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CABLE-STAYED BRIDGES Theory and Design SECOND EDITION M S Troitsky, DSc Professor of Engineering Concordia University, Montreal BSP PROFESSIONAL BOOKS OXFORD LONDON ED INB URGH BOSTON PALO ALTO MELBOURNE Copyright© M.S Troitsky 1977, 1988 All rights reserved No part of this publication may be reproduced, stored in a retrienl system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the copyright owner First Edition published by Crosby Lockwood Staples in 1977 Second Edition published by BSP Professional Books 1988 British Librarv Cataloguing i~ Publication Data Troitsky, M S Cable-stayed bridges: theory and design.Znd ed Bridges, Cable-stayed-Design and construction I Title 624'.55 TG405 BSP Professional Books A division of Blackwell Scientific Publications Ltd Editorial offices: Osney Mead, Oxford OXZ OEL (Orders: Tel 0865 240201) John Street, London WCIN ZES 23 Ainslie Place, Edinburgh El 13 6AJ 52 Beacon Street, Boston Massachusetts 02108, USA 66 L)tton Avenue, Palo Alto California 94301, USA 107 Barry Street, Carlton Victoria 3053, Australia Set by Cambrian Typesetters Printed and bound in Great Britain by Butler & Tanner Ltd, Frome and London ISBN 0-632-02041-5 Acknowledgements Special acknowledgement is herewith made to the following persons, companies, institutions and organizations for supplying the information and photographs for the many bridges discussed in this book: Alaska Department of I lighways, USA; British Railways Southern Region; Compagnie Fran~aise D'Entreprises Metalliques, France; Compagnie BaudinChateauneuf, France; Dip! Eng E Beyer, Landeshaupstadt Dusseldorf, Germany; Department of Public Works, Hobart, Tasmania; Mr A F Gee, Mott, I lay and 'l.nderson, Consulting Engineers, England; Dr A Kerensky, Freeman, Fox and Partners, Consulting Engineers, England; Dip! lng H Thul, Germany; The Institution of Engineers, Australia; Mr A Zanden, Rijkswaterstaat Directie Bruggen, Holland; Mr J \'irola, Consulting Engineer, Finland; lng J J 1\1 Veraart, Holland; Quebec Iron and Titanium Corporation; \lr Arvid Grant and Associates, Inc., Consulting Engineers, USA; Modjeski and Masters, Consulting Engineers, USA; Dr P.R Taylor, Buckland and Taylor Ltd, Civil and Structural Engineers, Canada I am especially grateful to the American Society of Civil Engineers li1r permitting me to use excerpts of the paper 'Tentative Recommendations for Cable-stayed Bridge Structures' Contents Preface to the second edition Vll Chapter The Cable-stayed Bridge System 1.1 1.2 1.3 1.5 1.6 1.10 1.11 1.12 Introduction Historical review Basic concepts Arrangement of the stay cables Positions of the cables in space Tower types Deck types Main girder and trusses Structural advantages Comparison of cable-stayed and suspension bridges Economics Bridge architecture References 19 20 21 24 25 26 29 31 34 36 39 Chapter Typical Steel Bridges 2.1 2.2 2.3 2.4 2.5 2.6 Two-plane bridges One-plane bridges Inclined tower bridges Railroad bridges Combined railroad-highway bridges Pipeline bridges Pontoon bridges References 42 69 91 95 99 103 105 108 iv COl\TE:'\TS Chapter 3.1 3.2 3.3 Concrete cable-stayed bridges Railroad concrete bridges Pipeline concrete bridges References Chapter 4.1 4.2 Typical Concrete Bridges 114 139 143 144 Typical Composite Bridges Introduction Composite cable-stayed bridges References 147 148 154 Chapter Typical Pedestrian Bridges 5.1 5.2 Introduction Cable-stayed pedestrian bridges References 155 155 173 Chapter Structural Details 6.1 6.2 6.3 6.4 6.5 6.6 6.8 6.10 6.11 6.12 6.13 Stiffening girders and trusses Towers Types of cable Modulus of elasticity of the cable Permissible strength of the cables Fatigue tests and strength of the cables Corrosion protection Behavior of the bent cable Cable supports on the towers Anchoring of the cables at the deck Stiffening girder anchorages Erection methods Adjustment of the cables References 175 176 180 185 191 191 195 195 198 203 211 213 217 221 Chapter Methods of Structural Analysis 7.1 7.2 7.3 7.5 Introduction Linear analysis and preliminary design Nonlinear analysis Dynamic analysis Application of computers References 223 223 224 227 229 230 CONTENTS V Chapter Approximate Structural Analysis Participation of the stiffening girder in the bridge system Optimum inclination of the cables The height of the tower and length of the panels The relation between the flanking and central spans 8.5 Number and spacing of the cables Multispan bridges 8.6 Multiple cantilever spans 8.7 Inclined cable under its own weight 8.8 Bridge systems 8.9 8.10 The degree of redundancy 8.11 Performance of the cable system 8.12 Linear analysis and preliminary design 8.13 Approximate weight of the bridge system 8.14 Approximate methods of analysis 8.15 Nonlinear analysis References 8.1 8.2 8.3 8.4 231 233 236 237 238 240 240 241 245 247 247 251 261 265 269 272 Chapter Exact Methods of Structural Analysis 9.1 9.3 9.4 9.5 9.6 9.8 9 Methods of analysis The flexibility method Force-displacement method Reduction method Simulation method Stiffness method Finite element method Torsion of the bridge system Analysis of towers References 273 274 282 297 309 317 323 328 345 361 Chapter 10 Model Analysis and Design 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 Introduction Basic concepts Planning Static similitude conditions Sectional properties and geometry of the model Design of the model Determination of influence lines Nonlinear behavior Post-tensioning forces in cables References 364 365 366 370 374 375 376 392 397 401 vi CONTENTS Chapter 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 Introduction Wind forces Static wind action Dynamic wind action Vibrations Vertical flexural vibrations Torsional vibrations Damping Wind tunnel model tests Prevention of aerodynamic instability Conclusions References Chapter 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 12.14 12.15 Wind Action and Aerodynamic Stability 404 407 408 410 413 416 421 428 435 440 446 446 Abbreviated Tentative Recommendations for Design of Cable-stayed Bridges Introduction Loads and forces Design assumptions Pylons Analysis Cables Saddles and end fittings Protection Camber Temperature Aerodynamics Fatigue Fabrication Erection Inspection References 450 450 451 452 452 453 454 455 455 455 456 456 457 457 458 459 Author Index 460 Subject Index 463 Preface to the second edition Since the first edition of was published a decade ago, there has been considerable development in the state of the art of cable-stayed bridges In this second edition, the contents have been revised to reflect recent developments in research, analysis, design and construction of new structures Although much of the data of the first edition has been retained, the arrangement of material has changed, chapters have been expanded and new ones have been added For the convenience of the users, the following changes and additions were made in the contents of the second edition The first edition contained seven chapters, while the second edition consists of twelve chapters, as follows: Chapter 1, The Cable-stayed Bridge System has an additional discussion on the problems of economics and aesthetics Chapter 2, Typical Steel Bridges contains additional data on new steel single and two-plane bridges, as well as pipeline and pontoon bridges Chapter 3, Typical Concrete Bridges contains additional data on new concrete structures Chapter 4, Typical Composite Bridges describes new deck types of cablestayed bridges Chapter 5, Typical Pedestrian Bridges presents additional types of pedestrian bridges Chapter 6, Structural Details provides additional structural details Chapter 7, Methods of Structural Analysis presents a discussion on the structural behavior of bridges and methods of analysis Chapter 8, Approximate Structural Ana(ysis treats methods of preliminary analysis Chapter 9, Exact Methods of Structural Analysis presents additional methods Chapter 10, Model Analysis and Design discusses experimental methods of design Chapter 11, Wind Action and Aerodynamic Stability provides expanded treatment considering aerodynamic action Chapter 12, Abbreviated Tentative Recommendations for Design of Cablestayed Bridges is a new addition Every effort was made to correct some errors detected in the first edition To my wife Tania Chapter The Cable-stayed Bridge System 1.1 Introduction During the past decade cable-stayed bridges have found wide application, especially in Western Europe, and to a lesser extent in other parts of the world The renewal of the cable-stayed system in modern bridge engineering was due to the tendency of bridge engineers in Europe, primarily Germany, to obtain optimum structural performance from material which was in short supply during the post-war years Cable-stayed bridges are constructed along a structural system which comprises an orthotropic deck and continuous girders which are supported by stays, i.e inclined cables passing over or attached to towers located at the main piers The idea of using cables to support bridge spans is by no means new, and a number of examples of this type of construction were recorded a long time ago Unfortunately, the system in general met with little success, due to the fact that the statics were not fully understood and that unsuitable materials such as bars and chains were used to form the inclined supports or stays Stays made in this manner could not be fully tensioned and in a slack condition allowed large deformations of the deck before they could participate in taking the tensile loads for which they were intended Wide and successful application of cable-stayed systems was realized only recently, with the introduction of high-strength steels, orthotropic type decks, development of welding techniques and progress in structural analysis The development and application of electronic computers opened up new and practically unlimited possibilities for the exact solution of these highly statically indeterminate systems and for precise statical analysis of their three-dimensional performance Existing cable-stayed bridges provide useful data regarding design, RFCOJ\L\IE:\JHTIO:\S FOR C:\BJ.I·:snn:D BR]])GES 455 end of a cable are broomed out, cleaned and immersed in a flux solution, then placed in the basket of the socket, which is then filled with molten zinc or with epoxy mixtures With swaged fittings, the cable end is inserted into a close-tolerance hole in the end of the fitting which is then placed in a die block of a hydraulic press The die block is closed under pressure and the softer steel of the fitting flows plastically around the harder steel wires 12.8 Protection Cable stays and their connections require protection as follows: (1) Corrosion-as a minimum all cables should have a protective coating equivalent to Class A zinc coating on all wires (2) Wrapping-individual strands should be bundled and wrapped to prevent water entry; this may be achieved with lead paste and soft galvanized wire or with a plastic or neoprene covering (3) Additional protection-in locations where de-icing salts or other chemicals are used, special precautions should be taken (4) Damage-may be caused by abrasion of the cable ends by the accidental impact of vehicles 12.9 Camber Girders should be cambered to follow the profile gradient line, considering the dead load and partial live-load deflections Camber provisions should be based on a theoretical analysis Cables should be capable of being jacked for final corrections 12.10 Temperature The thermal effects on the structure should be calculated, based on the ambient temperature at the time of erection A recommended ambient temperature variation may be as follows: (1) Moderate climates, to l20°F (2) Cold climates, -30 to l20°F 456 12.11 12.11.1 CABLE-STAYED BRIDGES Aerodynamics General When considering the effect of aerodynamic behavior of the bridge, wind tunnel tests are advisable 12.11.2 Cables and towers The critical wind velocity, ~,, associated with vortex shedding should be considered according to formula: NaD 5= - (12.4) where S = Strouhal number ~~ = shedding frequency equal to the natural frequency of the structural member D = projected dimension of the member Although vortex shedding causes limited amplitudes of motion, it should be considered for possible overstressing and fatigue 12.11.3 Bridge deck motion Wind tunnel tests are made to determine the wind velocity causing aerodynamic instability, using either full or sectional bridge models 12.11.4 Bridge deck configuration For the box section, plate girders and stiffened truss, the ratio of torsional to flexural frequencies should be greater than 12.12 Fatigue According to tests at Lehigh University, the fatigue life of the strand was defined as the number of cycles before the first wire broke and the loading range had more effect on the fatigue life than the magnitude of RECOMMENDATIONS FOR CABLE-ST.'\ YEO BRIDGES 457 maximum, minimum or mean loads Tentative conclusions for the fatigue characteristics of cables may be summarized as follows: (1) Strand diameter, wire size and grade have little effect upon the fatigue life (2) The fatigue limit should be expressed in terms of the load range, as a percentage of breaking strength (3) For a given load range, expressed as a percentage of breaking strength, the fatigue life increases with the number of wires in the strand (4) Zinc-cast end fittings lower fatigue life while swaged fittings can enhance the fatigue resistance of the strand (5) A fatigue limit expressed in terms ofload range indicates 15-30% of the breaking strength of the strand (6) A rapid increase in temperature of the strand can be noted at about 90% of the fatigue life under constant cyclic loading 12.13 Fabrication Fabrication includes manufacturing operations such as prestretching, measuring, cutting, socketing, and proofloading of end fittings 12.14 12.14.1 Erection Erection plans and calculations If no procedure for erection of the bridge is specified in the contract documents, the contractor should submit his proposed erection method to the design engineer for consideration with detailed geometry and stress computations 12.14.2 Erection devices and falsework Temporary bracing, stiffeners and falsework should be provided whenever required by erection procedures 12.14.3 Adequaq oftemporary connections and supports The above materials should be adequate as erection progresses 458 12.14.4 C: \BLE-STAYED BRIDGES Erection stresses Erection loads should include wind and erection equipment and stresses from the application of construction loads during erection should not exceed the allowable stresses 12.14.5 Cable installation Precautions should be taken during erection to avoid damaging the cables and their coating 12.14.6 Stay tension adjustment Provision should be made at the socket anchorages for cable length adjustment 12.15 12.15.1 Inspection General Material and workmanship should be subject at all times to inspection by the engineer 12.15.2 Co-operation Inspection should be made at the place of manufacture, fabrication, or erection, and the fabricator or contractor should co-operate with inspection personnel 12.15.3 Samples Samples of material for the cables may be requested by the engineer for separate testing 12.15.4 Limitations Inspection of cables should include additional testing to meet the needs for bridge construction RECO:\l'.IEI'\D\TIOI'\S FOR C>\BLE-ST:\YED BRIDGES 12.15.5 459 Records Records of physical and chemical properties of materials and test results on samples should be maintained 12.15.6 Field impection ofmaterials Inspection of cable material is advisable as it is removed from the reel and at the various stages of field fabrication and erection 12.15.7 Installation The inspector should determine that cables are installed with striping in the proper relative position 12.15.8 Perfimnance tests Performance tests under a simulated loading may be required which may be used to verify the performance or adequacy of the cables or other structural members under design loads References The American Society of Civil Engineers, 'Tentative Recommendations for Cable-Stayed Bridge Structures', ASCE J Struct Div., Proc., 103, No ST 5, 929-939, May, 1977 The American Society of Civil Engineers, 'Commentary on the Tentative Recommendations for Cable-Stayed Bridge Structures,' ASCEJ Struct Div., Proc., 103, No ST 5, 941-959, May, 1977 Author Index Advisory Board of the lnwstigation of Suspension Bridges, 447 '\lexander, A.J, 44R American Association of the State and Transportation Officials, 450 American Institute of Steel Construction, 40 American Iron and Steel Institute, 79 American Railway Engineering '\ssociation, 450 t\merican Society f(Jr Testing and 1\laterials, 180, 181, 367, 381 American Society of Civil Engineers, 450 Andra, W., 173, 222 Angelopoulos, T., 230 Argyris, J I 1., 230 Arnodin, F.J., 14 Aschenherg, I 1., 110 Bacchettal, A., 145 Bachelart, I 1., 173 Bakel, J F., 364, 40I Balhachevsky, G N., Ill Barges, J F., 403 Baumer, I 1., 109 13eaujoint, l\., 370, 402 Beggs, G E., 364, 401 13ell, R D., 173 Benkhorst, ]., 112 Beresford, F D., 173 13eyer, E., 108, 109, 110, 221, 272, 402, 403 Biggs, J ;vi., 229, 230 Birdsall, B., 401 13irnstiel, C., 227, 230 13leich, F., 411, 431, 432, 433, 447, 448 Boue, P., 109 13ragin, A.\'., 272 13reen, J E., 36 7, 402 13ridges, C P., 145 Brodin, S., 109 Brown, C D., 108, 222, 402 Brotton, D J\l., 227, 230, 361 Buckingham, E., 370, 403 Casudo, C F., 173 Cauchy, A., 334 Chandler, D B., 230 Cheung, Y K., 323, 362 Christopher, B G., 154 Clark, E., 401 Clements, L., 109 Clive, T I 1., 40 Connor, J.J., 361 Coulter, C S., 145 Daniel, II., Ill Datalnik, A., 403 David, J D., 403 Davis, I I E., 401 Davis, R E., 401 Deason, P 1'\l., 109 Demers, J G., Ill Demers, T B., Ill Dischinger, F., 17, 18, 40 Donnelly, J A., 173 Dreher, W., 112 Drewry, C S., 39 Dunne, P E., 230 Egeseli, E '\., 228, 230 Ency, W J., 364, 401 Ernst, I I J., I 08, I 10, 222, 225 Erunm, B G., 272 Esslinger, 1\1., 362 Fairbairn, W., 364 Falk, S., 297, 361, 362 Farquharson, F B., 438, 448 Faustus \' crantius, Feige, A., 222, 272, 402 Ferjencik, P., 113 Fialho, J F L., 402 Finsterwalder, U., 146 Fischer, G., 108, 363 Fleming, J F., 40, 228, 230 Forge, A., Ill Foster, D C., 367, 402 Frandsen, '\.G., 447 AUTHOR Il\DEX Fraser, R A., 438, 448 Freudenberg, G., 109, 110 Fuchs, D., 173 Fuchs, W., 109 Gandil, Ill Gee, A F., 144, 145, 146, 173 Gere, J M., 276, 361, 362 Gerold, W., 112 Gilbert, R., 448 Gimsing, N.J., 31, 32, 41, 240,272 Gisclard, A V., 14, 17, 40 Golub, II., 154 Gottschalk, 0., 64, 40 I Goschy, 13., 329, 362, 416, 421, 447 Graham, I I J., 146 Grant, A., 145 Hadley, I I !\1., 144 I Iagg, G., 113 I Iajdin, N., 112 Hass, B., I 10 I Iatley, T., Haupt, \\'., 23, 40, 70, 110 I Iavemann, I I K., II I Ieeb, A., I I2 Hess, I 1., 108, 363 Hohne, K.]., 109 Homberg, II., 36, 41, 109, 239,403 Homann, II., 109 Hooke, R., 223, 251 Hopper, C.]., 449 llossdorf, II., 402 Jeffer, R., 144 je\tovic, L.]., 112 Jolm