC) (Allemang and Brown 1982; Lieven and Ewins 1988). Because of the lack of information generated during the 1988 testing, only the first three vertical modes were used for the calculation of these criterion. The obatined magnitudes for the MAC factors were 0.997, 0.970 and 0.967 for the first, second and third mode, respectively. These results show that the correlation is better when comparing the first mode and the maximum differences are obtained for the third modal shape.
Figure 8. Modal shapes identified. On the other hand, the COMAC values calculated using the first three vertical mode shapes are presented in Table 3. Location numbers are referred to Figure 1. The values show a very good agreement for points near the center of the span. The major differences are obtained when comparing points near the piers. This might be produced by a change of section (steel to concrete) in these zones. Location 7 Value
9
11
15
19
23
25
28
29
30
0.947 0.975 0.997 1.000 0.973 0.961 0.985 0.997 0.997 0.670
Table 3. COMAC factors calculated with the vertical modal shapes. With respect to the recorded data obtained along the height of pylons 13 and 14, the analysis revealed a severe coupling effect of the longitudinal movements with the vibrations of the deck in the vertical direction, particularly for the first and third modes. Some results associated to the most relevant vibrations are presented in Table 4. Mode 1 2 3
Direction T 0.83 1.17-1.22 1.37-1.47
Direction L 2.30-2.40 2.78-3.03 -
Table 4. Significant natural frequencies for pylons (in Hz). 4.3 Cable Vibration Tests Ambient and forced vibration of cables produced records of movements that were utilized to derive frequency functions and dynamic parameters. Possible coupling of the vibration of the stays with the deck was considered identifying frequencies associated to higher modes and assuming a linear relationship of their magnitudes and the correspondent mode number (Robert et al, 1991). Calculated values were in the range of 0.59 to 2.17 Hz. With these values and based on the classical theory of cables, tension forces in the stays were calculated. These tension were compared with the ones measured by means of hydraulic jacks, a task that is carried out in the bridge every three or four years. In spite of some uncertainties in the weight and length of the cables, results showed differences in the range of 4 to 19%.
4.4 Results of Dynamic Vibration Tests As mentioned, additional dynamic tests were performed on the deck. Serial and parallel arrays of trucks were used and different crossing velocities were defined. Figure 9 shows a typical set of segments of time histories obtained during the crossing of a convoy of 5 trucks on the low velocity lane. These graphs correspond to the passing of the first truck. On the right side of each history a number is printed to identify the recording location. The similarity of acceleration records at points 23 and 24, on opposites sides of the bridge, and the change of sign of the longitudinal strains records, points C4 and R4, provided a broader insight of the high torsional stiffness of the superstructure and the induced flexure along its deck. Though Figure 9 only shows the time histories produced by the first truck, the remainder are very similar.
Figure 9. Selected time histories of strains and accelerations. The knowledge of the response of a bridge under static and dynamic loads prompted the calculation of a dynamic amplification coefficient for the strains. The average velocity of the trucks was in the range of 11 to 19 km/h. The average ratio of strains produced under the same dynamic and static loads was of 1.06. A pull back test was also carried out. A steel cable tied to the central span of the superstructure was released from a towing boat producing the free vibration of the bridge. Acceleration records were registered. With this information, the fundamental frequencies for the vertical and torsional component of the deck were identified again; their values were 0.38 and 1.01 Hz, respectively. The critical damping ratio of the deck was calculated using the logarithmic decrement. For the vertical vibration the estimated damping was 0.0028 and the correspondent one obtained in 1988 was 0.0045. For the torsional vibration these values are 0.0036 and 0.0052.
5. Numerical modelling Using a computer program (SAP90, 1995), a finite element model of the bridge was constructed. Cables and piers were modeled with truss and beam elements, respectively; shell elements were used for the box girder deck. The model comprised the superstructure between two hinges, including four piers and pylons 13 and 14. Static load conditions studied were self-weight and live loads produced by the trucks used during the testing program. Fundamental frequencies and modal shapes were also calculated using the mathematical models. The results of the experimental program were used to calibrate the finite element model.
6. Conclusions Results of two ambient vibration testing programs of a cable-stayed bridge were presented and compared. In spite of some differences observed, the whole sets of the two testing agree fairly well, although a general trend in the reduction of frequency values was observed. On the other hand, the results calculated numerically showed a fair agreement with the values experimentally obtained. The work presented is part of an entire structural safety evaluation program of the Tampico bridge. Results of this study and the numerical model will be used to propose maintenance and corrective actions in order to enhance the behavior of the bridge.
Acknowledgements This study was funded by CAPUFE. The authors acknowledge the support and encouragement of Juan Tellez and Miguel A. de la Cruz. Assistance of the technical staff of CAPUFE at Tampico is appreciated. G. Rodríguez, M. A. Mendoza also collaborated.
References [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8]. [9]. [10]. [11]. [12]. [13]. [14]. [15]. [16]. [17]. [18]. [19]. [20].
AEIC, S.C. 1988. Ambient vibration testing of the Tampico bridge, Technical report in spanish, Mexico Allemang R.J. and D.L. Brown 1982. A correlation coefficient for modal vector analysis. Proceedings, 1st International Modal Analysis Conference, Society for Experimental Mechanics, 110-116. Bethel, Conn. Bendat, J. S. and A. G. Piersol 1986. Random Data : Analysis and Measurements Procedures, Wiley Interscience, New York, N.Y. Gómez, E., D., M.A. Mendoza, D. Murià-Vila and Badillo E. 1998. Design and Implementation of an Acquisition and Signal processing System, Technical report in spanish, Instituto de Ingenieria, UNAM, Mexico. Gómez, R., D. Murià-Vila, R. Sánchez and J. A. Escobar 1998. Static and dynamic loading and mathematical modeling of the main central span of the Tampico bridge, Technical report in spanish, Instituto de Ingenieria, UNAM, Mexico. Gómez, R. , C. King, D. Murià-Vila and C. Montoya 1991. Numerical and experimental determination of dynamic properties of the Tampico bridge. Proceedings, International Symposium for Innovation in Cable-Stayed Bridges, 111-121, Fukuoka, Japan. Lieven, N. A. J. and D. J. Ewins 1988. Spatial Correlation of Mode Shapes, the Coordinate Modal Assurance Criterion (COMAC). Proceedings, 6th International Modal Analysis Conference, Society for Experimental Mechanics : 690-695, Bethel, Conn. Murià-Vila, D., R. Gómez and C. King 1991. Dynamic structural properties of the cable-stayed Tampico bridge, Journal of Structural Engineering, ASCE, 117 (11): 3396-3416 Robert, J.L., D. Bruhat and J. Gervais 1991. Mesure de la tension des cables par methode vibratoire, Bulletin de liaison de Laboratoire des Ponts et Chausseés, 173, mai-juin: 109114 SAP90 Structural Analysis Programs 1995, Computers and Structures Inc., Berkeley, California.
Dynamic Tests on Vasco da Gama Cable-Stayed Bridge Álvaro CUNHA Assistant Professor University of Porto Portugal
Elsa CAETANO Assistant University of Porto Portugal
Rui CALÇADA Assistant University of Porto Portugal
Raimundo DELGADO Associate Professor University of Porto Portugal
Summary This paper describes the dynamic tests performed on Vasco da Gama cable-stayed bridge so as to accurately identify its most significant modal parameters from the aerodynamic and seismic point of view. The main results obtained on the basis of ambient vibration and free vibration tests are presented and correlated with the corresponding parameters provided by the finite element model developed at the design stage. Moreover, the usefulness of application of a laser Doppler sensor to perform dynamic measurements on a large number of stay cables is also stressed, as well as the feasibility of experimental evaluation of dynamic amplification factors associated to the passage of heavy traffic.
1. The Vasco da Gama cable-stayed bridge
Figure 1: View of Vasco da Gama cable-stayed bridge The Vasco da Gama Bridge is the new Tagus River crossing in Portugal, 17300m long, including three interchanges, a 5km long section on land and a continuous 12300m long bridge, recently constructed close to the area of EXPO-98 international exhibition. It includes a cable-stayed component (Figure 1) over the main navigation channel with 420m central span and three lateral spans (62+70.6+72m) on each side, corresponding to a total length of 829.2m between transition piers. The bridge deck is 31m wide and is formed by two lateral prestressed girders, 2.6m high, connected by a slab and by transverse steel I girders. It is continuous along its total length and it is suspended at level 52.5m by two plans of 48 stays connected to each tower. The two towers are H shaped and 147m high above a massive zone at their base as protection against ship collision.
2. Objectives and tasks of the dynamic tests Due to the high proneness of long span bridges to be affected by aerodynamic instability problems, as well as to the high seismic risk of the Southern part of Portugal, the dynamic behaviour of Vasco da Gama cable-stayed bridge has been extensively studied using both experimental and numerical approaches[1,2]. In particular, dynamic tests have been performed by the University of Porto[3] in order to experimentally identify the most relevant modal parameters of the cable-stayed bridge from the aerodynamic and seismic behaviour point of view, and correlate them with the corresponding parameters provided by the 3-D numerical model developed by EEG (Europe Études Gecti, Villeurbanne, France), using the finite element program Hercules. These dynamic tests, described in this paper, involved the following main tasks: (i) preliminary measurements for evaluation of the levels of acceleration signals and identification of an appropriate reference section; (ii) development of an ambient vibration test for identification of natural frequencies and mode shapes, involving tri-directional measurements at 58 distinct points along the deck and towers; (iii) performance of response measurements under the passage of heavy trucks, passing over a hood plank, to increase the vertical accelerations; (iv) development of a free vibration test by sudden release of a mass of 60t suspended from the deck, in order to accurately indentify modal damping factors; (v) performance of dynamic measurements on some of the longest stay cables so as to identify global and local natural frequencies, both using conventional piezoelectric accelerometers and an interferometry laser sensor; (vi) experimental evaluation of dynamic amplification factors (DAFs) associated to the passage of heavy traffic at different speeds and along several lanes.
3. Ambient vibration test 29U 29D 28U
20U 19U 28D
18U 15U
27U 26U
LISBOA (North)
1U
2U
3U
1D 2D
4U 3D
5U 4D
6U 5D
7U
8U 26D
16U
12,13,14U
27D 9U 8D
10U 9D
11U
15D
19D
17U 16D
17D
21U 20D
22U 21D P4
18D PS
23U 22D
24U 23D
25U 24D
25D P6
P5 SETÚBAL (South)
12,13,14D
10D
11D
z x
y
7D 6D PN
P3
P2 P1
Figure 2: Schematic representation of the bridge with indication of the measurement sections used in the ambient vibration test This test was developed performing vibration measurements with two triaxial accelerographs at a given reference cross section (section 10, 1/3 span North) and with two other successively placed at 28 different mobile sections along the deck and towers (Figure 2). In all sections, the pairs of sensors were located laterally, upstream and downstream, always oriented according to the orthogonal referential xx (longitudinal direction), yy (transversal) and zz (vertical). Due to the relatively low level of signal captured, appropriate amplification factors were used, leading to a precision of at least 0.015mg (1g/216). The measurements were conducted in order to create time records with a sampling rate of 50Hz and enabling average spectral estimates with a frequency resolution inferior to 0.01Hz. Beyond these sensors, previously programmed and synchronised using a portable PC, an anemometer was still used to regularly measure the wind speed. With the purpose of increasing the signal level in the vertical component, vibration measurements were also carried out during the passage of a heavy truck, with a mass of 30t, over a hood plank, 4cm high, placed at 1/3 span. Inspection of the time records obtained showed a significant variation of the structural response during the ambient vibration test, which was essentially due to oscillations of the wind speed. The wind speed measured at midspan changed between 1 and 22m/s, leading to a ratio between maximum and minimum r.m.s. values of the vertical acceleration at the reference section of 28.
The identification of natural frequencies was based on the peak values of averages of normalised acceleration power spectra (NPSD) corresponding to each section (downstream, upstream, halfsum and half-difference signals), as well as on the coherence values associated to the simultaneous measurements at the several pairs of points[4]. The frequency resolution of the average spectral estimates obtained, on the basis of time records of 16 minutes, was 0.006Hz. Figure 3 shows average normalised auto spectra (ANPSD) and cross-spectra (ANCPSD), corresponding to vertical (Z) and transversal (Y) acceleration components, obtained as average of NPSD and NCPSD spectra associated to the measurement in 23 different sections, taking into account both the half-sum and the half-difference signals (upstream-downstream). Figure 4 also shows the amplitudes of NCPSD spectra and the corresponding coherence functions associated to simultaneous measurements at sections 10 and 16. Inspection of all the average spectral estimates obtained[3] permitted to identify the values of natural frequencies summarised in Table 1, in the range 0-1.15Hz, in correspondence with natural frequencies provided by the numerical model. 1.00E+00
1.00E+00 Half-sum Half-diff.
1.00E-01 ANPSD (Y)
ANCPSD (Z)
1.00E-01 1.00E-02 1.00E-03
1.00E-02 1.00E-03
1.00E-04 1.00E-05
1.00E-04 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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1
0
0.1
0.2
0.3
Frequency (Hz)
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
(a)
(b)
Figure 3: Average normalised spectra associated to: (a) vertical acceleration (half-sum and half-difference signals, upstream-downstream); (b) transversal acceleration (half-sum signal) 1.00E-01
0.4
1.00E-04
0.2
1.00E-05 1.00E-06
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1.00E-03
1
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1.00E-02
Coherence
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1
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1.00E-02
0.6
1.00E-03 0.4
1.00E-04
Coherence
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0.2
1.00E-05 1.00E-06
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
(b)
Figure 4: NCPSD spectra (amplitude) of the half-sum signal of (a) vertical acceleration and of (b) transversal acceleration at sections 10 and 16, and corresponding coherences The identification of modes of vibration with frequencies in the range 0-1.15Hz was based on the estimates of transfer functions (using estimator H1), and corresponding coherences, relating the ambient response at the reference section (half-sum and half-difference signals, upstreamdownstream) with the response at the other measurement sections along the deck and towers. The ratios between the values of those transfer functions related to each natural frequency (linear magnitude) associated to the several sections led to the absolute value of the modal components, the corresponding signal having been evaluated on the basis of the phase evolution. Figure 5 shows some of the identified modal shapes of the deck, also presenting the corresponding numerical modes, as well as some modal components identified using the free vibration test, described in the next section.
Calculated frequencies (Hz) 0.2624 0.3185 0.4287 0.4386 0.6268 0.6077 0.6268 0.7600
Identified frequencies (Hz)
Type of mode of vibration
0.298 0.341 0.437 0.471 0.572*/0.590*/0.599*/0.619*/0.624* 0.651 0.693*/0.707*/0.718*/0.755* 0.817* 0.895*/0.917* 0.985 1.129*
1st transversal bending 1st vertical bending 2nd vertical bending st 1 torsion + transversal bending 2nd torsion + transversal bending 3rd vertical bending nd 2 torsion + transversal bending 4th vertical bending 3rd torsion th 5 vertical bending 4th vertical bending
(*) – multiple modes, low signal level
Table 1: Identified and calculated natural frequencies Freq.=0.341Hz- 1st vertical bending mode
0.001
0.001
Vertical modal component
Transversal modal component
Freq.=0.298Hz- 1st transversal bending mode
0.0005 0
Numerical
-0.0005
Ambient vib.
-0.001
Free vib.
-0.0015 -0.002 -0.0025 -0.003 10950
11050
11150
11250
11350
11450
0 -0.001 -0.002 -0.003
Numerical Ambient vib. Free vib.
-0.004 -0.005 10950
11550
11050
11150
Point
Ambient vib. Free vib.
0.002
Vertical / transversal modal component
Vertical modal component
Numerical
0.003 0.001 0 -0.001 -0.002 -0.003 -0.004 11050
11150
11250
11350
11450
0 -0.001 -0.002
-0.004 -0.005 10950
11550
Numerical, Z Ambient vib., Z Ambient vib., Y Free vib., Z Free vib., Y
-0.003
11050
11150
Freq.=0.572Hz- 2nd torsion mode
11350
11450
11550
Freq.=0.619Hz- 2nd torsion + transversal bending mode
0.005
0.01
0.004
Numerical Ambient vib. Free vib.
0.003 0.002 0.001 0 -0.001 -0.002 -0.003
Numerical, Z Ambient vib., Y Numerical, Y Ambient vib., Z
0.008
Vertical / transversal modal component
Vertical modal component
11250
Point
Point
-0.004
0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008
11050
11150
11250
11350
11450
-0.01 10950
11550
11050
11150
11250
11350
11450
11550
Point
Point
Freq.=0.651Hz- 3rd vertical bending mode
Freq.=0.817Hz- 4th vertical bending mode 0.01
0.008
Vertical modal component
0.01
Vertical modal component
11550
0.001
0.004
Ambient vib., Z Numerical, Z Free vib., Z
0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 10950
11450
Freq.=0.471Hz- 1st torsion + transversal bending mode
0.005
-0.005 10950
11350
Point
Freq.=0.437Hz- 2nd vertical bending moment
-0.005 10950
11250
11050
11150
11250
11350
11450
Point
Figure 5(a): Some modal shapes of the deck
11550
0.008
Numerical
0.006
Ambient vib.
0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 10950
11050
11150
11250
Point
11350
11450
11550
Freq.=0.985Hz- 5th vertical bending mode
Freq.=0.895Hz- 3rd torsion mode 0.01
0.005
Vertical / transversal modal component
0.003 0.002 0.001
Vertical modal component
Ambient vib., Y Numerical, Y Ambient vib., Z Numerical, Z
0.004
0 -0.001 -0.002 -0.003 -0.004 -0.005 10950
11050
11150
11250
11350
11450
0.008
Experimental, Z Free vib., Z
0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 10950
11550
11050
11150
11250
11350
11450
11550
Point
Point
Figure 5(b): Some modal shapes of the deck
4. Free vibration test The free vibration test was performed not only to check the main results of the ambient vibration test previously developed, but essentially to permit an accurate identification of the damping factors associated to the modes of vibration with a more significant contribution to the dynamic response of the bridge, particularly under wind loading. For that purpose, a mass of 60t was suspended from one point of the deck close to the section 1/3 span North, near the upstream border, and was subsequently released, originating a vibratory phenomenon recorded during 16 minutes by 6 triaxial accelerographs, located at the sections 1/3 and 1/2 span (upstream and downstream). In order to verify that the wind would not affect the accuracy of evaluation of the structural modal damping factors, introducing a component of aerodynamic damping, the wind speed was permanently measured at midspan, connecting the anemometer to a spectral analyzer, the maximum wind velocity not exceeding 2.5m/s. The identification of natural frequencies was then made on the basis of the peaks of the FFTs of the acceleration time series (Figures 6-7). Each one of these series was formed by 32768 points sampled at 50Hz, corresponding to a time of acquisition of 655.36s, which led to a frequency resolution of 0.0015Hz. With regard to the mode shapes, these were identified applying a band-pass 10 poles Butterworth digital filter around each one of the natural frequencies identified, and comparing the amplitudes and phases of the filtered signals at different points of measurement. Figure 5 shows the modal components identified by this procedure, which are clearly in good agreement both with the mode shapes obtained by the ambient vibration test and with the modal configurations calculated numerically. 1 .0 0 E + 0 0
F F T a m p litu d e (m g
F F T a m p litu d e (m g )
1 .0 0 E + 0 0
1 .0 0 E -0 1
1 .0 0 E -0 2
1 .0 0 E -0 3
1 .0 0 E -0 4
1 .0 0 E -0 1
1 .0 0 E -0 2
1 .0 0 E -0 3
1 .0 0 E -0 4
0
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F re q u e n c y (H z )
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Frequency (Hz )
(a) (b) Figure 6: Amplitude of the FFT of the half-sum signal of vertical acceleration (upstreamdownstream) at (a) 1/3 span North and (b) 1/2 span
0 .9
1
1 .0 0 E + 0 0
F F T amplitude (mg
F F T am plitude (m g)
1 .0 0 E + 0 0
1 .0 0 E -0 1
1 .0 0 E -0 2
1 .0 0 E -0 3
1 .0 0 E -0 4
1 .0 0 E -0 1
1 .0 0 E -0 2
1 .0 0 E -0 3
1 .0 0 E -0 4
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F re q u e n c y (H z )
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1
F re q u e n c y (H z )
(a) (b) Figure 7: Amplitude of the FFT of the half-difference signal of vertical acceleration (upstreamdownstream) at (a) 1/3 span North and (b) 1/2 span At last, the identification of the modal damping factors was done on the basis of the decay of the envelope of the filtered signals obtained applying also a band-pass 10 poles Butterworth digital filter around each natural frequency in the range 0-1.0Hz (Figure 8). As the estimates of the modal damping factors depend on the level of vibration, different exponential regressions were performed in correspondence with different time intervals of the free response. Table 2 shows the average estimates obtained, as well as the respective intervals of variation. 1/2 s pan, ups tream, v e rtica l component B utte rw orth filter, 10 poles , F inf=0.4Hz ; F s up=0.5Hz
1/2 s pan, half-s um ups tream-dow ns tream, trans v. component Fitting of the 1s t tors ion damping modal coef. (logarithmic dec.) 2
1 0 .0 0
E n v e lo p e
8 .0 0
A c c e le ra tio n (m g )
A cce leration (mg)
6 .0 0 4 .0 0 2 .0 0 0 .0 0 -2 .0 0 -4 .0 0
F itte d c u rv e 2 0 0 -5 0 0 s
1 .5 1
ξ=0.24%
0 .5
-6 .0 0 -8 .0 0
0
-1 0 .0 0
100 100
150
200
250 300 T ime (s )
350
400
200
450
300
400
500
600
700
T im e (s )
(a) (b) Figure 8: Identification of the modal damping factor associated to the natural frequency 0.467Hz. Analysis based on the measured response at 1/2 span upstream Identified Modal damping factor (%) natural frequency (Hz) Mean value Int. of variation 0.295 1.23 0.87-1.73 0.338 0.21 0.16-0.40 0.456 0.23 0.19-0.27 0.467 0.24 0.14-0.36 0.591 0.34 0.30-0.39 0.647* 0.37 0.653* 0.20 0.707 0.78 0.71-1.12 0.814 0.48 0.45-0.54 0.982 0.74 0.67-1.24 (*) – Multiple modes; identification based on the half-power bandwith method due to the difficulty of application of digital filters
Table 2: Identified natural frequencies and modal damping factors
Type of mode 1st transversal bending 1st vertical bending 2nd vertical bending 1st torsion + transversal bending 2nd torsion + transversal bending 3rd vertical bending 2nd torsion + transversal bending 4th vertical bending 5th vertical bending
It’s worth mentioning that, beyond the application of the logarithmic decrement method, the frequency domain MDOF identification algorithm RFP (Rational Fraction Polynomial Method[5]) was still used, based on transfer functions relating the response measured at each point with the excitation. As the excitation was not actually measured when the mass of 60t was suddenly released from the deck, the transfer functions were evaluated assuming the input as an impulsive load, with unit magnitude, applied during a very short period of time, leading to a spectral content of the excitation with an almost constant intensity over the frequency range of interest. 1/3 span North, half -sum upstream / dow nstream, vertical component
1/3 span North, half -dif . upstream / dow nstream, vertical component
10000
10000 Measured
1000
Measured
1000
Identified
100
100
10
10
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Identified
1 0.2
0.3
0.4
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0.9
1
0.2
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Frequency (Hz)
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
Figure 9: Identification of modal parameters using the RFP method. Measured and synthesised transfer functions. Figure 9 shows two of the transfer functions obtained following this procedure, as well as the corresponding synthesised transfer functions, evaluated on the basis of the modal parameters identified using the RFP algorithm.
5. Dynamic measurements on stay cables 5.1 Identification of natural frequencies The performance of dynamic measurements on stay cables of cable-stayed bridges is often required to assess different problems of great interest in the context of the design, construction and maintenance of this type of structures, such as: (i) the evaluation of cable tensions, whose knowledge is critical to the correct alignment and distribution of internal forces in the finished bridge, and whose temporal evolution can provide interesting indications concerning the structural health; (ii) the assessment of fatigue problems in stay cables caused by long-term traffic loads; (iii) the evaluation of the level of importance of cable vibrations, that can occur due to vortex-shedding phenomena, parametric or rain-wind excitation; (iv) the experimental identification of local and global natural frequencies, contributing to validate and update finite element numerical models used to simulate the dynamic behaviour of the bridge under wind or seismic loads. The most common way of performing dynamic measurements in stay cables is based on the use of accelerometers conveniently attached to the external cable surface, which involves a rather hard and tedious set-up preparation when dealing with a large number of stay cables, as it is more and more common in modern cable-stayed bridges. Therefore, in the present study, the measurement of vibrations in stay cables was developed not only on the basis of conventional measurement equipment, but also applying an interferometry laser system that can play an interesting role in this context, avoiding the direct contact with the structure, and providing an excellent accuracy. The laser sensor used in this work[6] is an industrially engineered Doppler-based interferometer, which functions as a non-contacting velocity transducer capable of remote measurement of the velocity of a solid surface. The basic principle behind the laser Doppler technique used is that when a beam of coherent light is reflected from a moving surface, its frequency changes
according to the well-known Doppler effect. Although the fractional change of the frequency of the light wave is very small, it can be measured very accurately using optical interferometry in conjunction with electronic frequency measurement equipment, the velocity of the moving surface being directly derived from the frequency changes. In order to measure vibrations in some of the longest stay cables of Vasco da Gama cable-stayed bridge using conventional piezoelectric accelerometers, these were screwed on small metallic cubes, conveniently attached to the external surface of the stay cables with the help of metallic belts strongly tightened. This relatively boring preparatory operation, only possible as the bridge was not open to the normal road traffic yet, was systematically repeated in all the stay cables observed, placing the accelerometers 5m above the deck by means of a crane, and measuring vibrations in the vertical plane. The use of the laser transducer became however uncomparably easier, the only operation needed being the control of the position of the laser head, placed on the deck under each cable, in order to produce a laser beam hitting the cable surface. Figure 10 shows, for instance, average power spectra associated to the ambient response of one of the longest stay cables of the bridge, obtained with simultaneous measurements at the same point on the basis of the two types of sensors mentioned, using 16 averages and a frequency resolution of 0.0078Hz. Although those spectra are associated to different mechanical quantities measured (acceleration and velocity), they clearly evidence an excellent agreement in terms of identification of local natural frequencies of the cable, characterised by equally spaced well pronounced peaks. Moreover, some global natural frequencies of the bridge, corresponding to main peaks of the spectra in the range 0-1Hz, are also apparent, though not so clearly in the case of the laser sensor, as this transducer measures the relative velocity between the deck and the stay cable. The same conclusion can also be drawn when comparing the natural frequencies identified using the laser sensor with those obtained with conventional equipment in the free vibration test (Figure 10), the contribution of the global modes being naturally more significant in this case. 1.00E-04 Acceleration PSD (m^2/s^4)
Velocity PSD (m^2/s^2)
1.00E+00 1.00E-01 1.00E-02 1.00E-03 1.00E-04 1.00E-05 0
0.5
1
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2
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1.00E-05 1.00E-06 1.00E-07 1.00E-08 1.00E-09 0
4
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1
1.5
2
2.5
3
3.5
4
Frequency (Hz)
Frequency (Hz)
(a) (b) Figure 10: Average power spectra of the ambient response of a stay cable: (a) using the laser sensor; (b) using the accelerometer 40
1.00E+00
Acceleration (mg)
10
1.5
0 1
-10 -20
0.5
-30
Wind speed (m/s)
2
20
Acceleration FFT (mg)
2.5
30
1.00E-01 1.00E-02 1.00E-03 1.00E-04 1.00E-05
-40 0
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Time (s)
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700
800
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Frequency (Hz)
(a) (b) Figure 11: Response of the stay cable during the free vibration test of the bridge: (a) Cable response and wind speed at 1/2 span; (b) FFT of the cable response
3.5
4
The values of the first 5 natural frequencies of this stay cable, identified on the basis of these spectra using the two measurement systems referred, are virtually coincident (0.594, 1.180, 1.766, 2.367, 2.953Hz), the only difference observed in one of the natural frequencies being equal to the frequency resolution (0.0078Hz). 5.2 Evaluation of cable tensions Several techniques can be employed to evaluate cable forces, namely measurement of the force in a tensioning jack, application of a ring load-cell, topographic measurements, elongation of the cables during tension and installation of strain gauges in the strands. As referred by Casas[7], in spite of their simple theoretical bases, each of these methods is complex in its practical application and, in some cases, the level of accuracy is insufficient. A relatively simpler and less expensive method to estimate cable tensions in cable-stayed bridges is based on the vibrating chord theory, taking into consideration the identified values of natural frequencies of the stay cables, which leads to the following relation: T=
4mf n2 L2 n2
(1)
where T is the cable tension, f n is the n-th natural frequency, L is the cable length and m represents the mass of the cable per unit length. Application of this approach, taking L = 214.97m and m = 96.9kg / m , leads to an average value of cable tension, for the stay cable referred, of 6266kN using the laser sensor, whereas the accelerometer led to 6256kN.
6. Experimental evaluation of dynamic amplification factors The dynamic tests described herein still involved the experimental evaluation of dynamic amplification factors associated to the passage of heavy traffic. For that purpose, a truck with a mass of 30t has crossed the bridge several times at different speeds (15, 30, 45 and 60 km/h), both using a central and a lateral lane, the structural response being measured at sections 10, 13 and 16, upstream and downstream, in terms of vertical acceleration. Comparing the peak values of the response obtained at different speeds with the corresponding values associated to the lower velocity (15km/h), it was possible to estimate DAFs, which show a clear tendency to increase with the vehicle speed, as it is reported with more detail in [3]. Further investigation on this topic is being proceeded by the authors.
7. Conclusions The development of the dynamic tests described in this paper permitted to extract the following main conclusions: •
• •
The measurement system used in the ambient and free vibration tests, based on the use of independent triaxial accelerographs conveniently programmed and synchronised by a portable PC, revealed to be a very efficient and comfortable solution, avoiding the use of several hundred meters of electric cables and permitting the integral data acquisition in a relatively short period of time; The ambient vibration test provided a very accurate estimate of natural frequencies and mode shapes, despite the rather low level of signal captured, the low range of natural frequencies of interest (0-1Hz) and the relatively high number of different modes of vibration in that range; The free vibration test, based on the sudden release of a mass of 60t suspended from the deck, seemed to be quite useful as a complementary test that permitted not only to check the previous identification of natural frequencies and mode shapes, but essentially the very accurate identification of modal damping factors, whose knowledge is particularly relevant in terms of the study of the aerodynamic stability of the bridge;
•
•
•
•
There is, in general, an excellent correlation between modal parameters identified and the corresponding parameters calculated on the basis of the 3D finite element model developed at the design stage, though some small differences can be found, as it is the case of the multiple modes identified associated to the 2nd torsion + transversal bending numerical mode, related with local stay cable frequencies, or of the 3rd torsion mode, in which no transversal bending component was experimentally detected; Although no force measurement has been performed during the free vibration test, a standard MDOF identification algorithm (RFP – Rational Fraction Polynomial method) in the frequency domain could be applied with success, assuming the input as an impulsive load, with unit magnitude, acting during a very short period of time, leading to a spectral content of the excitation with an almost constant intensity over the frequency range of interest; The application of a laser Doppler velocity transducer reveals to be a rather accurate and easy to use non-contact vibration measurement technique, particularly appropriate to perform dynamic measurements in stay cables of cable-stayed bridges, providing a powerful form of systhematic and accurate evaluation of natural frequencies and cable tensions, which is a factor of significant importance, in particular, in terms of the long term health monitoring of this type of bridges; The experimental evaluation of dynamic amplification factors (DAFs) is an interesting field of research that deserves further investigation with the aim of testing the appropriateness of general design criteria defined in national or international codes or regulations concerning the evaluation of dynamic effects due to traffic loads on bridges.
8. Acknowledgements The authors wish to acknowledge the Portuguese Foundation for Science and Technology (FCT) and NOVAPONTE for all the support provided to the development of the present investigation, carried out in the context of the Research Project no. PBIC/CEG/2349/95, on the theme Experimental and Numerical Analysis of the Dynamic Behaviour of Cable-Stayed Bridges.
9. References [1] Grillaud G., Bourcier P., Barré C. and Flamand O., “Wind action on the Vasco da Gama cable stayed bridge”, Proc. of the 2nd European and African Conference on Wind Engineering, Genova, Italy, pp.1449-1456, 1997. [2] Branco F., Mendes P. and Guerreiro L., “Research studies for the Vasco da Gama Project”, IST Science & Technology, No.2, pp.3-7, April 1998. [3] Delgado R., Cunha A., Caetano E. and Calçada R., “Dynamic Tests of Vasco da Gama Bridge” (in Portuguese), Report under contract with NOVAPONTE, Faculty of Engineering of the University of Porto, 1998. [4] Felber A.J., “Development of a Hybrid Bridge Evaluation System”, Ph.D. Thesis, University of British Columbia, Canada, 1993. [5] Han M-C and Wicks A.L., “On the application of Forsythe polynomials for global modal estimation”, Proc. 7th Int. Modal Analysis Conference, pp.625-630, 1989. [6] Cunha A., Caetano E., Laje A. and Gomes A. “A laser system for the identification of dynamic parameters of civil engineering structures”, Proc. Int. Conf. Earthquake Resistant Construction and Design, pp.985-992, Berlin, 1994. [7] Casas J.R., “A combined method for measuring cable forces: the cable-stayed Alamillo Bridge, Spain, Structural Engineering International, Journal of the IABSE, Vol.4, No.4, pp.235-240, November 1994.
The Øresund stay cables : design for fatigue resistance and easy maintenance J.P. FUZIER Scientific Director Freyssinet International Vélizy, France
J.STUBLER Technical Director Freyssinet International Vélizy, France
D. GRATTEPANCHE Øresund Site Engineer Freyssinet International Vélizy, France
Summary The 16 km Øresund fixed link across the shallow channel between Denmark and Sweden includes a 7-8 km long bridge. The double-deck cable-stayed bridge with its 490 m main span appears to be the masterpiece of this viaduct. It is hence of primary importance to use a stay cable technology which provides high fatigue resistance and durable corrosion protection and allows easy maintenance without any interruption of the service. This paper deals with the installation specific procedure and the associated technology of these long cables. Such a technology offers the advantage of avoiding any limit to the sizes of the anchorages due to weight or to the dimensions of the jack. It allows the placing of the cables, even the longer ones, with very light equipments and provides the engineer and the owner a fully documented record of all the tensioning operations thanks to a microprocessor piloted robot. All necessary adjustments can then be carried out with great accuracy.
1. Introduction The Øresund bridge, like the other recent and major crossings (Normandie, Tagus, Second Severn, Ting Kau, Tsing Ma), requests a long life span. Very often, 100 or 120 years are considered for this type of structure ; the only way to meet such a demand is to provide a better quality product from the very beginning of the construction and to develop a surveillance concept since there are no material suppliers able to give a 120 years guarantee. This explains why the stay cable technology has been renovated during the last ten years. The cables supplied and installed on the Øresund bridge meet such requirements : - high fatigue resistance - high stiffness and mechanical strength - excellent corrosion protection - simplicity of installation - easy maintenance and replacement without any traffic disruption.
2. Technology description 2.1 General The stay cable system consists of parallel individually protected seven wire strands with wedge anchorages and additional corrosion protection system consisting of an outer HDPE pipe. The stay cable design is such that the replacement of any cable can be done, if required, strand by strand, in order to reduce to a minimum any traffic disruption. The anchorages are filled with wax. Cement grout filling is rejected because of the unability of cement grout to resist without cracking to stress variations produced by live loads. This cracking may induce fretting corrosion of the wires. The strands are individually protected as follows : - hot dip galvanization before wire drawing ; - extrusion around the strand of a high density polyethylene sheath (i.e. 1.5 mm thick minimum) after coating the wires with wax.
Fig 1.The Freyssinet monostrand 2.2 Independence of strands The high fatigue performances are obtained thanks to the absence of any steel to steel contact. All the strands are parallel in the anchorages. They are distributed according to a triangular network and they form a compact bundle in the typical section outside of the anchorage zone, thanks to deviators and clamping rings placed at a specified distance from each other. The transition zone between the bundle of strands and the individual anchorage of each strand consists of a guide-deviator which groups together the strands which are spaced apart in the anchorage (deviator function) and prevents any transverse movement at deck level or at pylon level in order to avoid bending in the anchorage because of the angular variations of the stay under service loads and wind effect (guide function).
The anchorage itself is made so that each strand is individually anchored by means of jaws blocked in a conical hole. There is no possibility of steel to steel contact inside the anchorage which avoids all risks of fretting corrosion. In the anchorage there is also a protection ensuring watertightness between the area where the strands are removed. Beyond the jaws, there is an over length of strands which enables tensioning or detensioning at any time.
Fig 2. The Freyssinet cable anchorage 2.3 Vibration limiting devices Helical ribs The streamlined sheaths covering the stays expose to the wind a cylindrical surface covered with two criss-crossed helical ribs. This arrangement, developed during wind tunnel tests carried out at the CSTB in NANTES for the Normandie bridge, prevents the vibration phenomena produced by vortex-shedding on rainy days, due to, under certain combinations of force and direction of the wind, the apparition of a water rivalet. This is the rain and wind phenomenon. Similar tests were performed at the Danish Maritime Institute for the Øresund bridge. Dampers Provisions have been taken to install, at a later stage if required, visco-elastic internal dampers. This installation can be carried out easily during regular maintenance operations.
3. Cable installation 3.1 General The 160 stays are distributed according to a regular harp layout with a constant 30° inclination. Each plane of stays consists of 10 x 2 twin-stays made of 73 strands each. The spacing between the twin-stays is equal to 670 mm. This cable concept based on independence of the strands leads to a simple and easy installation method which is installation at the site, strand by strand. 3.2 Installation Because of a tight schedule requesting that 2 x 73 HD15 stays are installed on a 6 days cycle, the following installation method has been selected : -
supply and installation, on each side of the deck, of a 40 m long self launching access platform. This platform provides access to two successive stay cables allowing to carry out, at the same time, erection of cable n+1 and finition of cable n ; lifting of HDPE sheath with the referenced strand ; threading of strands two by two in order to increase the productivity and to reduce the risk of delay in case of bad weather conditions ; the strand uncoilers are equipped with an hydraulic braking system permitting to adjust the tension of the threaded strand ; stressing strand by strand thanks to the patented Isotension system. A computer software allows the installator to provide a complete history of the cables.
Fig 3. Self launching access platform
3.3 Corrosion protection The strands in the free zone are galvanized, waxed with Injectelf and individually protected with an HDPE sheath. The top anchorage is injected with petroleum Injectelf wax. The bottom anchorages use the same dehumidification system already set up for the internal corrosion protection of the steel truss.
Fig 4. Self launching access plaform
IABSE REPORTS Available in June 1999
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Symposium - New York 1968
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IVBH BERICHTE Erhältlich im Juni 1999
Structural Precast Concrete Constructions préfabriquées en béton Vorfabrizierte Betonbauten On Wearing Surfaces for Steel Bridge Decks of Lightweight Construction Sur les revêtements pour les platelages métalliques légers Über Fahrbahnbeläge von stählernen LeichtFahrbahnen Final report – Rapport final – Schlussbericht On Concepts of Safety of Structures and Methods of Design Sur les notions de sécurité des structures et méthodes d’élaboration des projets Über neue Aspekte der Tragwerksicherheit und ihre Berücksichtigung in der Bemessung
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Main Trends in the Development of Steel Structures and Modern Methods of their Fabrication Tendances principales dans le développement des structures en acier et méthodes modernes de fabrication Wichtigste Entwicklungstendenzen im Stahlbau und moderne Herstellungsverfahren von Stahlkonstruktionen Introd. Report – Rapport introd. – Einführungsbericht Informatics in Structural Engineering Proceedings Ship Collision Problems with Bridges and Offshore Structures
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Organization of the Design Process Organisaiton du processus de projet Organisation des Planungsprozesses Proceedings
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Report Structural Eurocodes Report Length Effect on Fatigue of Wires and Strands Report Remaining Structural Capacity
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Report Extending the Lifespan of Structures
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IABSE Symposium – Kobe 1998 Volume 79 IABSE Colloquium – New Delhi 1999 Volume 80 IABSE Colloquium – Phuket 1999
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Long-Span and High-Rise Structures
Report Foundations for Major Bridges: Design and Construction Report Concrete Model Code for Asia Structural Concrete: Design, Materials and Construction, and Maintenance Report
Cable-Stayed Bridges – past, present and future
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