Holger Svensson CABLE-STAYED BRIDGES 40 Years of Experience Worldwide Holger Svensson CABLE-STAYED BRIDGES 40 Years of Experience Worldwide Prof. Dipl.-Ing. Holger Svensson Consulting Engineer Niederlausitzstraße 22 15738 Zeuthen Germany [email protected]
Translated by: Prof. Dipl.-Ing. Holger Svensson, Zeuthen, Germany Prof. Dr. Guido Morgenthal, Weimar, Germany (sections on dynamics) Review and Improvement: Paul Beverley, U.K.
Cover: Helgeland Bridge over Leirfjord, Sandnessjøen, Norway © Helga Rutzen, Düsseldorf, Germany
© 2012 Wilhelm Ernst & Sohn, Verlag für Architektur Library of Congress Card No.: applied for und technische Wissenschaften GmbH & Co. KG, Rotherstr. 21, 10245 Berlin, Germany British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.
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Introduction
Cable-stayed bridges are currently in a fast development, worldwide. have been designed in accordance with various codes, including DIN, While in 1986 about 150 major cable-stayed bridges were known, Eurocode, AASHTO, British Standard and others. The governing their number has increased to more than 1000 today. Their spans factor for the designs are ultimately the laws of nature which are have also increased by leaps. From 1975, when the span record was identical worldwide. 404 m, it jumped to 856 m in 1995 and today has reached 1104 m. A The selection of the cable-stayed bridges highlighted here is quite span limit is not yet in sight, and there are already designs for cable- subjective and consists of: stayed bridges with main spans up to 1800 m. As the economic range –– bridges in which the author participated or in which at least for suspension bridges is limited for very long spans, cable-stayed Leonhardt, Andrä and Partners (LAP) were involved, bridges are a focus of interest for bridge engineers worldwide. –– bridges with unusual structural details, and This book addresses experienced engineers as well as students. It –– bridges with record spans. has been developed from the scripts of the ‘Lectures on cable-stayed In general only completed bridges are treated. The discussion of pro- bridges’, which have been given by the author at the University of posals, as interesting as they may be, would go beyond the scope of Dresden for the 7th and 8th semester for bridge engineering students this book. since 2009. The book contains nearly 1300 figures, mainly in color, in accord- It aims to cover all aspects of the design, construction planning ance with the conviction of the author that a good picture is more and execution on site, dealing with principles that appear important meaningful than any description. This is especially true for the ap- to the author, based on his 40-year experience as a bridge engineer. pearance and for the construction. Additional details are given in the nearly 350 references. The author has named the engineers involved in as many bridges Key aspects of the book are: as possible. This should help to improve the public standing of engin- –– the historical development from precursors up to the present day, eers which is otherwise often neglected. The responsible engineers –– the structural details of beams, towers and especially the stay are also recognized as authors of the given references. A bridge is, of cables which are a crucial component of cable-stayed bridges, course, never the work of an individual – a whole design team is re- –– the preliminary design of cable-stayed bridges which provides the quired, which works in mutual trust with the engineers of the client best understanding of the flow of forces and permits initial sizing and with the engineers on site in order to successfully complete a and independent checking of a design, and bridge project. –– the erection of cable-stayed bridges, which is equally as important At the end of the book two DVDs are included, which record the as their final stage. 30 lectures that the author gives at Dresden University. With the exception of the cable sizing, codes are consciously not referred to. The investigated bridges are from all over the world and Holger Svensson, Zeuthen, 2012
Cable-Stayed Bridges. 40 Years of Experience Worldwide. First Edition. Holger Svensson. © 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG. 6 7
Acknowledgement
The author is grateful to the University of Dresden for the oppor (Freyssinet, France), Dr. Christian Braun (Maurer, Germany), tunity to hold lectures on cable-stayed bridges subsequently to his Dr. Marcel Poser (BBR, Switzerland), Mr Friedhelm Rentmeister active work, initially arranged by Professor Dr.-Ing. Jürgen Stritzke. (Bridon, UK) and Dr. Yoshito Tanaka (Shinko, Japan). The other The continuing support by Professor Dr.-Ing. Manfred Curbach, material used, especially drawings and photographies, originates Head of the Institute for Concrete Structures, and by Professor from the archives of the author and LAP. Dr.-Ing. Richard Stroetmann, Head of the Institute for Steel and Special thanks go to the author’s long-term colleagues and friends Timber Structures, as well as Dipl.-Ing. Peter Deepe and Dr.-Ing. Dr.-Ing. Imre Kovacs for the preparation of the sections on dynam- Uwe Reuter for the preparation of the video records of the lectures is ics and Dr.-Ing. E. h. Dipl.-Ing. Reiner Saul for the section on cable highly appreciated. sizing. The author is indebted to the following colleagues who generous- The publishers Wilhelm Ernst & Sohn and Wiley-Blackwell pro- ly provided him with information: Dr. Charles Birnstiel, USA, on the vided helpful support through the editor, Dipl.-Ing. Claudia Ozimek, Nienburg Bridge, M. Jacques Combault on the Rion-Antirion Bridge, supported by Ms. Sophie Bleifuß for the layout and Ms. Uta-Beate M. Jean-Marie Crémer on the Ben Ahin and Millau Bridges, Profes- Mutz for preparing the print. sor Dr. Guido Morgenthal on the Stonecutters and Sutong Bridges, The author translated the book into English himself with the ex- Dr.-Ing. Herbert Schambeck on the Metten and Flößer Bridges, ception of the sections on dynamics, which were done by Professor Dr.-Ing. Klaus Stiglat on early cable-stayed bridges in France and Dr. Guido Morgenthal. The translation was reviewed and improved M. Michel Virlogeux on the Normandy Bridge. Information on stay by Mr Paul Beverley, UK. The complete German and English text cables was provided by Dipl.-Ing. Werner Brand (DYWIDAG-Sys- was typed by Ms. Eva Gassmann and all graphics and their conver- tems International, Germany), Mr W. S. Cheung (Cabletek, South- sion into English was done by Ms. Mirela Beutel-Anistoroaiei; to all Korea), Dr. Hans Rudolf Ganz (VSL, Switzerland), M. Erik Mellier these the author is grateful for their indispensable skill and patience.
Cable-Stayed Bridges. 40 Years of Experience Worldwide. First Edition. Holger Svensson. © 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG.
9
The Author
Holger Svensson has extensive experience in the design, construc- tion engineering and on-site supervision of cable-stayed and other long-span bridges all over the world. In Germany he was involved in the checking of the Kocher Valley Bridge and the detailed design of the cable-stayed Flehe Bridge. In the USA he designed several cable-stayed bridges: Pasco- Kennewick (concrete), East Huntington (concrete), Sunshine Skyway (composite alternate), Burlington (composite) and the Houston Ship Channel Crossing at Baytown (composite). In Norway he was in charge of the design for the Helgeland Bridge and in Scotland he advised on the design of the Leven River Bridge, both concrete cable-stayed bridges. In Sweden he was checking engineer for the Höga Kusten suspen- sion bridge (main span 1210 m) and the Sunningesund and Ume Älv Prof. Dipl.-Ing. Holger Svensson composite cable-stayed bridges. P E, C Eng, FI Struct E, In Australia he advised on the design of the cable-stayed Glebe born 1945 near Hamburg, Germany Island concrete bridge in Sidney and on the My Tuan Bridge in 1969 Dipl.-Ing., Stuttgart University Vietnam for AusAID. 2009 – 2011 Lecturer and For the Asian Development Bank he reviewed the design and since 2012 Professor for cable- stayed bridges at the University construction of the record-breaking cable-stayed composite Yang Pu of Dresden, Germany Bridge (main span 602 m) in Shanghai, China. In Hong Kong he advised on the design and construction of the 1970 – 1971 Contractor Grinaker in South Africa and Botswana Kap Shui Mun Bridge to Lantau Airport. 1972 – 2009 Leonhardt, Andrä and He was also responsible for the design of several major girder and Partners, Consulting Engineers arch bridges in Germany and elsewhere. Design and checking of major, mainly cable-stayed bridges 1992 – 2009 Executive Director Registrations 1998 – 2008 Speaker of the Current: Member of the Chamber of Engineers in Berlin, Germany; Executive Board 2009 Chairman of the Board PE in the USA; CEng, FIStructE in Great Britain. Since 2010 Independent Consulting Formerly: MSAICE in South Africa; PEng in Canada; MHKIE in Engineer Hong Kong, China; RPEQ in Australia; TPEng. in Malaysia. Memberships 2003 to 2011 Vice-President of IABSE. Member of the Bridge Advisory Board of the German Railways. Member of the Jury for the German Bridge Prize. Member of the Jury for the German Structural Engineering Prize. Member of the German Convent for Building Culture. Publications More than 100 publications and 180 verbal presentations. Author of the book ‘Cable-Stayed Bridges – 40 Years of Experience Worldwide’, German Edition by Ernst & Sohn 2011, English Edition by Wiley-Blackwell 2012. Honours 1999 James Watt Medal, Institution of Civil Engineers, London. 2000 Henry Husband Prize, Institution of Structural Engineers, London. 2011 Emil Mörsch Commemoration Medal, German Concrete Society.
Cable-Stayed Bridges. 40 Years of Experience Worldwide. First Edition. Holger Svensson. © 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG. 10 11
Table of contents
1 Introduction ...... 16 2 The development of cable-stayed bridges ...... 46 1.1 Design fundamentals ...... 17 2.1 The precursors of cable-stayed bridges ...... 47 1.1.1 General ...... 17 2.1.1 Introduction ...... 47 1.1.2 Overall system ...... 19 2.1.2 Historical development ...... 47 1.1.2.1 Cable arrangement ...... 19 2.1.2.1 Historical designs ...... 47 1.1.2.2 Cable stiffness ...... 20 2.1.2.2 First examples and failures ...... 48 1.1.2.3 Geometry ...... 21 2.1.2.3 John Roebling and stiffened suspension bridges ...... 51 1.1.2.4 Support conditions ...... 21 2.1.2.4 Transporter bridges ...... 52 1.1.3 Tower shapes ...... 23 2.1.2.5 Approaching the modern form ...... 55 1.1.3.1 Two outer cable planes ...... 23 1.1.3.2 One central cable plane ...... 23 2.2 Steel cable-stayed bridges ...... 58 1.1.3.3 Spread central cable planes ...... 24 2.2.1 Introduction ...... 58 1.1.4 Beam cross-sections ...... 24 2.2.2 Beginnings ...... 58 1.1.4.1 Steel cross-sections ...... 24 2.2.3 The Düsseldorf Bridge Family ...... 59 1.1.4.2 Concrete cross-sections ...... 25 2.2.4 Further Rhine river bridges ...... 62 1.1.4.3 Composite cross-sections ...... 25 2.2.5 Special steel cable-stayed bridges ...... 70 1.1.4.4 Hybrid beams (steel/concrete) ...... 26 2.2.6 Cable-stayed bridges with record spans ...... 76 1.1.4.5 Double deck cross-section ...... 26 1.1.5 Stay cables ...... 26 2.3 Concrete cable-stayed bridges ...... 80 1.1.5.1 Systems ...... 26 2.3.1 General ...... 80 1.1.5.2 Cable anchorages ...... 26 2.3.2 Development of concrete cable-stayed bridges ...... 81 2.3.3 Bridges with concrete stays ...... 92 1.2 Aesthetic guidelines for bridge design ...... 30 2.3.3.1 Riccardo Morandi’s bridges ...... 92 1.2.1 Introduction ...... 30 2.3.3.2 Later examples ...... 92 1.2.2 Aesthetic guidelines ...... 30 2.3.3.3 Bridges with concrete walls ...... 94 1.2.2.1 Guideline 1: Clear structural system ...... 30 2.3.4 Cable-stayed bridges with thin concrete beams ...... 94 1.2.2.2 Guideline 2: Good proportions ...... 31 2.3.5 Record spans ...... 98 1.2.2.3 Guideline 3: Good order ...... 33 1.2.2.4 Guideline 4: Integration into the environment ...... 34 2.4 Composite cable-stayed bridges ...... 101 1.2.2.5 Guideline 5: Choice of material ...... 35 2.4.1 General ...... 101 1.2.2.6 Guideline 6: Coloring ...... 36 2.4.2 Cross-sections ...... 101 1.2.2.7 Guideline 7: Space above the bridge ...... 38 2.4.3 Special details ...... 104 1.2.2.8 Guideline 8: Recognizable flow of forces ...... 38 2.4.4 Economic span lengths ...... 104 1.2.2.9 Guideline 9: Lighting ...... 41 2.4.5 Beginnings ...... 105 1.2.2.10 Guideline 10: Simplicity ...... 41 2.4.6 Record spans ...... 105 1.2.3 Collaboration ...... 42 2.4.7 Latest examples ...... 111
2.5 Special systems of cable-stayed bridges ...... 118 2.5.1 Series of cable-stayed bridges ...... 118 2.5.1.1 Load transfer ...... 118 2.5.1.2 Intermediate piers ...... 118 2.5.1.3 Stiff towers ...... 118 2.5.1.4 Stayed towers ...... 118 2.5.1.5 Frames ...... 121 2.5.1.6 Accommodation of longitudinal deformations ...... 121 2.5.1.7 Examples ...... 123 2.5.2 Stayed beams ...... 130 2.5.2.1 Stayed from underneath ...... 130 2.5.2.2 Stayed from above (extradosed) ...... 130 2.5.3 Cable-stayed pedestrian bridges ...... 133 Cable-Stayed Bridges. 40 Years of Experience Worldwide. First Edition. Holger Svensson. © 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG. 12 Table of contents
3 Stay cables ...... 140 3.7 Cable sizing ...... 160 3.1 General ...... 141 3.7.1 General ...... 160 3.7.2 Sizing by permissible stresses ...... 160 3.2 Locked coil ropes ...... 141 3.7.2.1 Permissible stresses for static loads ...... 160 3.2.1 System ...... 141 3.7.2.2 Permissible fatigue range ...... 160 3.2.2 Fabrication ...... 142 3.7.2.3 Permissible stresses during cable exchange ...... 161 3.2.3 Modern corrosion protection systems ...... 142 3.7.3 Sizing in ultimate limit state ...... 161 3.2.3.1 General ...... 142 3.7.3.1 Ultimate limit state ...... 161 3.2.3.2 Galvanizing of the wires ...... 142 3.7.3.2 Fatigue ...... 161 3.2.3.3 Filling ...... 142 3.7.3.3 Cable exchange ...... 162 3.2.3.4 Paint ...... 143 3.7.3.4 Service limit state ...... 162 3.2.4 Inspection and maintenance ...... 143 3.7.4 Summary ...... 162 3.2.5 Damage ...... 143 3.2.5.1 Köhlbrand Bridge ...... 143 3.8 Cable dynamics ...... 163 3.2.5.2 Maracaibo Bridge, Venezuela ...... 145 3.8.1 General ...... 163 3.2.5.3 Flehe Rhine River Bridge ...... 146 3.8.2 Fundamental parameters ...... 164 3.2.5.4 Lessons from the damage ...... 146 3.8.2.1 Static wind load ...... 164 3.8.2.2 Natural frequencies ...... 165 3.3 Parallel bar cables ...... 146 3.8.3 Dynamic excitation ...... 165 3.8.3.1 Galloping oscillations ...... 165 3.4 Parallel wire cables ...... 147 3.8.3.2 Anchorage excitation ...... 166 3.4.1 System ...... 147 3.8.3.3 Parametric resonance ...... 168 3.4.2 Corrosion protection ...... 148 3.8.3.4 Buffeting ...... 168 3.4.2.1 Polyethylene (PE) pipes ...... 148 3.8.3.5 Vortex-induced vibrations ...... 169 3.4.2.2 Wrappings ...... 150 3.8.4 Countermeasures ...... 169 3.4.2.3 Grouting ...... 150 3.8.4.1 Dampers ...... 169 3.4.2.4 Damage ...... 151 3.8.4.2 Surface profiling ...... 174 3.4.2.5 Petroleum wax ...... 151 3.8.4.3 Cross ties ...... 174 3.4.3 Fabrication ...... 152 3.9 Cable installation ...... 175 3.5 Parallel strand cables ...... 153 3.9.1 General ...... 175 3.5.1 General ...... 153 3.9.2 Locked coil ropes ...... 175 3.5.2 System ...... 153 3.9.2.1 General ...... 175 3.5.3 Corrosion protection ...... 153 3.9.2.2 Example ...... 175 3.5.3.1 Traditional ...... 153 3.9.3 Parallel wire cables ...... 178 3.5.3.2 With dry air ...... 153 3.9.3.1 General ...... 178 3.5.4 Fabrication ...... 154 3.9.3.2 Example ...... 178 3.5.5 Durability tests ...... 154 3.9.4 Parallel strand cables ...... 179 3.5.5.1 Tensile strength and fatigue strength ...... 154 3.9.4.1 General ...... 179 3.5.5.2 Water tightness ...... 154 3.9.4.2 Example ...... 179 3.5.5.3 Sustainability ...... 154 3.9.5 Cable calculations ...... 184 3.5.6 Monitoring ...... 154 3.9.5.1 Cable deformations ...... 184 3.9.5.2 Measuring of cable forces ...... 184 3.6 Cable anchorages ...... 156 3.6.1 General ...... 156 3.6.2 Support of anchor heads ...... 156 3.6.3 Anchorage at the tower ...... 158 3.6.3.1 Continuous ...... 158 3.6.3.2 Composite cable anchorages at tower head ...... 158 3.6.3.3 Cable anchorage in concrete ...... 158 Table of contents 13
4 Preliminary design of cable-stayed bridges ...... 186 4.4 Protection of bridges against ship 4.1 Action forces for equivalent systems ...... 187 collision ...... 248 4.1.1 General ...... 187 4.4.1 Introduction ...... 248 4.1.2 System geometry ...... 187 4.4.2 Collision forces ...... 248 4.1.3 Normal forces of articulated system ...... 188 4.4.3 Protective structures ...... 252 4.1.4 Live loads on elastic foundation ...... 189 4.4.3.1 General ...... 252 4.1.4.1 Beam on elastic foundation ...... 189 4.4.3.2 Out of reach ...... 252 4.1.4.2 Buckling – non-linear theory ...... 190 4.4.3.3 Artificial islands ...... 253 4.1.5 Permanent loads on rigid supports ...... 192 4.4.3.4 Guide structures ...... 253 4.1.5.1 Dead load ...... 192 4.4.3.5 Independent protective structures ...... 258 4.1.5.2 Post-tensioning ...... 193 4.4.3.6 Strong piers ...... 261 4.1.5.3 Shrinkage and creep ...... 193 4.1.6 Towers ...... 195 4.5 Preliminary design calculations ...... 266 4.1.6.1 In the longitudinal direction ...... 195 4.5.1 General ...... 266 4.1.6.2 In the transverse direction ...... 195 4.5.2 Typical cable-stayed concrete bridge ...... 266 4.1.7 Stay cables ...... 197 4.5.2.1 System and loads ...... 266 4.5.2.2 Normal forces for articulated system ...... 267 4.2 Action forces of actual systems ...... 197 4.5.2.3 Bending moments ...... 269 4.2.1 Permanent loads ...... 197 4.5.3 Typical cable-stayed steel bridge ...... 270 4.2.1.1 General ...... 197 4.5.3.1 General ...... 270 4.2.1.2 Concrete bridges ...... 198 4.5.3.2 System ...... 270 4.2.1.3 Steel bridges ...... 199 4.5.3.3 Section properties and loads ...... 270 4.2.1.4 Towers ...... 202 4.5.3.4 Beam moments from live load ...... 270 4.2.2 Live loads ...... 202 4.5.3.5 Permissible beam moments ...... 271 4.2.3 Kern point moments ...... 204 4.5.3.6 Moments from dead load for articulated system ...... 271 4.2.4 Non-linear theory (second order theory) ...... 206 4.5.4 Cable-stayed bridge with side spans on piers ...... 272 4.2.5 Superposition ...... 208 4.5.4.1 System and loads ...... 272 4.2.6 Temperature ...... 208 4.5.4.2 Cable forces of articulated system ...... 273 4.2.7 Eigenfrequencies ...... 210 4.5.4.3 Bending moments for beam ...... 274 4.5.5 Cable-stayed bridge with harp arrangement ...... 275 4.3 Bridge dynamics ...... 211 4.5.5.1 With regular side spans ...... 275 4.3.1 General ...... 211 4.5.5.2 With side spans on piers ...... 276 4.3.2 Overview of wind effects ...... 213 4.5.6 Cable-stayed bridge with longitudinal A-tower ...... 276 4.3.3 Wind profile, turbulence and turbulence-induced 4.5.6.1 System and loads ...... 277 oscillations ...... 214 4.5.6.2 Normal forces for articulated system ...... 277 4.3.3.1 Wind parameters ...... 214 4.5.6.3 Cable sizing ...... 278 4.3.3.2 Natural modes of vibration of structures ...... 216 4.5.6.4 Bending moments for beam ...... 278 4.3.3.3 Section forces under turbulent excitation ...... 218 4.5.6.5 Post-tensioning ...... 278 4.3.4 Vortex-induced vibrations ...... 222 4.5.7 Slender cable-stayed concrete bridge ...... 279 4.3.5 Self-excitation and other motion-induced effects ...... 224 4.5.7.1 System and loads ...... 279 4.3.5.1 General description, background ...... 224 4.5.7.2 Stay cables ...... 280 4.3.5.2 Practical examples of bending-type galloping ...... 226 4.5.7.3 Beam moments ...... 283 4.3.5.3 Practical examples of torsional galloping ...... 228 4.5.7.4 Aerodynamic stability ...... 286 4.3.5.4 Flutter ...... 232 4.5.7.5 Towers ...... 287 4.3.6 Damping measures ...... 236 4.3.7 Wind tunnel testing ...... 240 4.3.7.1 General ...... 240 4.3.7.2 Overview of important types of wind tunnel testing ...... 240 4.3.8 Earthquake ...... 244 14 Table of contents
5 Construction of cable-stayed bridges ...... 290 6 Examples for typical cable-stayed bridges ...... 326 5.1 Examples ...... 291 6.1 Cable-stayed concrete bridges with 5.1.1 General ...... 291 precast beams ...... 327 5.1.2 Tower construction ...... 291 6.1.1 General ...... 327 5.1.2.1 Steel towers ...... 291 6.1.2 Pasco-Kennewick Bridge ...... 327 5.1.2.2 Concrete towers ...... 291 6.1.2.1 General layout ...... 327 5.1.2.3 Composite towers ...... 291 6.1.2.2 Construction engineering ...... 332 5.1.3 Beam construction ...... 292 6.1.2.3 Completed bridge ...... 344 5.1.3.1 General ...... 292 6.1.3 East Huntington Bridge ...... 346 5.1.3.2 Concrete beam ...... 293 6.1.3.1 General design considerations ...... 346 Free cantilevering ...... 293 6.1.3.2 Construction ...... 346 Launching ...... 299 6.1.3.3 Completed bridge ...... 349 Rotating ...... 299 Rotating on scaffolding ...... 302 6.2 CIP concrete cable-stayed bridge 5.1.3.3 Steel beams ...... 304 Helgeland Bridge ...... 352 Free cantilevering ...... 304 6.2.1 General layout ...... 352 Launching ...... 304 6.2.1.1 Introduction ...... 352 Transverse shifting ...... 305 6.2.1.2 Bridge system ...... 353 5.1.3.4 Composite beam ...... 305 6.2.2 Construction ...... 358 Free cantilevering ...... 305 6.2.2.1 Climate ...... 358 Launching ...... 309 6.2.2.2 Towers ...... 358 6.2.2.3 Beam ...... 360 5.2 Construction engineering ...... 312 6.2.2.4 Stay cables ...... 362 5.2.1 General ...... 312 6.2.2.5 Instrumentation ...... 366 5.2.2 Construction engineering by dismantling ...... 312 6.2.2.6 Completed bridge ...... 367 5.2.2.1 General ...... 312 6.2.3 Summary ...... 367 5.2.2.2 Dismantling from t = ∞ to t = 1 ...... 313 5.2.2.3 Dismantling of bridge ...... 313 6.3 Cable-stayed steel bridge With floating crane ...... 313 Strelasund Crossing ...... 369 Dismantling with derrick ...... 314 6.3.1 Design considerations ...... 369 5.2.2.4 Aerodynamic stability ...... 315 6.3.1.1 Bridge alternates ...... 369 5.2.3 Example for construction engineering ...... 316 6.3.1.2 Optimizing the cable-stayed solution ...... 371 5.2.3.1 Forward construction ...... 316 6.3.1.3 Structural details ...... 371 5.2.3.2 Construction engineering ...... 316 6.3.2 The cable-stayed bridge ...... 371 5.2.3.3 Construction manual ...... 316 6.3.2.1 Span lengths ...... 371 5.2.3.4 Control measurements ...... 316 6.3.2.2 Beam cross-section ...... 371 5.2.4 Design of auxiliary stays ...... 320 6.3.2.3 Wind barriers ...... 372 5.2.4.1 Symmetrical auxiliary stays for towers ...... 320 6.3.2.4 Tower ...... 372 5.2.4.2 One-sided auxiliary stays for towers ...... 321 6.3.2.5 Stay cables ...... 373 5.2.4.3 Auxiliary stays for beam ...... 321 6.3.2.6 Aerodynamic investigation ...... 373 5.2.4.4 Without auxiliary stays for beam ...... 321 6.3.3 Construction ...... 375 5.2.5 Auxiliary tie-backs for travelers ...... 323 6.3.3.1 Construction engineering ...... 375 6.3.3.2 Construction of the main bridge ...... 376 6.3.3.3 Completed bridge ...... 386 Table of contents 15
6.4 Composite cable-stayed bridge Index ...... 428 Baytown Bridge ...... 387 Bridge Index ...... 428 6.4.1 General layout ...... 387 References ...... 431 6.4.1.1 Bridge system ...... 387 Figure Origins ...... 439 6.4.1.2 Composite beam ...... 388 List of Advertisers ...... 441 6.4.1.3 Towers ...... 390 6.4.1.4 Stay cables ...... 390 Appendix: 40 years of experience with major bridges 6.4.1.5 Aerodynamic stability ...... 391 all over the world ...... 443 6.4.2 Construction ...... 391 Beginnings ...... 443 6.4.2.1 Foundations ...... 391 Bridges in Germany ...... 443 6.4.2.2 Towers ...... 391 Cable-stayed bridges abroad ...... 445 6.4.2.3 Beam ...... 392 New developments by competition ...... 446 6.4.2.4 Stay cables ...... 398 Checking of bridges ...... 449 6.4.2.5 Completed bridge ...... 398 Participation in Code Commissions ...... 452 6.4.3 Summary ...... 401 Current projects ...... 452 Summary ...... 453 6.5 Hybrid cable-stayed bridge References ...... 454 Normandy Bridge ...... 402 6.5.1 Design considerations ...... 402 6.5.1.1 Structural design ...... 402 6.5.1.2 Cable dynamics ...... 404 6.5.2 Construction ...... 404 6.5.2.1 Tower ...... 404 6.5.2.2 Concrete approach bridges ...... 406 6.5.2.3 Steel main span ...... 408 6.5.2.4 Cable installation ...... 408 6.5.2.5 Completed bridge ...... 410
6.6 Series of cable-stayed bridges ...... 411 6.6.1 Millau Bridge ...... 411 6.6.1.1 General ...... 411 6.6.1.2 Design ...... 412 6.6.1.3 Construction ...... 412 6.6.1.4 Completed bridge ...... 416 6.6.2 Rion-Antirion Bridge ...... 418 6.6.2.1 General ...... 418 6.6.2.2 Design ...... 418 6.6.2.3 Construction ...... 421 6.6.2.4 Completed bridge ...... 425
7 Future development ...... 426 Costs per m2
1 Introduction
Center span
Cable-Stayed Bridges. 40 Years of Experience Worldwide. First Edition. Holger Svensson. © 2012 Ernst & Sohn GmbH & Co. KG. Published 2012 by Ernst & Sohn GmbH & Co. KG. 1.1 Design fundamentals 17
Figure 1.1 (left side above) Relation between construction costs per m2 and main span length
1.1 Design fundamentals Girder Bridge Cable-Stayed Bridge 1.1.1 General The position of cable-stayed bridges within all bridge systems is given in Fig. 1.1. Their spans range between continuous girders and arch bridges with shorter spans at one end, and suspension bridges Moment with longer spans at the other. Influence Line The economic main span range of cable-stayed bridges thus lies between 100 m with one tower and 1100 m with two towers. What are the special advantages of cable-stayed bridges? First of all the bending moments are greatly reduced by the load Run of transfer of the stay cables, Fig. 1.2. By installing the stay cables with Moments their predetermined precise lengths the support conditions for a beam rigidly supported at the cable anchor points can be achieved and thus the moments from permanent loads are minimized, Fig. 1.3. Even for live loads the bending moments of the beam elastically Figure 1.2 Comparison of beam moments supported by the stay cables remain small. Negative live load moments may occur over the vertical bearings at the towers. They can be avoided by supporting the beam by the stay cables only, including in the tower region. The biggest positive and negative moments occur in the side spans near the hold-down piers, which may require special measures. Shear forces remain small. Large compression forces in the beam are caused by the horizon- tal components of the inclined stay cables. The normal forces in the main and side span equal one another so that only uplift forces have to be anchored in the abutments which act as hold-down piers. The largest horizontal components belong to the backstay cables, Fig. 1.3. The beam compression forces thus increase quickly at the beam ends and increase less quickly near the towers where they reach a maximum. For concrete beams this compression force is beneficial. Only in the bridge center, where the compression forces from cables are small, is additional longitudinal post-tensioning re- quired, which also has to overcome tension from friction, braking, etc. The cross-section of steel beams requires only little additional material to cover the overall compression forces. A second important advantage of cable-stayed bridges is their Figure 1.3 Bending moments and compression forces in beams ease of construction, Fig. 1.4: of cable-stayed bridges – Arch bridges with large spans are not stable during erection until the arch is closed and the horizontal support forces are anchored. They have to be temporarily supported, e. g. by auxiliary piers or temporary tie-backs. – Self-anchored suspension bridges, which may be required when their horizontal cable component cannot economically be an- chored due to bad soil conditions, need temporary supports of their beams until the main cables are installed. – In cable-stayed bridges, however, the same flow of forces is present during free-cantilever construction stages as after com- pletion. This is true for free cantilevering to both sides of the tow- er as well as for free cantilevering the main span only.
The third main advantage lies in the fact that cable-stayed bridges Figure 1.4 Erection systems for arches, self-anchored suspension bridges are inherently stiffer than suspension bridges. This is especially true and cable-stayed bridges 18 1 Introduction
for longitudinally eccentric loads, for which the main cables of a sus- pension bridge find a new equilibrium without increase of cable stresses (stressless deformations), whereas stay cables always have to a) suspension bridge be additionally stressed in order to carry any load. Suspension bridges are thus generally not suitable for high rail- way loads: their deformations become too large. The eigenfrequencies of cable-stayed bridges are significantly higher than those of suspension bridges. The torsional frequencies, which are especially important for the aerodynamic safety against b) cable-stayed bridge flutter, can further be increased by using A-towers which omit the with Twin-towers elasticity of the backstay cables, Fig. 1.5. The critical wind speed for the onset of flutter is thus higher for cable-stayed bridges than for suspension bridges. The diagram in Fig. 1.6 shows that for a main span of 500 m the critical flutter wind c) cable-stayed bridge speed for a typical cable-stayed bridge is about 200 km/h while for a with A-towers corresponding suspension bridge it is only 100 km/h. These advantages of cable-stayed bridges have become generally Figure 1.5 Eigenmodes of suspension bridges and cable-stayed bridges known worldwide since the 1970s, and since that time their number has increased strongly, Table 1.1. The total number of major cable- stayed bridges worldwide has currently reached about 1000. The main span length of cable-stayed bridges has also increased dramatically, the longest currently being 1088 m, Fig. 1.7 [1.1]. Fritz Leonhardt and his collaborators have disseminated the above findings in lectures and publications all over the world since the 1970s, [1.2 – 1.9].
Figure 1.6 Critical wind speeds of suspension bridges and cable-stayed bridges Table 1.1 Number of cable-stayed bridges until 2000
Sutong Stonecutters 1900 – 1960 1970 1980 1990 2000 ∑ 1950 Japan 1 8 12 21 China 17 17 Germany 2 5 6 2 15 USA 2 7 4 13 Netherlands 2 1 2 5 Span Length [m] France 2 2 4 USSR 1 1 2 4 Great Britain 1 1 2 4
Year of Completion other 3 9 21 33 ∑ 0 2 5 18 29 62 116 Figure 1.7 Development of main span lengths of cable-stayed bridges 1.1 Design fundamentals 19
1.1.2 Overall system 1.1.2.1 Cable arrangement Cable-stayed bridges have at least one forestay and one backstay cable per tower. The forestays act like two piers omitted in the main span. The first cable-stayed bridge across the River Rhine in the 1950s used relatively few stay cables, which comprised bundles of locked coil ropes, so that the distances between the cable anchorages at the beam were 40 to 60 m. Their anchorages and corrosion protection were difficult, and auxiliary tie-backs were required to overcome the large distances between the cables during construction. The bridge designer, Hellmut Homberg (see Fig. 2.78), used many individual stay cables with distances of only 4.5 m for the Bonn Figure 1.8 Development to multi-stay cable bridges North Bridge, which simplified decisively the structural detailing and the construction, Fig. 1.8. This design was trendsetting for the further development of cable-stayed bridges. The number of stay cables is chosen advantageously in such way that for each stay only one cable is required so that the anchorages at the tower and at the beam become most simple. With cable capacities now up to 20 MN, even for very wide bridges the distances between the cable anchorages at the beam can be 5 to 15 m, and even up to 20 m. Such small cable distances allow free cantilevering to be used without the need for auxiliary tie-backs dur- ing construction. The reduction of cable distances at the beam over the years is shown in Fig. 1.9. There are three basic cable arrangements in bridge elevation. With the fan arrangement, Fig. 1.10, all cables join at the tower head. With the harp arrangement, Fig. 1.11, all cables run parallel and are Figure 1.9 Development of cable distances at the beam anchored over the height of the tower. The true fan arrangement can not be realized practically if the condition has been set that, in the case of damage, each individual cable must be able to be exchanged by reversing the installation procedure. This exchangeability re- quires individual cable anchorages to have certain minimum dis- tances at the tower head. Figure 1.10 Fan system In such way an intermediate cable arrangement between harp and fan is created, Fig. 1.12, which should be as close as possible to the fan arrangement due to its economical advantages. The harp ar- rangement, however, is aesthetically advantageous because there are no visual intersections of the stay cables, even for two cable planes in a skew view. The arrangement of stay cables is also influenced by the relation- ship between side span and main span, and the location of the back- Figure 1.11 Harp system stay anchorages, e. g. by connecting them directly above the piers in the side spans. The harmonic cable arrangement plays an important role in the aesthetic appearance of a cable-stayed bridge and has thus to be studied carefully from the very beginning of a design. In addition to the basic arrangements mentioned above special configurations have been used. The early South Elbe River Bridge used a star-shaped cable ar- rangement for which the few cables were separated at the towers in Figure 1.12 Intermediate system fan – harp 20 1 Introduction
order to simplify their anchorages, Fig. 1.13 [1.10]. Since the stays Figure 1.13 South Elbe River Bridge, star-shaped cable arrangement are still anchored together at the beam, this solution was not repeated. For open cross-sections with low torsional stiffness two outer cable planes are required to carry eccentric live loads by a force couple. Hellmut Homberg (see Fig. 2.78) used mainly steel box gird- ers for his designs. They have a high torsional rigidity and permit a central cable plane and also have a high bending stiffness so that a Figure 1.14 Bonn North Bridge, Homberg’s window beam supported at the towers allows the removal of the first cables at both sides of the towers to some greater distance. This arrangement is called “Homberg’s window”, Fig. 1.14. The high negative bending moments above the tower piers can be carried by the box girder. This transfer of loads near the towers via shear and bending directly into the foundations is more economic than supporting the beam only by the cables. The Rhine River Bridge at Ilverich is located in the vicinity of Düsseldorf airport. The normally required tower height of 110 m could thus not be realized because of air traffic safety requirements. Figure 1.15 Rhine River Bridge at Ilverich, shortened towers In order to avoid cables at too uneconomically flat an angle, each tower was split into two V-shaped legs and the backstay and forestay cable forces are carried by a tie, Fig. 1.15 [1.12].
1.1.2.2 Cable stiffness The stiffness of cable-stayed bridges is governed by the stiffness of the stay cables, which is reduced by the cable sag, as given in the for- Sag mula (1-1) by Ernst [1.13] (Fig. 1.16): As E 0 As Eeff = (1-1) γ 2 l 2 E 1 + k 0 12 σ 3
As Cable Steel Area E0 Modulus of Elasticity for straight Cables Figure 1.16 Effective stiffness of stay cables Eeff E-Modulus of Cable with Sag γ Specific Weight of Cable including Corrosion Protection lk Horizontal Length of Cable σ Tensile Stress in Cable ] It gives the effective modulus of elasticity of a stay cable in relation 2 to a straight vertical cable E0, the specific weight of the cable γ, the horizontal projection of length lk, and the steel stress σ. The steel ]
stress is of major importance and occurs in the formula as the third 2 power, Fig. 1.16. The influence of the various parameters on the cable stiffness is shown in Fig. 1.17. In order to achieve a high cable stiffness, a high cable stress is re- quired. Therefore, high-strength steel as developed for prestressing Steel Stresses [N/mm tendons has to be used. The high dead weight of a concrete beam is Effective Stiffness of Cable [MN/mm advantageous in this respect. Assuming strands with a steel of 1660/1860 N/mm2 and assuming a factor of safety for the ultimate limit state of 2.2, a service load stress of 845 N/mm2 is reached. Assuming further a ratio of live load to dead load of 0.2, a cable stress Horizontal Cable Length [m] 2 of about 680 N/mm can be used for the permanent load stage which Figure 1.17 Relation between EEffective of cables, span lengths and governs the deflections of a cable-stayed bridge. steel stress 1.1 Design fundamentals 21
Fig. 1.17 shows that for such steel stresses the loss of cable stiffness is small.
1.1.2.3 Geometry Main spans In a first approximation the length of a side span comes to about 40 % of the main span for a concrete beam under road traffic loads. For a steel beam with railway loading this ratio may be reduced to 30 %. The governing factor for the span ratio is the stress in the back- stay cables. For the cable size required for the biggest backstay force with live load in the main span, the fatigue stress range for live load in the main and side span should not exceed the permissible range of, for example, 200 N/mm2, Fig. 1.18.
Tower heights High towers reduce the required amount of cable steel and the com- pression forces in the bridge beam up to a cable inclination of 45°, but increase the costs for the towers themselves. Figure 1.18 Relation between span ratios and backstay steel stresses Optimizations indicate that tower heights of about 1/5 of the main span above deck achieve minimum costs for the whole bridge, Fig. 1.19.
Stiff towers If the geometrical conditions require two equal spans with only one tower at the center, the tower height should be chosen so that the flattest cables have the usual inclination of about 27°. This gives a ratio of tower height to each main span of about 0.5. Since there are no typical backstays, which restrain the tower head, the tower has to be stiff by itself. This is best achieved by tow- ers that are A-shaped in the longitudinal direction, Fig. 1.20.
1.1.2.4 Support conditions Longitudinal The longitudinal support conditions for the beams of cable-stayed bridges are determined by the changes in lengths due to temperature, shrinkage and creep as well as longitudinal forces such as braking, wind and earthquake. A survey of the different support conditions Figure 1.19 Relationship between tower height and amount of cable steel with their advantages and disadvantages is given in Table 1.2 [1.14] for railway bridges which are especially sensitive in this regard. For railway bridges high above ground the main problem is the high braking loads which are best distributed equally to both towers. A rigid connection to each tower, however, may create too high tower moments from the beam changes of lengths due to temperature and shrinkage and creep. A compromise between these contradictory requirements are hy- draulic buffers, which act as rigid connections between beam and towers for short-term loads such as braking or earthquake, but offer no resistance for slowly applied loads such as temperature, shrinkage and creep. Their disadvantage is that they require monitoring and Figure 1.20 Olympic Grand Bridge, Seoul, Korea 22 1 Introduction
careful maintenance. A practical solution is to use high neoprene bearings which follow the beam deformations by inclination. Another possibility, chosen in Japan, is to connect both towers Figure 1.21 Transverse buffers at tower with long cables to the beam so that the cables are elastically re- strained by the beam deformations and thus both towers are equally loaded.
Transverse The governing load for cable-stayed bridges in the transverse direc- tion is wind on the cables, the towers and the beam. In many cases transverse buffers at the towers with little play can take the trans- verse beam loads, Fig. 1.21 [1.15]. Transversely post-tensioned bearings have been used where trans- verse movements are to be avoided, Fig. 1.22 [1.16]. In order to cater for the horizontal bridge rotations at the abut- ments due to wind, a transversely fixed rotational bearing can be lo- cated in the center of the end cross girder. Should there be piers in the side span, their bearings can normally slide in the transverse di- rection in order to avoid undue restraints from the main span.
Anchor piers At the anchor piers (hold-down piers) the uplift forces in the back- stay cables from unbalanced loads in the main span have to be anchored. The simplest solution is to connect the beam directly to the anchor pier with the help of a rotational connection, Fig. 1.23. The anchor piers are stressed down into the foundations and have to be flexible enough to follow the longitudinal changes of length in the beam [1.17]. For a sliding support of the beam at stiff abutments pendulums Figure 1.22 Post-tensioned transverse tower bearing have traditionally been used which extend deep into the abutments and are articulated at both ends. Especially with steel bridges it has to be taken into account that these pendulums may obtain both ten-
Table 1.2 Longitudinal support conditions
No. System Characteristics Advantages Disadvantages 1 Floating bridge beam Free deformations due to change Same stresses and deformations Large bending moments in of temperature for both halves of bridge towers and large horizontal Introduction of breaking forces movements of beam due to into cables and towers breaking and unsymmetrical live loads 2 One fixed bearing Free deformations due to change Less deformations than in Strong forces on hold-down pier of temperature system 1 Longitudinally unsymmetric All horizontal forces act on one Large temperature movements hold-down pier in other hold-down pier
3 Hydraulic buffers Two fixed bearings for short-term Small deformation of the sym- System with variying support at both towers loads metrical system conditions depending on period Floating system for long-term Transfer of breaking forces onto of loading loads both towers 1.1 Design fundamentals 23
sile and compression forces and thus have to be designed for fatigue. This is especially important for the end articulations. The fatigue problem can be avoided if the beam is post-tensioned through the bearings against the anchor piers and thus a minimum compression force on the bearings is always ensured, Fig. 1.24 [1.18]. The longitudinal movements have again to be accounted for.
1.1.3 Tower shapes The first cable-stayed bridges used steel towers. Since towers are mainly loaded by compression, concrete towers are more economi- cal and, therefore, mainly used today. Only if extremely bad founda- tion conditions would require very long piles, are the lighter steel towers used today.
1.1.3.1 Two outer cable planes Figure 1.23 Articulated hold-down pier The beams of cable-stayed bridges should normally be supported at the outsides in order to restrain the rotational deformations most ef- fectively. This requires two cable planes, supported by two tower legs, Fig. 1.25. For small and medium spans vertical tower legs may be used. To stiffen them transversely they can be connected with cross beams. For longer spans the two tower legs should lean towards one another above deck in an A-shape, which provides increased tor- sional rigidity to the beam and stiffens the towers for transverse loads. For bridge beams with a high clearance the two foundations for a straight A may be uneconomic. The two legs can then be pulled together underneath the beam to permit a common foundation.
1.1.3.2 One central cable plane Only if one central cable plane is used, the cables for short and medium spans are anchored at one single tower at the bridge center Figure 1.24 Prestressed pendulum
low level bridges (rivers) high level (sea)
Figure 1.25 Towers for two cable planes Figure 1.26 Towers for one cable plane 24 1 Introduction
which is designed against lateral buckling, Fig. 1.26. For large spans the central plane can be anchored in the extended tip of an A-tower.
1.1.3.3 Spread central cable planes If a cable-stayed bridge has to carry outer roadway lanes and central railway tracks it can be expedient to place the two tower legs in be- tween the rail tracks and the roadway lanes. This results in partially spread tower legs, Fig. 1.27 [1.19]. The two cable planes are arranged parallel to the tower legs.
1.1.4 Beam cross-sections Small cable distances result in small bending moments from the dead load in the beam. The live load moments are mostly restraint moments which decrease with the depth of the beam. Therefore, it is economic to choose a small depth for the beam, which is nearly in- dependent of the span length. The limiting condition is the safety Figure 1.27 Tower for partially spread central cable planes against buckling of the beam. A further condition is to ascertain a minimum deflection radius under concentrated loads. This can easily be achieved for traffic loads even with slender beams, but railway bridges require larger beam depth.
1.1.4.1 Steel cross-sections Steel cross-sections comprise an orthotropic deck supported by the main and cross girders. All beam members act together for the local and global loads.
Two outer cable planes Figure 1.28 Open steel cross-section Open cross-sections: For short to medium spans the torsion from eccentric live loads can be carried by a couple in the outer cable planes. Open cross-sections with little torsional resistance can thus be used, Fig. 1.28 [1.20]. Box girders: Long spans may require the use of a box girder even with two outer cable planes in order to achieve the required torsional stiffness. An example is the current world record span holder, the Sutong Bridge in China, with a main span of 1088 m, Fig. 1.29 [1.21]. Separate beams: The Stonecutters Bridge in Hong Kong has a central tower with two outer cable planes. In order to provide the necessary space for the tower, two separate beams connected by Figure 1.29 Steel box girder cross girders are used, Fig. 1.30 [1.22].
One central cable plane A central cable plane requires a box girder cross-section in order to carry the torsional moments. A typical example is the beam for the Rhine River Bridge at Ilverich, Fig. 1.31 [1.12].
Spread central cable planes Open cross-sections: For the two spread central cable planes at the Rhine River Bridge Mannheim-Ludwigshafen two box girders pro- vide the required torsional stiffness, and transverse bending is Figure 1.30 Separate steel beams connected by cross girders 1.1 Design fundamentals 25
With Diaphragm Without Diaphragm
Figure 1.31 Steel box girder carried by the cross girders, Fig. 1.32 [1.19]. The area between the two boxes is used by two tramway tracks which are lowered in one end region. Box girders: The railway tracks in the center of the Sava River Bridge Ada Ciganlija, Fig. 1.33 [1.23], remain on top. The two spread central cable planes are anchored at the outside of the central box. For introduction of the cable forces into the 45 m wide beam addi- Figure 1.32 Separate steel boxes tional webs are used.
1.1.4.2 Concrete cross-sections The shape of concrete cross-sections is determined from similar consi derations to steel cross-sections. It has, however, to be taken into account that concentrated tensile forces have to be carried by tendons.
Two outer cable planes Figure 1.33 Steel box girder with wide cantilevers Open cross-sections: The open cross-section of the Pasco-Kennewick Bridge has triangular boxes at the outsides for aerodynamic reasons, Fig. 1.34 [1.15]. Transverse bending is carried by cross girders which are post-tensioned across the whole beam width. Additional short tendons transfer the cable forces via the inclined slabs into the main girders. Box girders: For two cable planes and medium spans, box girders are generally not required. For the Posadas-Encarnación Bridge in Argentina a box girder was selected due to the eccentric railway track, Fig. 1.35 [1.24]. The transverse stiffening of the box was achieved by individually post- tensioned transverse stiffeners from precast elements which carry Figure 1.34 Open concrete cross-section tension and compression. Solid cross-sections: The elastic support of the beam from the stay cables provides a good distribution of heavy single traffic loads. For smaller spans a solid slab may be used, Fig. 1.36 [1.25]. In this case the transverse slenderness ratio comes to 1 : 23.5.
One central cable plane A central cable plane also requires, for concrete beams, a box girder to carry the torsional moments from eccentric live loads. For the Brotonne Bridge in France the cable forces are transmit- ted to the webs by post-tensioned diagonals, Fig. 1.37 [1.26]. The transverse distribution can also be achieved with cross gird- Figure 1.35 Concrete box girder ers, but larger quantities are required.
Spread central cable planes The cables of the two spread central cable planes of the Second Main River Bridge at Hoechst are directly anchored to the webs of the central box girder, Fig. 1.38 [1.27].
1.1.4.3 Composite cross-sections Composite cross-sections use a concrete roadway slab as the top flange of the steel main and cross girders, connected by shear studs. Figure 1.36 Solid cross-section 26 1 Introduction
Figure 1.37 Concrete box girder Figure 1.38 Concrete box girder
The concrete slab should always be under compression in both di- attached to the short upper cross girders between the directional rections: longitudinally by the compression forces from the inclined traffic lanes, Fig. 1.47 [1.31]. cables, transversely as the top flange of a single-span girder between The cable forces are transmitted by bending in the cross girders the two outer cable planes. Central cable planes should not be used into the truss diagonals, the required torsional stiffness being pro- for composite cross-sections. vided naturally by the truss. The roadway slab can be built cast-in-place or from precast ele- ments. The latter have the advantage that their shrinkage and creep 1.1.5 Stay cables is smaller after installation due to their advanced age. It has to be as- Stay cables are the characteristic structural components of cable- certained that the joints do not form weak spots during the life of stayed bridges. Their performance governs the behavior of the com- the bridge. A typical composite cross-section is given in Figs 1.39 plete bridge, not only in the final stage but also during construction. and 1.40 [1.28]. The durability of the stay cables determines the robustness of a cable- stayed bridge. 1.1.4.4 Hybrid beams (steel/concrete) Hybrid cable-stayed bridges comprise a steel beam in the main span 1.1.5.1 Systems and a concrete beam in the side spans. The heavier concrete beam The currently used stay cable systems are locked coil ropes, parallel serves as a counterweight to the lighter steel main span. Both cross- wire cables and parallel strand cables as outlined in Table 1.3. sections are coupled at or near the tower with shear studs and ten- For economic reasons parallel strand cables are mostly used dons if the compression force from the cables is not sufficient to worldwide today. Even in Germany, where until now mainly locked overcome local tensile forces from bending. coil ropes have been used, the latest two cable-stayed bridges were provided with parallel strand cables. They are fabricated rather simi- Two outer cable planes larly by all major fabricators worldwide, Fig. 1.48 [1.32]. The Normandy Bridge uses a flat steel box girder for aerodynamic The strands are anchored with profiled wedges in anchor blocks. stability in the main span of 856 m which is balanced by a similarly The depths of the wedge teeth increase gradually so that they anchor shaped concrete beam in the side spans, Fig. 1.41 [1.29]. The con- the strands safely, but reduce their fatigue strength only slightly. crete beams extend some 100 m on both sides into the main span, The corrosion protection for every single strand comprises the Fig. 1.42. following: – galvanizing of every single wire in the strand One central cable plane – filling the interstices between the single wires with grease For the Rhine River Bridge, Flehe, steel and concrete box girders are – surrounding each strand with a directly extruded PE-sheath. used with a central cable plane, Figs 1.43 and 1.44 [1.16]. They join Such strands are called monostrands. in the tower axis. A number of these monostrands are combined into a cable, for The side spans rest on outside piers. The support reactions are re- which all strands are covered additionally by a PE pipe, Fig. 1.48. At duced by the central backstays in the cable anchorage region. the transition from the free length to the anchorage region the strands spread out, the radial forces are contained by a clamp. A 1.1.4.5 Double deck cross-section damper may be positioned at this location. If a multi-lane freeway has to be carried together with two railway The installation of these stay cables takes place on site by assem- tracks the railway may be placed on the lower level. This requires bling the individual components. The monostrands are pulled into about an 8 m deep beam, for which a truss is often selected in order the PE pipe. Each strand is individually stressed in such way that to permit a free view for the railway passengers during the long ride. after complete cable assembly all strands have the same stress. It is possible to restress the complete cable with a large jack. Single Two outer cable planes strands may be exchanged later individually. For the Öresund Bridge in Denmark the cable forces are introduced by triangles into the lower and upper chord of the truss, Fig. 1.45 1.1.5.2 Cable anchorages [1.30]. The stay cables typically run through a steel pipe to their anchor These are arranged as outriggers so that the beam can pass points. There split shims prevent sliding of the anchor heads. The between the tower legs, Fig. 1.46. lengths of the cables and thus their forces can be adjusted by changes in the thickness of the shims. One central cable plane Support nuts around the anchor head can also be used for retain- The third Orinoco Bridge carries only a single railway track on the ing the anchor head and adjustment of cable lengths. lower chord. The truss can thus be supported by a single cable plane 1.1 Design fundamentals 27
Figure 1.39 Typical open composite cross-section
North Figure 1.41 Main span steel cross-section of the Normandy Bridge, France Pockets for Shear Studs
South
Figure 1.40 Typical composite beam Figure 1.42 Side span concrete cross-section of the Normandy Bridge, France
Figure 1.43 Main span steel cross-section for the Rhine River Bridge, Flehe, Germany
Figure 1.44 Side span concrete cross-section for the Rhine River Bridge, Flehe
Figure 1.45 Truss beam of the Öresund Bridge, Denmark–Sweden Figure 1.46 Cable anchorage of the Öresund Bridge 28 1 Introduction
At beam In concrete: A typical cable anchorage at a concrete beam is shown in Fig. 1.49 [1.15]. The cable forces are directly introduced into the main girder. The anchor head is supported by shims on pressure plates welded to the end of the steel pipe which transfer the cable forces either directly or via the steel pipe and shear rings into the concrete, where the tensile forces are covered by reinforcement. At the tip of the steel pipe the cable is centered and possibly dampened by an elastomeric ring. The weather-resistant closure of the steel pipe is ensured by a neoprene boot clamped to the steel pipe and the stay cable. In steel: A direct introduction of the cable forces into the main girder web is shown in Fig. 1.50 [1.33]. The web is extended with a butt weld through an opening in the top flange. A steel pipe is weld- Figure 1.47 Truss for the third Orinoco Bridge, Venezuela ed into this web extension to which the anchor head is attached with split shims or a support nut.
At the tower In concrete: The simplest way to anchor individual cables at the tip of a concrete tower is to overlap them and thus to anchor them by compression, Fig. 1.51. Usually the stay cables are anchored inside a tower box section, similar to that shown for a concrete beam. The tensile forces bet- ween forestays and backstays can be covered by short tendons, Fig. 1.52. In steel: If the ideal fan shape of the cables is to be achieved they have to be split sideways into several planes. An example is the steel anchor head in Fig. 1.53, within which the cable forces are intro- duced into the longitudinal plates. Usually the cables are spread vertically in their planes in order to obtain sufficient space for vertically aligned anchorages. This leads to a modified fan cable arrangement in elevation, Fig. 1.54. The tensile forces are also transferred into the longitudinal plates.
Table 1.3 Current stay cable systems
Characteristics Modern locked coil rope Parallel wire cable Parallel strand cable
E ∙ 10–6 [N/mm2] 0.170 0.205 0.195 2 fu [N/mm ] 1470 1670 1870 ∆σ [N/mm2] 150 200 200