cầu dây văng lý thuyết và thiết kế cầu dây văng

iv COl\TE:'\TS Chapter 3 Typical Concrete Bridges 3.1 Concrete cable-stayed bridges 3.2 Railroad concrete bridges 3.3 Pipeline concrete bridges Chapter 6 Structural Details 6.1 Stiffenin

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

8 John Street, London WCIN ZES

23 Ainslie Place, Edinburgh El 13 6AJ

52 Beacon Street, Boston Massachusetts 02108, USA

66 7 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

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 Baudin- Chateauneuf, France; Dip! Eng E Beyer, Landeshaupstadt Dusseldorf, Germany; Depart- ment 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

Chapter 1 The Cable-stayed Bridge System

1.1 Introduction

1.2 Historical review

1.3 Basic concepts

1 4 Arrangement of the stay cables

1.5 Positions of the cables in space

iv COl\TE:'\TS

Chapter 3 Typical Concrete Bridges

3.1 Concrete cable-stayed bridges

3.2 Railroad concrete bridges

3.3 Pipeline concrete bridges

Chapter 6 Structural Details

6.1 Stiffening girders and trusses

6.2 Towers

6.3 Types of cable

6.4 Modulus of elasticity of the cable

6.5 Permissible strength of the cables

6.6 Fatigue tests and strength of the cables

6 7 Corrosion protection

6.8 Behavior of the bent cable

6 9 Cable supports on the towers

6.10 Anchoring of the cables at the deck

6.11 Stiffening girder anchorages

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

Number and spacing of the cables

Multispan bridges

Multiple cantilever spans

Inclined cable under its own weight

Bridge systems

The degree of redundancy

Performance of the cable system

Linear analysis and preliminary design

Approximate weight of the bridge system

Approximate methods of analysis

9 7 Finite element method

9.8 Torsion of the bridge system

10.4 Static similitude conditions

10.5 Sectional properties and geometry of the model

10.6 Design of the model

10.7 Determination of influence lines

vi CONTENTS

Chapter 11 Wind Action and Aerodynamic Stability

11.1 Introduction

11.2 Wind forces

11.3 Static wind action

11.4 Dynamic wind action

11.5 Vibrations

11.6 Vertical flexural vibrations

11.7 Torsional vibrations

11.8 Damping

11.9 Wind tunnel model tests

11.10 Prevention of aerodynamic instability

11.11 Conclusions

References

Chapter 12 Abbreviated Tentative Recommendations

for Design of Cable-stayed Bridges

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

Chapter 11, Wind Action and Aerodynamic Stability provides expanded

treatment considering aerodynamic action

Chapter 12, Abbreviated Tentative Recommendations for Design of

Cable-stayed Bridges is a new addition

Every effort was made to correct some errors detected in the first edition

To my wife Tania

applica-The renewal of the cable-stayed system in modern bridge engineering was due to the tendency of bridge engineers in Europe, primarily Ger-many, 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 suppor-ted 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 suc-cess, 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 in-clined 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 struc-tural analysis The development and application of electronic computers opened up new and practically unlimited possibilities for the exact solu-tion 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,

Fig 1.1 Egyptian sailing

boat with rope-srjlyed

sail beam

2 CABU:-SfAYED BRIDGES

fabrication, erection and maintenance of the new system With the struction of these bridges many basic problems encountered in their engineering are shown to have been successfully solved However, these

con-important data have apparently never before been systematically presented

-In summary, the following factors helped make the successful ment of cab:e-staycd bridges possible:

develop-( 1) The development of methods of structural analysis of highly ally indeterminate structures and application of electronic computers (2) The development of orthotropic steel decks

static-(3) Experience with previously built bridges containing basic clements

a beam by inclined ropes or chains hanging from a mast or tower has been

known since ancient times The Egyptians1 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

1.2

bridge in Borneo

Fig 1 3 (bdow) Primitive bamboo bridge: in L aos

Indonesia

Figure 1.4 shows 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 H I 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 approxi-mately 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 CABLE-STAYED BRIDGES

Fig 1.8 Dryburgh Bridge, England, 1817

The system of inclined chains was adopted in a bridge built at Dry burgh Abbey across the Tweed River6 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 p destrians, and the motion of the chains appeared to be easily accelerated In 18 8, 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 J n this system he proposed using a fan-shaped 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, studied 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 h ight of the towers, the cost of both systems was approximately equal

Fig 1.9 Fan type stayed bridge proposed by Poyet , France, 1821

THE CABLE - STAYED BRIDGE SYSTEM 7

l'

I I

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

1823

8 CABL£-STAYED BRIDGES

Fig Lll Bridge ~cross the Saale River , Germany, 1824

~ """" ~ - - - · - "(EJ · -~ - · ==·"'

fig 1.12 Ti, • crton Bridge, England, 1837

Fig 1.13 Harp type stayed bridge by Hatle y, Eng land, 1840

THE CABLE-STAYED BRIDGE SYSTEM 9

In 1824, a bridge was erected across the Saale River at Nienburg,

Ger-many, with a 256ft (78.0 m) span and having the main girder stiffened by inclined members9 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 1 1)

1837 Motley10 built a bridge at Tiverton, England, a highly dant double cantilever with straight stays (Fig 1.12)

redun-The other type of stay arrangement, with parallel stays, now called

harp-shaped, was suggested by Hatley11 in 1840 (Fig 1.13) He

men-tioned that this system provided less stiffness than the fan-shaped one One interesting structure of the inclined-cable type is presented by the

bridge o er the Manchester Ship Cana.l12 in England (Fig 1.14) And in

1843, Clive13 proposed an original system of a cable-stayed bridge, shown

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 Bridge1 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, 1 873

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 sion bridges with such stays failed, on account of insufficient resistance

suspen-to wind pressure, and this led suspen-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 viewed in America by the famous bridge engineer Roebling In connec-tion with the stiffening truss, introduced by Roebling, and efficient lateral bracings, inclined stays proved more effective

re-The cables in suspension bridges designed by Roebling were always assisted by stays16 A network of diagonal stays occupied the same in-clined 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

Fig 1.18 The iagar.a suspension bridge, t:SA, 1855

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

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 the 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 dentally supplied This contribution to the strength of the bridge was explained in simple terms by the designer:

inci-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-ST A YEO 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 pension-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

sus-Bridges of this mixed system did not find wide application mainly because of their aesthetical imperfection, the mixture being less satis-factory than either of the two systems individually

In the system introduced by Arnodin, who built many French sion 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

suspen-The bridge over the Sa6ne River at Lyons designed by Arnodin17, 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 A vignon (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) each18 (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 geo-metrically 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, 1 888

Fig 1 22 The Rhone Ri,cr bridge at Avignon, France, 1 888

Fig 1.23 (bd o w) hommc Bridge over the

Bon-Blavcl River, Marbihan , France, 1 904

THE CABLE-STAYED BRIDGE SYSTEM 17 particularly adapted to railroad traffic In that system the inclined stays extend across the entire span and form a main carrying system in which the material is utilized in tension to the greatest possible extent

Bridges of this system found wide application in France and her former colonies A typical bridge of Gisclard's system is shown in Fig 1.25, and another well-known example is represented by the Cassagne Bridge, having a 512 ft (156 m) central span It was built in 1907 for a narrow gauge electric railroad (Fig 1.26) Due to its suitability, Gisclard's sys-tem showed distinctive advantages in a number of bridges

Applying the basic concept of Gisclard's system, the French engineer Leinekugel le Cocq20 proposed a bridge system having inclined cables and transfer of the horizontal components of the cables to the stiffening girder This system proved to be very economical and to give only small deformations A typical example of this system is the Lezardrieux Bridge over the Trieaux River in France built in 1925 (Fig 1.27) This cable-stayed bridge may be considered a prototype of the contemporary cable-stayed bridge, having a fan-type system

The structural system of this bridge is many times statically minate and performs as a three-dimensional system because, in addition

indeter-to the main girders, both a supporting deck and stringers also participate

in the performance of the main bridge system as one integral unit The bridge was designed with hinges at the quarter points of the stiffening girder under the assumption that the maximum bending moments at these locations act similarly as in suspension bridges However, as exact analysis shows, the bending moments at the above locations are small, and hinges are not only unnecessary but actually decrease the general stiffness of the whole bridge system

In 1938 Dischinger introduced stay cables into the design of a pension railroad bridge with a 2468 ft (753 m) span over the Elbe River, near Hamburg, Germany

sus-To reduce rather large deflections of the conventional suspension bridge system under heavy railroad loading, Dischinger introduced stay cables using high-strength wires, and accepted high stresses, reducing the sag of the cables which have visually a softening effect (Fig 1.28) Investigation by Dischinger established the fact that stiffness and aero-dynamic stability can be achieved by combining the main suspension cables with stays An absolute prerequisite for this is that the inclined cables must be subjected to considerable initial tension

Since World War II, the rapid advancement of bridge construction has brought about the need to develop a new concept in bridge design

In order to achieve economy of both material and cost, designers have gone back to the cable-stayed bridge concept A leading role in the new development of this bridge system was played by Dischinger21, who pub-lished the results of his studies in 1949

THE CABLE-STAYED BRIDGE SYSTEM 19

After 1950, several cable-stayed bridges were proposed at competitions for the reconstruction of bridges across the Rhine River in Germany Comparative estimates of the cost proved that these cable-stayed bridges were more economical than the suspension or the self-anchored suspen-sion bridges In 1952, Leonhardt22 designed the cable-stayed bridge across the Rhine in Dusseldorf, but the bridge was not built until 19 58

In the same period, the German firm Demag23, in collaboration with Dischinger, designed the Stromsund Bridge in Sweden, which, erected

in 1955, may be considered as the first modern cable-stayed bridge (Fig 1.29)

After the first two cable-stayed bridges of modern design had proved

to be very stiff under a traffic load, aesthetically appealing, economical and relatively simple to erect, the way was open for further wide and successful application The new system became rapidly popular among German bridge engineers and, about ten years later, in several other countries, too It is now increasingly applied by designers all around the world

The technical literature contains references to more than 50 bridges that have been built since 1955 or are being contemplated, incorporating the system of cable stays Approximately one-third have been built in Germany and others are located throughout the world A brief review of the development of cable-stayed bridges may be found in recent publica-tions on this subject24-26

1.3 Basic concepts

The application of inclined cables gave a new stimulus to the tion of large bridges The importance of cable-stayed bridges increased rapidly and within only one decade they have become so successful that they have taken their rightful place among classical bridge systems It is interesting to note how this development which has so revolutionized bridge construction, but which in fact is no new discovery, came about The beginning of this system, probably, may be traced back to the time when it was realized that rigid structures could be formed by joining triangles together It would be easy to refer to such examples in the history

construc-of bridge building, as shown in Figs l.l-1.7

Although most of these earlier designs were based on sound principles and assumptions, the girder stiffened by inclined cables suffered various misfortunes which regrettably resulted in abandonment of the system Nevertheless, the system in itself was not at all unsuitable The solution

of the problem had unfortunately been attempted in the wrong way

On the one hand, the equilibrium of these highly indeterminate tems had not been clearly appreciated and controlled, and on the other,

sys-Fig 1.30 Systems of cable

arrangement

20 CABLE-STAYED BRIDGES

the tension members were made of timber, round bars or chains They consisted therefore of low-strength material which was fully stressed only after a substantial deformation of the girder took place This may explain why the renewed application of the cable-stayed system was possible only under the following conditions:

( 1) The correct analysis of the structural system

(2) The use of tension members having under dead load a considerable degree of stiffness due to high pre-stress and beyond this still suf-ficient capacity to accommodate the live load

(3) The use of erection methods which ensure that the design tions are realized in an economic manner

assump-The renaissance of the cable-stayed system, however, was finally fully achieved only during the last decade

success-Modern cable-stayed bridges present a three-dimensional system sisting of stiffening girders, transverse and longitudinal bracings, ortho-tropic-type deck and supporting parts such as towers in compression and inclined cables in tension The important characteristics of such a three-dimensional structure is the full participation of the transverse con-struction in the work of the main longitudinal structure This means a considerable increase in the moment of inertia of the construction which permits a reduction in the depth of the girders and economy in steel

con-1.4 Arrangement of the stay cables

According to the various longitudinal cable arrangements, cable-stayed bridges could be divided into the following four basic systems shown in Fig 1.30

STAY SINGLE DOUBLE TRIPLE MULTIPLE VARIABLE SYSTEM

THE CABLE-ST A YEO BRIDGE SYSTEM 21

1 RADIAL OR CONVERGING SYSTEM

In this system all cables are leading to the top of the tower Structurally, this arrangement is perhaps the best, as by taking all cables to the tower top the maximum inclination to the horizontal is achieved and conse-quently it needs the smallest amount of steel The cables carry the maximum component of the dead and live load forces, and the axial component of the deck structure is at a minimum

However, where a number of cables are taken to the top of the tower, the cable supports or saddles within the tower may be very congested and a considerable vertical force has to be transferred Thus the detailing becomes rather complex

2 HARP OR PARALLEL SYSTEM

In this system the cables are connected to the tower at different heights, and placed parallel to each other This system may be preferred from an aesthetic point of view However, it causes bending moments in the tower In addition, it is necessary to study whether the support of the lower cables can be fixed at the tower leg or must be made movable in a horizontal direction

The harp-shaped cables give an excellent stiffness for the main span,

if each cable is anchored to a pier on the river banks as was done for Knie Bridge at Dusseldorf, Germany

The quantity of steel required for a harp-shaped cable arrangement is slightly higher than for a fan-shaped arrangement The curve of steel quantity suggests choosing a higher tower which will also increase the stiffness of the cable system against deflections

3 FAN OR INTERMEDIATE SYSTEM

The fan or intermediate stay cable arrangement represents a tion of the harp system The forces of the stays remain small so that single ropes could be used All ropes have fixed connections in the tower The Nord Bridge, Bonn, Germany, is a typical example of this arrangement

modifica-4 STAR SYSTEM

The star pattern is an aesthetically attractive cable arrangement However,

it contradicts the principle that the points of attachment of the cables should be distributed as much as possible along the main girder

1.5 Positions of the cables in space

With respect to the various positions in space which may be adopted for the planes in which the cable stays are disposed there are two basic arrangements: two-plane systems and single-plane systems (Fig 1.31 )

22 CABLE-STAYED BRIDGES

Fig 1.31 Space positions of cables

(a) Two vertical planes system (c) Single plane system (b) Two inclined planes system (d) Asymmetrical plane system

(c)

(d)

THE CABLE-STAYED BRIDGE SYSTEM 23

1 TWO VERTICAL PLANES SYSTEM

Two alternative layouts may be adopted when using this system: the cable anchorages may be situated outside the deck structure, or they may

be built inside the main girders

The first layout is the better of the two in that no area of the deck surface

is obstructed by the presence of cables and towers, as in the second case There is, however, a disadvantage in that the transverse distance of the cable anchorage points from the webs of the main girders requires sub-stantial cantilevers to be constructed in order to transfer the shears and bending moment into the deck structure Also the substructure, especially the piers for the towers, has to be longer, because in this case the towers stand apart and outside the cross-section of the bridge

Where the cables and towers lie within the cross-section of the bridge, the area taken up cannot be utilized as part of the roadway and may be only partly used for the sidewalk Thus an area of the deck surface is made non-effective and has to be compensated for by increasing the over-all width of the deck

2 TWO INCLINED PLANES SYSTEM

This system was first used for the Severin Bridge in Cologne, Germany, where the cables run from the edges of the bridge deck to a point above the centerline of the bridge on an A-shaped tower

This arrangement can be recommended for very long spans where the A-shaped tower has to be very high and needs the lateral stiffness given

by the triangle and the frame action Joining all cables on the top of this tower has a favorable effect regarding wind oscillations, because it helps

to prevent the dangerous torsional movement of the deck

3 SINGLE PLANE SYSTEM

Another system is that of bridges with only one vertical plane of stay cables along the middle longitudinal axis of the superstructure In this case the cables are located in a single vertical strip, which is not being used by any form of traffic

This arrangement requires a hollow box main girder with considerable torsional rigidity in order i:o keep the change of cross-section deformation due to eccentric live load within allowable limits It is therefore not necessary to increase the width of the superstructure when using the central box girder system This system which was proposed by Haupt27 can be used if there is a median space to separate two opposite traffic lanes In this way, no extra width is needed for the tower, and the cables

at deck level are protected against accidental impact from cars

The single plane system also creates a lane separation as a natural tinuation of the highway approaches to the bridge This is an economical and aesthetically acceptable solution, providing an unobstructed view

It should be noted that all the possible variations regarding the tudinal arrangements of the cables used with two plane bridges are also applied to single plane central girder bridges

longi-1.6 Tower types The various possible types of tower construction are illustrated in Fig 1.32, which shows that they may take the form of:

( 1) Trapezoidal portal frames (2) Twin towers

(3) A-frames ( 4) Single towers

Fig 1.32 Tower types

I Portal tower 4 A-frame tower

Portal type towers were used in the design of early cable-stayed bridges,

as in the case of suspension bridges, where the portal type was commonly used to obtain stiffness against the wind load which the cable transfers to the top of the towers However, later investigation of cable-stayed bridges indicated that the horizontal forces of the cables were in fact, relatively small, so that freely standing tower legs could be used without disadvant-age The inclined stay cables even give a stabilizing restraint force when the top of the tower is moved transversely

With single towers or twin towers with no cross-member, the tower is stable in the lateral direction as long as the level of the cable anchorages

is situated above the level of the base of the tuwer In the event of lateral

THE CABLE-ST A YEO BRIDGE SYSTEM 25

displacement of the top of the tower due to wind forces, the length of the cables is increased and the resulting increase in tension provides a restor-ing force Longitudinal moment of the tower is restricted by the restram-ing effect of the cables fixed at the saddles or tower anchorages

There are three different solutions possible regarding the support arrangement of the towers:

J TOWERS FIXED AT THE FOUNDATION

In this case large bending moments are produced in the tower The majority of cable-stayed bridges in Germany have, however, been built with the towers fixed at the base, and it is stated that the advantage of increased rigidity of the structure thus obtained offsets the disadvantage

of the high bending moments in the tower

Towers with fixed legs are relatively flexible, and loading and perature do not cause significant stresses in the structure In this case, the main girders pass between the frame legs and are supported on the transverse beam

tem-2 TOWERS FIXED AT THE SUPERSTRUCTURE

In the case of the single-box main-bridge system, the towers are generally fixed to the box With this arrangement it is necessary not only to rein-force the box but to provide strong bearings The supports also may resist the additional horizontal forces caused by the increased friction forces in the bearings

3 HINGED TOWERS

For structural reasons, the towers may be hinged at the base in the tudinal direction of the bridge This arrangement reduces the bending moments in the towers and the number of redundants, which simplifies analysis of the overall structure Also, in cases with bad soil conditions, linear hinges at the tower supports are provided, allowing longitudinal rotation, so that bending moments are not carried by the foundation

longi-1.7 Deck types

In the search for a more efficient bridge deck, a major advance has been made with the development of the orthotropic steel deck Most cable-stayed bridges have orthotropic decks which differ from one another only as far as the cross-sections of the longitudinal ribs and the spacing

of the cross-girders is concerned Typical ribs used in an orthotropic deck are shown in Fig 1.33

Cross-girders are usually 6-8ft (1.8-2.5 m) apart for decks stiffened by flexible ribs, and 15-18 ft (4.6 5.5 m) apart in the case of decks stiffened

26 CABLE-STAYED BRIDGES

Fig 1.33 Rib types

(a) Torsionally weak or

open type (b) Tersionally

stiff or box type

by box-type ribs possessing a high degree of torsional rigidity

The orthotropic deck performs as the top chord of the main girders or trusses It may be considered as one of the main structural elements which lead to the successful development of modern cable-stayed bridges How-ever, it is not intended to discuss the orthotropic system in detail because the analysis and design of this system have been treated extensively in the technicalliterature28• 29

For relatively small spans in the 200-300 ft (60-90 m) range it is venient to use a reinforced concrete deck acting as a composite section with the steel grid formed by the stringers, floor beams and main girders

con-An alternative solution is presented by a reinforced concrete deck acting monolithically with the main reinforced or prestressed concrete girders

1.8 Main girders and trusses The following three basic types of main girders or trusses are presently being used for cable-stayed bridges:

1 STEEL GIRDERS Bridges built with solid web main girders may be divided into two types: those constructed with !-girders and those with one or more enclosed box sections, as shown in Fig 1.34

Plated 1-girders with a built-up bottom flange comprising a number of cover plates have been used in some bridges It is considered that in this way, the required inertia of the section can be made to fit the moment envelope exactly, that no excess steel is being used, and thus the minimum weight of steel is attained It is felt, however, that this arrangement does not necessarily produce the most economical solution

THE CABLE-STAYED BRIDGE SYSTEM 27

Types of main girder Arrangement

cellular box girder

and sloping struts

Box girders in comparison often have portions of their span where a

certain minimum plate thickness has to be maintained to prevent local

buckling and to provide protection from corrosion, even though the

desired inertia does not require such thickness They do, however, have

the great advantage of simplicity of fabrication in comparison to plate

1-girders, and most important, a standard section with only the plate

thickness varying can be produced in series, which significantly reduces

fabrication costs Also, the inside surfaces are not exposed to the

atmo-sphere, and thus initial protective treatment and later maintenance costs

are reduced

Box girders may be rectangular or trapezoidal in form, i.e with web

plates vertical or sloping The trapezoidal section is often used in order

to keep the bottom flange area to the desired size, whilst the support to

the deck plate from the webs is provided at an optimum position

Although fabrication costs of the inclined web plates are higher, an

overall saving can often be achieved Both plate girder and box section

main girders are used for cable-stayed bridges, but it is felt that box

28 CABLE-STAYED BRIDGES

Types of stiffening truss

Fig 1.35 Deck supported

Highway and railroad ( project )

Highway and railroad ( project )

of loading and therefore reduce torsional rotations in the deck

2 TRUSSES During the last decade trusses have rarely been used in the construction

of cable-stayed bridges Compared to solid web girders, trusses present

an unfavorable visual appearance; they require a great deal of fabrication and maintenance, and protection against corrosion is difficult

Thus, except in special circumstances, a solid web girder is more factory both from an economical and an aesthetic viewpoint

satis-However, trusses may be used instead of girders for aerodynamical reasons Also, in the case of combined highway and railroad traffic, when usually double deck structures are used, trusses should be provided as the main carrying members of such bridges In Fig 1.35, typical bridge cross-sections incorporating trusses are shown

THE CABLE-STAYED BRIDGE SYSTEM 29

Twin box

I girders

3 REINFORCED OR PRESTRESSED CONCRETE GIRDERS

Fig 1.36 Reinforced and prestressed concrete girders

During the last decade a number of cable-stayed bridges have been built

with a reinforced or prestressed concrete deck and main girders These

bridges are economical, possess high stiffness and exhibit relatively small

deflections The damping effect of these monolithic structures is very

high and vibrations are relatively small Such outstanding structures as,

for instance, the Maracaibo Bridge in Venezuela, indicate that this new

bridge system possesses many excellent characteristics Typical

cross-sections of this system are shown in Fig 1.36

1.9 Structural advantages

The introduction of the cable-stayed system in bridge engineering has

resulted in the creation of new types of structures which possess many

excellent characteristics and advantages Outstanding among these are

their structural characteristics, efficiency and wide range of application

The main structural characteristic of this system is the integral action

of the stiffening girders and prestressed or post-tensioned inclined cables, which run from the tower tops down to the anchor points at the stiffening girders Horizontal compressive forces due to the cable action are taken

by the girders and no massive anchorages are required The substructure, therefore, is very economical

Introduction of the orthotropic system has resulted in the creation of new types of superstructure which can easily carry the horizontal thrust

of stay cables with almost no additional material, even for very long spans

In old types of conventional superstructures the slab, stringers, floor beams and main girders were considered as acting independently Such superstructures were not suitable for cable-stayed bridges With the orthotropic type deck, however, the stiffened plate with its large cross-sectional area acts not only as the upper chord of the main girders and of the transverse beams, but also as the horizontal plate girder against wind forces, giving modern bridges much more lateral stiffness than the wind bracings used in old systems In fact, in orthotropic systems, all elements

of the roadway and secondary parts of the superstructure participate in the work of the main bridge system This results in reduction of the depth

of the girders and economy in the steel

Another structural characteristic of this system is that it is geometrically unchangeable under any load position on the bridge, and all cables are always in a state of tension This characteristic of the cable-stayed systems permits them to be built from relatively light flexible elements-cables The important characteristic of such a three-dimensional bridge is the full participation of the transverse structural parts in the work of the main structure in the longitudinal direction This means a considerable increase in the moment of inertia of the construction, which permits a reduction of the depth of the girders and a consequent saving in steel The orthotropic system provides the continuity of the deck structure

at the towers and in the center of the main span The continuity of the bridge superstructure over many spans has many advantages and is actually necessary for a good cable-stayed bridge

Considering the range of applications in the domain of highway bridges, cable-stayed bridges fill the gap that existed between deck type and suspension bridges Orthotropic deck plate girders showed superior-ity over other systems in the case of medium spans For long spans, how-

THE CAB LE-ST A YEO BRIDGE SYSTEM 31 ever, they required considerable girder depth The cable-stayed bridge provides a solution to this problem, based on a structural system com-prising an orthotropic plate deck and a continuous girder

Comparative analysis of cable-stayed and suspension bridges indicates the structural superiority of this new system even for large spans, as is shown in the following section

1.10 Comparison of cable-stayed and suspension bridges The idea of suspended bridge structures is to support the bridge deck with cables However, the cable-stayed bridge differs from the suspen-sion bridge in the manner its deck is supported, and in resulting structural characteristics

In suspension bridges the deck is supported from loosely hung main cables with vertical suspenders, but in cable-stayed bridges the deck is supported directly from the towers with stay cables This provides a significantly stiffer structure Also generally the deflections are less, therefore the deck can be made lighter and more slender Structurally this improves cable-stayed bridge wind resistance and aesthetically the appearance

Comparison between modern types of suspension bridges and stayed bridges clearly indicates from several points of view that the cable-stayed bridge is superior to the suspension bridge Due to results of several competitions, the opinion became established that the cable-stayed bridge fitted into the gap between the plate girder beam, with spans of up to 700 ft (215 m), and the suspension bridge, with spans larger than 1400 ft (430 m)

cable-Comparison of the suspension and cable-stayed bridge systems indicates substantial progress in applications of cable-stayed bridges For example, in the competition for the Great Belt Bridge in Denmark in

196 7, eleven cable-stayed bridges received prizes from a total number of eighteen bridges Incidently, all those bridges have to carry not only highway but railway loading

In 1968 for the competition for the bridge across the Strait of Messina, Italy, a cable-stayed bridge with a 4264 ft (1300 m) main span was in the award group, as well as a number of suspension bridges In Japan, Hitsuishijima and Iwagurojima cable-stayed bridges will have spans of

607 + 1378 +607ft (185 + 420 + 184m) and traffic running on a level stiffening truss with roadway on the upper deck and railway on the lower deck The Arcash Kaikyo Bridge is planned to be the longest cable-stayed bridge, with a main span of 5838 ft (1780 m)

two-The superiority of the cable-stayed bridge over the suspension bridge may be based on a comparison of their structural characteristics, following an analysis as proposed and developed by Gimsing30•