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THE CANTILEVER' CONSTRUCTION

OF PRESTRESSED CONCRETE

BRIDGES

Jacques Mathivat Professeur au Centre des Hautes Etudes de la Construction, Pro/esseur a

[,Ecole Nationale de~ Ponts et Chaussees, Paris, France Translated by

Mrs C. J. Emberson

A Wiley-lntersciencePublication t

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JOHN WILEY AND SONS _. IJ .-~ .._.-.-.- .. ~.-....- .-.-._.-- - --- . --_.'._--~ '_.4 --1-_,,--__~ ..

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This book is the translation by Mrs. C. J. M. Emberson of the French original edition Conslruelion Par Eneorbellemenl Des Ponls En Beton Preconlrainl by. Jacques Mathivat. C Editions Eyrolles, 1979

61, boulevard Saint-Germain, 7SOOS Paris, France

EngUlh translation copyright C 1983 by John Wiley &, Sons Ltd.

All nabtl reserved.

No part of this book may be reproduced by uny means, nor transmitted. nor translated into a machine languaae without the written permission of the publisher.

Libra', o/Congrell Calaloglng In Publlcallon DaIQ: Mathivat. Jacques.

Th' ~JJlti1cvcr construction of prfstrelsed concrete bridges. Teanllation of: Construction par encorbcUemcnt des ponts en beton

precontraint. Bibliography: p. 333. 1. Bridges, Cantilever-Design and construction.

2. Bridges, Concreto-Design and construction. 3. Bridges, Prcfabricaled-Dcsian and constr~.ction. J. Title. TG385.M3713 1~83 624"~3.~. 82-23744 ISBN 0 471 10343 8

British Library Cataloguing In Publication DaJa: Mathivat, Jacques

The cantilever constniction of prestressed concrete bridges. 1. Bridges, cantilever '2. Concrete beams 3. Prestressed concrete . I. Title II. Construction par cncor~Ucment des ponts en beton precontraint. English . i-,\' . . ,.' 624' .35 TG38S

ISBN 0471 10343 8 Typeset by Pintail Studios Ltd., Ringwood, Hampshire. Printed in Great Britain by Pitma~ Press Ltd., Bath, Avon.

LIST OF CONTENTS

Foreword ............................... , . vii" ~

Chapter 1 General Background ..... ' . . 1 1. The Principle of Cantilever Construction . 1 2. History ~ 2 3. AdvantaJcs of the Process and Field of Application 13

Chapt,r 2 Deck Desfsn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1. MttbodaofConstruction from Piers and Abutments 21 2. Or.anization of the Cantilevers: Choice of Hinged or

Continuous Qeam System 33 3. Span Distribution ............................ 47 4. Forrp and Size of the Transverse Cross Section .......... S4 5. Loniitudinal Section of the Decks .. '. . . . . . . . . . . . . . . .. 76 6. Deck Cabling Arrangements .. ,..... . . . . . . . . . . . . . .. 79 7. Final Adjustment oftbe Structure ... . . . . . . . . . . . . . . .. 95 8. Deflections or the Balanced Cantilevers and Initial Compensating

'Hog ......................................... 97 9. Special Problems in Design and Calculation of Decks . . . . . . .. J02

Chapter 3 Delip for Deck StabDity during Construction ......,.. J26 1. Pier Structure and Deck Support Conditions 126 2. Piers with Flexible Diaphragms J30 3. Piers with a Double Line of Neoprene Be~rings ,.. J43 4. Deck Stability during Construction J59 S. Some Examples of Temporary Supports .. J77

Chapter 4 Cantilever 'Construction by in situ Concreting of the Segments J90 1. Different Construction Procedures for in situ Concreting of

Segments ...................... '. . . . . . . . . .. J90 v

_ ..,._..."""",,,~' _..J

vi C.:onlents

2. Construction by Mobile Concreting Carriage Carried by the Deck 190 3. Other Construction Procedures using in situ Concreting of the

Segments ................................. 209

Chapter 5 C,antilevcr Construction Method by Assembling Precast Segments . 212

1. Advantages of Precasting .. . . . . . . . . . . . . . . . . . . 2~.2 2. Segments with Glued Match-cast Joints . 212 3. Segment Precasting Methods .. 219 4. Methods of Segment Placing . 232 S. Problems specific to Segments with Match-cast Glued Joints 264 6. Limits and EvoIution of Construction by Prefabricated Segments . 267

Chapter 6 Cantilever Construction ofCable...stayed Bridges ...... 270 1. Transition between Cantilever Bridges and Cable-stayed Bridges 270 2. Difference between Cable Stays and Prestressina Cables of

Cantilever Bridges .......................... 272 3. Spacing of Stay Cables ..... ..... , ..... t 27S 4. History and Inventory or Br.idges with Multipleinclined Cables . 278 5. Field of Application of Cable-stayed Bridges-Aerodynamic

Stability ........................... 282 6.. Nonlinear Behaviour of Cable-stayed Bridges , ..... 285 7. Longitudinal Structure-General Arrangement . , .. ~ ... .288 . 8. SusJ)Cnsion ........... .. , .. 29S 9. Towers ............................ 305

10. Transverse Cross-section of the Structure , ........ 314 11. Construction Problems .......... 319i 12. Tenlporary use of Cable-staying during Construction of Other

Types of Structure ........................... 323

Bibliography .................................... 333

Index ......................................... t 336

FOREWORD

The first prestressed concrete bridges to be built by the progressive cantilever method were erected in Germany. a quarter of a century ago. This type of bridge has seen such rapid development that it nO\'1 has a virtual monopoly for spans from 60 to 1SO metres. The longest spans are. in Prance. 172 metres ror the two main bays of the Gennevilliers bridge and, in Japan, 240 metres for the bridge at Hanama. Two significant innovations may be credited to the French technique: the elimination of articulation at the centre of the span. through the stiffness provided by the prestressing or the two beams: and the prerRbrfc8tion or the scgn1cnts.

From 1971 to 1975, the French Department of Works supervised the c'onstruction of 73 bridges or this type. representing 403 000 square metres of bridge deck, while the motorway companies were responsible for 39 300 square metres. built by the same method. .

The advantages of this type of bridge which have led to its rapid development are essentially four in number.

First, the elimination of the arch. which means that noodwaters and con tingencies arising from burst dnrns can be accommodated. as the waterway is not impeded. Thi~ technique is well suited to the use of very high piers, the construction of which has become more economieal through the use of sliding formwork. Accordingly it has competed with. and virtually eliminated, large concrete arches.

Secondly, the scgrncnts can be prefnbricntcd, where the number required is sut' ficiently large to make this worthwhile. Prefabrication has several advantagesthe segments being factory made are of superior quality to those made at site and. by the time they are ~rcctcd, a considerable amount of shrinkage has already taken place, so that the prestressing is applied to hardened concrete.

The speed of operation permitted by this procedure should be noted; with segments cast in place, it is normal to complete two sections per week on each beam, or in exceptional cases two pairs per week; with the prefabricated method, three to four sections a day can be achieved.

vii

ix viii Foreword Foreword

Finally, the net cost has permitted successful competition with steel in what was the experience accumulated over a period of abOUI fifteen years. It will be of the once its exclusive domain. Furthermore, one should note the use of the technique greatest value to civil engineers and should lead to further advancements. for railway bridges and the possibility of extending its application by the use of MARCEL HUET,lightweight concrete. Ingenl!!"' Generai des Poms et Chaussees

Preside'" de Seclion au Consell Olmeral des Ponts el ChausseesBridges built by the progressive cantilever method present unusual design Presldenl de "Assoclallonproblems. The sheer volume of calculations involved is considerably more than in Fran~aise des Pants el Charpenles

other types of works. It stems from the large number of sections which have to be checked and the development of the static diagram of the work during ita cons truction. It also arises from the fact that the construction has to take account of the time factor, because of the overall duration of the project, during which the nonelastic properties of the materials have already begun to appear. The effects of creep of the concrete and relaxation of the steel lead to delicate problems of control of the beams and the continuous redistribution of stresses in the stru ctures. The development of such structures could not have progressed to such a high

degree without the systematic use of complex programs performed on the most advanced computers.

In the realm of major works the design concept is intimately bound up with the construction methods, and mention should be made orthe essential role played by contractors in the rapid and constant development of prestressed concrete bridges ' built by the progressive cantilever method. .. ! As always in the engineer's art, progress comes from the exploitation of the

valuable feedback given by each achievement, the analysis of difliculties encountered and the incidents overcome, either during the building phase or when the bridge is in service. The following four points can be mentioned, to which the greatest importance should be attached: - the continuity of the cable ducts, the correct evaluation of friction losses,

and the quality of grouting of the prestressing cables; - the spreading of the concentrated loads in the prestressing cables; - the introduction of a temperature gradient in the actions applied to the

structure; - and the redistribution of the hyperstatic stresses caused by concrete creep. Professor Jacques Mathivat has directed the concept and construction of a

large number of progressive cantilever bridges, and in this way he has been one of the leading architects of the evolution of this bridge-building technique. Today, he has an international reputation in the field. His book represents a synthesis of all

......: ...~.

,CHAPTER ONE

GENERAL BACI

2 The cantilever cOllstructioll ofprestressed concrete bridges Spnt19't19 on 0pier Concrete ~eQmenl~ p

../ / "" roweU'/l9 cobles

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Fig. 1.1 Diagram showin~ the principle of cantilever building

The segments may be concreted in situ in mobile forms. They can also be prefabricated. transported and set into place with the appropriate lifting devices.

2 HISTORY

2.1 Past history The concept of building a structure cantilevered from its supports is not new and has been in the mlnda of builden almost from the,bcginnina oC con.truction. The tirst cantilever bridge. were indeed timber bridges. In his writinp, Cacsar

mentions Gallic works built with tree trunks set orthogonaUy In horizontal rows, the latter being tilled with boulders acting as counterweights (lig. 1.2). Structurcs of this type can still be found in China, India and Tibet.

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Fig. 1.2 Cantilevered timber bridge (an impression from the art historian Viollet Le Due)

General background

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Fig, 1.4 Building methods for Thomas Pope's project

In moro recopt dmes, in 1811, the American engineer Thomas Pope designed a timber bridpwit!t.a 5~O'm span. This would have had a very shallow arch rcsting on two qJllOIJry .butm~nts from which it would have been built as a cantilever structure by assembling prefabricated components (tig. 1.3). . Fig. 1.4 shows the building methods conceived f, r this project.

2.2 Steel and reinCorced concrete structures

Cantilever techniques were first used for sleel structures during the last century when large arches and cantilevers were being built. With the introduction of

4 5 The cantilever constructioll a/prestressed concrete bridges

reinforced concrete many buiJders became interested in applying this technique, even to a limited extent, to this new material.

In 1928, Freyssinet was already building cantilever springings for the arches of the PlougasteJ bridge which has a span of ]85 m. The springings were subject to a high temporary overturning moment (47000 kNm) due to the ~eight or the centring during construction. In order to balance this moment. Freyssinet devised a system to link the two adjacent springings with steel ties. thus creating a form of temporary prestre~.s. These ties, which- were formed of wire cables, were kept under tension by defh..ction jacks bearing on a framework positioned at 'the centre of the piers (fig. 1.S). However, the first time this method was applied to reinforced concrete

structures in a manner similar to that used today was in 1930, when E. Baumgart undertook the building of the 68-m centre span of the Herval bridge across the

Overturning moment I due to weight of ~ centrmg T I

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Fig. 1.5. Cantilever construction of the Plougastel bridge springings (preysalnet)

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Fig. 1.6 Construction or the Donzire bridge (Caq'10t)

Genttal background

Rio Peixe in Brazil by the cantilever method. The reinforcing bars of the deck were extended by threaded sleeves as the concrete \vork progressed. Other works followed both in France and abroad. Caquot designed the biggest

cantilever reinforced concrete bridges in France, notably the bridge at Donzcrc. having a centre span of no Jess than 100 m (fig. 1.6). This method has not been extensively developed, however, on account of the

large amount of reinforcement needed to ensure the adequate strength of the cantilevers, and to contain the large incidence of cracki,ng in the top su rface of th,e deck.

2.3 Prestressed concrete structur.es

With the advent of prestressing, suited as it is to cantilever construction. th j~ process was to be exploited to the full. Freyssinet again used cantilever method5 of assembly for the sloping picrs ane

the first segments of the Luzancy bridge (S5-m span. 1945) and for the fiv< bridges across the river Marne (75-m span. I948-1 950)-anchored into the abut ment by prestressed cables-as also were the arch springings of the viaducts () the Caracas-La Guaira n10torway (1949-1950). The decks of the Marne bridges are formed of very shallow arches. composc<

of six prefabricated clements. Each half-arch comprises: a sloping jackleg. ; springing cantilever section formed of five segments. and a central half-bean (fig. J. 7). These elements are placed by a lifting system of two cable-stayed mast placed on the abutments and a tackle of rigged pulley blocks. OnJy the jack leg and the springings were cantilevered; the closing key of each arch was place. when the l wo half-arches were in position (ng. 1.8). The arch springers of the Caracas viaducts were built in lengths of about

quarter of the span, by concreting successive sections in suspended forms hangin rrom cablc~ (fig. 1.9). These cnbles were anchored to the roundntion~ of t he pier

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Fig. 1.7 Ussy bridge over the Marne River (Freyssinet)

6 The cantilever construction ofprestressed concrete bridges

Fig. 1.8 (0) and (b) Construction of the Marn~ bridges

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Fig. 1.9 Construction of the arch springers of the Caracas-La Guaira motorway viaducts

General bQckgroulld

of the approach viaducts and were supported by the main piers. which extended above the arch abutments. The central section of the arch was then built on a centring weighing 200 t, assembled at the bottom of the canyon and lifted by cables fixed to the ends of the already built arch springers (fig. 1.10).

However, it was Dr Flnsterwalder in Germany who inaugurated the cantilever method, with the construction of the prestressed concrete structures of Oa!dulnltcln and NC4:karrens (1950-1951). During the same period. the con tractor, BouSliron, aI,O used this method for the construction of the railway bridlO of 1. Voulto over the Rhone (1952) (fig. 1.11). From that date, the evolu tion or cantilever CODltru~on accelerated. The period 1952-1953 saw the con struction of .truct~OI u.~g prestresllng rods by the contractor Dycke,rhojJand Widman. in QcrmanY. l'hcy used travelling concreting skips supported by the cantJ1evon (WOrm. brid,e over the Rhine, 101-, 114 and 104m SpaMi Coblenz bridge oyer Ihe.Moselle, 102, 114 and l23m spans) (figs. 1.12 and 1.13). In France, the first cantilever construction by In situconcreting of the segments was on the Chazey bridge over the Ain (three spans, 41.2, 57.6 and 41.2 m long

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Fig. 1.10 (a) and (b) Positioning of the centring and keys of the midspan section

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9 ~ Tire cantilever construction ofprestressed concrete bridges ......... ~,~ -',",""'. ~'''''''n''''''''' __ -'--''''''''''''''t--''''''~'''''------''''''''~r ...!,~:~':. . _.: .~ :;..i..~.: 1 '~"j~~.,,,; ~.2""'~d.:.""'~x_~""""',4'~':'::'~'"\I:"''1'-'''-I":"

Fig. 1.11 Construction orla Voulte railway bridge

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10 Genera/background I I The cantilever COllstruction a/prestressed concrete bridges

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12 13

Fig. 1.1 6 Choisy-Ie-Roi bridae

The cantilever cons/ruction a/prestressed concrete bridges Genera/background

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;; This new construction method was soon used widely, and abroad some spectacular structures were built in this way: the Chnlon viaduct near Lausanne and the Rio Niteroi" Bridge in Brazil (totkllength 8 km). Recently several bridges1~, n' have been built in France using this procedure: q

- Saint-Cloud bridge across the Seine, a 1tOO-m..long curved structuret~ \~ involving a deck with a constant depth of 3.60 m and spans ranging trom

._.j"" 64 to 101.8 m; , I

L (b) Viaduct linking Ol~ron Island to the mainland ~:I - Saint-Andre-de-Cubzac bridge across the rivet Dordogne, 1200 m long, !','-, which has five spans of97 m over the piers; . Fig. J. J7 r ~~ - Calix viaduct in Caen, 1880 m long, has a central span of 156 m.

Cantilever techniques are likely to find new openings in years to come in the 3 ADVANTAGES OF THE PROCESS AND FIELD OF APPLICATIONdesign and the assembly of cable-stayed bridges. Brotanne bridge, below Rouen,

already sets a precedent, its 320 m main span is the IBtlest prestressed concrete ! span to date. The central part of this structure consists or a cable-stayed bridge 3.1

built by the cantilever method from the towers, using the multiple cables which The main advantage of cantilever construction is the elimination of centring and were arranged in a fan shf,.pe. falsework; this clears the space below the bridge. This process is therefore highly

14 The cantilever construction a/prestressed concrete bridges Genera/background I~

(a) Saint-Cloud bridlC .::;' "... ":.... ~~':~,--_..:,~:.;-;~f<

(b) Salnt-Andre-de-Cubzae bridle

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Fig, 1.18

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PlJ. 1.19 Brotonnc cable-.tayed bridp

suitablo for the following local conditions: - structures involving very high piers and which span wide and deep valleys

(COIdy COIItrinI); - rM'" wid! wild lAd sudden floods (dangerous to centring); - nocd to allow tho llow of. certain volume of traffic or to permit navigation . whilst construction i. in progress (hindering centring).

The technique ofcantilever construction also ofTtrs other advantages: - reduction in number and more efficient use of forms whose length is no

II'Cater than that of a segment; - improvementl in workmanship, due to mechaniza~ion of tasks within a

recurring cycle; - n~bility of execution which is linked to the possibility of speeding up the

construction by increasing the number of starting points for cantilevering; - improved rato of construction in the case of structures with prefabriclltc

16 The cantilever construction ofprestressed concrete bridges Genera/background 17 Spans (metres)

1 63000 .., o 10 20 30 40 50 GO 70 eo 90 100 110 120 130 140 130 160 170180

.Moq,t 140.00 ..,.. 24000 140.00 _ 5500~.I / 13.76 I I " B:._:...=::::t=~1f'~ Mmc::fi

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'--' Optimum ronge ~ Normal ronge l.__~ Exceptional ronge

Fig. 1.20 Field of application of the processes used to build major prestressed concrete bridges

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Fig. 1.22 Haman. bridgeFig. 1.21 Bendorf bridge

Prefabricated beams

Con'ileve

Incrementolfounchinq

Self - launChingC4!ntring

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come close to it,(J) namely: - the Hikoshima Ohashi bridge in Japan which has a main span of 236 m; - the Urato bridge, also in Japan, which has a main span of 230 m (fig. 1.23); - the bridge linking the Karor and Babefthuap islands Bast or the Philippines

has a main span of approximately 240 m. In France the three biggest cantilever bridges 8:fe:

- the GennevilJiers bridge across the Seine with a 172 m span (segments con

creted In situ);

- the-Calix viaduct in Caen with a 156 m span (prefabricated eoncrete seg

ments);

(I) For historic reasons the Maracaibo bridge is worthy or mention because, ror I long time. it ~as the pre~tressed concrete bridge with the longest span. Built with severa! cablestayed bays, its construction did not. however. involve CAntilever techniquea to I significant extent. . Fig. 1.23 (a) and (b) Urato bridge

19 cantilever construction ofprestressed concrell bridges . :.. 1~/1~J':~ V:" ~. .'.;'::;', , :....:~ .~.::.:;~{~;:.. .:Xt.:,~

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Fig- 1.24 Le Bonhomme bridge

Lightweight concrete

Fia. 1.25 Ottmarshcim bridge

- the Bonhomme bridge across the river Blavet, a structure with sloping piers. with a 18S m opening and with a 146 m deck span between piers (segments concreted in situ) (fig. 1.24).

A structure with precast segments currently under construction across the Ottmarshcim flood relief and navigation canal will have a span of approximately 172 m(fig. 1.25). Independent bays made of prefabricated beams placed in position by lifting

plant are usually cheaper than cantilever construction for spans below SO m. With spans over 60 m long, however, prefabricated beams are not used, due to the increase in the weight of the beams and the lifting plant. Besides, it is necessary to increase the number of longitudinal beams to limit their Wlit weight and, as a consequence, this decreases the rate ofconstruction. The same holds true for the other methods of construction, avoiding the use of

Generlll background

falscwork such u deck-launching and building on self-supporting centring and self-latIQching centrina; they become uncompetitive beyond spans ranging from SO to 60m. As far as small spans are concerned it should be noticed that in the case of long

prefabricated structures to be built in an urban environment at a low height, cantilever building is competitive for spans in the 40 m range. The viaducts of the Kleinpolderplein interchange in Rotterdam (fig. 1.26), of an overall length of 2 km, were indeed built by the cantilever method-with spans ranging from 27 to 3S m-by means of prefast concrete segments set in position by a launching girder. A similar method was used for the construction of the B3 motor\l,'ay viaducts in Paris, with spans of approximately 38 m. The use of lightweight aggrega/es (expanded clay or schist) in the concrete by

rcducina the dead wciaht of the deck can also permit a more economical construction of large spalll built by the cantilever method. Several structures have already been built in ligh/weight concrete in Germany

and mainly in HoUand. where several have spans around ISO m: - bridge over lake Fiihlingen (Germany)-J35 m span;

Fig. 1.26 Klcinpolderplein interchangein Rotterdam

'

20 The cantilever construction qfprestressed concrete brldps

- Houten Bridge over the Amsterdam-Rhine Canal (Honan~143.s m span;

- Ravensway and Zoolen Bridges over the Amsterdam-Rhine Canal (Holland)-150.5 m spans.

In France, the Ottmarsheim bridge is the first large cantilever structure in liabtweight concrete. CHAPTER TWO

DECK DESIGN

I METHODS OF CONSTRUCTION FROM PIERS AND ABUTMENTS

1.1 Cantnever construction generally starts from the main supports of the structure, namely the piers and abutments

J./.l Cantilever construction/rom piers 1.1.1.1 When starting from piers it is logical to build symmetrically outwards from the piers to avoid high asymmetric overturning moments in the piers. To meet this requirement, the structure must be built in a succession of balancing cantilever sections (fji~ 2.1). However, as the symmetrical sections either of in situ concrete or of precast conctete segments cannot be built simultaneously in practice, the piers must sustain bending stresses.

If the deck is built locked In with the piers, they can usually accommodate the asymmetric moments during construction more easily. If, on the other hand, the deck is designed to be continuous over the piers, it is necessary either to provide temporary fixity between the deck and the piers during construction (by means of wedges nnd stressed tendons), or to provide temporary supports from the piers. Details of providing temporary support to the deck during construction will be considered in Chapter Three.

1.1.1.2 In certain cases, it can be preferable to build asymmetrically from the piers. This can be achieved in a variety of ways: (a) By using a single temporary support pier, or by using one or several

temporary supports as building progresses, (fig. 2.2) as was adopted for the Medway bridge in England (fig. 2.3), a process usually requiring the use of temporary prestress.

(b) Section of deck poured in situ on centring to act as counter weight to cantilever-built sections. This arrangement is often used with three-spanned

21

22 The calltilever constructiOIl o/prestressed concrete bridges Deck design 23

Wind or construc;lion loodinQ ttttttttt

QverlurninQ ......+-.. momenl{ i '\ SeQment iii I Iii i ik...\!1

Contilever

BALANCED STRUCTURE BALANCED STRUCTURE

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'C".QFig. 2.1 Symmctrical construction >. III

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Seellon cost on CenlrirlQ ~ .' / Conlilever seclion J:! .., .....,-;,.;I'""""'..-..vk...7 1) ~

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__ Temporory _ Supplemenlory g .!:!

] support support +I 03 ..

+' I",03.,.

~ nil/II e illill I' g J = U.:II

--'Ip-J'L.+I.LI~~_-LL"_ ~11 f o _. 5 UFig. 2.2 Using tcmporary supports -:: ..., -

.1 8 Nstructurcs, when the centre span passes over a river or a highway which pre ~I h,cludes the use of staging. The bank spans arc then concreted in silu on the t centring and the centre span is built by the cantilever method (fig. 2.4). Structures built by this method include the bridge across the Rio Tocantins (Brazil), the bridge across the Rio Cuaiba (Brazil), the Goncclin bridge across tho river Isere, and the Port de Bouc bridge across the Aries canal.

(c) Counterloading or anchoring one cantilever span whilst building the adjacent span. This case more usually arises when building main river spans when the shore (or bank) spans are short. There are two possible solutions: /i

The first solution is to ballast the end of the bank cantilever or to provide a 11] counterweight (fig. 2.5). The bridges at Lacroix-Falgarde and Croix-Luizet,

24 25

The cantilever construcdon 0/prestressed concrete bridges

SlOQing

Section 7ret8d on centrin;

if~ Fig. 2.4 Bank span concreted on centrlns

$uppclrt ,.\ Support

Fig. 2.5 Ballastln& tM end ofone orthe cantilevers

and the structures spanning the Seine at Puteaux (fig. 2.6) are examples of this techniq ue.

The second solution is to anchor the end or the bank cantilever either by prestressed tie rods, or by a morlise-and-tenon joint linking abutment and deck. The prestressed tie rods are formed of prestressed cables, enclosed in articulating casings or tubes, which tie the deck to the abutment (or to the

"::>;;~:::::~~::~~~~::.

Fig. 2.6 Structure spanning the Seine at Puteaux bridge on Neuilly side. Longitudinal section

Deck design

Pre5lressed ''lie-rod

I Prestressing /,

'coble I'

. 1--PreSlress,ngcoble .......1

Fig. 2.7 Anchoring of one cantilever by prestressed tie rods

ground). The I~ngth of the tie rods' must be sufficient to ensure that the angular movements of the rods due to linear variations of the deck do not cause excessive fatigue stresses due to bending at the hinge points. On this account the components of the cables (steel wire or strands) are usua/ly arranged In a single row located in the axis of the hinge.

The mortise-and-tenon anchorage consists of extensions of the webs of the deck beams (forming the tenon) which slot into recesses fonned in the abutment (acting as mortises) (fig. 2.8). The bearing plates which allow free horizontal movement of the deck nrc fixed between the top of the tenon and the top element of the mortise in the case where the restraint is constantlyagainst an uplift of the deck.

If the tendency of movement of the deck is possible both upwards and downwards, the double restraint is adopted, the bottom bearing plates, which are placed after the top plates have been fixed, being forced against the bottom of the tendons by caulking or by tlatjacks (fig. 2.9).

The abutments of the Givors bridge, together with those of one of the two structures spanning the Seine at Puteaux (fig. 2.10), include mortise-and

tenon anchorages. To adopt such arrangements requires a detailed study of the structural capacity of both the abutment wall mortises and tHe tcnons. The deck reactions at the abutment must be calculated using a 50% overload factor on the estimated reactions.

With structures ofthis type and when aiming at limiting the uplift reactions

Downword mtroinl 1Double restrOlntl I, I I Ii' iii I ,

:J-'-Fig. 2.8 End anchorage by mortise and tenon

I

26 27

12Tl~

I

The canlileller conslrucliono!preslressed concrete bridges' Deck design

LONGITUDINAL SECTiON

Slllfenin9 membraneI freSlrnsillQ cobin

I111I,' i

, i_

Abutment ill 1 (a)

8~t30 3~5 30

(a)i llOT/CABLE ~ 1l0YCABLE 31ZT15Pr' "r 'J()+f. ~ ~ J t fl f

SECTIONAL PLAN .~f'F"i 1, 5ill f&:?l -,

1 ..:~~~~~::::;~~: :'~::.:::~:.::.;,.:.::

(b) Fig. 2.9 (a) and (b) Example of mortise and tenon anchorlle

of the deck on the abutment. it is expedient to build the centre span in lightweight concrete whilst the bank spans and the abutment springings are built in traditional concrete (fig. 2.11). Such a solution was adopted for Onmarsheim bridge and is planned for a structure across the Donmere canal at Tricastin (fig. 2.12).

(d) By means of temporary support strutting beams. enabling the sections of a cantilever span to be built symmetrically from each end in pairs. This particular solution implies that the deck is built as a succession of segments built symmetrically to the axis of each span. A temporary steel girder spanning the gap (a Bailey bridge for instance) supports the formwork and the se!f

(b)

Fig. 2.10 (a) and (b) Structures spanning the Seine at Putcaux bridge. Longitudinal section and detail of the abutment prestressing

Li9htweiCJht concrete Tradltionol cone/ere

A "1.7 to t.8

Fig. 2.11 Using lightweight concrete

_ ... _-... J .......~

--' 71 7\~-_: nTI5 j

_,' Temporory ~upporl

The cantilever construction ofprestressed concrete bridges28

203.00 ~

30.25 142.50 3025>'''~. \.. Ughlweighl concretl .. \ l:25.25 ..,P,I roo ....,.~"..::"._.- ~~. '50~=n~::::;!fS

. A

(0) i

(bl

TOP VIEW

I I L-==~::~ ~ l---i- r-j-- !.[--- A~---r---* 8I1 r ----------..r'-+--'-'-d>r-._._._._.t-H._- ...-J~. I__~=l--__ ~. L. rlt. r---F===, ----...---------1-=:=:::.~ ----~--_. y .

(c I Fig. 2.12 (8), (b), (c) Tricastlrt bridge project

weight of the segments under construction. and is also used as ." access way (fig. 2.13).The stability of the pier cantilever unit is ensured by I strUtting beam hanging from the steel formworlc. frame and bearing horizontally against temporary pedestals set into the deck (at each pier). The II Voulte llridge acrosS the Rhone is an example of this rare type of construction.

Deck design 29

Framewark suppart beam ( Bailey bridge 1 Supparl pedestal

Sirutting beam

Fig. 2.13 Construction of la Vouhe bridge

(e) By proceeding with cantilever construction on one cantilever once the next cantilever has been connected to the adjacent deck beam. This solution is onen adopted when the widths of adjacent spans vary. This solution has the disadvantage of entailing an arrangement of cables which becomes more complicated if th~.cantilever length greatly exceeds half the span.

/./.2 Cantfle~'er COllstructlon!rom tire abutments Cantilever construction springing from the abutments imposes high overturning moments on the latter which can be counterbalanced either by: (a) temporary supports set in front of the abutmenls (lig. 2.14) as adopled for the

8asse-Combelle nnd Pierre-l3cnite bridges; (b) by the abutment self weight acting as coumerlveight. In most cases the bank span cantilever is embedded in the abutment. and thus forms a stable unit (fig. 2.15). The abutment is Ihen said to be balanced.

The bridgc across the river Reallon, Verberie bridge, Bonpas bridge and the viaduct ofle Magnan (fig. 2.16) are examples of this type.

The deck can also be fixed nexibly at each end by means of a shorl balancing

Ballast

AnchoraQe in abutment

Fig. 2.14 Construction from an abutmenI with temporary support

Deck desigt' 31The c,mti/e~er constructloll C/fprcstressed C()1/crc/(! bridges30 Balanced abutment

/ ~

Fii. 2.15 Construction from a.balanced abutment

48.50 -\

I 15.00 \ 50-';: 14.50':

d . ......:--r ~\

-----__ ---k..Q.:&i::,.-&:r~n:_-~;~:~;\ --------- ;)-10 ---------=---i~ (blr._ I I ~ ... It I

i ~ 15.00 3.00 (a) and (b) Bridge across the Reallon river

1:JI=rLeon concrete infill

....... / 41.25I.. ; Ii

~l-r .i'::::~::~:;:~:::~::::::::::=:::::::::~::::::::~

NlOpre~, btOrirl91 ( c) Verb"i, bridge

(c.:) Vcrbcric briulIC

2000 6000 '.--"'-'~;-4. ".. -.. - _..._.. _._.. ~.

I I

Sond'9(O",1 fim/l9

.j

(d) Magnan viaduct Fig. 2.16

span incorporated into the abutment. In this case. free movement of the deck is ensured either by rubber or sliding bearings or by tie rods-with double hinges (liS. 2.17). Tho deck mUlt then be anchored or tied to the abutment since the uplift reac

lion is opposed by the dead weight of the abutment-which is eventually baUuted-or by the resistance of the foundation. It then becomes necessary to

Double- hinqed I'e-,od

Fig. 2.17 Flexible fIXing on abutment

. _ ':"".'!'.. l.... Ie.

32 The cantilever construction o/prestressed concrete bridges

AnchOr piles

1.0015.40

Anchoring span

24.50 Fig. 2.18 Saint-Jean bridge in Bordeaux-flexible anchorage of deck to abutment

~

---Tetnf,)OtOry support

\ Foundotion

Fig. 2.19 Temporary fixity (in the case or hinged arches)

Deck design

~.~

t~.~\~,\ ~~.:: .;:~~....~" ;. J~;;'

34 The canti/erer construction o/preslressed concrele bridges Deck design 35

Deck beam r~pin9 tie rods # Shd'nej h'"ges"

r=====rr==..

......, ... ,

""'/ 1/2 ~ ... {12~ i! n IT r

~IIIIIIII .iiii-f ....{~{~ .._-{ ~:~- { ~~ Fig. 2.22-Syslems wilh hinged canlilcvcrs-

--

36 37 The call/ite'"er construction o/prestressed concrete bridges

It should be noted that in the case of bridges with multiple spans, the introduction of a sliding hinge at the centre of each span requires the building of each cantilever into the abutments so as to maintain structural stability when subjected to asymmetrical loading. In this type of struct'Jre the lengths of the end spans are: either approximately half the length of intermediate spans when the bridge consists solely of balanced cantilever beams on piers (fig. 2.22); or approximately the length of intermediate spans when the bridge deck also involves cantilevers built in at abutments (fig. 2.23). Structures of this design are obviously simple as they are statically deterl1tlllate

under the combined effects of self-weight and prestress and become statically indeterminate only with respect to superstructures and additional toads once the central hinge has been incorporated. This makes design calculations easier as the statically indeterminate forces for each span thus amount only to the vertical reactions transmitted by the hinges. Moreover, after taking into account the permanent load, irrespective of the additional loading arrangement, these structures exhibit bending moments of constant sign. This results in a considerable simplification in the profile of the prestressing cables. Nevertheless, this system has many disadvantages: a lower ultimate strength

than a continuous structure. as each hinge behaves as a plastic hinge with a zero monlent of resistance; hinges are difficull to design and construct as they are delicate components with poor long-term performance; a multiplicity of expansion joints; risk of uplift of the deck over the abutments, when the span of the end bay is approximately half that of the adjacent bay-this can necessitate having the deck integrated \vith the abutment or the use of ballast (see paragraph 1.1.1.2(e); finally, and most important, progressive settlement of cantilevered ends during the nrst years of the working life of the structure, deformations caused by shrinkage, creep of concrete, and relaxation of prestressing tendons.

Even though the break brought about by this deflection in the longitudinal profile of the carriageway does not affect the mechanical properties of the deck, it is an inconvenience as far as the appearance of the structure and the user's comfort are concerned since both are highly sensitive to the slightest discontinuity.

The extent or this hrcak in J1rofitc can be reduced to n certain extent by estimating accurately the denection of the cantilevers and compensating for it by an initial compensating camber at the time of construction (fig. 2.25). This initial compensating camber will be visible at the completion of the

structure but it can be anticipated that after roughly three years, or thereabouts. the bridge \viU have attained the expected longitudin;tl profile. The d~13yed deflections in bridge structures \vith central hinges are of course

reduced when the structures are built using prefabrication techniques if the beam elements are used after a suitably long lapse of time. Sliding hiltges may also be replaced by sliding conllectiolls which allo\v for the

Deck design

Initiol compensating hog

+ _---- -_u -- - _

Fig.2.25 Initial compensating hog

Sliding hinge Sliding connectIon

&m Fig. 2.26 Sliding hinge and sliding connection

Bored moving piston

'~t't17/J ' -

I Stationary cylinder

Fig. 2.27 Arrangement used for the bridge over the river Escaut

deck longitudinal deformations whilst ensuring continuity 0/ deflection and rot(J/iol1 (fig. 2.26). An arrangemenl of this type was used for the hridgc over the castern Escaut rivcr. The ends of the opposing cantilevers were joined by hydraulic rams consisting of an oilfilled cylinder fixed to one cantilever with a moving piston-pierced with a small diameter bore-which was integral with the other cantilever (fig. 2.27). These rams allow for slow horizontal deformations due to linear movements of the bridge deck and can withstand rapid movements arising froln the impacl of notsClln or from the braking of vehicles. Such arriJngc tnellls C:111 h: lIsed to ensure the stubility of structures subjected to canhquakcs. They are unfortunately comparatively expensive as a result of their complexity.

FinaJly. with certain bridges whose final structural form is that of a hinged arch the cantile\'er beams are joined by genuine hinges transmitting the thrust; this is the case with the Grande-Cote bridge (fig. 2.28).

The cantilever conslruction ofpreslressed concrete bridges38

.,7!l.1.~

Fig.2,28 Static diagram ofla OrandeC6te bridge

2.2 Cantilever systems with suspended span i A variation of the hinged cantilever system is to connect two cantilevers by an

.'!i independent suspended span (fig. 2.29). In some cases, fcar of differential settling ! of the supports caused by the nature of the foundations can lead tu the adoption

of this solution rather than the continuous systems described in paraaraph 2,3. As with sliding hinges, the supports of the span suspended from the cantileverI ends must permit rotations and horizontal displacements. However. since these

supports transmit downward vertical reactions only, they can consist of Freyssinct concrete hinges or e1astomeric bearings, and will not have the drawbacks of central hinges (fig. 2.30).

The foUo\\'ina structures belong in this category: '- the bridge across Rio Ulua (Honduras) with three spans (60, 120 and 60 m

respectivdy) and with a suspended span of 36 m; - the bridge across the Rio Parana (Brazil) with a main structure of eiaht

bays of 109 m span and with suspended spans of 4S m. This system has certain advantages over centrally hinged cantilevers:

- by the reduction by half of the break in the longitudinal prom~ whose extent is already decreased by the smaller span of the cantilevcfs. S~pcnded

Suspended span Cantilever joint

\ ..

Fig. 2.29 Cantilever system with suspended span

39Deck deslgll

Prestressir\9 cobles

elorings (neoprene, Motion) Fia. 2.30 Diagram of a cantilever joint

spans also permit compensation of eventual differences of level of the candlever ends (fig. 2.31);

_ reduetion of tho bending moments at the support; this reduction is brought about by both the positive moment along the suspended span and the unit weight of the suspended span which is lower than that of the cantilevers (fig. 2.32).

The ratio I' /1 of the span of the suspended span to the total span may vary gt8atly: I' '36

Bridge across Rio Ulua: - =--=0.30I 120

I' 4S Bridge across Rio Parana: - == - =0.41I 109.

----- ~ -----~.~ -~..-"""- -1:--:':'-~~-..~ ------':::::~12

Fig. 2.31 Reduction in the break of the Jonsitudinal prorJ.1e

Hinged cantileversMfl

41 40 The cantilever construction o!prestressed concrete bridges

~ fa +*. I I I I :. 1/3 J!. I ~ J. 1/3 J I

Fig. 2.33 Suspended span with small end spans

This ratio is as high as 0.90 (=49.7/SS.3) at the Saint-Jean-de-Maurienne bridget but this hardly belongs to the category of cantilevering. This arrangement can be justified for a three bay structure when the end spans must be very short, amounting to approximately one-third of the centre span (fig. 2.33). Uplift forces above the abutment can be appreciably reduced by bringing the cantilever joints nearer to the pier.

The suspended span usually consists of independent I-beams or T-beams of the same number as the webs of the cantilever cross-section (fig. 2.34).

Apart from the above advantages, this structural form retains the same disadvantages (Io\ver ultimate strength, multiplicity of expansion joints) as the system with centrally hinged cantilevers.

Moreover.. it leads to the use of two different types of plant: launching girders

RIO ULUA Box beam Sus~tnded beam

16 t I. +16. I .' ~... ..:,~ 1~~84)lloO

orl . . .25:0 0' I I t --"1-40 ' 30.- C

J J ~

15or

,30 --

r

-

lJ 2'4,~ CD -~

S5tI 2.10 ii 2. ~ II 2.10 ~I I ...,...--...---... 1 I

8.10 RIO PARANA

12.50 t20or40I I 1.201~ +19 I

.., ,.. -f+

-~[.- t r , I

--15&tlJl 0 .... _40 _fGO l~ - 200r .g f6 12.05 i 2.75 ..,-re- .....

14~ I~ N I Suspended beamI. .I~.I

'Boxbeom Fig. 2.34 Transverse cross sections of the bridges across the Rio tnua and Rio

Parana

Deck design

are requited for the suspended span in addition to the equipment for cantilever construction.

2.3 Systems made continuous

This consists in cOMecting adjacent cantilevers by means of concreting, or by placing a precast segment called a 'keying' segment. as well as using prestressing cables which ensure that the cantilever beams are integrated and the structure continuous (fig. 2.35). This is b~ far the most satisfactory solution and is the reaSOn why all French cantilever bridges ha ve been made continuous since )961.

i m' '"T , /2 "' M 9F Keying segment ~ ~ Iii ===r 1,1 .r: .I

-. I

I.

J (

I.

.. I 4 I ;

I. ' .I

... f

Fig. 2.35 Systems made continuous

The ver/ical deflections in a continuous structure are indeed far smaller than those met in' hinged structures and the continuous structure also removes the disadvantages incurted by breaks in the longitudinal profite.

For instance, the vertical deformation caused by a uniformly distributed live load will be four times lower for a continuous structure with constant flexural stiffness and made of a very large number of identical spans, than for the same structure with central hinges.

This difference in behaviour of the two forms of structure, together with the influence of precasting techniques, is demonstrated by the centre span of the Choisy-Je-Roi bridge across the Seine, where the deflections at centre span have been calculated for two extreme bases of design: an in situ concrete beam with central hinge and a precast continuous beam. These deflections are summarized in the table below.

Figure 2.36 shows, for both bases of design, the cantilever deflection curves of the centre span under dead load and prestressing forces. The two diagrams of figure 2.31 show respectively the long-term deformations of both forms of structure under constant load, and their instantaneous deformations under additional loads. From figure 2.36, j.t transpires that the behaviour of the t\VO structures is similar in their statically determinate phase. Deflection y and the rotation 8 of the cantilevers are slightly lower in the structure with a central hinge, for which the prestress compensates a larger proportion of the dead load moments (82 instead of 58%).

42 43

'

The cantilever cO/u'tructlon o!prestressed concrele bridges

Comparisons of the deformations at midspan

Loads Hinacd beam cast In situ I Continuous precast beam Ely leE I Y I 8

(10 MPa) (mnl) (degrees) (lO~ MPa) (mm) (dc&rees) 46 3.62.4O.L. (Dead Load) 3 38 2.0

,3 3,6-38 -2.0I.P. (Initial prestress) -22 -1.2 (82% and 58% of

the D.L.) 3 . 0.4 3.6D.L.:::I.P. 16 0.8

Prestress variation - 8

1096 , Continuity prestress Superstructwoes 4.5 7

4.596

0.4 4.5 4.5

1496 - 7 + 2 I 0

0 Structure with no load (initial) 15 0.8 11 0.8

Long-term deformations I.S 27 1.4 1.S -4 0

Structure v.ith no load (final) 42 2.2 7 0.8

Addition aJ loads 4.5 22' 1.1 4.5 7 0

Under creep, however, as shown in figure 2.37, the continuous structure exhibit$ deformations without a break in the median line, whilst the hinged structure inevitably entails a 27-mm sag at centre span, together with a relative rotation of the cantilever ends of approximately 2.8 degrees. With some structures the differential deflection miUimetres.

at the connecting point may reach several hundred

Correcf and prestressed loodl

* P,"tr'lsed connection Omm.

30mm l

40mm...1

50mm' ,

UQiZ]i .A. .. AliA. ,,41 ~

10mmt-1--_....::

----------

20mmt-1----------

~~

Hinged structure cast Continuous precast in situ structwe

Fig. 2.36 Deformations under dead load and prestress

Deckde,;gn l

Hi~ ,'rue'ure co,t ContfnUOU$" preco$tin sllll ,t".,cture

DELAYEO DEFORMATIONS

:: 30mm

~ ADDITIONAL LOAD

~~ ~~' I

Pi... ~31 J.ona-CIrm ctcformations and deformations under imposed load

Thus. when submitted to imposed load, continuous structure,s are three times stifTer than articulated structures. These results i11ustrate the superiority of continuous structures: - due to the low valu, qf the longlerm deformations which must be taken

into account when determining the initial compensating camber. These deformations may be upwards. as in the case of the Choisy bridge. due to the size of the intesr,lion prestress of the centre span;

- owing to the lis' drastic consequences 0/a lack ofprecision ill the eSlima. lion of the modulus of de/ormation of the concrete, or of the prestressing force.

The above table ShoWI that with continuous structures, a 10% variation in the value of prestress in the beams has an influence upon the shape or the cantilevers prior to'~ssembly three times less than with hinged structures. - finally, and above all, deformations subsequent to assembly may affect the

general levels but no longer h~ve any effect upon the relative slopes of the two cantilevers. Creep notwithstanding. the continuity of the longitudinal profile can no Ionser be subsequently destroyed.

As far as the construction procedure is concerned the integral connection of the cantilever beams can be achieved in several ways (fig. 2.38)~ If the two cantilevers arc concreted simultaneously the keying segment will be

made by joining the two mobile gantries (fig. 2.38(a). In the opposite case, it will be possible either to support the mobile gantry On

the end of the completed cantilever (fig. 2.38(b) or to replace the keying segment

44 The cantilever construction o/prestressed concrete bridges

Cantilever beam cables Mobile concrelill9 gantry equipment

~. :::.:....

i :1

I

i .1

.,\. I Cantilever beam cables !.

il \ I. ;1 d t,

I it Integration cables .i .; (b) Keying segment concreted with one mobile gantryI II

I'\ I, Cantilever beam cables Keying joint I II' I

-j

I I" Spoce occupied by the coble

Inlegrolion cables tensioning jock

Temporary prestress ,/Key joint 1 ,j

l~ tl ":!

Inlegration cabl" .' I ~ (d) Keying joint for precast segments

Fig. 2.38 Integral connection or the cantilever beams

Keying segment Integration cables

(a) Keying segment concreted after connection or the two mobile gantries

(c) Kcying joint concreted with special form work

4~Deck design

by a joint which will be concreted when establishing continuity (fig. 2.38(a)). The size of this joint may vary between several hundred millimetres and approximately 2 metres (the overall dimension corresponds with the space occupied by the tensioning jack of the cantilever beam cables for the last concrete segments. t\ similar arrangement will be adopted if the cantilevers consist of precast elements: a joint 80 to 100 mm .thick will be left between the opposite faces of the two cantilevers and will be concreted at the time of integral connection (fig. 38(d. With this arrangement the placing of a central segment acting as a keying elemenl may occur. The continuity of the structure is ensured by prestressing cables (integration

cabies) tensioned after hardening of the concrete, of the segment, or of the keying joint. These cables which are mostly located in the lower flange of the beam produce statically indeterminate reactions which must be taken into account when designing the bridge. The bending moments due to linear phenomena (variations of temperature and moisture, shrinkage effects) may be increased if construction takes place with large differences in temperature occurring between the upper und lowcr nangcs of the cantilevcr. As temperature conditions cannot remain constunl during the hardening period of the cantilever concrete, the ends of the opposing cantilevers must be provisionally fixed on top of one another by it mechanical dcvicc (structural sections nnd steel joists) to avoid the disruption of thc joint.

TIlUs, continuous systems arc ultimately statically indeterminate under self weight and prestress and their degree of indeterminancy is higher than that or hinged systems. On the other hanu, as with any continuous construction, it is necessary 10

permillongitudinal expansion of the bridge by cll,reful consideration of the support conditions. without creating high bending moments at the piers. This problem can be solved either by the flexibility of the piers themselves, or by using elastomeric bearings or sliding supports. Bearing design and the infrastructure of the piers best suited for cantilever construction will be considered again in Chapter Three.

, With very long structures with multiple spans one has to incorporate joints in the cantilevers or suspended spans to ensure free horizontal movements. These expansion joints are commonly placed 300 to 600 m apart (fig. 2.30).

It is advisable to position these joints not at mid-span but in the area of points of

025 to 030 ~ Cantilever joint I I ' ~it-r9t~ . ' I II. l ,J, ( l .i. , ,I,j,

Fig.2.39 Continuous system with expansion joint

01 eapens,on jOin1

46 The call1ilever cOllstrucnon a/prestressed cOllcrete bridges

zero moment (that is almost at quarter-span) to reduce the magnitude of the deformations. This was done at Oleron viaduct, at la Seudre viaduct and, more recently, at the Saint-Cloud bridge. In order to permit cantilever construction of the beams including the expansion

joint, the latter is locked provisionally; prestressing cables pass through and are removed at the final phase. The calculations made for the Oleron viaduct show that, under permanent loads, vertical deformations are thus decreased in the ratio of 3 to 1 and angular changes in the ratio of 15 to L These ratios become 2.2 to I and 3 to 1respectively under imposed loading (fig. 2.40). The diagram in figure 2.41 corresponds to the case of a continuous bridge with

a large number of equal spans of constant inertia (span l), containing one hinge; it represents the curve of deflection of the hinged span under a uniformly distributed live load of 10 kN/m (=1 tim), for various hinge positions. It is seen that when the distance between the hinge and the nearest support is about 0.2 I, the deflection curve of the hinged structure can be compared with the deformation curve of the continuous structure. To round ofT the survey of hinged and continuous systems, attention is drawn

to a special case: the Chillon viaduct in Switzerland, over 2 km long. The structure expansion is accommodated by special joints similar to sliding hinges and located at the centre of certain spans. These joints arc fitted with devices maae of steel parts fixed to one cantilever and sliding into the other by means of sliding and oscillating supports (fig. 2.42).

s ., 2.

~ ~ II c .2

I ~ 7.

Standard span' 79.00m Fig. 2.40 Deck deformations under imposed load as a function of hinge position

(Oleron viaduct)

Deck design 47

'" _._,

o 0.11 0.21 03t 04/ 05t 06/ 0.7t 0.8/

,.,'

0.91 I

pon w,'hout hlnlle ~S .. I,__'--= ~:.,,+--.:t.::::p~.,.--r--r /.,;/ ~.... I I . ,~,,... ./

Art.0.31 ~. I I /' I ./ ,. 1'1"'/ ~. I "",)//'~.J /'1 .

Art. O.4t '~~ I /"'. Arl.O.51.

Fia 2.41 DcI'ormation of a continuous beam under constant load as a function of hin&e position

Retts,e, lor onchlH0ge

\,./ / KeYNl9 porls mode 01 52 Recesses 10 loke 'he keY'"9 perl"u, joists ""ed ,n tonerele With 'he shc'nq supports

Fia 2.42 Expansion joint of Chillon viaduct

3 SPAN DISTRIBUTION

3.1

Whenever possible, the lengths of standard spans are equal and the deck consists of a group of identical beams (fig. 2.43). What should then be the lengths or the end spans?

It m~t fU'lt be remembered that with a structure of a given length resting On its abutments by means of simple supports, the optimum end span is not equal to one-half the standard spans. For instance, in the case of a cast in situ three-span bridge. from the point of view of the distribution of bending moments in the structure. the economical value of the ratio between end span and centre spaD is bctwe= 0.75 and 0.80. With a similar structure built by the cantilever method and prestressed, otha- factors must be taken into account, namely the mode of application of the dead load, the prome of prestress with its statically indelerminate efTects, and the method of construction adopted for the part of the deck

..:",~~

48 The cantilet-'er construction ofprestressed concrete bridges Deck design 49

T T s~~n91 B~o~

0.651 I. I , (.. 1 ! I lq50~ i

Fig. 2.43 Deck consisting of a group t)f identical beams

close to the abutments. From experience one finds that the above mentioned ratio must be selected between 0.65 and 0.70. Similar conclusions can be applied to the end spans of structu res with multiple spans.

In the case of such a span distribution (solution a), the ends or the structure do not tend to rise under dead load and prescribed highway loading, the abutment reactions remaining broadly positive.

In reverse. if the' end spans are appreciably longer than half the adjacent spans, building the part or the deck included between the end of the bank beam and the abutment requires the use of falsework or temporary supports.

If. on the other hand, the end span is close to half the adjacent span, constructing the deck is made easier since it is fully cantilevered. However, special arrangements must be taken to avoid the deck hogging over its abutments (solution b).

As seen in paragraph 1.1.1.2(c) these arrangements can be made either by ballasting the end segments or by anchoring the deck to the abutments. In practicc, it is advisable to give end bays the smallest possible span compatible with the preservation of positive reactions on the abutments, in order to avoid involving a device to stppress uplift. This usually amounts to extending the cantilever of the end span by one or two segments which may be made by the cantilever method before connection to the adjacent span, without using temporary supports, the stability of the cantilever being temporarily assured by counterweigh ts.

When the structural form of the deck is a continuous beam and the connection of the end span is made before that of the adjacent .pan, the weight or the extra segmentJ bunt by the cantilever method balances the upward reaction at the abutment due to permanent load and to imposed load (increased by 1.5), as if they had been built on centring (soluti,on c). The structure is .,lin statically determinate. once the pro\isional fixing to the bank pier has been released.

When the connection of the end span occurs after that of the adjacent span, the c:nd result will be the same provided that the reactions on piers and abutments are adjusted by jacking and adjustment of relative levels of the bearings.

3.2

Even when it. is not possible to give equal \'ailies to all the spans, cantilever construction pro~des considerable flexibility in span distribution.

J.2.1

If the structure spans a gap where local conditions (such as river clearance) determine a span L of the central bay and where smaller end spans (length I) are found preferable because of their lower cost, the transition will be effected easily by an intermediate span). equal to the arithmetical means of the spans L and I (fig. 2.44) or \vill be close to that value.

A~t(L + I) The Oleron viaduct and Saint-Andre-deCubzac bridge across the Dordogne arc two examples of this type of structure (fig. 2.4 5).

IA a1/2(L+/ll Fig.2.44 Structure with two standard type spans

...., , I( 4l5190~ 1........1.. 5x95.30 ~ ... 4x57.90.. I ~ 36.70 74.05 74.05 36.70

F,ig.2.45 Examples of the Oleron viaduct and Saint-Andre..de-Cubzac bridge

so The Cal/li/ever construction o/prestressed concrete bridges

3.2.2

Generally, if the structure crosses a wide. deep valley it may be desirable for aesthetic reasons to make the spans vary regularly to match them to the apparent height of the piers (fig. 2.46). The spans [, of the structure are governed by the following condition:

/..

I: (_11+ 1 i, - d, + (-I)"d. =0 /.1

in which d: and d. represent the lengths of the portions of the end spans built on slaging. Tho: lenglhs of the differenl beams are equal to:

.iIC,

= \$I $1aQ8 - 2nd$l0Qt

Fig. 2.49 (a) and (b) Construction of the Givors and Gennevilliers bridges

_ ._ .. ...,... .,. ""...".......,....,.,..~lf~~

52 53 The cantilever construction o!prestressed concrete bridges

Webs

Abutme" s~men:s

Identicol pier segments

==:t-=--=--=t.=__ - I,!-

Asymmetrical pier segments

II

d\+d!.,

1/

Fig. 2.S0-Skew bridge with two beams-layout ofsegments

Deck design

both have a short centre span between two large spans. The cantilever construction of these structures made it necessary for the cantilever beams on either side of the short bay to be made in two stages as shown in figure 2.49. With such procedures it is necessary to rest the cantilever beams on simple supports during the second stage of construction in order to avoid the transmission of high bending moments to the piers.

3.2.4

Finally, it should be noted that the difficulties described above are increased if the structures are skew or curved and consist of two or more parallel beams.

With skew bridges (lig. 2.50) it is necessary to determine the length u of the precast segments so that the joints of the different parallel beams coincide. This result can be achieved by selecting u as equal to a multiple or a submultiple of the displncement 0 due to the skew, or by building asymmetrical pier segments.

If the skew varies from one support to the next it should first be ensured that the location of the transverse prestressing cables is compatible with the position of the joints whilst leading to as regular a distribution of prestress as possible. The prestressing cabt~ spacing e must then be a multiple of 0.

With curved bridges similar problems must be faced and arc made more severe by the trapezoidal shape of the precast segments resulting from the need to keep joints perpendicular to the longitudinal axis of the bridge (fig. 2.51).

I Transverse prestress,ng cables

Trope,o'dol segment

Tronsv~rse connect,ng Jo,nt

Fig. 2.SJ---Curved bridge with two beams-Iayoul of segments

54 The cantilever construction ofpreslressed concrele bridges

4 FORM AND SIZE OF THE TRANSVERSE CROSS SECTION

4.1 Cross-section type

The transverse section best suited to cantilever, construction is the box for the following reasons: (a) On the one hand, due to the construction procedure adoptcd, the bending

moments arc negative over most of the spans and very lar" in the rClion of the supports. As the bottom flanges must withstand high compressive forces, it is preferable to make a lower slab continuous betwcen webs; this disposition of material also allows the designer to take advantage of the intrinsic torsional strength of the box.

(b) On the other hand, box structures have a good mechanical efficiency (approximately 0.6) and a value of IIltilllate stre"gt" which depends less on the grade of concrete than 7:'sections. Thus, if at the tUllC of failure the force in the cables is equal to Fr, the depth of concrete in compression is y ~ F,/bRbr for a given value of the concrete crushing strenath R.,. In the case of a box bealn. the depth y is generally low on Dccount of the large value of the width b of the lower flange and the lever arm z is not reduced drasticaUy if Rbr does not achieve the expected value (ft 2.'2). With T beams" the depth y is close to that of the flange nnd a drop in R,., entails cOin ) pression in the \veb and, as a result, an appreciable reduction in the lever ann ~ z and consequently in the ultimate strength.l, (c) Finally. elastic and d.vllalnic stability of the bridge during cantilever construction is ensured luore satisfactorily with a box-section structure. which oOcrs a higher torsional rigidity. than a structure of open section. In service, the torsional rigidity Jessens the rotation of the transverse section under eccentric loads. It improves the distribution of imposed loads between the variousII:

zT:l-O~' Ilf ~ ,1;,

il zt.------""'-----.l " ~ ;~ ;.

I~ 1;, /)/3

Fig. 2.52 Ultinl~te behaviour of the cross-section of-a cnntiJcvc:r bridge

ssDeck des;g"

beams and permits the omission of intermediate cross-bracing. The torsion caused by the eccentricity of the load is then balanced by the beam torsional capacity instead of by cross-bracing.

It isquestiooable whether the box section in the centrespan region is necessary. Bending moments are moderatc and of positive sign (sagging) in that area. Asymmetrical Tsections arc therefore suitable and, in theoryt lead to maximal savings in the usc ofmatoriab (fig. 2.53).

In fact, thcreare few stNctures of this form in the world (except in Germany) for several reasOns:

_ poor transmission ofcompressive stress at change of section; - poor provision of clastic and dynamic stability with large spans: _ need to provide intermediate bracing if the resection is employed over a

substantial length: - ~inlcully of Illuintcnuncc (access for stun' and sc:rviccs etc.).

A few cantilever structures have a cross section other than box sections. 'In France, there is the Roquemaure bridge across the Rhone, whose deck con

,ists of twu thick ribs of variable depth and conncctccJ by a slab under the carriapWl1 (rll- ~.S4). The main span of this structure is 80 m. \

2130 '''~I

W- OJ1-C> if ,180

___._.. r_

5.40; I

W -'--4,95 -1-- 1170 ~~6~

Fig. 2.S3 Structure with a T-beam in the centre-span region

ar blt:tf ifI': .... "" .i

l a /)-//

---r:;rdJ c=J~ Fig. 2.54 Cross-section of the Roquemaure bridge

L

57 56 The cantilever construction ofprestressed conere!t bridges 4.2 Number and form of box beams

It is generally advisable to minimize the number ofcells which make up the crosssection. as each cell requires additional formwork. This leads to a significant spacing between webs: approximately .s to 7 m. Moreover, it is more economical to provide a small number of thick webs since each web includes a thickness of concrete 0 (corresponding to the deduction of the diameter of the prestressing ducts) \\'hich takes no part in shearing resistance and impairs the performance of the section in flexure. Furthermore, thick webs make easier the positioning of cable anchorage cones, ancNmprove conditions for the plaein. or concrete. I

- Box beam with two webs, each 400 mm thick. prestressed by cables made of 12 :\0 12.7 mm strands (4J = 70 mm) ! Total thickness of \vebs: 800 mm Effective thickness: 2(400 - 70) =660 mm;

- Box beam with three webs, each 290 mm thick Total thickness of webs: 870 mm Effective thickness: 3(290 - 70) == 660 Mm.

The two box beams are comparable as far as shear strength is concemed but using the box beam with two webs implies a saving of 7/81 == 8% in the volume of concrete in the webs. or approximately 3% in the total section of the beam. On theI:

; other hand, the prestressing cables can be anchored in the depth or the webs (thickness: 400 mm). whereas, with the three-webbed cross section. because of the insufficient thickness of the individual webs. the cables must be anchored either in the bottom \\eb flange junctions, or in a specially provided boss.

The h'eb spacing is, however, limited by the resistance of the top flange slab to transverse bending under live load. The cantilevered portions of the top flange must also be modest in order to avoid transmitting very high local bending moments to the webs (fig. 2.56). The induced moment m1, which increases with

4=t j=o 29:gg:29 Fig. 2.55 Box beams

m(~ r ~. Fig.2.56 High local bending moments to the web

.Deck design

LT LIT un1

58 The cantilever cOllstruction ofprestressed concrete bridges than the French regarding the transverse eccentricity of the military vehicle hishway loading.

The side cantilever of the Felsenaubriicke amounts to 7 m with a depth of 0.55 m at the root.

Beyond J8 In the association of two single-cell box beams connected by the deck slab permits a deck width up to 2S m; this covers the majority of current requirements (e.g. the Givors bridge and the Blois bridge) (fiS. 2.60). A few very large bridges may include three box beams such as the Saint-Jean bridge at Bordeaux (fig. 2.61), but with these structures, which are generally motorway bridges, it is usually preferred to design two independent parallel bridses each with two beams. separated by a central reservation (e.g. the upstream and downstream bridges of the Boulevard PCripherique in Paris) (fig. 2.62).

When the deck width is between 13 and 18 m, a particular problem arises. If a wide box beam with two webs i~ not adopted, a box beam with three w,bs appears in theory to be best suited, but often this type ofsection is not economical because of design problems, for the difficulties in mobile formwark, or far the preeasting equipment (cellular forms and segment-handling equipment).

1_.

Ieof' I~ 4'20 ~ (0)

-! 220i

y 4.50

I~I i ~I

... j:. fr! tr.,. - laW..,..

4.00

( b)

Deck desig" S9

2660~:~ .... _ __ .......... 110- _ I

!340 ~ . . e g7"'T .... ... .TTFWT'-.ijT7WTT\W"" r:lj.'" --,, ,,;s_-t-~~ :.:1

-'

~---... 3.79 250

I~ 900 900

Fig. 2.61 Cross..section of the Saint-Jean bridse at Bordeaux

32 eo 1201580 1580

....-----_. -------J-.1- ..--_. --I

o , ... -- -~l .,1.' '(~..-~ If') "'1 \~I t

I . 0 . ---! 3'50 So -0Q)Q) COG) I. 8.00 ".1. 9.00 -.1 .. 8.00

Fia.2.62 CrO$swscction of the downstream bridge of Paris Boulevard Peripherique

17.16 ....

o o I.D

!~ t

, ------1----

\ I .....

till(

IL- .. - _'000. ~ ; I~ 11. 38 __._._. ~!

Fig. 2.60 (a) and (b) Cross-sections of the Givors and Blois bridges FiB. 2.63 Cross-section of Oissel bridge across the Seine

60 61 The cantilever construction 0/prestressed concrete bridges

There are, however, se\'eral examples of this type of arrangement, including the Oissel bridge (fig. 2.63) and the Joinville bridge across the Seine (fig. 2.64) and the viaducts of the Paris BJ Sud motorway (fig.2.65), with structural sections of 17.2, 19.0 and 15.25 mwidth respectively. This section is also used with wider decks (I >20 m) as in the Genncvilliers

bridge across the Seine (fig. 2.66).

: 19.00 ..- .: 19.00_-1

-0 4 AA_. ~ __ A ~ ~36 t22C

52: - - - ill. I 181 I ---' T ~ -- I~ :1 9.48

6.03 Fig. 2.64 Cross-section ofJoinville bridge across the Seine

15.25 ~ I10( I ~ , ,~l~"IIi1lJiii111i1i11liiilii1l'" I

L 9.~O .1 Fig. 2.65 Cross-section of the viaducts or the B3 Sud motorway

.... 19.55 .,

o o ai

._--~--"- ~ 120 ~ 5~... 9.2~~t~_--illII JL~

Fig. 2.66 Crosssection of Gennevilliers bridge over the Seine

Deck design

Slab with transverse ribs Top slab with cellular section

~~ Warm air

rc:r:t:J Rib Iocotioni~

l~ ~I

L L/3 Fig. 2.67 Cross section with cellular or ribbed top slab

Another solution is to use a single-cell box bealn with two webs including a cellular top slab or transverse stiffening ribs (fig. 2.67). The first scheme allows large cellular lateral cantilevers and may be an advantage with structures liable to 00 tdTcctcd by frequent icing. as the different cells of the section produce thcrm:1I storage and may be used' in undernoor heating of the carriageway slab. The.: Chillon viaduct in Switzerland has a cross section of this type (fig. 2.68). The strength or the web in local bending induced by the force concentrated at the cantilever lower nange was examined carefully; it was necessary to increase the.: \veb reinforcement. The second scheme seems more advisable and the author proposed it for the

construction of the Saint-Andre-de-Cubzac bridges across the Dordognc (fig. 2.69). This choice resulted from comparative surveys of different section ~

13.00 ~ III

fI i;:r 1610 I

40-.. ...- ~50. t

1564 I

______.__ ~_r_ 1-.( ... - ~:

500 Fig. 2.68 Cross section of the Chilton viaduct in Swit lcrfand

62 The callti/ever cotlstructiotl Q/prestressed concrete bridges

1660 I~ 1

14 6bo J 7.78

Fig. 2.69 Crosssection of Saint-Andrc-de-Cubzac bridges

such as: two box beams each with two webs, a three-webbed box beam. and II two-webbed box beam with a ribbed upper slab.

Taking into account the nonnal width of the decks (equal to 16.6 m), and the need to reduce this width to 14.3 m for one of the access viaducts. this solution proved to be both the most practical, as far as construction was concerned, 11m! most attractive, economically speakina.

As compared with a structure consisting of two box beams, it has the advantage of avoiding transverse prestress, which is always costly for such widths, and of eliminating the concreting of the junction slab. Also, it considerably simplifies deck bearings and foundations.

Finally, it has a better mechanical efficiency than the three-webbed box beam and leads to a simpler design of mobile formwork or precasting moulds.

This type of transverse section, used for the first time in the construction or the Saint-Andrede-Cubzac bridges, has been used since in several structures which have all incorporated precast concrete seaments; these are: Sa/Ii"""",, bridge in Denmark, a 16.1 m wide bridge (fig. 2.70). In this bridae an improvement has been made in the design of the joints between precast segments. The contact surfaces of the half ribs were reduced by means of a lining laid out in the forms in order to secure a high average compression of the joint to be glued, wbich helped towards satisfactory gluing when the segments were connected. It had been suggested that a structure plaMed for construction in Denmark, the Vejle Fjord bridge (fig. 2. 71), ~hould be built with a 27.6 m wide deck with a ribbed top slab but this project was subsequently abandoned.

Finally, one can envisage designing a multicellular deck with two vertical central webs and two sloping webs. This cross-section would provide high torsional rigidity, and the shape of the side cantilevers would provide economiclll

63Deck design

16.10

I" I

1250

1-4.--...:Q9__ ._1 ~ .lU9.-...._. _ ..,.

PI,. 2.70 Cros. section of the Sellinlsund bridge

27.60

Fig. 2.71 Cross section of the V.ejle Fjord bridge

resistance against the action of concentrated loads. Unfortunately, it is unsuitable whcQ the depth varies; as a result, it leads to the substantial use of prestressing in the CI$C of structures with large spans.

Tbis solution was nevertheless adopted for la Voisnc viaduct built by the cantilever method with in situ concreting techniques, and which includes five spans with a maximum length of65 m (lig. 2.72). It was also adopted for the Paris

._. . . ?5J9 ._. . . .. ~.

r C 01'. ...

.11810 50 ~ I _.e.5.L-__...:

Fig. 2.72 Cross section of la Viosnc viaduct

.. --_._........~.

64 The cantilever construction a/prestressed concrete bridges

16.00.----------1.......

Fig.2.73 Cross section of the Metro viaducts of Mame-la-VaUee

T

20.40

Metro \iaducts at Marne-Ia..Valle"e with decks made or precast segments usually 11 m wide; they reach 16 m at the Neuilly-Plaisance Metro station owing to the addition of side cantilevers (fig. 2.73).

This solution was also adopted for the Saint-Cloud bridle across the seine both for architectural reasons and on account of the highly curved plan (R = 350 m) of the structure which prompted the designers to seek a structure with high torsional rigidity (fig. 2.74).

4.3 Decks with variable width

In an urban environment bridges are often found witb an increased width at their ends, to allow for the addition of s1iproads or for traffic management at an intersection.

A variation in the deck width may be facilitated by one of the follo\yjng processes:

(a) Width variation of the side cantilevers (fig. 2.75(a.

Deck design

~f\----r~@ L-J V~ : HOflZonloloddiloon ~IOddition

Standard section

WIdened sectIon

Standard sectIon

Widening

Fig. 2.7S (a). (b). (c) Deck widening

(b) Variation in the width of the reservation between box beams when there arc several of them (fig. 2.7S(b.

(c) Addition ofone or more extra webs (fig. 2.7Sc). Additional webs are usually built once the box beam has been made continuous they are constructed either by means of special mobile formwork, sliding on th beam or by formwork suspended from two beams or falsework supported a ground level.

The first solution was used a~ la Banquiere viaduct at Nice (fig. 2.76 and 2.77 whilst the second was adopted at the CoJlecteur bridge over the Seine at SainI Denis, and the last was employed for the Connans bridge across the Seine. \Vc1: may also be precast as those of the upstream bridge of the Boulevard Peripheriq u across the Seine (fig. 2.18).

66 67The calltilel'er construction o/prestressed concrete bridges Deck design

/

47.52 47.52

OouJbe J ~.

/a Section B8~

VARIABLE VARIABLE

Fig. 2.76 Widening scheme orla Banquicre viaduct

Fig.2.77 AS motorway-La Banquierc viaduct

Fig. 2.78 Upstream bridge of the Boulevard Peripherique (third web precast)

4.4 Type aCtransverse cross section-notation It is desirable that the top slab of the box girders should follow the transverse profde of the roadway in order to avoid carrying out an expensive and cum bersome reshaping process. There are several possible arrangements: - the IOYier flange is parallel to the top slap;

the cross section is a rectangle and the webs are perpendicular to the flanges (fig. 2.79(a. This is the most satisfactory solution from the point of vic\y of the reinforcement of the beam;

- the cross section is apara//elogram (fig. 2.79(b. Reinforcement is not identical from one web to the next. In both cases a wedge must be provided under the pier segment in order to

compensate for the cant, and to position the bearings on a horizontal plane. - the lower flange is horizontal (fig. 2.79(c.

~ .._~........ ... ..', ,,- ' ... ..---.~- .......... ~-~.""-~

68 6 The cantilever constroction a/prestressed concrete bridges

o 0 Cf \ ~a J1T:~a btr~a

90 90 I """' I ~ ~iii~wed9' in position Fig. 2.79 (a), (b), and (e) Wcb arrangcment in relation to the flanlcs

This solution, which implies webs of different height, is to be avoided as it makes the design of prestressing cables considerably more complex.

When the cross section consists of two box beams built separately these are usually connected by an upper slab, concreted once the box beams have been constructed. This slab must be at least 500 mm wide to allow the taking up of differences of level between the two box beams u wen as eventual threading of the transverse prestressing cables. Figure 2.80 shows the standard cross section of a bridge constructed by the

cantilever method, with the usual notation.

4.5 Web thickness (a) Webs must provide resistance to shearing forces and permit proper placing of the concrete as well as. fairly often. the anchorage of prestressing cables. Thcy musl therefore have the following characteristics.

4.5.1

A thickness at supports limited by the shearing condition:

t b ~ t~ where t~ =permissible shear stress in concrete.

Port cost ill silll ofter construction of the two box beams

Fig. 2.80 Standard cross section-notation

Deck design

The web is subjected to shear stresses due to shearing force V (t 1) and to tr torsional moment M, (t2 )

t b = t l + t 2

VH t l = /(0- ~) H. J: Firs~ moment and second moment of area of tl

section.

t 2

M, ----

- 20(0 _~) { ~:

0: Diameter of cable ducts. Area enclosed in the section mean outline.

In a deck with variable stiffness the critical sections with respect to shearing for' are generally situated at approximately onesixth span. The use of prestressed stirrups, which induce a vertical compression in the we

permits an increase of the value of the permissible shear stress t b and a decrea of the web thickness a. Prestressed stirrups are made of single win monostrands, or of bars, positioned in sleeves and grouted to prevent corrosi< (fig. 2.81). Some monostrands are supplied directly from the works in pins. sleeves and coated with a corrosionproof grease.

Anchorage Active ,anchO,age

Area prestressed verticolly

Bar

- Sleeve (4), l

A,..t:"'I')''''.l~ rY1".".I"~

, I . I I-_._-

- nr)0r0i.!,.,"'21~~!q ~1:1:~I~Areo prestressed ~~:III~ . :~i~!~

~I~I .I ~- ~.~ Strcssed stirrups

vertocolly

"

Manowires

Zone of anchorage bybondi"9

71

:!

I' ~

!

70 The cantilever construction ofprestressed concrete bridges

The stirrups made of bonded wires or strands used with prefabricated webs arc more economical due to the fact that no sleeve is needed ('1 co 0).

Variations of depth in the beam also result in a reduction of the shearing force, thanks to the effect of the vertical component of the compression in tho lower flange (the so-called Rcsal correction). When variations in heisht are Important it

. is usually possible to maintain a constant web thickriess along the length of the beam and this greatly simplulCs the formwork.

Sloping cable profiles in the region of the supports reduces still further the shear force because of the vertical component of the prestressing force.

4.5.2 A minimum thickness compatibie with good concreting (fig. 2.82) The stirrups usually with a 10- or 16mm diameter, must have a minimum cover of 20 mm. Concreting shafts (>60 mm) must be left on both sides of the cables to allow for the penetration of internal vibrators, giving a minimum diameter of SO mm. Thus:

a ) ~ + 2(20 + ~t + ~I + 60)(mm) where ~I =diameter of distribution steel or:

250 mm with a 12 ~ 8 cable,(!) ~ 10 stirrups and ~ 8 distribution steel 280 mm with a 12 T 13 cable,m ~ 16 stirrups and ~ 10 distribution steel.

Longitudinal wires (4)1)Stirrups (t/>.)

Coble (t/>l

Concreting shoft ( for vibrations) --Web face

~1161 '" 1611~ t/>!W!I cfll.JUt-

Fig. 2.82 Web minimum thickness

'12 ~ 8 indicates a cable of twelve 8-mm wires_ :12 T 13 indicates a cable of twelve t-in. strands, or 12.7 mm distribution steeL

Deck design

The above condition Is often inadequate with webs of great depth. It is indeed Clsential that the concrete fills the form adequately over the whole depth of the web. Concretina ports set half way up the forma and towards the inside of the box beam mako placina easier. When the webs are sloping vibration can be Improved by luidinl the internal vibrators inside latticed ducts.

Ouyon sullests an empirical formula for webs with a depth less than 6 m:

h a;> 36 + 50 + +(mm)

In this way we have 240 mm for a depth of S m and cables 12 ~ 8. Ifthe webs arc Inclined at a large angle to the vertical, it is advisable to increase the values liven in the above formula.

With depths equal to 6 m, or slightly higher, it does not seem sound to go below 300 mm if the webs include 12 T 13 cables (Pont du Bonhomme: webs of 300 mm for a depth oJ 7 m). and below 240 mm if there arc no cables in the webs.

Boyond 7mth. Ouyon formula can be replaced by:

a ~ - + 80 + ~(mm) " 22

The webs of Gennevilliers bridge which are sloping and penetrated by 12 T I~ cablu(II are 400 mm thick for a depth of 9 m. At Bendorf bridge the vertical web! are 370 nun thick for a depth of 10.45 m (the prestressing cables do not go down into the webs, which are prestressed by sloping prestressed stirrups).

If the webs arc precast and concreted flat their thickness may be reduced, a! with the Brotonne bridge where the webs which are prestressed by bonded wire! have a minimum thickness of 200 mm.

4.5.3 An adequate thickness allowing for the anchorage cables, if these are stoppeo of at the surface of the segments in the depth of the webs. Approval certificates gi\'t for each prestressing procedure, minimum values. to be observed, apart frorr special arrangements (end plates, wire wrapping, elc.).

These values are equal to 230 mm with 12 ~ 8 cables and to 360 mm witl I:! T 13 cables (approximately I.SD; D being the external diameter of tho anchorage).

4.6 Span and IhJckness Ci) of the upper flange In a cantilever bridge whose transverse cross-section usually consists of bo.

72 The cantilever cons/rue/ion o/prestressed concrete bridges Deck design 73

beams, the upper flange is fIXed to the webs because of the presence or the lower nange which acts as a tie rod and thus laterally restrains the webs (fig. 2.83).

As a result, the upper flange whose dimensions are determined by its resistance to transverse bending under live loads, may have quite large spans (comm