cầu dây văng lý thuyết và thiết kế cầu dây văng

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.
1. Bridges, Cable-stayed-Design and

construction
I. Title
624'.55
TG405

BSP Professional Books
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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 0. 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 1 The Cable-stayed Bridge System
1.1
1.2
1.3
1. 4
1.5
1.6
1. 7
1. 8
1. 9
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

1
2
19
20
21
24
25
26

29
31
34
36
39

Chapter 2 Typical Steel Bridges
2.1

2.2
2.3
2.4
2.5
2.6
2. 7

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
3.1
3.2
3.3

Concrete cable-stayed bridges
Railroad concrete bridges
Pipeline concrete bridges
References

Chapter 4
4.1
4.2

Typical Concrete Bridges

114
139
143
144

Typical Composite Bridges

Introduction
Composite cable-stayed bridges
References

147
148

154

Chapter 5 Typical Pedestrian Bridges
5.1
5.2

Introduction
Cable-stayed pedestrian bridges
References

155
155
173

Chapter 6 Structural Details
6.1
6.2
6.3
6.4
6.5
6.6
6. 7
6.8
6. 9
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 7 Methods of Structural Analysis

7.1
7.2
7.3
7. 4
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 8 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 9 Exact Methods of Structural Analysis
9.1
9. 2
9.3
9.4
9.5
9.6
9. 7
9.8
9. 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 1

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,


2

CABU:-SfAYED BRIDGES

fabrication, erection and maintenance of the new system. With the construction of these bridges many basic problems encountered in their
engineering are shown to have been successfully solved. However, these
important data have apparently never before been systematically presented.
In summary, the following factors helped make the successful development of cab:e-staycd bridges possible:
( 1) The development of methods of structur al analysis of highly statically indeterminate structures and application of electronic computers.
(2) The development of orthotropic steel decks.

(3) Experience with previously built bridges containing basic clements
of cable-stayed bridges.
(4) Application of high-strength steels, new methods of fabrication and
erection .
(5) The ability to analyse such structures through model studies.

1.2 Historical review

Fig. 1.1

Egyptian sailing

boat with rope-srjlyed

sail beam

The history of stayed beam bridges indicates that the idea of supporting
a beam by inclined ropes or chains hanging from a mast or tower has been
known since ancient times. The Egyptians 1 applied the idea for their
sailing ships as shown in Fig. 1.1.
In some tropical regions of the world primitive types of cable-stayed
bridge, such as shown in Figs. 1.2 and 1.3, were builrl. Inclined vines
attached to the trees on either bank supported a walk which was woven
of vines and bamboo sticks.


Fig. 1.2 Primithe bamboo
bridge in Borneo
Fig. 1.3 (bdow) Primitive
bamboo bridge: in Laos

Fig. 1.4 Bamboo bridge with bamboo stays O\'Cr Serajoc Ri,er 10 Ja,a,
Indonesia

F igure 1.4 s hows a primitive bridge of bamboo stays interwoven with
vi11es with the ends fastened to trees ar each side. This crude structure
indicates that its builders had a vague idea of some of the principles of
bridge engineering.
In 1617, Faustus Verantius proposed a bridge system ha,'ing a timber
deck supported by inclined eyebars3 ; see Fig. 1.5.
I

t HI I \

Fig. 1.5 Bridge stiffened by eye bars, designed by Faustus Vcrantius,
Italy, 1617.


THE CABLE-STAYED BRIDGE SYSTEM

5

Like all bridge designs of this epoch, it exhibits many departures from
what .a structural analysis would dictate; nevertheless, it contains the
main features and basic principles of a metal suspension bridge stiffened
by stays.
In 1784, a German carpenter, Immanuel Loscher4 in Fribourg
designed a timber bridge of I OS ft (32 m) span consisting of timber stays
attached to a timber tower (Fig. 1.6).

In 1817, rwo British engineers, Redpath and Brown, built the King's
,\leadows Bridge5 , a footbridge in England which had a span of approximately II 0 ft (33.6 m), using sloping wire stay cable suspension members
attached to cast iron towers (Fig. 1.7).
Fig. 1.6 All-timber bridge stiffened by inclined timber stays, designed by
Loschcr in Germany, 1784.

Fig. l.i

King's i\lc;ado"s Bridge, England, 1817


6

Fig. 1.8

CABLE-STAYED BRIDGES

Dryburgh Bridge, England, 1817

The system of inclined chains was adopted in a bridge built at Dry burgh
Abbey across the Tweed River 6 in 1817. It had a 260ft (79.3 m) span,
and was 4ft ( 1.2 m) wide (Fig. 1.8).
It was observed that the bridge had a \'ery noticeable vibration when
crossed by pedestrians, and the motion of the chains appeared to be easily
accelerated. In 18 18, six months after the completion of the bridge, it was
destroyed by a violent gale.
Around 1821, the French architect Poyet7 suggested hanging the
beams up to rather high towers with wrought iron bars. Jn this system he
proposed using a fan-s haped arrangement of the stays, all being anchored
at the mp of the tower (Fig. 1.9).

Poyct's idea was further developed by the famous French engineer
Navier who, in 1823, stud ied bridge systems stiffened by inclined chains8
(Fig. 1.1 0).
By comparing both the weights of the deck and the inclined chains,
Navier found that for a given span and height of the towers, the cost of
both systems was approximately equal.
Fig. 1.9

Fan type stayed bridge proposed by Poyet, France, 1821.


THE CA BLE-STAYED BRIDGE SYSTEM

l'

II

Fig. 1.10 Chain-stiffened bridge systems proposed by 'a vier, France,
1823

7


8

CABL£-STAYED BRIDGES

Fig. Lll

~.. """"~- ---- ...... ·-

"(EJ·

Bridge ~cross the Saale River, Germany, 1824

.

-~ -

fig. 1.12 Ti,•crton Bridge, England, 1837

Fig. 1.13

Harp type stayed bridge by Hatley, England, 1840

·==·"'


THE CABLE-STAYED BRIDGE SYSTEM

9

In 1824, a bridge was erected across the Saale River at Nienburg, Germany, with a 256ft (78.0 m) span and having the main girder stiffened by
inclined members 9 . However, this bridge had excessive deflections under
loading and the foUowing year it collapsed under a crowd of people
because of failure of the chain-stays (Fig. 1. 11).
1837 Motley 10 built a bridge at Tiverton, England, a highly redundant double cantilever with straight stays (Fig. 1.12).
The other type of stay arrangement, with parallel stays, now called
harp-shaped, was suggested by Hatley 11 in 1840 (Fig. 1.13). He mentioned that this system provided less stiffness than the fan-shaped one.
One interesting structure of the inclined-cable type is presented by the

bridge over the Manchester Ship Cana.l 12 in England (Fig. 1.14). And in
1843, Clive 13 proposed an original system of a cable-stayed bridge, shown
in Fig. 1.15.
Fig. 1.14 The Manchester Ship Canal Bridge, England

;,. ___

t

,

- - - ---- -------- 106 -00

,

.

-- ----------)+<(-- ---

'

Fig. 1.15 Bridge system proposed by Clive, England, 1843

I

'

--~

I

10

CABLE-STAYED BRIDGES

Fig. 1.16 The Franz joseph Bridge over the Moldau River in Prague,
Czechoslovakia, 1868

In 1868 the Franz Joseph Bridge, designed by Ordish and LeFeuvre 1.\
was built over the Moldau R iver at Prague, Czechoslovakia (Fig. 1.16).
This bridge actually represents a combination of a cable-stayed and a
classical suspension bridge.
A new form of suspension was introduced in this bridge, using sloping
rods running directly from the panel points of the floor system to the
tops of the towers, the direct tension members being supported and held
in position by catenary cables between the towers. These have no other
purpose than to sustain the weight of the direct tension bars. Here is a
very interesting idea of supporting an intermediate joint by an inclined
bar which transfers the tension to the longest stay of the other half of the
span.
The Albert Bridge 1 5 over the Thames at Chelsea with a main span of
400ft (122 m) and dating back to 1873, was built by Ordish, using his
system (Fig. 1.17). In this bridge the suspension system comprises tie
Fig. 1.17 The Albert Bridge over the River Thames, England, 1873


THE CABLE-STAYED BRIDGE SYSTEM

11

members converging at the top of the towers. There are three sloping
tie members on each side of the center span and four on each side of the
end spans.
The short historical review presented here indicates that the idea of
the stayed beam bridge is very old. However, it was not successfully
applied until the twentieth century. The reasons for such slow progress
have to be found in the collapse of several of the first built cable-stayed
bridges.
Inclined stays were first introduced in England and widely used there
in the early part of the nineteenth century. However, a number of suspension bridges with such stays failed, on account of insufficient resistance
to wind pressure, and this led to the partial abandonment of that type in
England.
It should be noted that in many cases these early cable-stayed bridges
actually possessed structural defects which led to their destruction. This
was mainly due to the misunderstanding on the part of the designers
of the actual structural behavior of such bridges and of the defects in
their construction. Cables, for instance, were usually of an insufficient
cross-section and were not tightened during erection. Consequently,
cables performed their proper function only after substantial deformation
of the whole structure under the action of the load. This aspect of their
behavior led to the opinion that cable-stayed bridges were exceptionally
flexible and not safe. It was Navier who reported on these failures and
suggested using suspension bridges instead of cable-stayed bridges.
Navier's statement led bridge engineers to prefer the suspension-type
bridge.
In the second half of the nineteenth century inclined stays were reviewed in America by the famous bridge engineer Roebling. In connection with the stiffening truss, introduced by Roebling, and efficient
lateral bracings, inclined stays proved more effective.
The cables in suspension bridges designed by Roebling were always
assisted by stays 16 . A network of diagonal stays occupied the same inclined plane as that of the cables. The purpose of these stays was twofold.

They not only assisted the cables greatly in the support of the bridge, but
they also supplied the most economical and efficient means for stiffening
the floor against cumulative undulations that may be started by the action
of the wind.
In 1855 Roebling built the first successful railroad suspension bridge
in the world across the Niagara River (Fig. 1.18). The total load was
divided between the cables and an extensive system of radiating stays.
The application of a system of stays provided all the stiffness required for
the passage of trains at a rapid rate, as well as stability against the wind
action.
Roebling also provided a generous system of inclined stays in the


)2

CABLE-STAYED BRIDGES

Fig. 1.18 The

iagar.a suspension bridge, t:SA, 1855

Fig. 1.19 The Ohio River bridge at Cincinnati, USA, 1867


Fig. 1.20 The Brooklyn Bridge, USA, 1883

construction of the Ohio Bridge (Fig. 1.19). Nearly one-half of the total
weight of the roadway and the live load was carried by diagonal stays of
wire rope, running straight from the tops of the towers to successive
points along the floor. The main cables, themselves stiffened by this

arrangement, really had to carry only about one-half of the total weight of
the roadway and load. The stays served effectively to strengthen the floor
and to prevent or check vibration during the passage of heavy loads and
in high winds.
Perhaps the most distinctive feature of the Brooklyn Bridge (Fig. 1.20)
is the system of inclined stays radiating downward from th e tops of the
towers to the floor of the span. Roebling introduced them primarily for
the critical function of adding rigidity to the ~pan, and then ingeniously
took advantage of the additional load-carrying capacity which they incidentally supplied. This contribution to the strength of the bridge was
explained in simple terms by the designer:
The floor, in connection with the stays, will support itself without the
assistance of the cable, the supporting power of the stays alone will be ample
to hold up the floor. If the cables were removed, the bridge would sink in the
center, but would not fall.

As we know today, the designers of the old days had not yet been able
to calculate the forces in the inclined cables correctly, and they also underestimated the influence of hyperstat:ic behavior and of the sag of the stays.


14

CAB LE-STAYEO BRIDGES

Consequently, the stayed-beam bridge system was condemned and
abandoned, and only at the beginning of the twentieth century, with the
introduction of wire cables, high-grade steel and the further development
of the structural theory, was it possible to re-introduce the cable-stayed
system.
A few bridges of a mixture of the stayed-bridge system and the suspension-bridge system were built in France in the nineteenth century by
the famous engineer Arnodin. In this system, diagonal stays radiate from

the tower tops with no vertical hangers in this interval. This system
reduces deflections of the stiffening girders, and permits the use of smaller
heights of the stiffening girder. This arrangement of loading distorts the
curve of the cables from the catenary, but substantially reduces the
amount of load upon them.
Bridges of this mixed system did not find wide application mainly
because of their aesthetical imperfection, the mixture being less satisfactory than either of the two systems individually.
In the system introduced by Arnodin, who built many French suspension bridges in the second half of the nineteenth century, the inclined
stays extend from the towers to near the quarter-points of the span, while
the middle portion of the span is suspended from the cables.
The bridge over the Sa6ne River at Lyons designed by Arnodin 17 , has
a span of 397 ft (121 m) (Fig. 1.21). Diagonal stays are shown at ends
radiating from the tower tops with no vertical hangers in this interval.
Of similar conception was the bridge over the Rhone River at Avignon
(Fig. 1.22).
In 1904 Arnodin built over the Blavet River, the Bonhomme Bridge
778ft (237m) long with a main span of 535ft (163m) and side spans of
121 ft (37 m) each 18 (Fig. 1.23). The main span was divided into three
parts, the central portion being hung from five continuous cables on each
side, and the two end portions from six diagonal cables on each side.
The original idea of Poyet to use fan-shaped arrangements of the stays
was modified, improved and successfully employed by Arnodin in the
transporter bridge built in 1903 at Nantes (Fig. 1.24). The lightness of
the suspension system with cables radiating from the tops of the slender
tapering towers creates the impression of an elegant structure.
The first rational solution for cable-stayed bridges which satisfied the
necessary stiffness and economic conditions, was proposed by Gisclard 19 ,
a French engineer, in 1899. He introduced a new system consisting
basically of inclined and horizontal cables. His system presents geometrically stable cable trusses. The inclined cables do not transfer the
horizontal component of the cable force onto the stiffening girder. This

system actually represents a three-hinged arch, having diagonals made of
cables.
The Gisclard system is less appealing to the eye, but appears to be


Fig. 1.21 Bridge over the
Saone River at Lyons,
Frnnce, 1888

Fig. 1.22 The Rhone
Ri,cr bridge at Avignon,
France, 1888

Fig. 1.23 (bdow) Bonhommc Bridge over the
Blavcl River, Marbihan,
France, 1904


16

CABLE-STAYED BR IDGES

s.oo

't.

...
•

fo,OO

0
0

.,0

Fig. 1.24 Transporter bridge at Nantes, France, 1903

E

D

Fig. 1.25 Typical bridge of Giscla.rd's system

127' -1 1"

·'·

511' -10"

127 ' -11"

830. -0"

Fig. 1.26 (abow)
The Cassagnc
Bridge, France,
1907

Fig. 1.27 (rigltl)

Lezardricux
Bridge, France,
1925

!6 "'"'1-~3' /,4~.~~~~~3~6~7'~-0'~'~~~~~~,~66'-3'1
~~.~.~~·----~~--------·~
~99.

-6"

,j